Pardee Wiki - User contributions [en]

Energy

2026-08-27T18:27:08Z

Megan.Livengood:

Please cite as: Hughes, B. B., Solórzano, J., & Rothman, D. S., Irfan, R. I., Sahadevan, D. (2025, November 11). IFs energy model documentation. Pardee Center for International Futures, Josef Korbel School of Global and Public Affairs, University of Denver. [[Energy|https://pardeewiki.du.edu/index.php?title=Energy]]

Further information on this topic is provided in a [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_10 dedicated chapter], which offers additional context, analysis, and supporting information.

1. Introduction

1.1 Overview

The International Futures system (IFs) represents energy and electricity through integrated dynamics that span multiple IFs models: energy, economy, environment, and infrastructure. It captures patterns of energy consumption and electricity use, the drivers behind them, and the production of energy from both fossil and non-fossil sources using different technologies. IFs also incorporates trade in energy, using both a pooled approach and a bilateral version. The model accounts for the environmental implications of fossil fuel use, while broader development and sustainability outcomes such as access to electricity and improved fuel use, are also represented.

Here we document the IFs energy model - a partial equilibrium model operating on physical energy, balancing consumption and production through a price variable that adjusts in response to supply-demand dynamics, with energy stocks serving as a buffer. Investment decisions are signalled by price and by cost, with cost shaped by resources, reserves, and technologies, and these dynamics in turn inform the treatment of the energy sector in the broader Economic Model. Ultimately, computations in the physical energy model feed into the Economic Model by replacing its sectoral calculations with the corresponding financial variables from the physical energy model.

Gross domestic product (GDP) from the Economic Model provides the basis for energy demand calculations. Energy demand elasticity represents the responsiveness of demand to prices, which evolve over the long run with changes in technology and resource availability. Thus, the physical constraints on the supply side are very important in determining the dynamics of the energy model.

IFs distinguishes nine energy production categories: oil, natural gas, coal, hydropower, nuclear, solar, wind, geothermal and other renewables. The other renewables category includes tidal, wave, biodiesel and biogas. For each category both conventional and unconventional sources are considered, but these have only been fully implemented for oil. Currently, the model does not generate projections for consumption or trade by specific energy types. IFs rather computes aggregated regional or national energy demands and prices, on the assumption of high levels of long-term substitutability across energy types and a highly integrated market. The model also conducts energy trade only in a single, combined energy category. Finally, at the moment, there is no full reconciliation between the production of energy and electricity generation (see the IFs

Infrastructure Model Documentation for a description of the electricity aspects of IFs).

1.2 Dominant Relations

Energy demand (ENDEM) is a function of GDP and the energy demand per unit of GDP (ENRGDP). Energy production (ENP) is a function of capital stock in each energy type, the capital/output ratio (QE) for that energy type, and a capacity utilization factor (CPUTF).

The following key dynamics are directly linked to the dominant relations:

* '''DEMAND:''' Energy demand per unit of GDP depends on GDP per capita, energy prices, and an autonomous trend in energy efficiency. The first two of these are computed endogenously, the latter exogenously. The user can control the price elasticity of energy demand ('''''elasde'''''), speed at which energy price changes affect demand ('''''ehw''''') and the autonomous trend in efficiency of energy use ('''''enrgdpgr'''''). The user can also use an energy demand multiplier ('''''endemm''''') to directly modify energy demand.

* '''PRODUCTION''': For fossil fuels and hydro, there are upper bounds on production. For fossil fuels, these are based on reserve-to-production ratios, as well as user-specified upper bounds ('''''enpoilmax''''', '''''enpgasmax''''', and '''''enpcoalmax'''''). For hydro, the upper bound relates to hydropower potential. The model user can also control production using an energy production multiplier ('''''enpm''''') to directly modify energy production by energy type. The user may also indirectly increase energy production through additional investment ('''''eninvm'''''), which will incorporate economic trade-offs. In contrast, a production multiplier ('''''enpm''''') comes without any cost to increased production.For renewable categories other than hydro, the model uses potential capacity ('''''resor''''') in lieu of reserves or resources. This reflects availability or potential based on data or estimated from drivers such as land area. Unlike fossil fuels, where '''''resor''''' represents finite physical resources that directly constrain production, renewable potentials are effectively unlimited; instead of setting an upper bound, they influence capital costs and investment dynamics.

* '''CAPITAL/OUTPUT RATIO''': The capital/output ratio provides a measure of production cost, with declines reflecting efficiency gains and reduced capital intensity. User-controllable parameters ('''''etechadv''''' and '''''etechadvuncon'''''), applied to each fuel type, implement these cost declines due to technological improvements at the global level. For fossil fuels, this is counteracted by a factor that increases the capital/output ratio as the amount of remaining resources decreases. The user can further modify the capital/output ratios with the multipliers ('''''qem''''' and '''''qeunconm''''').For renewable energy sources such as wind, solar, and geothermal, the capital/output ratio is equivalent to the levelized cost of electricity (LCOE) generation from these sources, though users can still modify capital output ratios with multipliers ('''''qem''''' and '''''qeunconm'''''). These energy sources are primarily used to generate electricity (except for geothermal, which can also provide direct heat).[1]

* '''CAPITAL:''' Energy capital, by fuel type, is initialized based on the initial levels of production and capital/output ratios. Energy capital depreciates at a rate determined by the lifetime of energy capital ('''''lke''''') and grows with investment. Total desired investment in energy capital is influenced by many factors, including existing capital, domestic and global energy demand, the production of other renewables, changes in the global capital/output ratio, world and domestic energy stocks, expected overall profits in the energy sector, and imports. Users can control the effect of expected profits ('''''eleniprof''''' and '''''eleniprof2''''') and world energy stocks ('''''elenpr''''' and '''''elenpr2'''''). Desired investment by energy type increases with individual profit expectations, but also by limits related to reserve production factors (for fossil fuels and hydro), any exogenous restrictions on maximum production (for fossil fuels), ultimate potential (for hydro), and other, unspecified factors (nuclear). Users can influence the effect of profit expectations by fuel type (via '''''elass''''') as well as influence the desired investment by energy type ('''''eninvtm'')''', or in the aggregate (via '''''eninvm'''''). The user can also specify an exogenous growth rate for energy investment by fuel type ('''''eprodr'''''). The Economic Model ultimately determines whether all of the investment needs can be met; in case of shortfalls, the investment in each type of energy is reduced proportionately.

* '''RESOURCES/RESERVES/STOCKS''': IFs separately represents ultimate resources and reserves, where the latter are the amount of energy resources available to be produced. Resources and reserves, both conventional and unconventional, are set in the pre-processor. The user can modify the default assumptions on ultimate resources, either directly ('''''resor''''', '''''resoruncon''''') or via the use of multipliers ('''''resorm''''', '''''resorunconm'''''). Reserves decline with production and increase with discoveries. The rate of discovery depends on the ultimate resources remaining, the intensity of current production, world energy prices, and a base rate of discovery ('''''rdi'''''). The user can control the effect of world prices on discovery ('''''elasdi'''''), augment the base rate of discovery ('''''rdinr'''''), and use a multiplier to affect the rates of discovery ('''''rdm'''''). Finally, IFs keeps track of any production not used in the current year, i.e., stocks, and shortages.

* '''ENERGY PRICES''': Domestic energy prices are influenced by world stocks, domestic stocks, and the ratio of capital to production at the global level. The user can control the effect of domestic stocks on prices ('''''epra''''' and '''''eprafs'''''). Users can also include a “cartel premium” ('''''encartpp''''') and a carbon tax ('''''carbtax'''''). More directly users can set domestic energy prices exogenously for just the first year ('''''enprixi''''') or for multiple future years ('''''enprix'''''). The world energy price is calculated as a weighted sum of the domestic prices.

* '''TRADE''': The energy model also provides representation and model-user control over energy trade. The levels of imports (ENM) and exports (ENX), measured in physical terms (bboe), depend upon levels of production and demand, as well as past propensities to import and export energy. The user can set maximum limits on of energy imports ('''''enml''''') and energy exports ('''''enxl'''''), as well as general limits on trade ('''''trademax''''').

----[1] Conventional sources refer to oil extracted through standard drilling methods, while unconventional sources include those requiring advanced techniques such as shale oil extraction.

[2] LCOE is expressed as the cost per kilowatt-hour of electricity generated and is computed by dividing the total electricity produced over the lifetime of a plant by the sum of its capital costs, operations, and maintenance expenditures (IRENA, 2024). We will revisit the implications of variable renewable energy (VRE), including system integration costs and their effect on capital/output ratios in more detail later.

'''1.3 Structure and Agent System'''

''Table 1: Model Structure and Agent System.''
{| class="wikitable"
|'''System/Subsystem'''
|Energy
|-
|'''Organizing Structure'''
|Partial market
|-
|'''Stocks'''
|Capital, resources, reserves

|-
|'''Flows'''
|Production, consumption, trade, discoveries, investment
|-
|'''Key Aggregate Relationships'''

(Illustrative, not comprehensive)
|Production function with exogenous technology change;

Energy demand relative to GDP;

Price determination
|-
|'''Key Agent-Class'''

'''Behavior Relationships'''

(Illustrative, not comprehensive)
|Government taxes, subsidies
|}

2.'''Flow Charts'''

This section presents several block diagrams that are central to the energy model: an energy system overview, energy production and energy consumption.

2.1 '''Energy Overview'''

The production growth process in energy is simpler than that in Agriculture or the full Economic Model. Because energy is a very capital-intensive sector, production depends only on capital stocks and changes in the capital-output ratio, which represents technological sophistication and other factors (such as decreasing resource bases) that affect production costs.

The key equilibrating variable is again inventories. It works via investment to control capital stock and therefore production, and via prices to control domestic consumption. Production and consumption, in turn, control trade. Specifically, as inventories rise, investment falls, restraining capital stock and energy production, and thus holding down inventory growth. As inventories rise, prices fall, thereby increasing domestic consumption, which also holds down inventory growth.

''Figure 1: IFs Energy Model Overview.''

2.2 '''Energy Production Detail'''

Energy production is computed from the capital stock invested in energy and the capitaloutput ratios, adjusted by a capacity utilization factor and bounded by production limits specific to each energy type. Exogenous parameters allow users to modify both the drivers of production and the production volumes themselves. The capital-output ratios are affected by the amount of remaining resources as a share of the initial levels, technological progress, and user-controlled multipliers. The capacity utilization factor is influenced by domestic stocks and shortages.

''Figure 2: Energy Production in IFs''

2.3 '''Energy Capital and Investment Detail'''

The capital stock by energy type decreases through depreciation and grows with new investment. Investment growth in the capital stock, though influenced by several factors, is driven primarily by energy profits and existing stocks. It can be adjusted through a user-defined scenario multiplier and is capped by production constraints linked to reserves availability for fossil fuels and resource potential for renewables. The user can use a direct multiplier on total energy investment, multipliers on energy investment by energy type to influence investment or specify a desired rate of growth in investment by energy type.

For renewable energy sources like wind, solar and geothermal, the capital-output rations are tied to the levelized cost of electricity (LCOE). In case of variable renewable energy (VRE) sources such as solar and wind, there comes an additional set of challenges associated with intermittency, dispatchability and storage. For renewables, the capital– output ratio corresponds to the LCOE with adjustments for system integration costs such as transmission, storage, and balancing in the case of variable renewables. Addressing these challenges requires additional expenditures on transmission, distribution, and balancing capacity. LCOE data published in the literature does not always incorporate such system integration costs, which can be substantial at higher penetration levels of VRE and also affect production costs (Hirth et al., 2015; Ueckerdt et al., 2013).

If these additional system costs are not considered, the model’s forecasts for such renewable sources may overestimate the pace of cost reductions driven by technological learning and economies of scale, while at the same time underestimating the true investments required for large-scale deployment of wind and solar power.

''Figure 3: Energy Capital and Investment in IFs''

'''2.4 Energy Demand Detail'''

Energy demand is estimated as a function of the energy demand per unit GDP (in PPP terms) and total GDP (in PPP terms), with adjustments related to energy prices and improvements in energy use efficiency. The energy demand per unit GDP depends on GDP per capita (in PPP Terms). The improvement in energy use efficiency is a combination of autonomous trend in efficiency of energy use ('''''enrgdpgr''''') and an additional amount that accelerates the improvements for (non-exporting) countries that have efficiencies below the global average. The price effect takes into account both the domestic and global prices of energy, as well as any carbon tax ('''''carbtax'''''). The user can control the price elasticity of energy demand ('''''elasde''''') and the historical weight used to smooth energy prices ('''''ehw'''''). Finally, the user can also use an energy demand multiplier ('''''endemm''''') to directly modify energy demand.

''Figure 4: Energy Demand in IFs''

2.5 '''Energy Resources and Reserves Detail'''

IFs distinguishes between ultimate resources and reserves, where the latter represent the amount of energy actually discovered and available for production. Ultimate resources are initially determined in the pre-processor, but the user can override these estimates using either absolute values (resor, resoruncon) or multipliers (resorm, resorunconm). There is also a parameter controlling the portion of unconventional oil that is economic to produce (enresunce). For non-renewable energy types, i.e., fossil fuels, reserves increase with discoveries and decrease with production. The rate of discovery includes a base rate (rdi) and an annual increment (rdinr). There are further adjustments related to the world energy price, the remaining resources, and the current rate of production. The user can control the effect of world prices on discovery (elasdi) and can also intervene with a discovery multiplier (rdm).

''Figure 5: Energy Resources and Reserves in IFs''

3.'''Equations'''

This section will present and discuss the equations that are central to the functioning of the energy model: supply, demand, trade, stocks, price, investment, economic linkages, capital, natural resources and energy indicators. Here we follow the order of calculations in all years but the first, noting specific calculations that are made in the first year or preprocessor as necessary. A table has been added as an appendix to this document, linking the variables to the historical data series used to initialize them.

'''3.1''' '''Energy Demand'''

The key energy demand variable in IFs, ENDEM, tracks total primary energy demand. For the most part, IFs does not represent the transformation of this primary energy into final energy forms, or end-user energy demand. The one exception relates to electricity use, which is described in the documentation of the Infrastructure Model.

In the first year, total primary energy demand is calculated as an apparent demand based on a balancing equation that equates energy demand with supply, defined as production plus net trade, and a balancing energy stock. While the supply side is obtained from historical data, the initial value for the stock is estimated from an aggregate stock base, obtained by adding demand and supply, on which a desired stock level (dstlen, 10% by default) is applied and then augmented by the expected growth in production following standard practice in storage planning.

𝐸𝑁𝑆𝑇𝑟,𝑡=1 = (∑𝑒 𝐸𝑁𝑃𝑟,𝑒,𝑡=1 + 𝐸𝑁𝐷𝐸𝑀𝐸𝑠𝑡𝑟) ∗ 𝑑𝑠𝑡𝑙𝑒𝑛 [1]

𝐸𝑁𝐷𝐸𝑀𝑟,𝑡=1 = ∑𝑒 𝐸𝑁𝑃𝑟,𝑒,𝑡=1 + 𝐸𝑁𝑀𝑟,𝑡=1 − 𝐸𝑁𝑋𝑟,𝑡=1 − 𝐸𝑁𝑆𝑇𝑟,𝑡=1 ∗ 𝐴𝑉𝐸𝑃𝑅𝑟,𝑡=1

''Where,''

• ''ENP'', ''ENM'', ''ENX'', ''ENST'', and ''AVEPR'' are energy production, energy imports, energy exports, estimated energy stocks, and an average of the expected growth in production across all energy types (e) for a country, or region (r) in the first year (t) of the projection horizon. The calculations of the initial values of these variables are described later in the Equations section under the appropriate headings.

Note that this calculation does not directly use the historical data on total primary energy demand and there can be a significant difference between the initialized value of ENDEM and the actual historical data for the base year. This information is used by the variable ENDEMSH, which is described in the Infrastructure documentation.

In future years, the calculation of total primary energy demand begins with an estimate of the predicted amount of energy demand per unit of GDP (in PPP terms), compendemperunit, as a function of GDP per capita (in PPP terms).[4] This function is show in the figure below[5]
----[3] Since energy demand is not yet computed for the first year, an estimate (ENDEMEst) is obtained from the energy balance equation, with the stock term based solely on the supply side.

[4] Here, IFs uses GDP from the previous time cycle, with an estimate of growth, to calculate GDPPCP, because the recursive structure of IFs computes current GDP later. The current value of population, POP, has already been computed at this stage.

[5] The exact equation is compendemperunit = 0.0023428 -0.0003878*ln(GDPPCP).

''Figure 6: Relationship between compendemperunit and GDP per capita''

A small amount, 0.0005 barrels of oil equivalent (boe), is added to this computed value to account for the fact that the demand data used to estimate the function above is less than apparent demand globally.

The initial data for countries is unlikely to fall exactly on this function. To reconcile this fact, IFs calculates values for both predicted energy demand per unit GDP in the first year, compendemperuniti, and empirical demand per unit GDP (in PPP terms) in the first year, actendemperuniti.[6] Over a time period of 75 years, controlled by the parameter '''''enconv''''', IFs gradually adjusts the difference between these two values so that the estimate of energy demand per unit GDP (in PPP terms) eventually does fall on the function.

IFs then calculates an initial estimate of total energy demand, endemba, by multiplying this adjusted value of energy demand per unit GDP (in PPP terms), endemperunit, by GDP (in PPP terms).[7]
----[6] There is also an adjustment to the empirical demand that occurs during the initialization. Due to data inconsistencies and/or the exclusion of non-traded energy sources such as traditional biomass from production data, energy demand initialized using the balance method described above can turn out to be very low for some countries. The initialization code adjusts the base-year ENDEM for such cases to ensure that energy demand per unit of GDP at PPP is not less than a fifth of the value computed using the energy intensity function.

[7] IFs uses GDP from the previous time cycle here, because the recursive structure of IFs computes current GDP later.

IFs then considers the effect of price on total primary energy demand. IFs keeps track of the global energy price as both an index (WEP, base year = 100) and as an actual dollar value (WEPBYEAR, $ per BBOE). It also tracks a country level energy price index<div id="ftn2"><div id="ftn2">
(ENPRI, base year =100). Finally, it can also consider a tax on carbon, expressed by the variable CarTaxEnPriAdd, which has the units $ per BBOE.

The calculation of the effect of prices on total energy begins with the calculation of a variable called renpri. renpri is a moving average country-level price index that starts at the level of the country level price index in the base year, ENPRII, and then tracks changes in world energy prices and country-level carbon taxes. The historical weight is controlled by the parameter ehw, so that:

renpri𝑟,𝑡 = 𝒆𝒉𝒘 ∗ renpri𝑟,𝑡−1 + (1 − 𝒆𝒉𝒘)

(𝑊𝐸𝑃𝑡−1+CarTaxEnPriAdd𝑟,𝑡−1∗𝑊𝐸𝑃𝑡=1

𝑊𝐸𝑃𝐵𝑌𝐸𝐴𝑅𝑡=1)
</div></div>''where''

• ''renpri'' is the moving average country level price index

• '''''ehw''''' is the weight given to the historical value of renpri

• ''WEP'' is the global energy price index

• ''WEPBYEAR'' is the global energy price in $ per BBOE

• ''CarTaxEnPriAdd'' is the country level carbon tax in $ per BBOE of total energy and is calculated as the exogenous value of the carbon tax in $ per ton of carbon, '''''carbtax''''', times a production weighted average of the carbon contents of oil, gas, and coal, '''''carfuele , where e is 1-3''''':

∑𝑒(𝐸𝑁𝑃𝑟,𝑒 ∗ 𝒄𝒂𝒓𝒇𝒖𝒆𝒍𝒆)

CarTaxEnPriAddr = ∗ 𝒄𝒂𝒓𝒃𝒕𝒂𝒙𝒓

 ∑𝑒 𝐸𝑁𝑃𝑟,𝑒

The parameter specifying the price elasticity of energy demand, '''''elasde''''', is adjusted based on the relationship between renpri and and ENPRII to yield a new parameter, elasadjusted.

𝐸𝑁𝑃𝑅𝐼𝐼𝑟

elasadjustedr = 𝒆𝒍𝒂𝒔𝒅𝒆𝒓 ∗

renpri𝑟

== Energy Supply ==

The computation of energy production (ENP) is considerably easier than that of gross sectoral production in the economic model or of agricultural production in the agricultural model.  Only capital is considered important as a factor of production (not labor, land, or even weather).  Energy production is initially estimated by dividing the quotient of capital in each energy category (ken) and the appropriate capital-to-output ratio (QE).  A multiplier, '''''enpm'' ''', can be used to increase or decrease production.  This yields:

:<math>ENP1_{r,e}=\frac{ken_{r,e}}{QE_{r,e}}*\mathbf{enpm_{r,e}}</math>

The dynamics of the capital-to-output ratios, QE, are discussed in [[Energy#Resources_and_Reserves:_Capital-to-Output_Ratios_and_Discoveries|this section]].

Known reserves (RESER) and exogenously specified maximums pose constraints on production of certain energy types.  The affected energy types are oil, gas, coal, and hydro.  The impact of reserves is felt via a limit on the fraction of reserves that can be produce in any year. Specifically, the reserve-to-production ratio may not fall below the value of '''''prodtf'' ''', which is initially set in the pre-processor, but can be overridden by the user.  In addition, as the actual reserve-to-production ratio approaches this limit, its rate of decrease is limited.  The exogenously specified maximums apply only to oil, gas, and coal, and are given by the parameters '''''enpoilmax'' ''', '''''enpgasmax'' ''', and '''''enpcoalmax'' '''.  This yields a second estimate for energy production, given as:

:<math>ENP2_{r,e}=MIN(\frac{RESER_{r,e}}{MAX(\mathbf{prodtf}_{r,e},sResProdR_{r,e}-1)},enpmax_{r,e})</math>

''where''

*e only applies to oil, gas, coal, and hydro
*''enpmax'' takes on the value '''''enpoilmax'' ''', '''''enpgasmax'' ''', and '''''enpcoalmax'' ''',depending upon the fuel.
*sResProdR is the reserve-to-production ratio from the previous year; this limit only takes effect when sResProdR falls below 30 and remains above '''''prodtf'''''

IFs then selects the minimum of ENP1 and ENP2 as the estimate of energy production ENP.  The dynamics of energy reserves are discussed in [[Energy#Resources_and_Reserves:_Capital-to-Output_Ratios_and_Discoveries|this section]].

Two final adjustments are made to energy production.  The first accounts for capacity utilization, ''CPUTF'', and the second only comes into play when a restriction is placed on energy exports.  Since these are not calculated until the calculation of energy stocks and shortages, they are described in the appropriate places in the [[Energy#Domestic_Energy_Stocks|Domestic Energy Stocks]] section and the [[Energy#Energy_Prices_and_Final_Adjustments_to_Domestic_Energy_Stocks_and_Capacity_Utilization|Energy Prices and Final Adjustments]] section. 

== Energy Trade ==

The energy model in IFs keeps track of trade in energy in physical quantities; the trade in energy in monetary terms is handled in the economic model.  As opposed to the agricultural model, where trade in crops, meat, and fish are treated separately, the energy model considers trade in energy in the aggregate.  Furthermore, it only considers production from oil, gas, coal, and hydro as being available for export.  Finally, as with other aspects of trade, IFs uses a pooled trade model rather than representing bilateral trade.

The first estimate of energy imports and exports by country are determined based upon a country’s propensity to export, propensity to import, and moving averages of its energy production and demand.

The moving average of energy production, identified as smoothentot, is calculated simply as a moving average of production of energy from oil, gas, coal, and hydro. In the first year of the model:

:<math>smoothentot_{r,t=1}=EnTot_{r,t=1}=\sum_eENP_{r,e,t=1}</math>

''where''

*e is oil, gas, coal, and hydro

In future years,

:<math>smoothentot_{r,t}=0.9*smoothentot_{r,t-1}+0.1*\sum_eENP_{r,e,t}</math>

''where''

*e is oil, gas, coal, and hydro

The moving average of energy demand, identified as smoothpendem has a few more nuances, particularly after the first year.  In the first year, IFs calculates:

:<math>smoothpendem_{r,t=1}=ENDEM_{r,t=1}</math>

In future years, rather than using the value of ENDEM calculated earlier, the model uses a slightly different measure of energy demand, referred to as pendem.  pendem differs from ENDEM in two main ways:

1. rather than using the moving average country-level price index, renpri, to calculate the effect of prices on energy demand, it uses only current values:

:<math>PEnPri_{r,t}=WEP_{t-1}+CarTaxEnPriAdd_{r,t-1}*\frac{WEP_{t=1}}{WEPBYEAR_{t=1}}</math>

2. it does not include the additional boost in energy efficiency beyond '''''enrgdpr'' ''' in calculating the autonomous changes in energy efficiency

Thus, in future years, we have

:<math>smoothpendem_{r,t}=0.8*smoothpendem_{r,t-1}+0.2*pendem_{r,t}</math>

A country’s propensities to import and export energy are given by the variables MKAVE and XKAVE.  These are moving averages of the ratios of imports to an import base related to energy demand and exports to an export base related to energy production and demand, respectively.  MKAVE is initialized to the ratio of energy imports to energy demand in the first year.  A maximum value, MKAVMax is also set at this time to the maximum of 1.5 times this initial value or the value of the parameter '''''trademax'' '''.  XKAVE is initialized to the ratio of energy exports to the sum of energy production from oil, gas, coal and hydro and energy demand from all energy types in the first year.  Its maximum value, XKAVMAX is set to the maximum of this initial value and the parameter '''''trademax'' '''.  The updating of MKAVE and XKAVE occur after the calculation of imports and exports, so we will return to that at the end of this section.

The initial estimates of energy exports, ENX, and energy imports, ENM, are calculated as:

:<math>ENX_r=MIN(XKAVE_r,XKAVMAX_r)*exportbase_r</math>

:<math>ENM_r=MIN(MKAVE_r*pendem_r,MKAVMAX_r*smoothpendem_r)</math>

''where''

:<math>exportbase_r=smoothentot_r+smoothpendem_r</math>

At this point, IFs makes some adjustments to energy imports and exports depending upon whether a country is considered in energy surplus or deficit.  Where a country sits in this regard involves considering domestic and global stocks in addition to current production and demand.

Domestic energy stocks are computed as the sum of stocks carried over from the previous year, while also considering any shortages

:<math>stocks_{r,t}=ENST_{r,t-1}-ENSHO_{r,t-1}</math>

A stock base is also calculated as 

<math>StBase_r=smoothpendem_r+smoothpendemr</math>

The ratio of stocks to StBase can be defined as domesticstockratio. A moving average of a trade base, smoothtradebase, is also calculated for each country:

:<math>smoothtradebase_{r,t}=MAX(ENDEM_r,0.9*smoothtradebase_{r,t-1}+0.1*2*(ENX_r+ENM_r))</math>

''where''

:<math>smoothtradbase_{r,t+1}=MAX(ENDEM_{r,t=1},2*(ENX_{r,t=1}+ENM_{r,t=1}))</math>

Global energy stocks, GlobalStocks, and the global stock base, GlobalStBase, are the sum of the domestic stocks and stock bases across countries, and the value of the globalstockratio is defined as GlobalStocks divided by GlobalStBase.

For each country, the level of deficit or surplus, endefsurp, is calculated as:

:<math>endefsurp_r=(globalstockratio-domesticstockratio_r)*StBase_r</math>

This implies that if a countries stock ratio is less (greater) than the global average, it is considered in deficit (surplus).

If a country is in deficit, i.e., endefsurp > 0, IFs will act to reduce its exports and increase its exports.  The recomputed value of exports is:

:<math>ENX_r=MAX(0.5*ENX_r,ENX_r*(1-\frac{endefsurp_r}{smoothtradebase_r}))</math>

In words, the decrease in energy exports is determined by the ratio of the level of deficit to the smoothed trade base, but can be no greater than 50 percent.

The recomputed value of imports is:

:<math>ENM_r=ENM_r*(1+\frac{endefsurp_r}{smoothtradebase_r})</math>

with a maximum level given as:

:<math>ENMMax_r=ENM_r+(\frac{pendem_r*MKAVMAX_r-ENM_r}{5})</math>

Similarly, if a country is in surplus, i.e., endefsurp < 0, IFs will act to increase exports and reduce imports.  The amount of increase in exports is controlled, in part, by the exchange rate for the country, EXRATE, specifically its difference from a target level of 1 and its change from the previous year.  As with other adjustment factors of this type, the ADJSTR function is used, yielding a factor named mul.  After first multiplying ENX by a value that is bound from above by 1.05 and from below by the maximum of 0.95 and mul, the recomputed value of ENX is:

:<math>ENX_r=ENX_r*(1-\frac{endefsurp_r}{smoothtradebase_r})</math>

Here, a maximum level is given as:

:<math>ENXMax_r=ENX_r+(\frac{exportbase_r*XKAVMAX_r-ENX_r}{5})</math>

''where'' this maximum value is computed prior to the adjustments to ENX noted above.

The recomputed value of imports is:

:<math>ENM_r=MAX(0.5*ENM_r,ENM_r*(1+\frac{endefsurp_r}{smoothtradebase_r}))</math>

In words, the decrease in energy imports is determined by the ratio of the level of surplus to the smoothed trade base, but can be no greater than 50 percent.

Because of the frequent use and importance of government trade restrictions in energy trade, model users may want to establish absolute export ('''''enxl'' ''')  or import ('''''enml'' ''') limits, which can further constrain energy exports and imports.  An export constraint may also affect the production of oil and gas as described in the next section.

As it is unlikely that the sums of these values of ENX and ENM across countries will be equal, which is necessary for trade to balance.  To address this, IFs computes actual world energy trade (WET) as the average of the global sums of exports and imports.

:<math>WET=\frac{\sum_rENX_r+\sum_rENM_r}{2}</math>

and recomputes energy exports and imports, as:

:<math>ENX_r=WET*\frac{ENX_r}{\sum_rENX_r}</math>

:<math>ENM_r=WET*\frac{ENM_r}{\sum_rENM_r}</math>

This maintains each country’s share of total global energy exports and imports.

IFs can now update the moving average export (XKAVE) and import (MKAVE) propensities for the next time step.  This requires historic weights for exports ('''''xhw'' ''') and imports ('''''mhw'' '''), yielding the equations:

:<math>XKAVE_{r,t+1}=XKAVE_r*\mathbf{xhw}+(1-\mathbf{xhw})*\frac{ENX_r}{exportbase_r}</math>

:<math>MKAVE_{r,t+1}=MKAVE_r*\mathbf{mhw}+(1-\mathbf{mhw})*\frac{ENM_r}{smoothpendem_r}</math>

A further adjustment is made related to the import propensity, MKAVE, related to the difference between this propensity and a target level, ImportTarget, and the change in this difference since the previous year.  This target starts at the level of MKAVE in the first year and gradually declines to 0 over a 150 year period.  As in many other situations in IFs, this process makes use of the ADJUSTR function to determine the adjustment factor.  The value of mulmlev is not allowed to exceed 1, so its effect can only be to reduce the value of MKAVE.

Finally, XKAVE and MKAVE are checked to make sure that they do not exceed their maximum values, XKAVMAX and MKAVMAX, respectively.

[1] The previous year’s values of WEP and CarTaxEnPriAdd are used as the current year’s values are not calculated until later in the model sequence. 

== Domestic Energy Stocks ==

IFs sets a target for energy stocks in each country as a fraction of a domestic stock base, StBase, which was defined earlier as the sum of a moving average of energy demand, smoothpendem, and a moving average of the production of oil, gas, coal, and hydro, smoothentot.  This fraction is defined by the parameter '''''dstlen'' '''.

Stocks are initialized in the first year as '''''dstlen'' '''multiplied by the initial domestic stock base, which is the sum of production of all energy types and an estimated value of apparent energy demand.

:<math>ENST_{r,t=1}=\mathbf{dstlen}*(\sum_cENP_{r,e,t=1}+ENDEMEst_{r,t=1})</math>

''where''

*e includes all energy types
*ENDEMEst is calculated as:

:<math>ENDEMEst_r=(1-\mathbf{dstlen}*AVEPR_r)*\sum_eENP_{r,e,t=1}+ENM_{r,t=1}-ENX_{r,t=1})</math>

''where''

*e includes all energy types
*AVEPR is a weighted average energy production growth rate

In future years, IFs begins by summing the moving average energy demand, smoothpendem, across countries, storing this value as WENDEM and the same for moving average energy production from oil, gas, coal, and hydro, smoothentot, which it stores as WorldEnp.  It also sums the moving average energy demand just for countries that have low propensity for exports, XKAVE < 0.2, and stores this value as WEnDemIm.

At this point, IFs adjusts energy production by multiplying by a capacity utilization factor, CPUTF, which is assumed to be the same for all energy types in a country.

:<math>ENP_{r,e}=ENP_{r,e}*CPUTF_r</math> [1]

The value of CPUTF is initialized to 1 in the first year.  How it changes in time is described in the next section after the description of the calculation of the domestic price index.

An initial estimate of energy stocks, ENST, is then calculated as the previous year’s stocks augmented by production and imports and reduced by use and exports

:<math>ENST_r=ENST_{r,t-1}+-ENDEM_r-ENX_r</math>

If after this calculation, there are excess stocks, i.e., ENST > '''''dstlen'' ''' * StBase, and there is an export constraint, given by '''''enxl'' ''', adjustments are made to the production of oil and gas[2], and, in turn, to energy stocks.  The total reduction in oil and gas production is given as the amount of excess stocks, with a maximum reduction being the total amount of oil and gas production.  This total amount of reduced production is then shared proportionately between oil and gas.  The total reduction is also removed from ENST.

Later, after the determination of prices, ENST is modified to: 1) ensure that they are not less than zero and 2) to account for any global shortfalls.  These modifications are described in the next section.
<div>
----
<div id="ftn1">
[1] This is the first of the two adjustments to energy production noted at the end of the [[Energy#Energy_Supply|Energy Supply]] section.

[2] This is the second of the two adjustments to energy production noted at the end of the [[Energy#Energy_Supply|Energy Supply]] section.
</div></div>
== Energy Prices and Final Adjustments to Domestic Energy Stocks and Capacity Utilization ==

IFs keeps track of separate domestic, ENPRI, and world, WEP, energy price indices, that apply to all forms of energy.  These are initialized to a value of 100 in the first year.  It also tracks the world energy price in terms of dollars per BBOE, WEPBYEAR, which is initialized as a global parameter.

A number of pieces are needed for the calculation of energy prices.  These include a world stock base, wstbase, world energy stocks, wenst, world energy production by energy type, WENP, world energy capital, WorldKen, and a global capital output ratio, wkenenpr.  These are calculated as follows:

:<math>wstkbase=\sum_rStBase_r</math>

:<math>wenstks=\sum_r(ENST_r-ENSHO_{r,t-1})</math>

:<math>WENP_e=\sum_rENP_{r,e}</math>

:<math>WorldKen=\sum_r\sum_e(ken_e*\frac{CPUTF_r}{MAX(5,\mathbf{lke_e})})</math>

:<math>wkenenpr=\frac{WorldKen}{WorldEnp}</math>

''where''

*ENSHO is domestic energy shortage (described below)
*ken is capital for each energy type
*'''''lke'' ''' is the average lifetime of capital for each energy type

In cases when at least one country has an exogenous restriction on the production of oil, i.e., enpm(oil) < 1 for at least one country, a few additional variables are calculated:

:<math>GlobalShortFall=\sum_r\sum_eMax(0,ENP_{r,e,t-1}-1.05*ENP_{r,e,t})</math>

:<math>WorldEnProd=\sum_eWENP_e</math>

:<math>ShortFallSub=GlobalShortFall*MIN(10,\frac{WorldEnProd}{WENP(oil)})</math>

Otherwise these three variables all take on a value of 0.

These values are used to calculate an adjustment factor driven by global energy stocks that affects domestic energy prices.  The effect in the current year, wmul, is calculated using the ADJSTR function, which looks at the difference between world energy stocks, wenstks and the desired level, given by '''''dstlen'' ''' * wstbase, and the change in world energy stocks from the previous year.  The presence of an exogenous restriction on the production of oil has two effects on the calculation of wmul.  First, the value of ShortFallSub affects the two differences that feed into the ADJSTR function.  Second, the elasticities applied in the ADJSTR function are tripled.

The adjustment factor calculated in the current year is not applied directly to the calculation of domestic energy prices.  Rather, a cumulative value, cumwmul, is calculated as:

:<math>cumwmul_t=cumwmul_{t-1}*(1+(wmul-1)*\mathbf{eprohw})</math>

Other factors affect the domestic energy price index – domestic energy stocks, possible cartel price premiums, '''''encartpp'' ''', the first year value of the world energy price index, IWEP, changes in the global capita output ratio from the first year, whether the user has set a global energy price override. '''''enprixi'', '''and whether there are any restriction on oil production.

The domestic energy stocks affect a country-specific “markup” factor, MarkUpEn.  This starts at a value of 1 and changes as a function of the value of mul, which is calculated using the ADJSTR function.  Here the differences are those between domestic energy stocks and desired stocks, given as '''''dstlen'' ''' * StBase, and the changes in energy stocks from the previous year.  Shortages from the previous year are also taken into account.  The user can also control the elasticities used in the ADJSTR function with the parameters '''''epra'' ''' and '''''eprafs'' '''.  This markup evolves over time as

:<math>MarkUpEn_{r,t}=MarkUpEn_{r,t-1}*mu</math>

The domestic energy price index, ENPRI, is first calculated as:

:<math>ENPRI_r=\mathbf{X}*mul_r*cumwmul+\mathbf{encartpp}</math>

''where''

*'''X''' = '''''enprixi'', '''when this parameter is set to a value greater than 1 and IWEP otherwise

It is then recomputed as:

:<math>ENPRI_r=MIN(ENPRI_r,ENPRI_{r,t-1}+\mathbf{encartpp}_t-\mathbf{encartpp}_{t-1}+\mathbf{X})</math>

''where''

*'''X''' is 100 whenthere is a restriction on oil production in at least one country and 20 otherwise

Furthermore, ENPRI is not allowed to fall by more than 10 in a given year.

It is possible for the user to override this price calculation altogether.  Any positive value of the exogenous country-specific energy price specification ('''''enprix'' ''') will do so.

It is only now that a country’s energy stocks and shortages are finalized for the current year.  If ENST is less than 0, then a shortage is recorded as ENSHO = -ENST and ENST is set to 0.  In addition, for countries that have a low propensity for exports, XKAVE < 0.2, a share of any global shortfall is added to their shortage, with the share determined by the country’s share of moving average energy demand among those countries:

:<math>ENSHO_r=ENSHO_r+GlobalShortFall*\frac{smoothpendem_r}{WEnDemIm}</math>

The energy shortage enters the Economic model in the calculation of gross sectoral production.

The same differences in domestic stock from their target level and their change since the previous year, taking into account shortages from the previous year, are used to update the value of capacity utilization in energy, CPUTF, which was introduced earlier.  The multiplier affecting CPUTF, Mul, is calculated using the ADJSTR function, with elasticities given by '''''elenpst'' ''' and '''''elenpst2'' '''.  In addition, the capacity utilization is smoothed over time.

:<math>CPUTF_{r,t}=0.5*CPUTF_{r,t-1}+0.5*Mul</math>

This value is further assumed to converge to a value of 1 over a period of 100 years and is bound to always have a value between 0.2 and 2.

This still leaves the need to calculate the world energy price.  IFs actually tracks a world price including carbon taxes, WEP, and a world price ignoring carbon taxes, WEPNoTax.  Carbon taxes are ignored in cases where the energy price is set exogenously using '''''enprix'' '''.

In both cases, the world energy price is a weighted average of domestic energy prices:

:<math>WEP=\frac{TENP}{TENPRI}</math>

:<math>WEPNoTax=\frac{TENP}{TENPRINoTax}</math>

''where''

:<math>TENP=\sum_r\sum_eENP_{r,e}</math>

:<math>TENPRINoTax=\sum_r\sum_e(ENPRI_r*ENP_{r,e})</math>

:<math>TENPRI=\sum_r\sum_e((ENPRI_r+CarTaxEnPriAdd_r*\frac{WEP_{t=1}}{WEPBYEAR_{t=1}})*ENP_{r,e})</math>

''where''

*WEP and WEPBYEAR convert CarTaxEnPriAdd from $/BBOE to an index value
*the term with CarTaxEnPriAdd is ignored in countries with exogenous energy prices in a given year
*CarTaxEnPriAdd is 

Finally, the value of WEPBYEAR is computed as:

:<math>WEPBYEAR=WEPBYEAR_{t=1}*\frac{WEP}{WEP_{t=1}}</math>

== Energy Investment ==

Investment in energy is relatively complex in IFs, because changes in investment are the key factor that allows us to clear the energy market in the long term.  It is also different and perhaps slightly more complex in IFs than investment in agriculture.  Whereas the latter involves computing a single investment need for agricultural capital, and subsequently dividing it between land and capital, in energy a separate demand or need is calculated for each energy type, based on profit levels specific to each energy type.

We begin by calculating a total energy investment need (TINEED) to take to the economic model and place into the competition for investment among sectors.  This investment need is a function of energy demand, adjusted by a number of factors, some global and some country-specific. To begin with, TINEED is calculated as

:<math>TINEED_r=ENDEM_r*mulendem*\frac{wkenenpri_t}{wkenenpri_{t-1}}*mulkenenpr*mulwst*mulstocks^{0.5}*mulrprof_r*mulrenew_r*sendeminvr_r</math>

''where''

*mulendem is the ratio of global energy demand per unit GDP in the current year to that in the previous year

:<math>mulkenenpr=\frac{WENDEM_t/WGDP_t}{WENDEM_{t-1}/WGDP_{t-1}}</math>

*wkenenpri is the ratio of global energy capital to global energy production

:<math>wkenenpr=\frac{WorldKen}{WorldEnp}</math>

*mulkenenpr is the ratio of wkenenpr in the current year to that in the previous year

:<math>mulkenenpr=\frac{wkenenpr_t}{wkenenpr_{t-1}}</math>

*mulwst and mulstocks are factors related to global energy stocks. mulwst is calculated using the ADJSTR function, where: the first order difference is that between global energy stocks, wenstks, and desired global energy stocks, DesStocks = '''''dstlen'' ''' * wstbase; the second order difference is between the level of world energy stocks in the current year and those in the past year; and the elasticities are given by the parameters '''''elenpr'' ''' and '''''elenpr2'' '''. mulstocks is also related to global energy stocks, but is more directly related to the desired level of global energy stocks:

:<math>mulstocks=\frac{DesStocks}{MAX(0.5*DesStocks,MIN(4*DesStocks,enstks))}</math>

Note that mulstocks will always take on a value between ¼ and 4.

*mulrprof is a function of the expected level of profits in the energy sector as a whole in a country, EPROFITR.  Energy profits are calculated as the ratio of returns, EnReturn, to costs, ProdCosts.  EPROFITR is actually a moving average of these profits relative to those in the base year, with a historical weighting factor controlled by the parameter '''''eprohw'' '''.  In full, we have:

:<math>EnReturn_r=WEPNoTax*\sum_eENP_{r,e}</math> [1]

:<math>ProdCost_r=\sum_e\frac{ken_{e,r}}{MAX(5,\mathbf{lke_e})}</math>

:<math>EnReturn_r=\frac{EnReturn_r}{ProdCost_r}</math>

:<math>EPROFIT_{r,t}=\mathbf{eprohw}*EPROFIT_{r,t-1}+(1-\mathbf{eprohw})*\frac{EnReturn_{r,t}}{EnReturn_{r,t=1}}</math>

We can now calculate mulrprof using the ADJSTR function.  The first order difference is between the current value of EPROFITR and a target value of 1; the second order difference is the change in the value of EPROFITR from the previous year; the elasticities applied to these differences are given by the parameters '''''eleniprof'' ''' and '''''eleniprof2'' '''.

*mulrenew is a function of the share of other renewables in the energy mix in a country.  It is assigned a value of 1 unless the production of energy from renewables exceeds 70% of total energy demand.  If so, we have:

:<math>mulrenew_r=MAX(0.5,1-(\frac{ENP_{r,renew}}{ENDEM_r}-0.7)*1)</math>

Given these conditions, mulrenew can take on values between 0.5 and 1, with larger values associated with larger amounts of renewable production.

*sendeminvr is a moving average of the ratio of investment need to energy demand in a country, with an accounting for changes in the global capital production ratio since the first year and is updated as[2]:

:<math>sendeminvr_{r,t+1}=0.95*sendeminvr_{r,t}+0.05*\frac{TINEED_{r,t}}{ENDEM_{r,t=1}}*\frac{wkenenpr_{t=1}}{wkenenpr_t}</math>

After this initial calculation, two further adjustments are made to TINEED.  The first is a reduction related to a possible reduction of inventory, invreduc, carried over from the previous year.  The calculation of invreduc is described later in this section, where we look at reductions in investment in specific energy types due to resource constraints or other factors. The effect on TINEED is given as:

:<math>TINEED_r=TINEED_r-MIN(0.7*invreduc_{r,t-1},0.6*TINEED_r)</math>

Thus, the reduction in TINEED can be no more than 60 percent.

Finally, the user can adjust TINEED with the use of the multiplier '''''eninvm'' '''.

Before this total investment need, TINEED, is passed to the Economic model, there is a chance that it may need to be further reduced.  This depends on the calculation of a bound, TINeedBound.  TINeedBound arises from a bottom-up calculation of the investment needs for each energy type individually, ineed.  These depend upon the profits for each energy type and any possible bounds on production related to reserves and other factors.

As with the estimate of total profits to energy, the returns by energy type depend upon production and costs. 

:<math>EnReturnS_{r,e}=\frac{ENP_{r,e}}{EnCost_{r,e}}</math>

For the non-fossil fuel energy types – hydro, nuclear, and other renewable – EnCost is based solely on capital depreciation

:<math>EnCost_{r,e}=\frac{ken_{r,e}}{\mathbf{lke_e}}</math>

''where''

*e = hydro, nuclear, renew

For the fossil fuel energy types – oil, gas, and coal – we must also consider any possible carbon taxes. EnCost is calculated as 

:<math>EnCost_{r,e}=\frac{ken_{r,e}}{\mathbf{lke_e}}+ENP_{r,e}*\mathbf{carfuel}_e*\mathbf{carbtax}_r+MAX(-0.5*\frac{ken_{r,e}}{\mathbf{lke_e}},ENP_{r,e}*(\mathbf{carfuel}_e-AvgCarFuel)*emtax_r)</math>

''where''

*e = oil, coal, gas
*'''''carfuel'' ''' is the carbon content of the fuel in tons per BBOE
*AvgCarFuel is the unweighted arithmetic average of the carbon content of oil, gas, and coal
*'''''carbtax'' ''' is an exogenously specified country-specific carbon tax in $ per BBOE
*emtax is the number of years since the first year plus one multiplied by 2

The change in eprofitrs from the first year is then calculated as:

:<math>eprofitrs_{r,e}=\frac{EnReturnS_{r,e,t}}{EnReturnS_{r,e,t=1}}</math>

An average return, avgreturn, is calculated as the weighted sum of the individual returns:

:<math>avgreturn_r=\sum_e(ENP_{r,e}*EnReturnS_{r,e})smoothentot_r</math>

Investment need by energy type, ineed, grows in proportion to capital and as a function of relative profits.

:<math>ineed_{r,e,t}=ineed_{r,e,t=1}*\frac{ken_{r,e,t}}{ken_{r,e,t=1}}*eprofitrs^{elass_{r,e}}_{r,e}</math>

''where''

*'''''elass'' ''' are country and energy-specific user controlled parameters

At this point, ineed is checked to make sure that it does not fall by more than 20% or increase by more than 40% in any single year. 

Also, if the user has set an exogenous target for production growth, i.e., '''''eprodr'' ''' > 0, all of the above is overridden and ineed is calculated as:

:<math>ineed_{r,e}=\frac{ken_{r,e}*(1+\mathbf{enprodr}_e)}{\mathbf{lke}_e}</math>

These investment needs are checked to make sure that they do not exceed what the known reserve base can support.  This applies only to oil, gas, coal, and hydro. An initial estimate of the maximum level of investment is given by:

:<math>maxinv_{r,e}=(\frac{RESER_{r,e}}{\mathbf{prodtf}_{r,e}}-\frac{ken_{r,e}}{QE_{r,e}}+\frac{ENP_{r,e}}{\mathbf{lke}_e})*QE_{r,e}</math>

''where''

*e = oil, gas, coal, or hydro
<div>
The first term in parentheses, when multiplied by QE, indicates the amount of capital that would be necessary in order to yield the maximum level of production given the lower bound of the reserve production ratio, '''''prodtf'' '''. The second term is simply the current level of capital and the third term indicates the level of depreciation of existing capital.  This implies that countries will not make investments beyond those that would give it the maximum possible level of production for a given energy type.

At the same time, IFs assumes there is a minimum level of investment, which is basically 30% of the capital depreciated during the current year:

:<math>mininv_{r,e}=0.3*\frac{ENP_{r,e}}{\mathbf{lke}_e}*QE_{r,e}</math>

''where''

*e = oil, gas, coal, or hydro

In cases where the current production of oil, gas, or coal already equals or exceeds the exogenously specified maximum for a country – '''''enpoilmax'' ''', '''''enpgasmax'' ''', or '''''enpcoalmax'' ''' – maxinv is set equal to mininv.  This again avoids useless investment.

A further constraint is placed on the maximum investment level in capital for hydro production.  This is done by simply replacing RESER/'''''prodtf'' ''' in the calculation of maxinv with the value ENDEM * EnpHydroDemRI * 2, where EnpHydroDemRI is the ratio of energy produced by hydro in the base year to total energy demand in that year.  In other words, the growth in energy production from hydro in the current year from the first year cannot exceed twice the growth in total energy demand over that period, even if reserves are available, and capital investments are restricted accordingly. 

:<math>maxHydroProd_{r,t}=2*\frac{ENDEM_{r,t}}{ENDEM_{r,t=1}}*ENP_{r,Hydro,t=1}</math>

The constraints placed on investment in nuclear energy differ somewhat from these other fuels. IFs does not have an explicit measure of reserves for nuclear.  Rather, it is assumed that the growth in capital in nuclear energy cannot exceed 1 percent of existing capital plus whatever is required to account for depreciation:

:<math>maxinv_{r,e}=(0.01*\frac{ken_{r,e}}{QE_{r,e}}+\frac{ENP_{r,e}}{\mathbf{lke}_e})*QE_{r,e}</math>

''where''

*e = nuclear

Also, the minimum level of investment for nuclear energy is assumed to be 50 percent of the capital depreciated in the current year, rather than 30 percent as with oil, gas, coal, and hydro.

There is no limit to the investments in capital for other renewables.

Given these restrictions, the investment needs for oil, gas, coal, hydro, and nuclear are updated so that mininv <= ineed <= maxinv.  Any reductions from the previous estimates of ineed are summed across energy types to yield the value of invreduc, which will affect the estimate of TINEED in the following year as described earlier.

The final estimates of ineed for each energy type are summed to yield TINeedBound.  If TINEED is greater than TINEEDBOUND, then TINEED is recalculated as the average of the two:

:<math>TINEED_r=0.5*(TINEED_r+TINeedBound_r)</math>

This value of TINEED is passed to the Economic model as IDSenergy, 

:<math>IDS_{r,s=energy}=sidsf_r*TINEED_r</math>

''where''

*sidsf is an adjustment coefficient converting units of energy capital into monetary values. This gradually converges to a value of 1 after a number of years specified by the parameter '''''enconv'' '''.

In the Economic model, the desired investment in energy must compete with other sectors for investment (see more about linkages between the Energy and Economic models in section 3.7).  Once these sectoral investments are determined, a new value for investments in the energy sector, IDSs=energy, is passed back to the Energy model.  The adjustment coefficient is then applied to yield:

:<math>inen_r=\frac{IDS_{r,s=energy}}{sidsf_r}</math>

In the meantime, the desired investment for each energy type can be modified with a country and energy-type specific parameter '''''eninvtm'' ''', and a new value of TINEED is calculated as the sum of these new levels of desired investment.  The amount of the available investment, inen, going to each energy type is then calculated as:

:<math>ineed_{r,e}=inen_r*\frac{ineed_{r,e}*\mathbf{eninvtm}_{r,e}}{TINEED_r}</math>

i.e., all energy types receive the same proportional increase or decrease in investment.

These investments are then translated into units of capital, KEN_Shr,

:<math>KENShr_{r,e}=ineed_{r,e}-\frac{ken_{r,e}}{\mathbf{lke}_e}</math>

The new level of capital is determined as:

:<math>ken_{r,e,t+1}=(ken_{r,e,t}+KENShr_{r,e})*(1-CIVDM_r)</math>

''where''

*CIVDM is an exogenous factor reflecting civilian damage from war

Note that there is no guarantee that KEN_Shr is positive, so it is theoretically possible for ken to fall below 0; IFs checks to make sure that this does not happen.
</div>
----
<div id="ftn1">
[1] World energy price is used to provide stability. The no tax world energy price is used as taxes do not contribute to returns.

[2] Note the careful use of the time subscripts. sendeminvr is not updated until after the computation of the initial value of TINEED, so the initial calculation of TINEED needs to use the previous year’s value of sendeminvr. Furthermore, the updating of sendeminvr occurs after TINEED has been adjusted to reflect any inventory reductions, but before the investment multiplier, '''''eninvm'' ''', is applied.
</div>
== Economic Linkages ==

The economic model and the two physical models have many variables in common.  As in the agricultural model, IFs generally uses the values in the physical model to override those in the economic model.  To do so, it computes coefficients in the first year that serve to adjust the physical values subsequently. The adjustment coefficients serve double duty - they translate from physical terms to constant monetary ones, and they adjust for discrepancies in initial empirical values between the two models.

[[Energy#Energy_Investment|The Energy Investment section]] already described how desired investment, TINEED, is passed to the Economic model using the adjustment coefficient sidsf.  The adjustment coefficient, ZSR is used to convert production: 

:<math>ZS_{r,s=2}=ZSR_r*WEPBYear_{r,t=1}*\sum^EENP_{r,e}</math>

''where''

:<math>ZSRI_r=\frac{ZS_{r,s=2,t=1}}{WEPBYear_{r,t=1}*\sum^EENP_{r,e,t=1}}</math>

ZSR is a convergence of ZSRI to a value of 1 in 30 years and WEPBYear converts the energy units, which are in BBOE to dollars.

The adjustment coefficient SCSF is used to convert consumption:

:<math>CS_{r,s=2}=SCSF_r*ENDEM_r*0.6</math>

where

:<math>SCSF_r=\frac{CS_{r,s=2,t=1}}{ENDEM_{r,t=1}*0.6}</math>

Note that this assumes that consumer make up a constant 60 percent of consumption of total primary energy.  Also SCSF remains constant over time.

For stocks, imports, and exports, WEBPBYear serves as the adjustment coefficient

:<math>ST_{r,s=2}=WEPBYear_{r,t=1}*ENST_r</math>

:<math>XS_{r,s=2}=WEPBYear_{r,t=1_r}*ENX_r</math>

:<math>MS_{r,s=2}=WEPBYear_{r,t=1}*ENM_r</math>

Finally, the indexed price (with a base of 1) in the energy sector of the economic submodel (PRI) is simply the ratio of current to initial regional energy price (ENPRI) time the value of PRI in the first year.

:<math>PRI_{r,s=2}=PRI_{r,s=2,t=1}*\frac{ENPRI_r}{ENPRI_{r,t=1}}</math>

== Resources and Reserves: Capital-to-Output Ratios and Discoveries ==

=== Capital-to-Output Ratios ===

Resource base is important in selected energy categories of IFs: conventional oil, natural gas, coal, hydroelectric power, and unconventional oil.  Resources are not important in the nuclear category, which represents an undefined mixture of burner, breeder and fusion power.

Resource costs, as represented by the capital required to exploit them, increase as resource availability in the resource-constrained categories decreases.  The capital-to-output ratio captures the increased cost.  Kalymon (1975) took a similar approach.

More specifically, the capital-to-output ratio (QE) increases in inverse proportion to the remaining resource base (as the base is cut in half, costs double'''; '''as it is cut to one fourth, costs quadruple).  The model multiplies the initial capital output ratio by the initial resource base (RESOR) times a multiplier (RESORM) by which a model user can exogenously increase or decrease model assumptions.  It then divides that product by initial resources minus cumulative production to date (CUMPR).

Total available resources by energy type, ResorTot, are calculated as:

:<math>ResorTot_{r,e}=\mathbf{resorm}_{r,e}*\mathbf{resor}_{r,e}+\mathbf{resorunconm}_{r,e}*\mathbf{resoruncon}_{r,e}</math>

''where''

*'''''resor'' ''' and '''''resoruncon'' ''' are exogenously assumed levels of the ultimate amount of conventional and unconventional forms of each energy type.  There is no assumption about conventional resources for nuclear and only oil and gas include unconventional resources
*'''''resorm'' ''' and '''''resorunconm'' ''' are multipliers that can be used to change the amount of assumed ultimate resources by energy type

All energy types begin with basic capital-to-output ratios, BQE and BQEUC.  These are initially set equal to the same values of QE and QEUNCON, which are derived in the pre-processor, and then evolved according to exogenous assumptions about technological advance for each energy type:

:<math>BQE_{r,e,t}=BQE_{r,e,t-1}*(1-\mathbf{etechadv}_e)</math> [1]

:<math>BQEUNCON_{r,e,t}=BQEUNCON_{r,e,t-1}*(1-\mathbf{etechadvuncon}_e)</math>

Recall that technological improvements result in declining amounts of capital required for each unit of energy produced.

The initial translation of this basic capital-to-output ratio to the value actually used to determine energy production varies by energy type.

This is most straightforward for nuclear and unconventional energy, which do not take into account remaining resources:

:<math>QE_{r,e,t+1}=BQE_{r,e,t}*\mathbf{qem_{r,e}}</math>

''where''

*e is nuclear
*'''''qem'' ''' is an exogenous multiplier

:<math>QEUC_{r,e,t+1}=BQEUC_{r,e,t}*\mathbf{qeunconm_{r,e}}</math>

''where''

*e is oil or gas
*'''''qeunconm'' ''' is an exogenous multiplier

For hydro and other renewables, QE depends upon the remaining resource, which is defined as the difference between the total resource available and a moving average of the difference in production vis-à-vis production in the first year.  In other words, it is not cumulative production that is important, but rather the portion of resources used annually.

:<math>QE_{r,e,t+1}=BQE_{r,e,t}*\frac{ResorTot_{r,e}}{resorrem_{r,e}}*\mathbf{qem_{r,e}}</math>

''where''

:<math>resorrem_{r,e}=ResorTot_{r,e}-ENPGR_{r,e}</math>

:<math>ENPGR_{r,e}=SmoothENP_{r,e}-ENP_{r,e,t=1}</math>

:<math>SmoothENP_{r,e,t}=0.8*SmoothENP_{r,e,t-1}+0.2*ENP_{r,e}</math>

*e = hydro or renew

For oil, gas, and coal, the logic is similar, but the definition of remaining resources is somewhat different: 

:<math>resorrem_{r,e}=MAX(ResorTot_{r,e}-CUMPR_{r,e},MaxFac_{r,e})</math>

:<math>CUMPR_{r,e,t}=CUMPR_{r,e,t-1}+ENP_{r,e}</math>

:<math>MaxFac_{r,e}=0.1*ResorTot_{r,e}</math>

Furthermore, the capital-to-output ratio is calculated as a moving average

:<math>CompQE_{r,e}=BQE_{r,e}*(\frac{ResorTot_{r,e}}{resorrem_{r,e}})^{0.4}</math>

:<math>QE_{r,e,t+1}=(0.8*QE_{r,e,t}+0.2*CompQE_{r,e})*\mathbf{qem_{r,e}}</math>

''where''

*e is oil, gas, or coal

=== Discoveries ===

Energy reserves decrease with production and increase with discoveries, the latter of which are limited by remaining resources and other factors.  This only applies to oil, gas, and coal.

:<math>RESER_{r,e,t+1}=RESER_{r,e,t}+rd_{r,e}-ENP_{r,e}</math>

The rate of discovery, rd, is initially computed as a function of a number of factors related to global energy prices, remaining resources, global and domestic production, and several exogenous assumptions

:<math>rd_{r,e}=rdiaug_e*wepterm*reterm_{r,e}*\mathbf{rdm_{r,e}}</math>

'' where''

*e = oil, gas, coal
*'''''rdm'' ''' is a country and energy-specific exogenous multiplier
*rdi_aug is an energy-specific factor driven entirely by exogenous assumptions about initial rates of discovery, '''''rdi'' ''', and annual increments, '''''rdinr'' ''':

:<math>rdiaug_e=\mathbf{rdi}_e+\mathbf{rdinr}_{r,e}*(t-firstyear)</math>

*wepterm is a global factor driven by the growth in world energy prices from the first year and an exogenously defined elasticity, '''''elasdi'''''

:<math>wepterm=1+\frac{WEP_t-WEP_{t=1}}{WEP_{t=1}}*\mathbf{elasdi}</math>

*reterm is a country and energy-specific factor representing an average of a country’s remaining resources as a share of original resources and its share of current production

:<math>reterm_{r,e}=0.5*(\frac{ResorTot_{r,e}-CUMPR_{r,e}-RESER_{r,e}}{\sum_e(ResorTot_{r,e,t=1}-RESER_{r,e,t=1})}+\frac{ENP_{r,e}}{WENP_e})</math>

A further assumption is that the rate of discovery cannot exceed 4 percent of the remaining resources in a country, where remaining resources are specified as:

:<math>resorrem_{r,e}=ResorTot_{r,e}-CUMPR_{r,e}-RESER_{r,e}</math>

''where''

*e = oil, gas, coal
*For oil the amount of unconventional oil in ResorTot is also affected by the parameter '''''enresunce'' '''[2]
<div>[1] There used to be an additional impact of ICT broadband that would further reduce the BQE for other renewables, but that is currently not active in the model. <div id="ftn1">
[2] This only affects Canada, which has a value of '''''enresunce'' ''' = 0.3. Why this is not included in the QE calculations is unclear.
</div></div>
== Energy Indicators ==

Among useful energy or energy-related indicators is the ratio (ENRGDP) of energy demand (ENDEM) to gross domestic product (GDP).

:<math>ENRGDP_r=\frac{ENDEM_r}{GDP_r}</math>

Global production of energy by energy type (WENP) is the sum of regional productions (ENP).

:<math>WENP_e=\sum^RENP_{r,e}</math>

Global energy production is the basis for examining the build-up of carbon dioxide and Climate Change, as described in the documentation of the Environmental model.

The ratio of oil and gas production globally to total energy production (OILGPR) helps trace the transition to other fuels.

:<math>OILGPR=\frac{WENP_{e=1}+WENP_{e=2}}{\sum^EWENP_e}</math>

Global energy reserves (WRESER) and global resources (WRESOR) are sums by energy type across regions, the latter taking into account any resource multiplier (RESORM) that a user specifies to modify basic model resource estimates.

:<math>WRESER_e=\sum^RRESER_{r,e}</math>

:<math>WRESOR_e=\sum^R(RESOR_{r,e}*RESORM_e)</math>

= Energy Bibliography =

Kalymon, Basil A. 1975. "Economic Incentives in OPEC Oil Pricing Policy." ''Journal of Development Economics'' 2: 337-362.

Naill, Roger F. 1977.''Managing the Energy Transition.'' Vols. 1 and 2. Cambridge, Mass: Ballinger Publishing Co.

Stanford University. 1978. ''Stanford Pilot Energy/Economic Model.'' Stanford: Department of Research, Interim Report, Vol. 1.

Agriculture

2026-08-27T18:21:15Z

Megan.Livengood:

Please cite as: Dale S. Rothman, Hughes, Barry B., and Kanishka Narayan. 2017. ''"IFs Agriculture Model Documentation." ''Working paper 2017.07.04. Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <[https://pardeewiki.du.edu/index.php?title=Agriculture]>

Further information on this topic is provided in a [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_9 dedicated chapter], which offers additional context, analysis, and supporting information.

The IFs agricultural model tracks the supply and demand, including imports, exports, and prices, of three agricultural commodities: crops, meat, and fish. Crops, meat and fish have direct food, animal feed, industrial and food manufacturing uses. The agricultural model is also where land use dynamics and water use are tracked in IFs, as these are key resources for the agricultural sector.

The structure of the agriculture model is very much like that of the economic model. It combines a growth process with a partial economic equilibrium process using stocks and prices to seek a balance between the demand and supply sides. As in the economic model, no effort is made in the standard adjustment mechanism to obtain a precise equilibrium in any time step. Instead stocks serve as a temporary buffer and the model chases equilibrium over time.

The most important linkages between the agriculture model and other models within IFs are with the economic model. The economic model provides forecasts of average income levels, labor supply, total consumer spending, and agricultural investment, all of which are used in the agriculture model. In turn, the agriculture model provides forecasts on agricultural production, imports, exports, and demand for investment, which override the sectoral computations in the economic model. The agricultural model also has important links to the population and health models, using population forecasts and providing forecasts of calorie availability.

= Dominant Relations =

Agricultural production is a function of the availability of resources, e.g. land, livestock, capital, and labor, as well as climate factors and technology. Technology is most directly seen in the changing productivity of land in terms of crop yields, and in the production of meat relative to the input level of feed grain. The model also accounts for lost production (such as spoilage in the fields or in the first stages of the food supply chain), distribution and transformation losses and consumption losses (which account for food lost at the household levels) which are all determined by average income.

Agricultural demand depends on average incomes, prices, and a number of other factors. For example, changing diets can affect the demand for meat, which in turn affects the demand for feed crops. The industrial demand for crops, some of which is directed to the production of biofuels, is also affected by energy prices.

Production and demand, along with existing and desired stocks and historical trade patterns determine the trade in agricultural products. The differences in the supply of crops, meat, and fish (production after accounting for losses and trade) and the demand for these commodities are reflected in shifts in agricultural stocks. Stock shortages feed forward to actual consumption, which is addressed in the population model of IFs. Stocks, particularly changes in stocks, are a key driver of changes in crop prices. Crop prices are also influenced by the returns to agricultural investment and therefore to the basic underlying cost structure. Meat prices are tied to, and track world crop prices, while changes in fish prices are driven by changes in fish stocks.

Stocks and stock changes also play a role, along with general economic and agricultural demand growth, in driving the demand for agricultural investment. The actual levels of investment are finalized in the economic model of IFs and subject to constraints there. The investment can be of two types – investment for expanding and maintaining cropland (extensification) and investment for increasing crop yields per unit area (intensification). The expected relative rates of return determine the split.

The final key dynamics addressed in the agriculture model relate to land, livestock, and water. The latter of these is very straightforward, driven only by crop production. Changes in livestock are determined by changes in the amount of available grazing land, changes in the demand for meat, and the ability of countries to meet this demand as reflected in changing stocks.

In the IFs model, land is divided into 5 categories: crop land, grazing land, forest land, ’other’ land, and urban or built-up land. First, changes in urban land are driven by changes in average income and population, and draws from all other land types. Second, the investment in cropland development is the primary driver of changes in cropland, with shifts being compensated by changes in forest and "other" land. Third, changes in grazing land are a function of average income, with shifts again being compensated by changes in forest and "other" land. Finally, conservation policies can influence the amount of forest land, with any necessary adjustments coming from crop and grazing land. 

= Structure and Agent System =

{| class="tableGrid" style="width:100%;" cellspacing="0" cellpadding="5" border="1"
|-
| style="width: 50%" | <div>'''System/Subsystem''' </div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Agriculture</div>
|-
| style="text-align: left" | <div>'''Organizing Structure'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Partial market equilibrium</div>
|-
| style="text-align: left" | <div>'''Stocks'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Capital, labor, accumulated technology, agricultural commodities, land</div>
|-
| style="text-align: left" | <div>'''Flows'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Production, loss, consumption, trade, investment</div>
|-
| style="text-align: left" | <div>'''Key Aggregate ''' '''Relationships '''</div><div>(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Production function with endogenous technological change  </div><div> </div><div>Price determination</div>
|-
| style="text-align: left" | <div style="text-align: left">'''Key Agent-Class Behavioral ''' '''Relationships'''</div><div style="text-align: left">(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" |
Household crop, meat, and fish consumption

Industry crop use

Livestock producers crop use

|}

= Flow Charts =

== Overview ==

The agriculture model combines a growth process in production with a partial equilibrium process that replaces the agricultural sector in the full-equilibrium economic model unless the user disconnects it. The model represents three agricultural commodities: crop, meat, and fish.

The key equilibrating variables are the stocks of the three commodities. Equilibration works via investment to control capital stock and via prices to control domestic demand.

Specifically, as food stocks rise, investment falls, restraining capital stock and agricultural production, and thus holding down stocks. Also, as stocks rise, prices fall, thereby increasing domestic demand, further holding down stocks. Domestic production and demand also influence imports and exports directly, which further affect stocks.

== Agricultural Production ==

=== Crop Production ===

Crop production is most simply a product of the land under cultivation (cropland) and the crop yield per hectare of land. Yield is determined in a Cobb-Douglas type production function, the inputs to which are agricultural capital, labor, and technical change. Technical change is conceptualized as being responsive to price signals, but the model uses food stocks in the computation to enhance control over the temporal dynamics of responsiveness.  Specifically, technology responds to the imbalance between desired and actual food stocks globally.  In addition there is a direct response of yield change to domestic food stocks that represents not so much technical change as farmer behavior in the fact of market conditions (e.g. planting more intensively). Overall, basic annual yield growth is bound by the maximum of the initial model year's yield growth and an exogenous parameter of maximum growth.

This basic yield function is further subject to a saturation factor that is computed internally to the model̶–investments in increasing yield are subject to diminishing rather than constant returns to scale. Moreover, changes in atmospheric carbon dioxide (CO2) will affect agricultural yields both directly through CO2 and indirectly through changes in temperature and precipitation. Finally, the user can rely on parameters to increase or decrease yield patterns indirectly with a multiplier or to use parameters to control the saturation effect and the direct and indirect effects of CO2 on crop yield.

[[File:CropproductionFlowchartKN.png|frame|center|text-bottom|571x500px|Agricultural Production Flowchart]]

=== Meat and Fish Production ===

Meat and fish production are represented far more simply than crop production. Meat production is simply the product of livestock herd size and the slaughter rate. Meat production includes production of non-meat animal products (eg. Milk and eggs). The herd size changes over time in response to global and domestic meat stocks, as well as changes in the demand for meat and the amount of grazing land.

Fish production has two components: wild catch and aquaculture. The former is based on actual data and an exogenous parameter that allows the user to influence rate of catch. Aquaculture is assumed to continue to grow at a country-specific growth rate; a multiplier can also be used to increase or decrease aquaculture production.   

[[File:Meat and fish production FlowchartKN.png|frame|center|text-bottom|571x500px|Meat and Fish Production Flowchart]]

== Agricultural Demand ==

=== Overview ===

Agricultural demand is divided into crops, meat, and fish. Crop demand is further divided into industrial, animal feed, and human food demand. 

Food demand from crops, meat and fish are responsive to calorie demand, which in turn responds to GDP per capita (as a proxy for income).  The division of calorie demand between demand for calories from crops and from meat and fish changes in response also to GDP per capita (increasing with income). Caloric demand is used as the basis to compute food demand through conversion to food demand in terms of grams per capita. The caloric value of demand is also used to compute food demand in terms of proteins per capita. 

In addition to food demand, demand for feed, industrial demand for meat, crops and fish and food manufacturing demand are also computed. When all components of agricultural demand are computed, the price of the food elements of it are checked to assure that the total household demand for food does not exceed a high percentage of total country-level household consumption expenditures.

=== Calorie Demand ===

Crop use for food and meat demand are both influenced by calorie demand. Total per capita calorie demand is driven by GDP per capita, but can be limited by calorie availability as well as by an exogenous parameter specifying maximum calorie need.[[File:Calorie Demand FlowchartKN.png|frame|center|text-bottom|571x500px|Calorie demand flowchart]]

The calculations of demand for meat, fish and food crop determine the ultimate division of calorie sources.  There is also a limit to the share of calories that can come from meat. The demand for calories from crops is simply the residual obtained by subtracting the demand for calories from meat and fish from the demand for total calories. Caloric value of demand is used to compute food demand in terms of grams per capita and in terms of proteins per capita.  Caloric value of demand is adjusted for elasticities to prices for all three categories namely crops, meat and fish.

The user can manipulate calorie demand through the use of an exogenous calorie multiplier and can reduce undernourishment to 5 percent of the population over time through the usage of two other hunger elimination parameters.

=== Food Demand for Crops, Meat and Fish ===

Food demand is driven by the demand for calories. A conversion factor translates calorie demand into food demand in terms of grams per capita.  Crop prices and an elasticity affect the resultant food demand.  So too does a constraint on the maximum calories per capita and the size of the population. 

[[File:Food demand flowchart KN.png|frame|center|text-top|571x500px|Food demand flowchart]]

=== Industrial Demand ===

Industrial demand (examples would be textile use of cotton or beverage inputs use of barley) is driven primarily by GDP per capita and population.   Another important use in recent years has been for biofuels, and that demand component is responsive to world energy price and an elasticity.

Crop prices also influence total industrial demand for crops.  A maximum per capita demand parameter constrains the total and an exogenous multiplier allows users to alter the total.

[[File:IndustrialdemflowchartKN.png|frame|center|text-bottom|200x300px|Industrial demand flowchart]]

=== Feed Demand  ===

The total feed demand for the livestock herd is dependent on the weight of the livestock herd and per unit weight feed requirements.  The per unit feed requirements increase with GDP per capita as populations move from meat sources such as chickens to more feed intensive ones such as pork and especially beef.  But they also are reduced by change in the efficiency of converting feed to animal weight.

Some of the food requirements of livestock are met by grazing, thereby reducing the feed requirements.  The feed equivalent of grazing depends on the amount of grazing land, the productivity of that land (computed in the initial year and highly variable across countries), and grazing intensity (which increases with crop prices).

Finally, the feed demand can be modified directly by an exogenous demand parameter that modifies industrial crop demand. The feed demand for meat and fish are calculated using ratios of the food demand to feed demand which are calculated in the initial years of the model. In addition to industrial demand and feed demand, food manufacturing demand is also calculated in the model on the basis of the food demand for all three categories (meat, crops and fish)

[[File:FeeddemandKN.png|frame|center|564x476px|Feed demand flowchart]]

=== Total Agricultural Demand ===

Total Agricultural demand is the sum of demand for crops to serve industrial, animal feed, food manufacturing and human food purposes. 

[[File:Total Ag demand KN.png|frame|center|564x500px|Total Agricultural Demand Flowchart]]

=== Financial Constraint on Food Demand ===

Total food demand in million metric tons consists of the sum of crop demand, meat demand and food demand and fish demand.  It can be, however, that the monetary value of those calculated demands is greater than the financial ability of households to pay for them.  When that is the case, the food ,meat and fish demand are proportionately reduced. [[File:Financial constraint on food demand KN.png|frame|center|575x400px|Visual representation of financial constraint on food demand]]

=== Agricultural Investment and Capital ===

The level of total desired agricultural investment are driven by the rate of past investment as a portion of GDP, changes in global crop demand as a portion of GDP, and global crop stocks relative to desired levels. We have experimented also with tying investment to profit rates in agriculture, thereby linking it also to prices relative to costs. The user can use a multiplier to increase or decrease the desired level of investment.  This desired amount of investment is passed to the economic model, where it must ‘compete’ with demands for investments in other sectors.  The economic model returns a final investment level for use in agriculture. 

Investment in agriculture has two possible targets. The first is capital stock. The second is land. The split between the two destinations is a function of the relative returns to cropland development and agricultural capital, the latter of which is determined by the increased yield that could be expected from an additional unit of agricultural capital.

[[File:AginvandcapitalFlowchartKN.png|frame|center|564x476px|Visual representation of agricultural investment and capital]]

== Land Dynamics ==

In IFs, land use is divided into 5 categories: cropland, grazing land, forest land, "other" land, and urban or built-up land. Four key dynamics are involved in land use change. First, changes in urban land are driven by changes in average income and population, and draws from all other land types. Second, the investment in cropland development is the primary driver of changes in cropland, but this is also influenced by the cost of developing cropland, the depreciation rate, or maintenance cost, of cropland investment, and a user-controllable multiplier. The costs of developing cropland increase as the amount of cropland increases and, therefore, there is less other land available for conversion. Shifts in cropland are compensated by changes in forest and "other" land. Third, changes in grazing land are a function of average income, with shifts again being compensated by changes in forest and "other" land. Finally, conservation policies can influence the amount of forest land, with any necessary adjustments coming from crop and grazing land. [[File:Land dynamics.png|frame|center|Visual representation of land dynamics]]

= Agricultural Equations =

=== Overview ===

Briefly, each year the agriculture model begins by estimating the production (pre and post-production loss) of crops, meat, and fish. It then turns to the demand for these commodities. This begins with a computation of caloric demand from crops, meat, and fish, which is translated into demand for food going directly to consumers. Other demands for crops, meat, and fish are for feed, industrial uses (e.g. biofuels), and food manufacturing. Losses in the production, distribution and consumption of agricultural commodities are also accounted for. This is followed by computations for trade. The model then considers the balance between the demands and the available supply based on production, imports, and exports. Any excess supply increases stocks. In the case of excess demand, stocks are drawn down; this can result in shortages if there are not enough stocks, which leads to an inability to meet all of the demands. Levels of, and changes in, stocks influence prices for the coming year, as well as desired investment, which are passed to the economic model, which determines the actual amount of investment that will be available. With this knowledge, the model can then estimate values for changes in land development, agricultural capital, and livestock for the coming year.

=== Agricultural Supply ===

Crop, meat, and fish supply have very different bases and IFs determines them in separate procedures.

==== Crop Production ====

Crop production, pre-loss, (AGPpplf=1) i is the product of total yield and land devoted to crops (LDl=1).

<math>AGPppl_{r,f=1}= YL_r*LD_{r,l=1}</math>

We focus here on the determination of yield; the amount of land devoted to crops is addressed in the sections below.Yield functions are almost invariably some kind of saturating exponential that represents decreasing marginal returns on inputs such as fertilizer or farm machinery. Such functions have been used, for instance in World 3<ref>Meadows, Dennis L. et al. 1974. Dynamics of Growth in a Finite World. Cambridge, Mass: Wright-Allen Press.</ref> , SARUM<ref>Systems Analysis Research Unit (SARU). 1977. SARUM 76 Global Modeling Project. Departments of the Environment and Transport, 2 Marsham Street, London, 3WIP 3EB</ref>, the Bariloche Model <ref>Herrera, Amilcar O., et al. 1976. Catastrophe or New Society? A Latin American World Model. Ottawa: International Development Research Centre.</ref>, and AGRIMOD <ref>Levis, Alexander H., and Elizabeth R. Ducot. 1976. "AGRIMOD: A Simulation Model for the Analysis of U.S. Food Policies." Paper delivered at Conference on Systems Analysis of Grain Reserves, Joint Annual Meeting of GRSA and TIMS, Philadelphia, Pa., March 31-April 2.</ref>. IFs also uses a saturating exponential, but relies on a Cobb-Douglas form. The Cobb-Douglas function is used in part to maintain symmetry with the economic model but more fundamentally to introduce labor as a factor of production. Especially in less developed countries (LDCs) where a rural labor surplus exists, there is little question that labor, and especially labor efficiency improvement, can be an important production factor.

===== Pre-processor and first year =====

In the pre-processor, agricultural production is initialized using data from the FAO food balance sheets. For details of the series that are used in this initialization, refer Annex 1 of this document. In the first year of the model, total crop production is calculated by adjusting the initialized value of crop production for production losses, as the FAO data are for post-loss production. Yield (YL) is computed simply as the ratio of total crop production (AGPpplf=1) to cropland (LDl=1). It is bound, however, to be no greater than 100 tons per hectare in any country.

In addition to yield, a number of other values related to production are calculated in the first year of the model that are used in forecast years.

First, a scaling factor cD is calculated in the first year of the model. This is basically the constant in the Cobb-Douglas formulation for estimating yields. It is based upon the base year yield (YL), capital (KAG), and labor supply (LABS). The labor supply is adjusted using a Cobb-Douglass alpha exponent (CDALF) which is explained in detail below.  cD is similar to the shift factors elsewhere in the model, which are used to match predicted values in the base year to actual values.  It does not change over time. It is computed using the following equation,

<math>cD_r= YL_{r,t=1}/ KAG_{r,t=1} ^ {CDALF_{r,s=1}} * LABS_{r,S=1,t=1} ^ {(1-CDALF_{r,s=1})}</math>

Second, a target growth rate in yield is computed (TgrYli) which is used in forecast years to restrict the growth rate of the yield. This target growth is a function of current crop demand (AGDEM), expected crop demand (Etdem), and a target growth rate in cropland.

<math>Tgryli_{r}= (Etdem/AGDEM_{r,s=1}) -1-tgrld_{r} </math>

where,

'''''tgrld''''' is a country-specific parameter indicating target growth in crop land

Etdem is an initial year estimate of the sum of industrial, feed and food demand for crops in the following year

===== Forecast years =====

In forecast years, IFs computes yield in stages. The first provides a basic yield (Byl) representing change in long-term factors such as capital, labor and technology. The second stage uses this basic yield as an input and modifies it based on prices, so as to represent changes in shorter-term factors (e.g. amounts of fertilizer used, even the percentage of land actually under cultivation). Finally, in a third stage, yields are adjusted in response to changing climate conditions.

'''''First stage (Adjustment for long-term factors)'''''

The basic yield (Byl) relates yield to agriculture capital (KAG), agricultural labor (LABS), technological advance (Agtec), a scaling parameter (cD), an exponent (CDALF), and a saturation coefficient (Satk).

<math>Byl_{r}= cD_{r}*(1+Agtec_{r} )_{t-1}* KAG_{r}^ {CDALF_{r,s=1}} * LABS_{r,s=1} ^ {(1-CDALF)_{r,s=1}} * Satk_{r} </math>

The equations for KAG and LABS are described elsewhere (see the sections below  and the economic model, respectively). 

*cD is the scaling factor calculated in the first year of the model. Its calculation is described in the section above

*CDALF is the standard Cobb-Douglas alpha reflecting the relative elasticities of yield to capital and labor.  It is computed each year in a function, rooted in data on factor shares from the Global Trade and Analysis Project, driven by GDP per capita at PPP.<ref>Following table is used to update CDALF, GDP/Capita (PPP) Versus Cobb-Douglas Alpha (GTAP 5)</ref>

Agtec is a factor-neutral technological progress coefficient similar to a multifactor productivity coefficient. It is initially set to 1 and changes each year based upon a technological growth rate (YlGroTech). Its computation is described below.

 <math>Agtec_{r}= Agtec_{r,t-1}*(1+ YlGroTech_{r})</math>

*The saturation coefficient Satk is a multiplier of the Cobb-Douglas function and of the technological change element. It is the ratio of the gap between a maximum possible yield (YLLim) and a moving average of yields to the gap between a maximum possible yield and the initial yield, raised to an exogenous yield exponent ('''''ylexp'''''). With positive parameters the form produces decreasing marginal returns.

<math>Satk_{r+1}=(YLLim_{r}-Syl_{r}/YLLim_{r}-YL_{r,t=1})^ {ylexp}</math>

where,

Sylr is a moving average of byl, the historical component of which is weighted by 1 minus the user-controlled global parameter '''''ylhw'''''.

'''''ylexp '''''is a global parameter

The maximum possible yield (YLLim) is estimated for each country and can change over time.  It is calculated as the maximum of 1.5 times the initial yield (YLr,t=1) and the multiple of an external user-controlled parameter ('''''ylmax''''') and an adjustment factor (YLMaxM).

<math>YLLim_{r} = max (ylmax_{r}* YLMaxM_{r}, 1.5* YL_{r,t=1})</math>

where,

'''''ylmax''''' is a country-specific parameter

The adjustment factor YLMaxM allows for some additional growth in the yields for poorer countries

<math>YLMaxM_{r} = 1*((1-DevWeight_{r})+(YL_{r}/YlMaxFound)^ {0.35* DevWeight_{r}})</math>

where,

DevWeightr is GDPPCPr/30, with a maximum value of 1

YlMaxFound is the maximum value of YL found in the first year

{| border="1" cellspacing="0" cellpadding="0"
|-
| style="width:575px;" |
'''Box1: Computation of technological growth rate for yield'''

The algorithmic structure for computing the annual values of YlGroTech involves four elements: 
<ol style="list-style-type:lower-alpha;">
<li>The difference between a targeted yield growth calculated the first year and the portion of that growth not initially related to growth of capital and labor (hence the underlying initial technology element of agricultural production growth); call it AgTechInit.</li>
<li>The gap between desired global crop stock levels and actual stocks (hence the global pressure for technological advance in agriculture); call it AgTechPress. This contribution is introduced by way of the ADJUSTR function of IFs.<ref>The ADJSTR function, used throughout the model, is a PID controller that builds in some anticipatory and smoothing behavior to equilibrium processes by calculating an adjustment factor. It considers both the gap between the current value of the specific variable of interest, here crop stocks, and a target value, as well as change in the gap since the last time step. Two parameters control the degree to which these two "differences" affect the calculation of the adjustment factor. In this case, these are the global, user-controllable parameters elfdpr1 and elfdpr2.</ref></li>
<li>The difference between the productivity of the agricultural sector calculated in the economic model and the initial year's value of that (hence reflecting changes in the contributions of human, social, physical, and knowledge capital to technological advance of the society generally); call if AgMfpLt.</li>
<li>The degree to which crop production is approaching upper limits of potential; this again involves the saturation coefficient (Satk).</li>
</ol>

The algorithmic structure of this is:

<math>YlgroTech_{r} = F(AgTechInit_{r},AgTechPress_{r},AgMfpLt_{r},Satk_{r})</math>

|}

'''''Second stage of yield calculation (short term factors)'''''

Before moving to the next stage, a check is made to see if the growth in byl is within reason.  Specifically, Byl is not allowed to exceed the moving average of Byl (Syl) times a given growth rate (YlGrbound).  This bound is the maximum of a user-controlled global parameter  '''''ylmaxgr''''' and an initial country specific target growth rate (Tgrylir).<ref>There is also an adjustment whereby ylmaxgr is reduced for countries with syl>5, falling to a value of 0.01 when syl>=8. Also, for countries with a yield greater than world yields, the additional growth rate in yields due to change in agricultural investment is restricted to a value that is equal to ylmaxgr.</ref>

At this point, the basic yield (Byl) is further adjusted by a number of factors.  The first of these is a simple country-specific user-controlled multiplier  '''''ylm'''''. This can be used to represent the effects of any number of exogenous factors, such as political/social management (e.g., collectivization of agriculture).

<math>YL_r= YL_r*ylm </math>

The basic yield represents the long-term tendency in yield but agricultural production levels are quite responsive to short-term factors such as fertilizer use levels and intensity of cultivation. Those short-term factors under farmer control (therefore excluding weather) depend in turn on prices, or more specifically on the profit (FPROFITR) that the farmer expects. Because of computational sequence, we use domestic food stocks as a proxy for profit level. Note that this adjustment is distinct from the adjustment above where global stocks affect the technological growth rate.

The stock adjustment factor uses the ADJSTR function to calculate an adjustment factor related to the current stocks, the recent change in stocks, and a desired stock level.  The desired stock level is given as a fraction (Agdstl) of the sum of crop demand (AGDEMf=1) and crop production (AGPf=1). Agdstl is set to be 1.5 times '''''dstl''''', which is a global parameter that can be adjusted by the user.

The focus in IFs on yield response to prices differs somewhat from the normal use of price elasticities of supply. For reference, Rosegrant, Agcaoili-Sombila, and Perez (1995: 5) report that price elasticities for crops are quite small, in the range of .05 to .4.<ref>Rosegrant, Mark W., Mercedita Agcaoili-Sombilla, and Nicostrato D. Perez. 1995. "Global Food Projections to 2020: Implications for Investment." Washington, D.C.: International Food Policy Research Institute. Food, Agriculture, and the Environment Discussion Paper 5.</ref>

'''''Third stage of yield calculation (Adjustment for a changing climate)'''''

In the third stage, IFs considers the potential effects of a changing climate on crop yields. This is introduced through the variable ENVYLCHG[[#_ftn4|[4]]] which is calculated in the environmental model. This variable consists of two parts: the direct effect of atmospheric carbon dioxide concentrations and the effects of changes in temperature and precipitation.

<math>ENVYLCHG_{r,f} =(((CO2Fert_{t}/100)+1)*((DeltaYClimate_{R,t}/100)+1)-1)*100</math>

The direct effect of atmospheric carbon dioxide assumes a linear relationship between changes in the atmospheric concentration from a base year of 1990 and the percentage change in crop yields.

<math>CO2Fert_{t+1} = envco2fert *((CO2PPM- CO2PPM_{t=1990})/CO2PPM_{t=1990} )</math>

where,

'''''envco2fert''''' is a global, user-controllable parameter

CO2PPMt=1990 is hard coded as 354.19 parts per million

The effect of changes in annual average temperature and precipitation are based upon two assumptions: 1) there is an optimal temperature (Topt) for crop growth, with yields falling both below and above this temperature and 2) there is a logarithmic relationship between precipitation and crop yields.  The choice of this functional form was informed by work reviewed in Cline (2007)<ref>Cline, William R. 2007. Global warming and agriculture: Impact estimates by country. Washington, DC: Peterson Institute for International Economics.</ref>.  Together, these result in the following equation:

<math>ClimateEffect_{t+1} = 100*{({e^{(-0.5*(T0_{r}+ DeltaT{r} - Topt)^2)/SigmaTsqd}*ln(P0_{r}*(DeltaP_{r}/100+1))/e^{(-0.5*(T0_{r}-Topt)^2/SigmaTsqd}*ln (P0_r))-1}} </math>

where,

T0 and P0 are country-specific annual average temperature (degrees C) and precipitation (mm/year) for the period 1980-99.

DeltaT and DeltaP are country specific changes in annual average temperature (degrees C) and precipitation (percent) compared to the period 1980-99.  These are tied to global average temperature changes and described in the documentation of the IFs environment model.

Topt is the average annual temperature at which yield is maximized.  It is hard coded with a value of 0.602 degrees C.

SigmaTsqd is a shape parameter determining how quickly yields decline when the temperature moves away from the optimum. It is hard coded with a value of 309.809.

CO2Fert and ClimateEffect are multiplied by each other to determine the effect on crop yields.

There are two final checks on crop yields.  They are not allowed to be less than one-fifth of the estimate of basic yield (Byl) and they cannot exceed the country-specific maximum ('''''ylmax''''') or 100 tons per hectare. Finally crop production is adjusted for production losses to arrive at post loss production (AGP). Losses are discussed in detail in the sections below

==== Meat Production ====

Meat production in IFs is the sum of animal meat production and non-meat animal products (AGPMILKEGGSR). Animal meat production in a particular country is a function of the herd size and the slaughter rate and non-animal meat products are calculated by applying a ratio MilkEggstoMeatIR which is calculated in the first year of the model as the ratio of non-meat animal production to the meat production. Meat production is then adjusted for production losses which are described in detail in the sections below.

<math>AGP_{r,f=2} =((LVHERD_{r}* slr)+ AGPMILKEGGS_r )- AGLOSSPROD_{r,f=2}</math>

where,

LVHERD is the size of livestock in a particular country in a particular year

'''''slr '''''is the slaughter rate which is a global parameter

AGLOSSPROD is the meat production loss.

===== Pre-processor and first year =====

In the pre-processor, meat production is initialized in the model using data from the FAO food balance sheets. Total meat production and animal meat production (which is the sum of bovine meat production, mutton and goat meat production, pig meat production, poultry meat production, and other meat production) are initialized separately. If data on all of the animal meat sub-categories is unavailable, then animal meat production is calculated as 30 percent of total meat production. Animal production is also not allowed to exceed 99% of the value of total meat production.

 

AGPMILKEGGSR, which is the non-meat animal production is then calculated as total meat production minus total animal meat production. The non-meat production ratio MilkEggstoMeatIR is calculated as the ratio of the initialized value of AGPMILKANDEGGSR and meat production in the first year. This is used in forecast years to calculate the value of non-meat animal production, and is held constant over time.

<math>MilkEggstoMeatI_{r} = AGPMILKEGGS_{r}/(AGP_{r,f=2}- AGPMILKEGGS_{r})</math>

The size of the livestock (LVHERDR) is also computed in the first year using the initialized value of pre-loss meat production. This value of LVHERDR is used in forecast years to compute meat production.

<math>LVHERD_{r} = (AGPppl_{r,f=2} - AGPMILKEGGS_{r} )/slr </math>

For a detailed discussion on the dynamics of livestock herd, refer to this [[Section|section]].

===== Forecast years =====

Pre-production loss values for meat production are calculated in IFs as meat production (AGPpplR,f=2) and production of non-meat animal products (AGPMILKANDEGGSR). Meat production, in metric tons, is given as the multiple of the herd size (LVHERDR) and the slaughter rate ('''''slr'''''). The latter is a global parameter. These values are then adjusted for production losses for meat (AGPRODLOSSR,f=2) to arrive at post production loss values (AGPR,f=2). The same meat production loss percentage is also applied to the non-meat production to arrive at post loss production values for the variable. The dynamics of production losses are discussed here.

<math>AGP_{r,f=2} = AGPppl_{r,f=2} - AGLOSSPROD_ {r,f=2}</math>

where,

<math>AGPppl_{r,f=2} = (AGPMILKANDEGGSppl_{r} +( LVHERD_{r}*slr)) </math>

Production of non-animal meat products is computed using the non-meat production ratio which is applied to the animal meat production.

<math>AGPMILKANDEGGSppl_{r} = MilkEggstoMeatI_{r} *( LVHERD_{r} * slr)</math>

The dynamics of the [[Livestock|livestock]] herd are described below.
<div></div>
==== Fish Production ====

The production of fish has two components, wild catch and aquaculture. Fish caught through aquaculture is treated as a stock in the model and is a function of a growth component.  Wild catch on the other hand is treated as a flow in the model.

===== Pre-processor and first year =====

Data for fish catch and aquaculture is derived through two main sources, namely the FAO food balance sheets and the FAO Fishstatj software. Data for fish production, imports and exports is initially extracted from the FAO Food Balance Sheets. However, no breakout is available for fish caught as wild catch and fish caught through aquaculture. This bifurcation is available in the dataset from the FAO Fishstatj database. The data from the FAO food balance sheets is broken down into fish catch (AGFISHCATCH) and aquaculture (AQUACUL) using data from the FAO fishstatj dataset.

In the first year, the values for pre-loss production of wild fish, AGFISHCATCHppl and aquaculture, AQUACULppl, are calculated by adding in a level of catch loss, which is not reflected in the FAO and Fishstatj data. Separate parameters, '''''aglossprodperc'''''f=3 ''and '''aglossprodperc'''f=4, ''are used for wild catch and aquaculture.

===== Forecast years =====

The amount of aquaculture (AQUACUL) in forecast years can be modified by the user. Production is assumed to grow over time. The default growth rate in the first year for all countries is 3.5 percent, but this value can be modified by the user, by country, with the parameter '''''aquaculgr'''''. This growth rate declines to 0 over a number of years given by the global parameter '''''aquaculconv'''''. Users can change the amount of aquaculture production, by country, with the multiplier '''''aquaculm<ref>In every year of the model, the effect of aquaculm is removed on the aquaculture variable. This is because the multiplier in this case is used on a stock rather than a flow due to which the effect of the multiplier needs to be removed in each time step.</ref>'''''. Finally, this is adjusted for production losses from aquaculture with Aquaculloss

<math>AQUACUL_{r} = (AQUACULppl_{r,t-1} * (1+ aquaculgr_{r,t} )* aquaculm_{r})- Aquaculloss_{r} </math>

where

''aquaculgrr,t declines from '''aquaculgr'''r,t=1'' to 0 over '''''aquaculconv''''' years

Wild catch is initialized in the pre-processor as the variable AGFISHCATCH. The pre- production loss of wild catch is computed after applying a multiplier '''''fishcatchm''''' and this is adjusted for losses (Catchloss) to arrive at post production loss wild fish catch.

<math>AGFISHCATCH_{r} = (AGFISHCATCHppl_{r,t-1} * fishcatchm_{r} )- Catchloss_{r} </math>

Total, post-production loss fish production (AGP) is then given as:

<math>AGP_{r,t=3} = AQUACUL_{r} + AGFISHCATCH_{r} </math>

==== Losses and waste ====

Losses can occur at several places along the chain from production. In earlier sections, we mentioned losses at the production stage. Losses can also occur in the process of transmission and distribution from the producer to the final consumer and at the consumer stage. The latter is sometimes referred to as food waste, but for our purposes, we will use the term loss for all three stages: production, transmission and distribution, and consumption.

The FAO Food Balance Sheets provide data on losses during transmission and distribution, but not at the production or consumption stages. Until we are able to find data showing a clear relationship between these losses and GDP per capita, or some other explanatory factor, we make an assumption of production losses and consumption losses of 10% for all countries. The user can make changes in these values with the parameters '''aglossprodperc''' and '''aglossconsperc''' respectively. The former can be set for crops, meat, wild catch, and aquaculture separately. The latter combines wild catch and aquaculture as fish, as we do not have separate data on the consumption of wild caught versus farmed fish. More details on the use of these parameters and the actual calculation of production and consumption losses are provided in sections 3.1.1-3.1.3 and 3.2.1, respectively.

Turning to transmission and distribution losses, some agricultural commodities will never make it from the producer to the final consumer because of pests, spoilage, etc.  The FAO food balance sheets provide data on food lost to waste for crops and meat , but not for fish. Thus, for now we assume that there are no losses in this stage for fish. For crops and meat, though we were able to establish relationships between transmission and distribution losses and GDP per capita. These are shown in the figures below:

----

===== Pre-processor and first year =====

The initial values for transmission and distribution losses are taken directly from the FAO Food balance sheets. For those countries without data, an assumed loss of 1 ton (0.000001 MMT) is used. These are given by the variable AGLOSSTRANS[[|r, f=1-3]]. As with consumption, wild catch and aquaculture are combined into a single category, fish, as we do not have separate data; also, for the moment the value of AGLOSSTRANSr, f=3 is set to 0 for all countries.

In the first year, a ratio of [[Transmission/distribution_loss_to_food_demand|transmission/distribution loss to food demand]], FDEM,  is computed as:

<math>AgLossTransToFoodRatI_{r,f=1to3} = AGLOSSTRANS_{r,f=1to3} / FDEM_{r,f=1to3} </math>

===== Forecast years =====

In future years, for crops and meat, the initial estimate for transmission and distribution losses are calculated as follows:

·         Predictions are made for the ratio of transmission/distribution loss to food demand as a function of GDP per capita (predaglosstrans) for the first year and the current year.

·         The ratio of the predicted values for the current year to the predicted value for the first year is multiplied by AgLossTransToFoodRatI.

·         That result is multiplied by FDEM for the current year to get losses in MMT.

·         That result is multipled by the parameter '''aglosstransm''', to get a final value.

 

This can be expressed as:

<math>AGLOSSTRANS_{r,f=1,2,3} = FDEM_{r,f=1,2,3,t=1} * predaglosstrans_{r,f=1,2,3,t}/predaglosstrans_{r,f=1,2,3,t=1}*AgLossTransToFoodRatioI_{r,f=1,2,3}*aglosstransm_{r,f=1,2,3}</math>

Some further adjustments may be made to AGLOSSTRANS in the process of balancing global trade and balancing domestic supply and demand. These are discussed later in this documentation.

== Agricultural Demand ==

IFs computes demand, or uses, for three agricultural categories—crops, meat, and fish.  These commodities are used for direct human consumption (FDEM), animal feed (FEDEM), industrial uses, e.g. biofuels (INDEM), and food processing and manufacturing (FMDEM). IFs also tracks the losses in transmission and distribution (AGLOSSTRANS). Total demand (AGDEM) is the sum of these five use categories and is given in MMT per year.

The sections above describe the calculation of AGLOSSTRANS, so that is not repeated here. The calculation of the demand for direct human consumption, FDEM begins with estimates of daily per capita calorie demand for crops, meat, and fish. Briefly, IFs first estimates total per capita calorie demand, which responds to GDP per capita (as a proxy for income). The division of total demand between demand for calories from crops and from meat and fish also changes in response to GDP per capita (more meat and fish demand with increasing income). Finally, the division of calories from meat and fish is calculated based on historic patterns. Using country and commodity specific factors, the daily per capita calorie demands are converted to grams per capita per day and protein per capita per day. The grams per capita per day are then multiplied by the size of the population, POP, and the number of days in a year, 365, to arrive at FDEM.

The other demands, FEDEM, INDEM, and FMDEM are driven by factors such as the size of the livestock herd, LVHERD, and the use of crops for fuel production. In cases where information is lacking, these demands are determined in relation to FDEM. Finally, there may be some modifications to all of the demand categories due to shortages or other factors, as described in the rest of this section.

==== Daily per capita demands – calories, grams, and protein ====

IFs tracks one set of variables for agricultural demands, or uses, on a daily per capita basis. These are. specifically, calories (CLPC), protein (PROTEINPC), and grams (GRAMSPC), for each category – crops, meat, and fish.

===== Pre-processor and first year =====

Daily calories per capita (CLPC), by category, are initialized in the IFs pre-processor using data from the FAO food balance sheets. Data on daily protein per capita and grams per capita are also read into the pre-processor.<ref>Note that although daily grams per capita are read in and used in the pre-processor, these are recalculated in the first year of the model</ref> If data are available for crops, meat, and fish, total values for calories, protein, and grams are calculated as sums of the three categories. For countries where no data are available for one or more of the categories, the model follows a set of procedures to fill in the missing data. These procedures uses, among other things, 1) equations that relate total calories per capita per day and the share of these calories from crops versus meat and fish to GDP per capita and 2) other ratios derived from global averages of those countries with data. Later in the pre-processor, CLAVAL, which represent the total calories (across all categories) per day for the population as a whole is also calculated.

The equation for total calories as a function of GDP per capita is stored as "GDP/Capita (PPP 2011) Versus Calorie Demand (fixed-effect)" and is illustrated below.<ref>Equation is CalPerCap = 2468.972+155.778*ln(GDPPCP). Because this equation was estimated using a fixed-effects model, the intercept does not have the same meaning as in a regular regression. Rather, it is the average of the fixed-effect across countries with data. This is not a problem for countries with data, as the shift factor in the first year will account for this. For countries without data, however, this can give a misleading estimate of initial daily calories per capita.</ref>

[[File:Calorie Demand vs GDP per capita.png|frame|center|200x250px|Calorie demand vs GDP per capita at PPP (fixed effect)]]

The equation for the share of calories from meat and fish as a function of GDP per capita is stored as " GDP/Capita (PPP 2011) Versus CLPC from MeatandFish (2010) Log"

Both of these are in a logarithmic form, indicating that both total calories and the share of calories from meat and fish increase with GDP per capita, but at a decreasing rate. As the data do not show a clear pattern for the breakdown between meat and fish, which is largely due to cultural patterns and geography, the model uses historical values rather than an estimated equation, as discussed below. In the pre-processor, an average global value is used for countries without data.

In the first year of the model, one of the first things that occurs is a recalculation of GRAMSPC as GRAMSPC = FDEM/(POP * 365) * 100000. This is to ensure the consistency between the daily per capita variable, GRAMSPC, and the annual national value, FDEM. This is necessary because FDEM may have been modified in the pre-processor as part of ensuring a balance between the initial year supply of agricultural produces and their use. This is described in more detail in Box 1.

In addition, a number of additional values related to calories to be used in the forecast period are calculated.

#CalActPredRat: the ratio between actual calories available and the predicted value.<ref>In the model this is currently calculated as CLAVAL/caldem, where caldem = the predicted value of total CLPC (after accounting for calmax) times the total population. It could just as easily be calculated as the predicted value of total CLPC (after accounting for calmax) divided by the actual value of total CLPC from the pre-processor.</ref> It is used as a multiplicative shift factor. The predicted level of is estimated using the equation for total calories per capita as a function of GDP per capita described above. This is bound from above by an assumed maximum value, given by the global parameter '''''calmax'''''. The value of calactpredrat gradually converges to 1 over a period given by the global parameter '''''agconv '''''and appears in future equations with the name AdjustForInitialDevc.
#MeatAndFishActPredRat: the ratio between actual share of calories from meat and fish to the predicted value. It is used as a multiplicative shift factor. The predicted level of is estimated using the equation for share of calories from meat and fish per capita as a function of GDP per capita described above.
#MeatToMeatFishRatI: the ratio between calories from meat and calories from meat and fish. It is used to separate the future estimates of calories from meat and fish into separate values for meat and fish.
#ProtToCalRatI: the ratio of daily per capita protein to daily per capita calories, by category. It is used to convert future estimates of calorie availability to protein availability. If for some reason the initial estimate of ProtToCalRatI is 0 for any category, the median value for that category based on 2010 is used.
#GramsToCalRatI: the ratio of daily per capita grams to daily per capita calories, by category. It is used to convert future estimates of calorie availability to a value in grams, which is then used to estimate aggregate demand for food for direct human consumption. If for some reason the initial estimate of GramsToCalRatI is 0 for any category, the median value for that category based on 2010 is used.

===== Forecast years =====

In the forecast years, daily per capita calorie demand begins with a prediction of a total demand, CalPerCap, as a function of average income using the equation above, with a maximum value given by '''''calmax'''''. Two other values are also calculated at this point. First, a base level of calories per capita, CalBase, is also calculated, which is given as the minimum of 3000 or '''''calmax'' '''minus 300. Second, because comparative cross sections show a growth of around 7.6 calories per capita per year independent of average income, a factor representing this increase (CaldGr) is calculated as:

<math>CaldGr_{r,t} = CaldGr_{r,t-1} +7.638*((calmax-MAX(CalBase,MIN(calmax, CalPerCap_{r} )))/(calmax-CalBase)</math>

Thus, depending on the exact values of '''''calmax''''', CalBase, and CalPerCap, CaldGr grows each year by a value that centers around 7.6 calories. This value is then added to the predicted value in calculating the total demand for calories.

The equation also takes into account '''''calmax'' '''and the multiplicative shift factor on calories per capita calculated in the first year of the model. The latter is named AdjustForinitialDevc, which, as noted previously, is calculate as the value of calactpredrat gradually converging to 1 over a period given by the global parameter '''agconv'''

<math>TotalCalPerCap_{r} = MIN('''''calmax''''',(CalPerCap_{r} + CaldGr_{r})* AdjustForInitialdevc_{r})* POP_r</math>

Finally, a value for the total calories per day, CalDem, is calculated by multiplying TotalCalPerCap times POP.

The next step is to divide the total calories between crops and meat plus fish. First, a predicted value of the share of total calories going to meat and fish, MeatAndFishPctPred, is calculated as a function of GDP per capita, using the equation described earlier. Second, the ratio of between actual share of calories from meat and fish to the predicted value, MeatAndFishActPredRat, calculated in the first year is potentially modified. Specifically, a new variable, AdjustForInitialDevm, is assigned either the intial value of MeatAndFishActPredRat, or a value that reflects convergence of MeatAndFishActPredRat to a value of 1 over a period given by the global parameter '''agconv'''. The countries for which convergence does not occur are the South Asian countries – India, Nepal and Mauritius –  which are traditionally low meat consuming countries. The actual share of calories from meat and fish is then calculated as:

<math>MeatAndFishPctAct_{r} = MeatAndFishPctPred_{r} * AdjustForInitialDevm_r</math>

A minimum value of 3.5 percent is also imposed.

With this value for MeatAndFishPctAct, the model can divide the total calories between crops and the combination of meat and fish. Using the value for MeatToMeatFishRatioI, calculated in the first year, the model can then estimate the calories from meat and fish separately. The values are stored in the variable CLPC(r,f)

At this point, these values are adjusted for changes in world food prices and elasticities to demand for these prices.

<math>CLPC_{r,f=1-3} = CLPC_{r,f=1-3} *(WAP_{f=1-3}/WAP_{f=1-3,t=1} )^{X}</math>

'''where,'''

WAPf=1-3 are the global food prices for crops, meat, and fish

X is the price elasticity of demand and takes on the value of '''''elascd''''', '''''elasm''''', and '''''elasfd'' '''for crops, meat, and fish, respectively

Given these adjustments, TotalCalPerCap is recalculated as the sum of CLPC for crops, meat, and fish.

Finally, a parameter '''''clpcm'' '''is applied to the final value of calories per capita that allows the user to manipulate demand for calories in addition to two parameters (that allow the user to eliminate hunger in a particular country over time) which are described below.

 The parameters '''''malnelimstartyr '''''and '''''malnelimtargetyr '''''allow the user to reduce hunger in any country over a specific period of time. The activation of these parameters by the user, calculates the required cumulative growth rate in calories to eliminate hunger (reduce the undernourished population to 5 percent of the total population) ClPCcum. This cumulative growth rate is calculated using a logarithmic function that computes the growth rate relative to the household income and unskilled labor in a country.<ref>The function used is as follows, Exp((Log(5) - 46.95226 + 0.18422 * Log(HHINC / labsups)) / -5.643)</ref>  Also, the user can activate a switch '''''malelimprecisesw''''', which calculates the specific number of calories required to eliminate hunger for the most undernourished part of the population. An individual who consumes less than 1000 calories per day but is still alive is assumed to be the most undernourished person in the population.

Therefore the final equation is as follows,

<math>CLPC_{r,f} = (CLPC_{r,f} *clpcm_{r,f} * ClPCcum_{r} )+ Caldef_{r,f} </math>

where,

'''''clpcm '''''is a multiplier that can be used to affect the demand for calories

ClPCcum is the cumulative growth rate required in calories per capita to eliminate hunger over a specific time period determined by malnelimstartyr and malnelimtargetyr

Caldef is the cumulative number of calories required to eliminate hunger for the most undernourished part of the population. This is calculated through the activation of '''''malelimprecisesw'''''.

At this point, i.e., after dealing with the hunger targets, the values for daily grams per capita (GRAMSPC) and daily protein per capita (PROTEINPC) are calculated by multiplying the values for CLPC by GramsToCalRatI and ProtToCalRatI, respectively. Recall that these values were computed in the first year.

A final adjustment to CLPC, PROTEINPC, and GRAMSPC can occur as a result of shortages. This begins with a reduction in FDEM, as described in the  Stocks section below, which is then translated into new values for GRAMSPC, which are then used to recalculate CLPC and PROTEINPC.

One final variable, CLAVAL, which represent the total calories (across all categories) per day for the population as a whole is then calculated as total calories per capita times the population.

==== Agricultural demand for direct human consumption (FDEM'')'' ====

FDEM represents the amount of agricultural commodities going directly to consumers, presumably for consumption.

===== Pre-processor and first year =====

The pre-processor reads in data from the FAO Food Balance Sheets and initializes values for the amount of agricultural commodities used for direct human consumption, FDEM. If these data are missing for any commodity, a value is calculated by multiplying the daily grams per capita by the size of the population (POP) and the numbers of days in a year (365), and then divided by 100000 to get the units correct. As noted in Box 1, certain adjustments may be made to ensure consistencies between supply and demand in individual countries, as well as between imports and exports across countries.

No adjustments are made to FDEM in the first year.

===== Forecast years =====

In the forecast years, FDEM is initially calculated based upon the calculation of daily grams per capita described in this section below:

<math>FDEM_{r,f=1-3} = GRAMSPC_{r,f=1-3} * POP_{r}* 365/100000</math>

There are two situations where the value of FDEM might be adjusted. The first case is where more than 85 percent of consumers’ expenditures are on food stuffs. If this is the case, the values of FDEM for crops and meat and fish are reduced proportionately, as described in this section below.

The second case is when a country faces absolute shortages, i.e., the total domestic supply, AGDEM, is not adequate to meet all of the demands, FDEM + FEDEM + INDEM + AGLOSSTRANS even after drawing down stocks to 0. Here, each of these demands/uses are reduced proportionately to restore the balance as described in Section 3.4: Stocks. In both cases, the decreases in FDEM are fed forward to reduce the actual calories available, as described here.

=== Feed demand for crops, meat and fish ===

Feed demand, FEDDEM, represents: 1) the amount of crops that are used to complement what livestock receive from grazing, and 2) an unspecified use of meat and fish, which appears in the FAO Food Balance Sheets.

===== Pre-processor and first year =====

The pre-processor reads in data from the FAO Food Balance Sheets and initializes values for the amount of agricultural commodities used as feed for other agricultural production, usually meat. If data are missing, a minimum value of 1 ton, or .000001 MMT is used.

An initial adjustment to feed demand for crops can occur in the pre-processor. This occurs when the production from grazing land is not being fully utilized. Specifically, this is when the amount of equivalent feed from grazing land, i.e. grazing land productivity, here named GLandCAP, implies a lower than assumed minimum value of 0.01 tons of crop equivalents per hectare, here named MinLDProd. The implied value of GLandCap is calculated as the difference between the total feed requirement for the number of livestock minus the feed demand divided by the amount of grazing land.

<math>GLandCAP_{r} = LiveHerd_r* fedreq_r-FEDDEM_{r,f=1}/ LDGraz_{r} </math>

'''where,'''

LiveHerd is the size of the livestock herd (discussed in this section )

LDGraz is the amount of grazing land (discussed in this section under Land Dynamics)

FEDDEMr,f=1 is the value for demand for crops for feed

''Fedreq is an estimate of the per animal feed requirements, which is a function of GDP per capita. The function is depicted in the figure below<ref>The specific equation is stored as “GDP/Capita (PPP) Versus Feed Requirements” and is defined by the two points (GDP/capita, fedreq) = (0, 2.5) and (30, 3.5).</ref>:''

[[File:Feed demand for crops 2.png|frame|center|Feed demand as a function of GDP per capita at PPP]] If the value of GLandCAP is less than the minimum, MinLDProd—currently hard coded as 0.01 tons of crop equivalents per hectare, based on values for the Saudi desert), then CFEDDEMr,f=1 is recalculated as the difference between the total feed requirement for the number of livestock minus the amount of feed equivalent produced by grazing using the minimum productivity.

<math>CFEDDEM_{r,f=1} = LiveHerd_{r} * fedreq_{r} - MinLDProd* LDGraz_{r}</math>

Note that this occurs when the feed from crops meets most, if not all, of the total feed requirements, implying little or no need for feed equivalents from grazing land. Also a minimum value of 0.01 MMT is set for CFEDDEM.

Finally, as noted in Box 1, certain adjustments may be made in the pre-processor to ensure consistencies between supply and demand in individual countries, as well as between imports and exports across countries.

In the first year, the model once again checks to make sure that the grazing land productivity exceeds a minimum value and this time stores this value for future use. A parallel equation to that in the pre-processor is used to get an initial estimate for grazing land productivity, now named GldCap:

<math>GLdCAP_{r} = (LVHERD_{r,t=1} * Fedreq_{r,t=1} -FEDDEM_{r,t=1})/LD_{r,l=2,t=1}</math>

'''where,'''

LVHERDr,t=1 replaces LiveHerd from the equation in the pre-processor

LDr,l=2,t=1 replaces LDGraz from the equation in the pre-processor

FEDDEMr,f=1 replaces CFEDDEMr,f=1 from the equation in the pre-processor

Fedreqr is the same as in the equation in the pre-processor

Now, if the model estimates that GldCAP is below the minimum level, still called MinLDProd and hard coded to a value of 0.01, a new value of GldCAP  calculated:

<math>GLdCAP_{r} = LVHERD_{r,t=1} * Fedreq_{r,t=1} -FEDDEM_{r,t=1}/LD_{r,l=2,t=1} </math>

'''where,'''

LVHERDr,t=1, LDr,l=2,t=1, FEDDEMr,f=1, and fedreqr are defined as above

'''''fedreqm'''r is a multiplier required to ensure that the grazing land productivity meets the difference between the total feed requirement and that provided by crops in the initial year. It is calculated as:''

<math>fedreqm_{r} = LD_{r,l=2,t=1} * MinLDProd + FEDDEM_{r,t=1} /(LVHERD_{r,t=1} * fedreq_{r,t=1} )</math>

Note that this value is always greater than or equal to 1 given the condition for making the adjustment. When no adjustment is made, fedreqm is set to 1. These values of GldCAP and fedreqm, calculated in the first year, are held constant for all forecast years

Finally, one other value is calculated in the first year – FeedToFoodRatI, which is the ratio between FEDDEM and FDEM. This is calculated for crops, meat, and fish, but is only used for the latter two categories in the forecast years, as described below.

==== Forecast years ====

In the forecast years, FEDDEM is calculated as a function of the size of the livestock herd (LVHERD), the feed requirements per unit livestock (fedreq), the amount of grazing land (LDl=2), and the productivity of grazing land (GldCAP), but adjustments are also made reflecting the effect of global crop prices on grazing intensity (WAPf=1), changes in the efficiency with which feed is converted into. meat, and the adjustment factor fedreqm calculated in the first year. There is also a parameter with which the user can cause a brute force increase or decrease in FEDDEM ('''feddemm''')

The model first calculates the amount of crop equivalent produced from grazing land using the following equation:

<math>GLFeedEq_{r} =(LD_{r,l=2} * GLdCAP_{r} )*( WAP_{f=1} / WAP_{f=1,t-1} )^{elglinpr} </math>

'''where''''',''

''LDr,l=2 is the amount of grazing land; the dynamics of this variable is discussed in section 3.10: Land Dynamics''

''GldCAPr is the country value for grazing land capacity initialized in the first year''

''WAPt,f=1 is global price for crops; and''

'''''elglinpr''' is a global parameter for the elasticity of livestock grazing intensity to annual changes in world crop prices; the basic assumption is that increasing prices should lead to increased grazing intensity and therefore greater productivity of grazing land<ref>The code, as written, ignores price effects that would reduce GLFeedEq. Since elglinpr is generally positive, this implies that decreases in world crop prices are ignored.</ref>''

''This production of crop equivalents from grazing land is then subtracted from total feed requirement in the following equation:''

''<math>FEDDEM_{r,f=1} =(LVHERD_{r} * Fedreq_{r} * fedreqm_{r}*max{0.5,(1-livhdpro/100)^(t-1) }-[GLFeedEq]_r )*feddemm</math>''

'''where,'''

LVHERD, fedreq, and fedreqm are as previously described. LVHERD and fedreq are updated each year as described in section 3.11: Livestock Dynamics and as a function of GDP per capita, respectively. fedreqm, determined in the first year, does not change over time.

'''''livhdpro''' is a global parameter related to the rate at which the productivity of crops in producing meat improves over time. This part of the equation implies that the amount of feed needed to produce a unit of meat declines over time to a minimum of half the original amount required''

'''''feddemm''' is a country-specific multiplier that can be used to increase or decrease crop demand for feed purposes''

For meat and fish, a simpler process is used. The feed to food ratio, FeedToFoodRatI, calculated in the initial years of the model is used to calculate the share of feed demand for meat and fish respectively.

<math>FEDDEM_{r,f} = FeedToFoodRatI_{r,f} * FDEM_{r,f}</math>

Note that there is no multiplier equivalent to '''feddemm'''for meat and fish.

Finally, as with FDEM, FEDDEM may be adjusted to account for excessive consumer spending on food, as described in Box 2 or due to shortages in crops, meat, or fish as described in Section 3.4: Stocks.

=== Industrial demand for crops, meat and fish ===

Industrial demand, INDEM, represents the amount of crops, meat, and fish that are used in industrial processes.

==== Pre-processor and first year ====

The pre-processor reads in data from the FAO Food Balance Sheets and initializes values for the amount of agricultural commodities used in industrial processes. If data are missing, a minimum value of 1 ton, or .000001 MMT is used.

Finally, as noted in Box 1, certain adjustments may be made in the pre-processor to ensure consistencies between supply and demand in individual countries, as well as between imports and exports across countries.

[[File:Industrial demand for crops.png|frame|center|Industrial demand for crops]] In the first year, two values related to industrial demand for crops are calculated. The first of these is a multiplicative shift factor (INDEMK), which is calculated as the ratio of actual to predicted industrial demand for crops.  The predicted value is given by a function that relates per capita industrial demand to GDP per capita, which is shown above.<ref>Equation is INDEM = 0.0376 + 0.000704 * GDPPCP</ref> This multiplicative shift factor remains constant over time. As with FEDDEM, one other value is calculated in the first year – IndToFoodRatI, which is the ratio between INDEM and FDEM. This is calculated for crops, meat, and fish, but is only used for the latter two categories in the forecast years, as described below.

==== Forecast years ====

In the forecast years, for crops, the initial value of industrial demand is updated using the table function above to get a predicted value for industrial demand per capita, which is then multiplied by population (POP) and the multiplicative shift factor (IndemK). At this point, a region-specific multiplier ('''indemm''') can either increase or decrease the initial estimate of INDEM.

A first adjustment to INDEM is related to the world energy price (WEP) and reflects the use of crops for fuel production. Specifically, as the world energy price increases relative to the price in the first year, the industrial demand for crops increases.

<math>INDEM_{r} = INDEM_{r} *(1+ WEP_{t}/WEP_{t=1}) *FoodforFuel)</math>

'''Where'''

WEP is world energy price

FoodforFuel is the elasticity of industrial use of crops to world energy prices. It starts at a value given by the global parameter '''elagind''', and declines to a value of 0 over 50 years.

The second adjustment relates to the world crop price (WAPf=1); as this increases relative to the price in the first year, industrial demand for crops declines.

<math>INDEM_{r} = INDEM_{r} *(WAP_{f=1,t}/WAP_{f=1,t=1} )^{elascd}</math>

''''Where''''

WAP is world crop price

'''''elascd''' is a global parameter specifying the elasticity of crop demand to global food prices''

A third adjustment is based on an assumed cap on per capita industrial demand for crops (IndemCapperPop—hard coded as 2. Specifically, INDEM is not allowed to exceed IndemCapperPop * POP.

For meat and fish, industrial demand is initially calculated by applying the Industrial demand to food ratio, IndToFoodRatI (calculated in the initial year of the model) to the value of food demand.

<math>INDEM_{r,f} = IndToFoodRatI_{r} * FDEM_{r,f} </math>

Note that there is no multiplier equivalent to '''indemm'''for meat and fish.

Finally, as with FDEM and FEDDEM, INDEM may be adjusted to account for excessive consumer spending on food, as described in section 3.2.5 or due to shortages in crops, meat, or fish as described in this Section below.

=== Food manufacturing demand ===

The final demand category, FMDEM, relates to the use of crops, meat, and fish in food manufacturing and processing.

==== Pre-processor and first year ====

The pre-processor reads in data from the FAO Food Balance Sheets and initializes values for the amount of agricultural commodities used in food manufacturing and processing.<ref>Note that the FAO Food Balance Sheets include data for agricultural commodities used for food manufacturing and as seed separately. We combine these into a single food manufacturing category.</ref> Note that If data are missing, a minimum value of 1 ton, or .000001 MMT is used.

As noted in Box 1, certain adjustments may be made in the pre-processor to ensure consistencies between supply and demand in individual countries, as well as between imports and exports across countries.

Paralleling the case for INDEM, FEDDEM, and AGLOSSTRANS, one other value is calculated in the first year –FManToFoodRatI, which is the ratio between INDEM and FDEM. This is calculated for crops, meat, and fish, and used for all three in the forecast years, as described below.

<math>FMDEM_{r,f} = FManToFoodRatI_{r,f} * FDEM_{r,f} </math>

==== Forecast years ====

In the forecast years, for all three categories, demand is calculated using the Food manufacturing to food demand ratio, FManToFoodRatI, calculated in the first year of the model and the value of food demand.

<math>FMDEM_{r,f} = FManToFoodRatI_{r,f} * FDEM_{r,f} </math>

As with FDEM, INDEM, and FEDDEM, FMDEM may be adjusted to account for any shortages in crops, meat, or fish as described in Section 3.4: Stocks. It is not currently affected by excessive consumer spending on food, as described in Box 2

=== Total agricultural demand and final adjustment to demand ===

==== Pre-processor and first year ====

AGDEM, which represents the sum of all uses. It is initialized in the first year of the model to ensure the balance with production, imports, and exports:

<math>AGDEM_{r,f=1-3,t=1} = AGP_{r,f=1-3,t=1} + AGM_{r,f=1-3,t=1} - AGX_{r,f=1-3,t=1} </math>

==== Forecast years ====

In the forecast years, AGDEM, is recalculated as the sum of the final values of feed, industry, and food demand and transmission losses:

<math>AGDEM_{r,f=1-3} = FEDDEM_{r,f=1-3} + INDEM_{r,f=1-3} + FDEM_{r,f=1-3} + FMDEM_{r,f=1-3} + AGLOSSTRANS_{r,f=1-3} </math>

Note that this occurs after any adjustments to the demand values as a result of excessive consumer spending on food, (described below), but before adjustments as a result of shortages, describe in Section 3.4: Stocks. Thus, it can be the case that the final value of AGDEM may exceed the sum of the individual demand values.

'''Final agricultural demand adjustment based on levels of consumer spending'''

One final adjustment is made to the agricultural demand variables in the forecast years.

If the preliminary estimate of total food demand in monetary terms (csprelim), is too large of a share of consumption, i.e., if

<math>CsPrelim_{r} = CSF_{r} *(FDEM_{r} * WAP_{f=1,t=1} + FDEM_{r,f=2} * WAP_{f=2,t=1} + FDEM_{r,f=3} * WAP_{f=3,t=1} )>0.85*C_{r,t=1}</math>

'''Where,'''

CSF is the ratio of consumer spending in the agricultural sector in the first year (CSr,s=1,t=1) to DemValr, a weighted sum of demands for agricultural products for food in the first year;

<math>DemVal_{r} = FDEM_{r,t-1} *WAP_{f=1,t-1} + FDEM_{r,f=2,t-1} * WAP_{f=2,t-1} + FDEM_{r,f=3,t-1} * WAP_{f=3,t-1} </math>

C is total household consumption in the first year

When this is the case, a series of steps are taken to bring these values back in line.

#The necessary reduction (NecReducr), which is in monetary terms, is calculated as CsPrelimr – 0.85*Cr
#A reduction factor (ReducFact) for meat and fish, assuming cuts would disproportionately be there,  is calculated as,

<math>ReducFact_(r,)=(NecReduc_{r}/csprelim)*2</math>

with a maximum value of 1 or full elimination

#The physical demands for crops for meat and fish in tons (FDEM, categories 2 and 3) are reduced by reducfact, and the values of the meat and fish reduction are saved for the next step

<math>Meatreduc_{r} = FDEM_{r,f=2} *ReducFact_{r}</math> <math> Fishreduc_{r} = FDEM_{r,f=3} *ReducFact_{r}</math>

<math>FDEM_{r,f=2,3} = FDEM_{r,f=2,3} *(1-Reducfact)_{r}</math>

#An estimate of the necessary reductions in crops for food, in monetary terms is estimated by subtracting the savings obtained through the reduction in meat demand

<math>FoodReduc_{r}= NecReduc_{r} - MeatReduc_{r}* CSF_{r} *WAP_{f=2,t=1} - FishReduc_{r} * CSF_{r} *WAP_{f=3,t=1} </math>

The physical demand for crops for food (FDEM) is then reduced as follows

<math>FDEM_{r,f=1} = Max(0.1*FDEM_{r,f=1} , FDEM_{r,f=1} - FoodReduc_{r}/(CSF_{r} *WAP_{f=1,t=1} ))</math>

Note that this ensures that FDEM is not reduced by more than ninety percent.

Finally, given the changes above, the total demand is recalculated as the sum of the final values of feed, industry, and food demand and transmission losses

<math>AGDEM_{r,f} = FEDDEM_{r,f} + INDEM_{r,f} + FDEM_{r,f} + FMDEM_{r,f} + AGLOSSTRANS_{r,f}</math>

{| cellpadding="0" cellspacing="0" width="100%" align="center" border="1"
|-
|
'''Box 1: Adjustments in the Pre-processor to Ensure Proper Balances'''

The pre-processor reads in data from the FAO Food Balance Sheets and initializes values for the amount of agricultural commodities used for direct human consumption, FDEM, feed (FEDEM), industry (INDEM), food manufacturing (FMDEM), as well as transmission losses (AGLOSSTRANS). All of these are measured in MMT per year. At the same time, it reads in data for production (AGP), imports (AGM), exports (AGX), and total domestic supply (AGDOMSUPP)[1].

A set of conditions should be meet for these variables for each category:

#AGDOMSUPP = AGP + AGM – AGX. This says that total domestic supply equals production plus imports minus exports. This equivalence can be broken if there are changes in stocks, which we will see in forecast years. Currently, however, we assume there are no such changes in the first year. Thus it may be necessary to make adjustment for the equivalence to hold in first year. This is done in the pre-processor, by keeping AGDOMSUPP the same and applying the following three rules:<ol style="list-style-type:lower-alpha;">

*If AGDOMSUPP > AGP + AGM – AGX, i.e., stocks were being drawn down, increase AGP and AGM while reducing AGX.
*If AGDOMSUPP < AGP + AGM – AGX, i.e., stocks were being added to, decrease AGP and AGM while increasing AGX.
*Make sure that AGP, AGM, and AGX do not fall below a minimum value.
*Sum of AGM across countries = Sum of AGX across countries. This says that imports and exports need to match. If they do not, the model calculates the average of the two sums and adjusts AGM and AGX in each country proportionately.
*AGP + AGM – AGX = FDEM + FEDEM + INDEM + FMDEM + AGLOSSTRANS. This says that the total domestic supply, which accounts for production losses, has to match the total uses (including losses in transmission and distribution).

The pre-processor includes procedures to ensure that these three conditions hold for the initial values in each country. This can lead to minor adjustments in the values for the supply and demand categories. These processes can also lead to changes in related variables, including the production of non-animal meat products (CAGPMILKEGGS), fish catch (AGFISHCATCH), aquaculture production (AQUACUL), the size of the livestock herd (LVHERD), and the breakdown of land areas (LD). The latter occurs because we do not want these processes to change crop yields (YL). 

|}

== Trade ==

Consistent with the approaches within both the economic model and the energy model, trade of agricultural products in IFs uses a pooled approach rather than a bilateral one.   That is, we can see the total exports and imports of each country/region, but not the specific volume of trade between any two.  Offered exports and demanded imports from each country/region are responsive to the past shares of export and import bases and are summed globally.  The average of the totals is taken as the actual level of global trade and the country exports and imports are normalized to that level. 

Price differentials across countries do not influence agricultural trade. Although the IFs project has experimented over time with making such trade responsive to prices, there is an increasing tendency globally for food prices to be more closely aligned across countries than was true historically.  Moreover, the use within IFs of local relative food surpluses or deficits (as indicated by stock levels) to adjust trade patterns is an effective proxy for the use of prices.

The initial year values of the imports (AGM) and exports (AGX) of the three agricultural commodities in physical quantities are determined in the pre-processor. Since we only have historical data on the imports and exports of fish in monetary terms, these need to be converted to physical terms. This is done by multiplying the monetary values, which are in $billion, by 1000*/2200 to get physical values in million tons. In addition, exports of fish are limited to be less than 70 percent of total fish available and imports less than 1 percent of total fish available. For each of the three agricultural commodity groupings, if there is an imbalance between global imports and global exports in the preprocessor, the latter takes precedence and national imports are adjusted to bring global imports into line with global exports.

In the first year, seven variables are set related to trade for each commodity: XKAVE, MKAVE, XKAVMAX, MKAVMAX at the country level and wxct=1, wmdt=1, and WAPt=1 at the global level.

XKAVE and MKAVE are moving average values of export and import propensity, respectively. They are specified as the ratio of agricultural exports and imports to a base value (xbase) for each commodity. For exports, this is basically the sum of production and demand for that commodity; for imports, it is just demand.

<math>XKAVE_{r,f=1-3,t=1} = AGX_{r,f=1-3,t=1}/(AGP_{r,f=1-3,t=1} + AGDEM_{r,f=1-3,t=1} )</math>

<math>MKAVE_{r,f=1-3,t=1} = AGM_{r,f=1-3,t=1}/ AGDEM_{r,f=1-3,t=1} </math>

XKAVMAX and MKAVMAX are maximum values of XKAVE and MKAVE. For crops and meat, XKAVMAX is set to 1.1 times XKAVE, but is not allowed to exceed a value of 0.7; MKAVMAX is set to 1.5 times XKAVE, but also is not allowed to exceed a value of 0.7. For fish, XKAVMAX is set to 1.1 times XKAVE, with a bound of 0.95; MKAVE is set to 1.5 times MKAVE, with a bound of 2. These values are held constant for all future years.

XPriceTermLag, and MPriceTermLag are set to 0 for all commodities. wxc and wmd are the total world agricultural exports and imports; these are set to a value of 1 in the first year. WAP is the initial world price index for each commodity, which is set to 100.

In the forecast years, the process for determining agricultural imports and exports involves the following steps:

#Estimating the agricultural export capacity and agricultural import demand for each country.
#Reconciling the differences between global agricultural export capacity and global agricultural import demand.
#Computing the actual levels of agricultural exports and agricultural imports for each country

The agricultural export capacity is estimated by multiplying the export propensity (XKAVE) by the current year’s production and demand. It is also limited by XKAVMAX:

<math>AGX_{r,f=1-3} = MIN(XKAVE_{r,f=1-3}, XKAVMAX_{r,f=1-3} )*(AGP_{r,f=1-3} + AGDEM_{r,f=1-3} )</math>

Similarly, the agricultural import demand is estimated by multiplying the import propensity (MKAVE) by the current year’s demand, with a limit set by MKAVMAX

<math>AGM_{r,f=1-3} =MIN(MKAVE_{r,f=1-3}, MKAVMAX_{r,f=1-3} )* AGDEM_{r,f=1-3} </math>

For each country, values are also estimated for its net surplus or deficit (surpdef) for each commodity. This is based on the following factors: 1) post-loss production, 2) domestic demand, 3) the difference between current and desired stocks, and 4) a trade term

<math>surpdef_{r,f=1-3} = AGP_{r,f=1-3} * (1-LOSS_{r,f=1-3}) -AGDEM_{r,f=1-3}
+ cumstk_{r,f=1-3} - agdstl*(AGP_{r,f=1-3} + AGDEM_{r,f=1-3})
+TradeTerm_{r,f=1-3}
)</math>

The first three factors are straightforward. Production minus demand reflects a basic net surplus, which is then adjusted by any net surplus in stocks. The TradeTerm is related the relative role a country plays in global imports and exports and is given as:

<math>TradeTerm_{r,f=1-3} =(AGM_{r,f=1-3}/wmd_{f=1-3,t-1} - AGX_{r,f=1-3}/wxc_{f=1-3,t-1} )*(wmd_{f=1-3,t-1}+ wxc_{f=1-3,t-1})/2</math>

The TradeTerm is positive (negative) when a country has a larger (smaller) share of the global imports than it does of the global exports of a particular commodity and vice versa. Since the TradeTerm is added to surpdef, it acts as a balancing mechanism; countries that appear as relatively larger (smaller) importers get a positive (negative) boost to their estimated net surplus, which tends to reduce (increase) imports as shown below.

At this point, the global sum of exports and imports across countries will likely differ. Therefore, a procedure is required to balance these. In preparation for this one more global variable and several country-level variables are calculated. The global variable is globalsurdefrate, which is the ratio of the sum across countries of net surplus divided by the sum across countries of demand and production, which is the stock base.

<math>globalsurdefrate_{f=1-3} =(\sum_r(surpdef_{r,f=1-3} )/(\sum_r(AGDEM_{r,f=1-3} + AGP_{r,f=1-3}))</math>

The country-level variables are as follows:

The first term modifies the country’s net surplus, increasing (decreasing) it when the global net surplus is negative (positive).

<math>countryextrasurdef_{r,f=1-3} = surpdef_{r,f=1-3} - globalsurdefrate_{f=1-3} *(AGDEM_{r,f=1-3}+ AGP_{r,f=1-3})</math>

The second term modifies how rapidly the net surplus is closed.

<math>countryextrasurdefadj_{r,f=1-3} = countryextrasurdef_{r,f=1-3}/5</math>

The third term is simply the ratio of exports to the sum of imports and exports.

<math>exportshare_{r,f=1-3} = AGX_{r,f=1-3}/(AGX_{r,f=1-3} + AGM_{r,f=1-3} )</math>

The next step is to calculate whether it is necessary to increase (decrease) imports and decrease (increase) exports for each country, and by how much. Whether a country needs to increase its initial estimates of imports and decrease its initial estimates of exports, or vice versa, is determined by the sign of countryextrasurdef. If this value is negative, i.e., the country has a net deficit, it will need to reduce exports and increase imports. The opposite holds for when countryextrasurdef is positive.

As for the amount by which imports and exports need to be increased or decreased, this is a function, in general, of the size of the necessary adjustment and the export share:

<math>AGX_{r,f=1-3} = AGX_{r,f=1-3} + countryextrasurfdefadj_{f=1-3} * exportshare_{r,f=1-3}</math> <math>AGM_{r,f=1-3} = AGM_{r,f=1-3}- countryextrasurfdefadj_{f=1-3} * (1-exportshare_{r,f=1-3})</math>

Note that the sign of countryextrasurdef and the fact that exportshare is a value between 0 and 1 ensure that when exports increases, imports fall, and vice versa.<ref>Two other variables, defadjmul and ImportBoost, are included in the calculations to make some finer adjustments to the changes in exports and imports; these relate to the observed behavior for specific countries and are not discussed in detail here.</ref>Finally, in this adjustment process, exports and imports are not allowed to fall by more than half or more than double.

This process may not fully reconcile global trade, so a final adjustment is made by setting world trade (WT) as the average of global exports and imports and then adjusting the country values accordingly:

<math>WT_{f=1-3} =(\sum_r(AGX_{r,f=1-3}) +\sum_r(AGM_{r,f=1-3}) )/2</math> <math> AGX_{r,f=1-3} = AGX_{r,f=1-3} * WT_{f=1-3}/(\sum_r(AGX_{r,f=1-3}) )</math> <math> AGM_{r,f=1-3} = AGM_{r,f=1-3} * WT_{f=1-3}/(\sum_r(AGM_{r,f=1-3}) )</math>

IFs can now update the moving average export (XKAVE) and import (MKAVE) propensities for the next time step. The weights given to history are set by the global parameters '''xhw'''and '''mhw'''. For small exporters, i.e., where exports are less than one tenth of the sum of production and demand, '''xhw'''is reduced by 40 percent, allowing for faster adjustment. XKAVE and MKAVE are updated as

<math>XKAVE_{r,f=1-3,t+1} = XKAVE_{r,f=1-3}+(1-xhw)* AGX_{r,f=1-3}/(AGP_{r,f=1-3} + AGDEM_{r,f=1-3} )</math>

<math>MKAVE_{r,f=1-3,t+1} = XMAVE_{r,f=1-3}+ {1-mhw} * AGM_{r,f=1-3}/AGDEM_{r,f=1-3} </math>

For crops, the import propensity is bound from below by a factor given by potential GDP (GDPPOT), demand (AGDEM), the conversion factor between agricultural imports in physical terms and dollar values (msf, see section on links to the economic model), and the initial world price for agriculture (WAP).

<math>XKAVE_{r,f=1-3,t+1} => (0.6*GDPPOT_{r})/(AGDEM_{r,f=1-3} * msf_{r}*WAP_{f,t=1})</math>

Finally, XKAVE and MKAVE are bound from above by XKAVMAX and MKAVMAX, respectively.

== Stocks ==

==== First year ====

Due to a lack of good historical data, in the first year, stocks for all three agricultural commodities are assumed to equal desired stocks. These are set to a fraction (agdstl) of total production (AGP) and demand (AGDEM) for each commodity.

<math>FSTOCK_{r,f=1-3} =(AGP_{r,f=1-3} + AGDEM_{r,f=1-3} )*Agdstl</math>

Where

Agdstl is a parameter used to set desired stock levels for agricultural commodities.  It is set to be 1.5 times '''dstl''', which is a global parameter that can be adjusted by the user

==== Forecast years ====

In future years, basic stock levels (CumStk) increase with production (AGP), decrease with demand or consumption (AGDEM), and adjust for net imports (AGM-AGX).

<math>CumStk_{r=1-3} = FSTOCK_{r,f=1-3,t-1} + StkAdj_{r,f=1-3}</math> <math>StkAdj_{r,f=1-3} = AGP_{r,f=1-3} - AGDEM_{r,f=1-3}+ (AGM_{r,f}- AGX_{r,f=1-3})</math>

Of course, the actual stock values (FSTOCK) are not allowed to go negative. If the basic stock level is negative, stocks are set at zero and a shortage (Sho) exists, which affects calorie availability. If the basic stock level is positive there is no shortage and stocks equal the basic level.

<math>if cumstk_{r,f=1-3}<0 then Sho_{r,f=1-3} =-StkAdj_{r,f=1-3} and FSTOCK_{r,f=1-3}= 0</math> <math>if cumstk_{r,f=1-3} > 0 then Sho_{r,f=1-3} = 0 and FSTOCK_{r,f=1-3} = cumstk_{r,f}</math>

Also, if shortages are greater than 0, a reduction factor (ReductionFactor''')'''is computed which is then used to adjust demand and losses.

<math>if SHO_{r,f}>0, ReductionFactor_{r,f} =(AGDEM_{r,f}- SHO_{r,f})/ AGDEM_{r,f}</math> <math> FDEM_{r,f}= FDEM_{r,f} * ReductionFactor_{r,f} </math> <math> FEDDEM_{r,f} = FEDDEM_{r,f} * ReductionFactor_{r,f} </math> <math> INDEM_{r,f} = INDEM_{r,f} * ReductionFactor_{r,f} </math> <math> FMDEM_{r,f} = FMDEM_{r,f} * ReductionFactor_{r,f} </math> <math> AGLOSSTRANS_{r,f} = AGLOSSTRANS_{r,f} * ReductionFactor_{r,f} </math>

== Calorie Availability ==

Daily per capita calorie availability (CLPC) is initialized in the pre-processor. Where available, data is taken from the FAO<ref>Note this occurs in DATAPOP, not DATAAGRI. The historic data series is SERIESCalPCap. Missing data are estimated based on access to water and sanitation or average income.</ref> It is multiplied by population (POP) to yield total daily calorie availability and brought into the model with the name CLAVAL. We already saw that this first year value is used in the calculation of two country-specific factors: 1) calactpredrat, which is a shift factor determined as the ratio of calorie availability to predicted calorie demand in the first year, and 2) sclavf, which is a conversion factor relating the total annual demand for food crops and crop equivalents from meat to daily calorie availability.

In the forecast years, CLAVAL is calculated using the final value of calories per capita.

<math>CLAVAL_r= CLPC_{r,f=4}* POP_{r} </math>

Calorie availability combines with regional calorie need in the population model for the calculation of possible starvation deaths (a seldom used variable because in official death statistics people do not die of starvation but rather of diseases associated with undernutrition); the population and health models therefore look instead to the impact of calorie availability on undernutrition and health.

== Prices ==

IFs keeps track of both national (FPRI) and world (WAP) price indices for each of the three agricultural commodities. All of these are set to an index value of 100 in the building of the base.

The national crop price indices (FPRI, category (1) respond to: 1) changes in global costs of crop production, the latter being expressed as the ratio of global accumulated capital investment in crops to global production and 2) changes in the level of domestic crop stocks. The first factor should provide a long-term basis for rising or falling prices tied to changing technology and other factors of production; the second factor generally should represent shorter-term market variations from that long-term level.

The impact of global costs is given by dividing the ratio of global investment in crops to global production (wkagagpr) in the current year to that same ratio in the first year.  The effect of stocks on crop prices (Mul) is calculated using the same ADJSTR function introduced in the description of crop supply, which considers the difference between both the current crop stocks and a desired vale and between current crop stocks and those in the previous year. Two parameters control the degree to which these two ‘differences’ affect the calculation of the adjustment factor. In this case, these are the global, user-controllable parameters '''fpricr1'''and '''fpricr2'''. All together the equation for domestic crop price indices in the coming year is given as

<math>FPRI_{r,f=1,t+1} = WAP_{f=1,t=1} * wkagagpr_{r,t}/wkagagpr_{r,t=1} * Mul_{r} </math>

The domestic crop price indices are also bound between 0.01 and 1000.

The national meat price indices are linked the global crop price. Specifically, they are given as a moving average of the global crop price index

<math>FPRI_{r,f=2,t+1} = fprihw* FPRI_{r,f=2,t} +(1-fprihw)* WAP_{f=1,t}</math>

Where

'''''fprihw''' is a global parameter used to control the speed at which the domestic meat price changes.''

The national fish price indices are all set equal to the global fish price index. The determination of the global fish price is similar to that for the national crop price, but here the stock of interest is the global stock and there is no effect related to costs. The ADJSTR function is used once again to calculate the adjustment factor (MUL), this time focusing on the desired global fish stock, the difference between this and the current global fish stock, and the change in the global fish stock in the past year. Again, two parameters control the degree to which these two "differences" affect the calculation of the adjustment factor. In this case, these are the global, user-controllable parameters '''fprim1'''and '''fprim2'''. The global and national fish prices are thus calculated as

The world price indices for crops and meat are computed, in the following year, as a weighted average of the domestic prices, with the weights given by crop and meat production:

<math>WAP_{r,f=1-2,t+1} =(\sum_r(FPRI_{r,f=1-2,t+1} * AGP_{r,f=1-2,t+1} ) )/(\sum_r(AGP_{r,f=1-2,t+1}) )</math>

== Returns and Profits ==

IFs estimates the net returns in agriculture (AGReturn) for each commodity as the ratio of gross returns (GReturn) to production costs (ProdCost and MProdCost). The agricultural profit ratios (FPROFITR) are then estimated as the ratio of AGReturn in the current year to its value in the initial year. At some points in the evolution of IFs we have used FPROFITR as a guide to rates of investment (see the calculation of mulrprof in All but First 2: Investment); the current formulation for investment does not do so. For completeness, however, we provide a description of these processes in the model, as they still exist as live code.

==== Pre-processor and first year ====

In the first year, values for FPROFITR, sfprofitr, and FPRofitR are all set to 1.

==== Forecast years ====

The production costs for crops are estimated as the cost of cropland, priced at the cost of new land development (CLD), plus the investment in agricultural capital (KAG). The net revenues are given as total yield times the domestic crop price index. This results in

<math>ProdCost_{r,f=1,t} = LD_{r,l=1,t} * CLD_{r,t}+ KAG_{r,t} </math>

<math>GReturn_{r,f=1,t} = (byl_{r,f}* LD_{r,f=1} * FPRI_{r,f=1} * (AGLOSSPROD_{r,f=1} /AGP_{r,f=1}))/ProdCost_{r,f=1,t}</math>

For meat, production costs are estimated by the value of the crop equivalents produced by grazing and the cost of feed, where the value is given by the domestic meat price index. The net revenues are based on the size of the herd and the domestic meat price index. This results in

<math>MProdCost_{r,f=2,t} =(LD_{r,l=2,t} * GLDCAP_{r,t} + FEDDEM_{r,t} )* FPRI_{r,f=2,t+1} </math> <math> GReturn_{r,f=2,t}=(LVHERD_{r,t} * FPRI_{r,f=2,t+1})/ProdCost_(r,f=2,t)</math>

For fish, the production costs are simply estimated by the total production of fish times the domestic meat price index. The net revenues are given as the total production of fish times the domestic fish price index. This implies

<math>MProdCost_{r,f=3,t}= FISH_{r,t} * FPRI_{r,f=2,t+1} </math> <math>GReturn_{r,f=3,t} =(AGP_{r,f=3}* FPRI_{r,f=3,t+1})/ProdCost_{r,f=3,t}</math>

The net returns for each commodity can then be calculated as

<math>AGReturn_{r,f=1-3,t} = GReturn_{r,f=1-3,t}/ProdCost_{r,f=1-3,t} </math>

These net returns are used to account for changes in profits over time, using the variable FPROFITR, which influences investment in agriculture. This variable is calculated for each commodity as

<math>FPROFIT_{r,f=1-3,t} = AGReturn_{r,f=1-3,t}/ARGeturn_{r,f=1-3,t=1} </math>

A similar variable (wfprofitr) is calculated at the global level as a production weighted average of country/region values, but only for crops.

== Investment ==

Investment in agriculture is relatively complex in IFs, because changes in investment are the key factor that allows us to clear the agricultural market in the long term. It is very similar to investment in energy, except that we do not need to compute type-specific investments—capital in agriculture is only used for the production function of crops.

We calculate a total agricultural investment need (INAG) to take to the economic model and place into the computation for investment among sectors. This calculation involves multiple factors.  These begin with an initial estimate or targeted level of investment (TInAg) that is the product of the ratio of investment to GDP in the previous year times the GDP in the current year.

Three factors modify that basic or target investment level.  Two of those are global and one is regional.  The first global factor is a multiplier linked to year-to-year change in the ratio of agricultural demand to GDP (WAgDemRMul); typically agricultural demand grows more slowly than GDP.  The second is a multiplier responsive to the level of global stocks (MulWSt); if those drop below target levels it would increase production globally and vice versa.  The model could use a global price average instead of stocks, but in the recursive structure stocks determine prices and therefore use of stocks accelerates responsiveness of investment.  Similarly, the regional factor represents a multiplier tied to regional stock levels (MulSt).

<math>TInAg_{r,t} = INAG_{r,t-1}/GDP_{r,t-1} * GDP_{r,t}* WAgDemRMul_{t} * MulWSt_{t}* MulSt_{r,t}</math>

where, <math> WAgDemRMul_{t} =((\sum_r(AGDEM_{r,t} )/WGDP_{t} )/((\sum_r(AGDEM_{r,t-1})/WGDP_{t-1})</math>

To elaborate, MulWSt and MulSt are adjustment factors related to global and domestic crop stocks, respectively. Both use the PID ADJSTR function described earlier, just as changes in prices use it in order to set prices that change year-to-year so as to chase supply-demand equilibration over time. For MulWSt, the controlling parameters in the PID function for stocks versus targets and changes in stocks are hard coded with values of -0.3 and -0.9, respectively. For MulSt, these parameters are hard coded with values of -0.2 and -0.4, respectively.

Experience with that initial estimate, however, shows that it can be overly responsive to one or more of the multiplicative adjustment factors, thereby setting up behavior that oscillates.  Therefore the next step is to compute a smoothed rate of investment as a share of GDP (SmInAgR).  That rate gives more weight (60 percent) to the final investment rate in the previous year than it does to the rate that results from the initial target investment calculation.  The overall result of this process is to smooth changes in the rate of investment over time.  Desired investment (INAG) is the product of that smoothed rate and GDP.

<math>INAG_{r,t}= SmInAgR_{r,t} * GDP_{r,t} </math>

where,

<math>SmInAgR_{r,t} = INAG_{r,t-1}/GDP_{r,t-1} *0.6+ TInAg_{r,t}/GDP_{r,t} *0.4)</math>

To further prevent too rapid of a shift in demand for agricultural investment, INAG is not allowed to increase by more than 30 percent or decrease by more than 25 percent from the actual investment in the current year. A second check ensures that the demand is no less than 0.5 percent and no greater than 40 percent of current agricultural capital (KAG).

At this point a user-controlled country-specific multiplier '''aginvm'''can boost or reduce INAG. One final check ensures that as long as GDP in the country is larger than it was in the first year, the demand for agricultural investment is not allowed to decline at an annual rate of more than 1 percent per year from the first year.

Investment need (INAG) then enters the economic model, which returns a value reconciled with all other investment needs and that feeds into further calculations in the agriculture model.

== Economic Linkages ==

Several variables, such as gross production, stocks, consumer spending, trade, prices and investment, are common to both the economic model and the two physical models. But hardly ever will the economic and physical models produce identical values, even during the first time step when both utilize "data." Thus, although we want the physical model value to override that of the economic model, it cannot simply replace it. Instead IFs extensively uses a procedure of computing an adjustment coefficient during the first time step. That coefficient is the ratio of the value in the economic model to the value in the physical model. In subsequent years IFs uses that coefficient to adjust the value from the physical model before its introduction into the economic model.

Gross production (ZS) in the agricultural sector illustrates this procedure. The value of gross production in the agricultural model is the sum of the products of agricultural production (AGP) and prices (WAP) in each agricultural category. Multiplying that times an adjustment factor (ZSF) computed in the first time stop to assure inter-model consistency produces gross production for the economic (ZS). World average prices (WAP) are used in all the economic/physical model conversions because they assure that global sums (e.g. of exports and imports) will balance.<ref>s in the subscript represents economic sector. s = 1 is defined as the agriculture sector.</ref>

<math>ZS_{r,s=1}=ZSF_{r}*\sum_f(WAP_{f,t=1}*AGP_{r,f,t} ) </math>

'''Where,'''

<math>ZSF_{r} =ZS_{r,s=1}/(\sum_f(WAP_{f,t=1}*AGP_{r,f,t=1} ) )</math>

Similarly, food stocks in each category (FSTOCK) and an adjustment factor (FSF) produce stocks (ST) for the economic model.

<math>ST_{r,s=1}=FSF_{r}*\sum_{f}(FSTOCK_{r,f,t}* WAP_{f,t=1} ) </math>

'''Where,'''

<math>FSF_{r} = ST_{r,s=1}/(\sum_{f}(FSTOCK_{r,f,t=1}* WAP_{f,t=1} ) )</math>

A similar translation is made for consumer spending on agricultural commodities, recognizing that not all crop demand is directly by consumers.

<math>CS_{r,s=1} = CSF_{r} *(FDEM_{r,t} * WAP_{f=1,t=1} +\sum_{f=2,3}(AGDEM_{r,f,t}* WAP_{f,t=1} ) )</math>

'''Where'''

<math>CSF_{r} = CS_{r,s=1} /(FDEM_{r,t=1}* WAP_{f=1,t=1} +\sum_{f=2,3}(AGDEM_{r,f,t}* WAP_{f,t=1} ) )</math>

In the same fashion exports (AGX) and imports (AGM) from the agricultural model allow calculation of exports (XS) and imports (MS) for the economic model.

<math>XS_{r,s=1}= xsf_{r} *\sum_f(AGX_{r,f,t}* WAP_{f,t=1} ) </math>

'''Where'''

<math>xsf_{r}= XS_{r,s=1}/(\sum_{f}(AGX_{r,f,t=1}* WAP_{f,t=1} ) )</math>

and

<math>MS_{r,s=1} = msf_{r} *\sum_f(AGX_{r,f,t}* WAP_{f,t=1} ) </math>

'''where'''

<math>msf_{r}= MS_{r,s=1}/(\sum_f(AGN_{r,f,t}* WAP_{f,t=1} ) )</math>

A check and, if necessary, adjustment is made ensure that the monetary values of imports and exports match up at the global level.

<math>XS_{r,s=1} = XS_{r,s=1} * ((\sum_{r}(XS_{r,s=1} ) +\sum_{r}(MS_{r,s=1} ) )/2)/(\sum_{r}(XS_{r,s=1} ) )</math>

and

<math>MS_{r,s=1}= MS_{r,s=1} *((\sum_{r}(XS_{r,s=1} ) +\sum_r(MS_{r,s=1} ) )/2)/(\sum_{r}(MS_{r,s=1} ) )</math>

With respect to prices, the agriculture model passes to the economic model a value (PRI), which reflects the ratio of the current domestic crop price index to the initial world crop price index.

<math>PRI_{r,s=1} = FPRI_{r,f=1}/ WAP_{r,f=1,t=1} </math>

Finally, investment need (INAG) is passed to the economic model under the variable name IDS, category 1 (agriculture).

== Capital Dynamics ==

The economic model of IFs returns a (potentially) modified value of IDS, category 1, reflecting the total amount of capital available for agriculture. This value is assigned to the variable IAval, which overrides the value of INAG calculated earlier (earlier it was basically investment demand; after return from the economic model it becomes investment supply).<ref>Fs does have a global parameter agon that can be used to break the link between the agriculture and economic model, in which case INAG is not overwritten. This is done by setting agon to a value less than 0.5. Doing so treats the agriculture model as a partial equilibrium model rather than a general equilibrium model.</ref> The agriculture model divides the investment available for agriculture (IAval) into investment for cropland development and investment for other agriculture capital. The coefficient IALK indicates the portion going to cropland development.

IALK is set to a default value of 0.25 for all countries in the pre-processor. In forecast years, IALK changes from this initial value depending on change in the ratio of return on land (RETR) to return on capital (RETK).

IFs calculates the return rate on land as the crop yield (YL) in the first year divided by the current cost of developing a unit of cropland (CLD).

<math>RETLD_{r} = YL_{r,t=1}/ CLD_{r,t} </math>

The return on capital depends on the difference between the hypothetical level of crop yield (HYL) that could be obtained from an additional unit investment in agricultural capital and the crop yield without that increment (CompYl). Recalling how crop yield is estimated, the hypothetical crop yield is given as

<math>HypothYl_{r} = cD_{r} * agtec_{r} *(KAG_{r+1})^( ALPHA_{r} )*(labagi_{r} )^((1-ALPHA_{r} ) )* satk_{r}</math> <math> CompYl_{r} = cD_{r} * agtec_{r} *(KAG_{r} )^(ALPHA_{r} )*(labagi_{r} )^((1-ALPHA_{r} ) )* satk_{r}</math>

and the return on capital is given as

<math>RETCap_{r} = LD_{r,l=1} *(HypothYLl_{r}- CompYl_{r} )</math>

The ratio of the return to land to the return to capital (RETRAT) is given as

<math>RETRAT_{r} = RETLD_{r}/ RETCap_{r} </math>

The adjustment of IALK uses the same first and second order adjustment mechanism that we have seen before with the ADJSTR function. Here the ‘target’ level is the ratio of the return to land to the return to capital in the first year.

<math>IALK_{r,t+1} = IALK_{r,t=1} *(1+(RETRAT_{r}-RETRAT_{r,t=1}/1))^{eliasp1}*(1+(RETRAT_{r}-RETRAT_{r,t-1}/1))^{eliasp2}</math>

'''where,'''

'''''eliasp1''' and '''eliasp2''' are global parameters''

Two final checks are made on the value of IALK. First, it is not allowed to exceed a value related to the cost of replacing depreciated investment in land and bringing a portion of grazing or forested land into production.

<math>IALK_{r,t+1} =< ((0.04* LD_{r,l=3} +0.04* LD_{r,l=4} +dkl* LD_{r,l=1} )* CLD_{r})/ IAval_{r} </math>

Second, IALK is bound between 0.1 and 0.8.

Finally the model updates agricultural capital (KAG) for the next year by subtracting depreciation as represented by agricultural capital lifetime ('''lks'''), adding the residual (non-land) investment, and adjusting for any civilian damage from warfare (CIVDM – see international politics model documentation).

<math>KAG_{r,t+1} = KAG_{r,t}- KAG_{r,t} /lks_{s=1} + IAval_{r}*(1-IALK_{r,t+1} )*(1- CIVDM_{r})</math>

== Land Dynamics ==

 Land in IFs is divided into five categories—crop, grazing, forest, urban, and other land. Historical data on total land area (LDTot), crop land (LDl=1), grazing land (LDl=2), forest land (LDl=3), and other land (LDl=4) are taken from FAO data. Historical data on urban land (LDl=5) is taken from WRI.

==== Pre-processor and first year ====

A few adjustments to the historical data are made in the pre-processor.

*In the pre-processor total production of food is reconciled with the total trade. In cases where, demand is greater than domestic supply of crops, crop production is increased to reconcile demand with supply of food production. Crop land is also increased proportionately. 
*If urban land is more than three quarters the area of other land, land is shifted from urban to other land
*If no data is available for crop land, the same is set to 30 percent of total land area. If no data is available for grazing land, same is set to 5 percent of total land area. If no data is available for other land, same is set to 30 percent of total land area.

After these changes, total land area is recomputed as the sum of the area of the individual land categories.

The pre-processor also reads in a value for potentially arable land ('''landarablepot'''), which affects the amount of potential cropland in the model. The share of agricultural capital going to land (IALK) is set to 0.25 in the pre-processor.

One final parameter is estimated related to land in the pre-processor. This is the target rate of growth of cropland ('''tgrld'''). When data is available, this is currently estimated as the growth rate of cropland between the year 2015 and the year 2005.

<math>tgrld_{r} =(LD_{r,l=1,yr=2015}/LD_{r,l=1,yr=2005} )^{1/10}-1</math>

When no data are available for cropland in either 2015 or 2005, the target rate of growth of cropland is estimated as a function of average income

<math>tgrld_{r} =0.009-0.011*MIN(1,GDPPCP_{r}/30)</math>

with a maximum growth rate given as a function of cropland as a share of total land

<math>tgrld_{r} =< tmaxgrow_{r} =0.015-0.01*MIN(1,0.5* LD_{r,l=1}/LDTot_{r} )</math>

Finally, this target growth rate is restricted to fall between -0.003 and +0.01.

In the first year, IFs estimates an initial unit cost of cropland development (CLD) as

<math>CLD_{r,t=1}=(IDS_{r,s=1,t=1} * IALK_{r,t=1})/(LD_{r,l=1,t=1}*(dkl+tgrld_{r} ) )</math>

'''where,'''

IDS is the total investment in agriculture

IALK is the share of agricultural investment going to cropland development

'''''dkl''' is a global parameter indicating the depreciation rate of investment in cropland, essentially a maintenance cost for existing cropland''

'''''tgrld''' is the target growth rate for cropland''

A related factor (SCLdF), to be used in determining the cost of land development in future years, is also calculated in the first year

<math>SCLdF_{r} = CLD_{r,t=1}/LD_{r,l=1,t=1} </math>

==== Forecast years ====

IFs calculates changes in land use for the coming year as a result of four key dynamic processes. First, changes in urban land may result from income and population changes. Second, economic shifts related to investment, particularly in the agricultural sector, can affect the amount of cropland. Third, IFs there can be expansion or retirement of grazing land for undefined reasons. Finally, in certain scenarios, specific changes in forest land can result from policies related to issues such as conservation and environmental protection.

====== Changes in urban land from income and population changes ======

Changes in urban land result from changes in population and income. IFs first estimates a predicted level of urban land (LandUrbanPred), which is then compared to current urban land. Any changes are assumed to affect all other land types proportionately, unless this leads to not enough land in a particular category. The growth with income is based on an estimated relationship between income and urban land per capita (LandUrbanR)

The predicted level of urban land (LandUrbanPred) is then given as

<math>LandUrbanPred_{r} = LD_{r,l=4,t=1} *(POP_{r,t}/POP_{r,t=1} )*(LandUrbanR_{r,t}/LandUrbanR_{r,t=1} )</math>

The change in urban land (NUrbLD) is then calculated as

<math>NUrbLD_{r} = LandUrbanPred_{r} - LD_{r,l=4}</math>

Limits are placed on the change in urban land area. First, if urban land is growing, the amount of increase in a single year cannot exceed 1/100th of a variable that is related to the change in the non-urban share of all other land from the base year (NonUrbanShrR)

<math>NonUrbanShrR_{r} = (NonUrbanShr_{r,t}/NonUrbanShr_{r,t=1} )^{2}</math>

'''where,'''

<math>NonUrbanShr_{r,t=1,t} =(\sum_{l}LD_{r,l=1-4,t} )/(\sum_{l}LD_{r,l=1-5,t} )</math>

Second, if urban land is declining, it is not permitted to fall below 10,000 hectares. Third, the changes in Urban land are assumed to affect all other land categories proportionately

<math>Reduc_{r,l=1-4} = NUrbLD_{r} * LD_{r,l=1-4}/(\sum_{l}LD_{r,l=1-4} )</math>

However, this is not allowed to result in the area for a given land category falling below 1,000 hectares. Thus, there may be a slight reduction in the amount of new urban land in certain cases.

====== Changes in cropland due to investment and/or depreciation. ======

The changes in cropland are driven by the economics of land. Specifically, they are a function of the profitability of cropland. Also, they are assumed to affect, at least directly, only the forest and the other land categories.

A maximum amount of cropland expansion each year (MaxLandExpansion) is fixed by the amount of forest land, the amount of other lands, the amount of potential arable land, and the existing amount of cropland. The maximum amount of expansion must be at least 2/100th of the existing cropland, but beyond that it cannot exceed either the total amount of forest and other land or the difference between 110% of the potential arable land (landarablepot) and current cropland.

The change in the amount of cropland and the initially estimated share of agricultural investment going to cropland in the following year are computed differently depending upon the maximum amount of cropland expansion relative to the amount of existing cropland and the current level of average income in a country. Specifically, if the maximum amount of cropland expansion is less than 10 percent of existing cropland then it is assumed that there is no change in cropland (lddev = 0) and that no agricultural investment is targeted for cropland development (IALK = 0).

If the condition mentioned in the previous paragraph is met, i.e., there is an ‘adequate’ amount of land for expanding cropland, the amount of change in cropland (lddev) is initially calculated as

<math>LdDev_{r} =(((IAval_{r} * IALK_{r})/CLD_{r} )* ldcropm_{r})-(LD_{r,l=1}*dkl)</math>

'''where'''

IAval is the total amount of funds available for investment in agriculture which is equal to IDS

IALK is the share of agricultural investment going to cropland development

CLD is the unit cost of cropland development

'''''dkl''' is the depreciation rate of investment in cropland (essential a maintenance cost for existing cropland)''

'''''ldcropm''' is a country-specific multiplier that can be used to increase or decrease changes in cropland''

Note that this equation takes into account the need to maintain existing cropland. Also, at this point, the value of LdDev is bound from below to ensure that it does not imply a greater than 10 percent decrease in existing cropland. For relatively poor countries (GDPPCP < 10), the constraint is even stricter. Specifically, IFs calls for a shift in funds to ensure that no cropland is lost. The desired shift in funds is given as

<math>DesShift_{r} =-CLD_{r} * LdDev_{r} </math>

The actual shift in funds is limited to 90 percent of the available funds, however, where the available funds are the investment in agriculture not initially designated for cropland development

<math>Shift_r = MIN(0.9* IAval_{r} *(1-IALK_{r} ),DesShift_{r} )</math>

The value of lddev given the actual shift in funds is given as

<math>LdDev_{r} = LdDev_{r} + Shift_{r}/ CLD_{r} </math>

In addition, the share of investment in agriculture designated for cropland development is updated to be

<math>IALK_{r}= IALK_{r}+ Shift_{r}/IAval_{r} </math>

The changes in cropland are linked to changes in land in the forest and ‘other’ categories. The amount coming from/going to forests reflects the share of forest land relative to ‘other’ land, as well as the current level of development. For countries with a GDP per capita higher than 15,000 dollars and where LdDev is less than 0, more is given back to forest land and the ForShrPar is set to 0.25.

<math>LDDEVFor_{r}=LdDev_{r}* LD_{r,l=3}/(LD_{r,l=3} + LD_{r,l=4} )* ForShrPar_{r}</math>

'''where,'''

 ForShrPar is given by the function depicted below;

[[File:Changes in cropland due to Investment and or Depreciation.png|frame|center|Changes in crop land due to investment and or depreciation]]

The solid line holds when land is being converted from forests to cropland (lddev > 0) and the dotted line holds when land is being converted from cropland to forests (LdDev < 0). In either case, this implies that the less of the change is related to forest land than would be expected by its share.

Two other qualifiers are that the changes in forest land (LDDEVFor) and the changes in ‘other’ land cannot exceed 90 percent of existing land in these categories and the shifts cannot result in either land category falling below 1,000 hectares. These limits feedback to the change in cropland, finally resulting in the following

<math>LdDev_{r}= LDDEVFor_{r} + LDDEVOth_{r}</math>

<math>LD_{r,l=1}= LD_{r,l=1}+ LdDev_{r}</math>

<math>LD_{r,l=3}= LD_{r,l=3} - LDDEVFor_{r} </math>

<math>LD_{r,l=4}= LD_{r,l=4}- LDDEVOth_{r} </math>

Turning back to the future cost of cropland development, this is estimated differently based only on whether there is ‘adequate’ room for cropland land expansion, defined as when the maximum amount of cropland expansion is greater than 10 percent of existing cropland. If this is the case, the future price of cropland is estimated as

<math>CLD_{r,t+1}= CLD_{r,t=1}* LD_{r,l=1,t}/ LD_{r,l=1,t=1} * RemRat_{r}^{0.2}</math>

'''where'''

RemRat is the ratio of the maximum land for expansion in the first year to the maximum land for expansion in the current year, with a maximum value of 10

<math>RemRat_{r} = MaxLandExpansion_{r,t=1}/MAX(0.1* MaxLandExpansion_{r,t=1},MaxLandExpansion_{r,t} ) </math>

This basically states that the price of cropland development grows linearly with growth in cropland and exponentially with declines in available land for cropland expansion.

Alternatively, if the maximum amount of cropland expansion in a given year is less than or equal to10 percent of existing cropland, the cost of bringing new land under cultivation is assumed to grow at the maximum of either 2 percent per year from the cost in the first year or the growth of cropland from the first year. Furthermore, it is not allowed to decline. Thus

<math>[CLD]_{r,t+1}=MAX(CLD_{r,t}, CLD_{r,t=1} * LD_{r,l=1,t}/ LD_{r,l=1,t=1} , CLD_{r,t=1}*(1+2*(t-2015)/100))</math>

====== Changes in grazing land ======

IFs assumes that relatively poor countries (GDPPCP < 10) will continue to develop additional grazing land, whereas relatively rich countries (GDPPCP > 15) will retire grazing land. No change is expected in countries with average income between $10,000 and $15,000. The annual expansion of grazing land in poor countries is initially estimated as 0.5 percent of the amount of grazing land in the first year. The retirement of grazing land in richer countries is initially estimated as 0.2 percent of current grazing land.

As with cropland, any changes in grazing land will be compensated by changes in forest and ‘other’ land. Each category is initially assumed to be affected proportionately, e.g.,

<math>ForestShr_{r}= LD_{r,l=3}/(LD_{r,l=3} + LD_{r,l=4} )</math>

Unlike the case for changes in cropland, there is no adjustment to the forest share as a function of income or the direction of change in grazing land. As with the changes in cropland, however, the changes in forest and ‘other’ land cannot exceed 90 percent of existing land in these categories and the shifts cannot result in either land category falling below 1,000 hectares. Again, these limits feed back to the change in grazing land.

====== Change in forest land due to a policy choice ======

The model user can also force the land in forest area to increase or decrease at the expense of crop and grazing land via a forest multiplier '''forestm'''. The change in forestland, LDSHIFT, is bound. In the case of an increase, i.e., '''forestm'''> 1, the amount of added land is limited to 20 percent of crop and grazing land; in the case of a decrease, i.e., '''forestm'''< 1, the amount of forest land removed is limited to 20 percent of existing forest land.

<math>- LD_{r,l=3}/5< LANDSHIFT_{r} <(LD_{r,l=1}+ LD_{r,l=2})/5</math>

<math>LD_{r,l=3}= LD_{r,l=3}+ LANDSHIFT_{r}</math>

The amount of land taken from cropland and grazing land is proportional to the amount of each.

<math>CropShare_{r}=LD_{r,l=1}/(LD_{r,l=1}+ LD_{r,l=2} )</math>

<math>LD_{r,l=1}= LD_{r,l=1}+LANDSHIFT_{r}* CROPSHARE_{r}</math>

<math>LD_{r,l=2}= LD_{r,l=2}+ LANDSHIFT_{r} *(1-CROPSHARE_{r})</math>

====== Final checks and renormalization of land use ======

Two final adjustments are made to the land area values to clean up any quirks that might have be introduced in the previous processes. First, the values for each category are bound between one thousand and ten billion hectares. Second, the values are normalized so that the sum of the categories equals the total amount of land.

<math>[LD]_{r,l=1-5,t+1}=LD{r,l=1-5} * LD_{r,l=1-5}/(\sum_{l}LD_{r,l=1-5} )</math>

Finally, a value for world forest area (WFORST) is calculated at the end of this process by summing forestland area across all countries.

<math>WFORST_{t+1}=\sum_{l}LD_{r,l=3} </math>

== Livestock Dynamics ==

In addition to capital and land, the other "stock" or "level" variable with important temporal dynamics is the livestock herd (LVHERD).

==== Pre-processor and first year ====

In the pre-processor, as explained earlier, the values for total meat production and animal meat production are initialized. From these values, IFs calculates the value for livestock by dividing the total animal meat by the slaughter rate ('''slr''')

==== Forecast years ====

The value of LVHERD is calculated by using pre-production loss meat production (AGPppl), adjusting the same for animal products produced (AGPMILKEGGS). This gives total animal meat production. The animal meat production is then divided by the slaughter rate '''slr<ref>For details on the base year value of meat production, which is based on historical data related to production, imports, exports, and assumptions about expected meat consumption and production losses, see the description of agricultural data initialization in the pre-processor.</ref>'''

<math>LVHERD_{r}=(AGPppl_{r,f=2}- AGPMILKEGGS_{r})/slr</math>

== Water Dynamics ==

Water use begins with data on total water withdrawals from FAO Aquastat.  These are divided by the size of the population to get an estimate of water use per capita.

In future years, water use per capita is forecast to increase in parallel with crop production per capita.  Specifically, an expected level of water use per capita as a function of crop production per capita (see figure below) is calculated for crop production in the current year (CropPC) and crop production in the first year (CropPCI).  The ratio of these values is multiplied by the water use per capita in the first year (WatUsePCI) to get water use per capita in the current year (WatUsePC).  This is multiplied by population (POP) to get total water use (WATUSE)

<math>WatUsePC_{r}= WatUsePCI_{r}*f(CropPC_{r} )/f(CropPCI_{r} </math>

<math>WATUSE_{r}= WatUsePC_{r} * POP_{r}</math>

[[File:Water dynamics.png|Water Use per capita compared to GDP per capita]]

= Data Tables read in Agricultural Pre-Processor – DATAGRI.BAS =

{| border="1" cellspacing="0" cellpadding="0" width="0"
|-
| nowrap="nowrap" style="width:234px;height:35px;" |
'''Table'''

| nowrap="nowrap" style="width:142px;height:35px;" |
'''Definition'''

| nowrap="nowrap" style="width: 212px; height: 35px;" |
'''Original Source'''

| style="width: 406px; height: 35px;" |
'''Variable to which series relates in PP/How the series is used in the PP'''

|-
| style="width:234px;height:20px;" |
SeriesLandArea

| style="width:142px;height:20px;" |
Land Area

| style="width: 212px; height: 20px;" |
WDI

| style="width: 406px; height: 20px;" |
LandArea

|-
| style="width:234px;height:69px;" |
SeriesMalnChil%WeightWB

| style="width:142px;height:69px;" |
Percentage of children under 5 malnourished based on weight; US benchmark

| style="width: 212px; height: 69px;" |
World Health Organization.

| style="width: 406px; height: 69px;" |
Malnourished children

|-
| style="width:234px;height:35px;" |
SeriesMalnPop%WB

| style="width:142px;height:35px;" |
Percentage of population malnourished

| style="width: 212px; height: 35px;" |
FAO

| style="width: 406px; height: 35px;" |
Malnourished population

|-
| style="width:234px;height:20px;" |
SeriesLandCrop

| style="width:142px;height:20px;" |
Land, crop

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
LDCrop

|-
| style="width:234px;height:20px;" |
SeriesLandForest

| style="width:142px;height:20px;" |
Land, forest

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
LdFor

|-
| style="width:234px;height:20px;" |
SeriesLandGrazing

| style="width:142px;height:20px;" |
Land, grazing

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
LdGraz

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdAqAnimalsFSJ

| style="width:142px;height:69px;" |
Total Aquatic Animals Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdAqPlantsFSJ

| style="width:142px;height:69px;" |
Total Aquatic Plants Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdCephalopodsFSJ

| style="width:142px;height:69px;" |
Total Cephalopods Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdCrustaceansFSJ

| style="width:142px;height:69px;" |
Total Crustaceans Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdDemersalFSJ

| style="width:142px;height:69px;" |
Total  Demersal Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdFreshwaterFSJ

| style="width:142px;height:69px;" |
Total Freshwater Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdMarineFSJ

| style="width:142px;height:69px;" |
Total Marine Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdMolluscsFSJ

| style="width:142px;height:69px;" |
Total Molluscs Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdPelagicFSJ

| style="width:142px;height:69px;" |
Total Pelagic Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdAqAnimalsFSJ

| style="width:142px;height:69px;" |
Total Aquatic Animals Catch Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdAqPlantsFSJ

| style="width:142px;height:69px;" |
Total Aquatic Plants Catch Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdCephalopodsFSJ

| style="width:142px;height:69px;" |
Total Cephalopods Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdCrustaceansFSJ

| style="width:142px;height:69px;" |
Total Crustaceans Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdDemersalFSJ

| style="width:142px;height:69px;" |
Total Demersal Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdFreshwaterFSJ

| style="width:142px;height:69px;" |
Total Freshwater Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdMarineFSJ

| style="width:142px;height:69px;" |
Total Marine Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdMolluscsFSJ

| style="width:142px;height:69px;" |
Total Molluscs Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdPelagicFSJ

| style="width:142px;height:69px;" |
Total Pelagic Capture Production (tonnes) from Fishstatj

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Break down data from FAO into aquaculture and catch stat using data from fish stat j

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyAqPlantsFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity of Aquatic Plants (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyBodyOilFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity ofl Body Oil (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyLiverOilFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity of Fish Liver Oil (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyMealFAO

| style="width:142px;height:52px;" |
Domestic Supply Production of Fish Meal (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil EXports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsMealFAO

| style="width:142px;height:52px;" |
Total Fish Meal Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsMealFAO

| style="width:142px;height:52px;" |
Total Fish Meal Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdAqPlantsFAO

| style="width:142px;height:52px;" |
Production Quantity of Aquatic Plants (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdBodyOilFAO

| style="width:142px;height:52px;" |
Production Quantity of (Fish) Body Oil (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdLiverOilFAO

| style="width:142px;height:52px;" |
Production Quantityt of Fish Liver Oil (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdMealFAO

| style="width:142px;height:52px;" |
Production Quantity of Fish Meal (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedMealFAO

| style="width:142px;height:52px;" |
Total Fish Meal used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilMealFAO

| style="width:142px;height:52px;" |
Total Fish Meal used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayCephalopodsFAO

| style="width:142px;height:69px;" |
Total Cephalopods Fish Quantity used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayCrustaceansFAO

| style="width:142px;height:69px;" |
Total Crustaceans Fish used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayDemersalFAO

| style="width:142px;height:69px;" |
Total Demersal Fish consumed for Calories/cap/day (kcal/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayFreshwaterFAO

| style="width:142px;height:69px;" |
Total Freshwater Fish consumed for calories/cap/day (kcal/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishCalPerCapPerDayMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayPelagicFAO

| style="width:142px;height:69px;" |
Total Pelagic Fish consumed for Calories/capita/day (Tonnes)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyAqAnimalsFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity ofAquatic Animals (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyCephalopodsFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity of Cephalopods Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyCrustaceansFAO

| style="width:142px;height:52px;" |
Domestic Supply of Crustaceans Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish used for Food(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyFreshwaterFAO

| style="width:142px;height:52px;" |
Total Domestic Supply of Freshwater Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyMarineFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity of Marine Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyMolluscsFAO

| style="width:142px;height:52px;" |
Total Domestic Supply of Molluscs Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyPelagicFAO

| style="width:142px;height:52px;" |
Domestic Supply Quantity of Pelagic Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsCephalopodsFAO

| style="width:142px;height:52px;" |
Total Exports of Cephalopods Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish Exports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishFoodSupplyPerCapPerDayCephalopodsFAO

| style="width:142px;height:69px;" |
Total Cephalopods Fish Quantity used for Food/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishFoodSupplyPerCapPerDayCrustaceansFAO

| style="width:142px;height:69px;" |
Total Crustaceans Fish used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish for Food Supply/cap/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish used for Food Supply/cap/day  (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Food Suply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFoodSupplyPerCapPerDayPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsCephalopodsFAO

| style="width:142px;height:52px;" |
Total Imports of Cephalopods Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportsPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish Imports (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdAqAnimalsFAO

| style="width:142px;height:52px;" |
Production Quantity Aquatic Animals (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdCephalopodsFAO

| style="width:142px;height:52px;" |
Production Quantity of Cephalopods Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdCrustaceansFAO

| style="width:142px;height:52px;" |
Production Quantity of Crustaceans Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdDemersalFAO

| style="width:142px;height:52px;" |
Production quantity of Demersal Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdFreshwaterFAO

| style="width:142px;height:52px;" |
Total Domestic Freshwater Fish Production (tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdMarineFAO

| style="width:142px;height:52px;" |
Production Quantity of Marine Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdMolluscsFAO

| style="width:142px;height:52px;" |
Production Quantity of Molluscs Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdPelagicFAO

| style="width:142px;height:52px;" |
Production quantity of Pelagic Fish (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishProteinPerCapPerDayCephalopodsFAO

| style="width:142px;height:69px;" |
Total Cephalopods Fish Quantity used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishProteinPerCapPerDayDemersalFAO

| style="width:142px;height:69px;" |
Total Demersal Fish consumed for Protein/cap/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishProteinPerCapPerDayFreshwaterFAO

| style="width:142px;height:69px;" |
Total Freshwater Fish consumed for protein/cap/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishProteinPerCapPerDayPelagicFAO

| style="width:142px;height:69px;" |
Total Pelagic Fish consumed for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedCephalopodsFAO

| style="width:142px;height:52px;" |
Total Cephalopods Fish Quantity used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish used for Feed(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish used for feed  (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFeedPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish used for Feed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodCephalopodsFAO

| style="width:142px;height:52px;" |
Total Cephalopods Fish Quantity used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish used for Food(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish for food  (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilCephalopodsFAO

| style="width:142px;height:52px;" |
Total Cephalopods Fish Quantity used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish used for other Utilities(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish used for other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedCephalopodsFAO

| style="width:142px;height:52px;" |
Total Cephalopods Fish Quantity used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish used for Feed(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish used for Seed  (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoSeedPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish used for Seed (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportQuantityFAOTrade

| style="width:142px;height:52px;" |
Quantity of fish exported(Tonnes) from FishstatJ

| style="width: 212px; height: 52px;" |
FAO, FishstatJ

| style="width: 406px; height: 52px;" |
AGXFishQuantTradetbl

|-
| style="width:234px;height:35px;" |
SeriesAgFishExportValueFAOTrade

| style="width:142px;height:35px;" |
Export value of fish ($1000 US)  from FishstatJ software

| style="width: 212px; height: 35px;" |
FAO, FishstatJ

| style="width: 406px; height: 35px;" |
Fish imports and exports

|-
| style="width:234px;height:35px;" |
SeriesAgFishImportQuantityFAOTrade

| style="width:142px;height:35px;" |
Quantity of fish imported (Tonnes) from FishstatJ

| style="width: 212px; height: 35px;" |
FAO, FishstatJ

| style="width: 406px; height: 35px;" |
Fish imports and exports

|-
| style="width:234px;height:35px;" |
SeriesAgFishImportValueFAOTrade

| style="width:142px;height:35px;" |
Import value of fish ($1000 US)  from FishstatJ software

| style="width: 212px; height: 35px;" |
FAO, FishstatJ

| style="width: 406px; height: 35px;" |
Fish imports and exports

|-
| style="width:234px;height:52px;" |
SeriesAgCropExportQuantityFAOTrade

| style="width:142px;height:52px;" |
Quantity of Crops exported (Tonnes) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Crop trade

|-
| style="width:234px;height:52px;" |
SeriesAgCropExportValueFAOTrade

| style="width:142px;height:52px;" |
Value of Crops exported (1000$ US) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Crop trade

|-
| style="width:234px;height:52px;" |
SeriesAgCropImportQuantityFAOTrade

| style="width:142px;height:52px;" |
Quantity of Crops Imported (Tonnes) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Crop trade

|-
| style="width:234px;height:52px;" |
SeriesAgCropImportValueFAOTrade

| style="width:142px;height:52px;" |
Value of Crops Imported(1000$ USD) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Crop trade

|-
| style="width:234px;height:52px;" |
SeriesAgMeatExportQuantityFAOTrade

| style="width:142px;height:52px;" |
Quantity of meat exported (Tonnes) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Meat trade

|-
| style="width:234px;height:52px;" |
SeriesAgMeatExportValueFAOTrade

| style="width:142px;height:52px;" |
Value of meat exported (1000$ US) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Meat trade

|-
| style="width:234px;height:52px;" |
SeriesAgMeatImportQuantityFAOTrade

| style="width:142px;height:52px;" |
Quantity of Meat Imported (Tonnes) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Meat trade

|-
| style="width:234px;height:52px;" |
SeriesAgMeatImportValueFAOTrade

| style="width:142px;height:52px;" |
Value of Meat Imported (1000$ US) from FAO Trade Domain

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Meat trade

|-
| style="width:234px;height:20px;" |
SeriesAgProdCereals

| style="width:142px;height:20px;" |
Cereal production

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Crop production (AGP)

|-
| style="width:234px;height:35px;" |
SeriesAgProdFruitsExclMelons

| style="width:142px;height:35px;" |
Production of fruit, excluding melons

| style="width: 212px; height: 35px;" |
FAO

| style="width: 406px; height: 35px;" |
Crop production (AGP)

|-
| style="width:234px;height:20px;" |
SeriesAgProdPulses

| style="width:142px;height:20px;" |
Pulses production

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Crop production (AGP)

|-
| style="width:234px;height:35px;" |
SeriesAgProdRootsTub

| style="width:142px;height:35px;" |
Root and tuber production

| style="width: 212px; height: 35px;" |
FAO

| style="width: 406px; height: 35px;" |
Crop production (AGP)

|-
| style="width:234px;height:35px;" |
SeriesAgProdVegMel

| style="width:142px;height:35px;" |
Vegetable, melon production

| style="width: 212px; height: 35px;" |
FAO

| style="width: 406px; height: 35px;" |
Crop production (AGP)

|-
| style="width:234px;height:20px;" |
SeriesLandOther

| style="width:142px;height:20px;" |
Land, other

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
LdOth

|-
| style="width:234px;height:35px;" |
SeriesLandBuiltGFNcorine

| style="width:142px;height:35px;" |
Land Area, Artificial Land

| style="width: 212px; height: 35px;" |
CORINE Land Cover

| style="width: 406px; height: 35px;" |
LdUrbTbl

|-
| style="width:234px;height:52px;" |
SeriesLandBuiltGFNgaez

| style="width:142px;height:52px;" |
Land Area, Settlement and Infrastructure

| style="width: 212px; height: 52px;" |
Global Agro-Ecological Zones (GAEZ) Model

| style="width: 406px; height: 52px;" |
LdUrbTbl

|-
| style="width:234px;height:35px;" |
SeriesLandBuiltGFNglc

| style="width:142px;height:35px;" |
Land Area, Infrastructure aggregated

| style="width: 212px; height: 35px;" |
Global Land Cover (GLC) 2000

| style="width: 406px; height: 35px;" |
LdUrbTbl

|-
| style="width:234px;height:103px;" |
SeriesLandBuiltGFNsage

| style="width:142px;height:103px;" |
Land Area, Buit area

| style="width: 212px; height: 103px;" |
Sustainability and the Global Environment (SAGE) at University of Wisconsin

| style="width: 406px; height: 103px;" |
LdUrbTbl

|-
| style="width:234px;height:20px;" |
SeriesAgProdMeat

| style="width:142px;height:20px;" |
Meat production

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Meat production (AGP)

|-
| style="width:234px;height:20px;" |
SeriesAgFruVegEx

| style="width:142px;height:20px;" |
Fruit, vegetable exports

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Food imports

|-
| style="width:234px;height:20px;" |
SeriesAgFruVegIm

| style="width:142px;height:20px;" |
Fruit, vegetable imports

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Food imports

|-
| style="width:234px;height:35px;" |
SeriesLandPotentialArable

| style="width:142px;height:35px;" |
total potential arable land

| style="width: 212px; height: 35px;" |
FAOTERRASTAT

| style="width: 406px; height: 35px;" |
LandArablePot

|-
| style="width:234px;height:341px;" |
SeriesWaterAnRenResources

| style="width:142px;height:341px;" |
Annually renewable water resources

| style="width: 212px; height: 341px;" |
FAO: Water Resources, Development and Management Service. AQUASTAT Information System on Water in Agriculture: Review of Water Resource Statistics by Country.  [http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm].

| style="width: 406px; height: 341px;" |
Water resources

|-
| style="width:234px;height:341px;" |
SeriesWaterAnWithdrawals

| style="width:142px;height:341px;" |
Annual water withdrawals/use (1990=70-99;2000=update, mostly 2000)

| style="width: 212px; height: 341px;" |
FAO: Water Resources, Development and Management Service. AQUASTAT Information System on Water in Agriculture: Review of Water Resource Statistics by Country.  [http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm].

| style="width: 406px; height: 341px;" |
Water use

|-
| style="width:234px;height:341px;" |
SeriesWaterAnRenResourcesOld

| style="width:142px;height:341px;" |
Annually renewable water resources

| style="width: 212px; height: 341px;" |
FAO: Water Resources, Development and Management Service. AQUASTAT Information System on Water in Agriculture: Review of Water Resource Statistics by Country.  [http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm http://www.fao.org/waicent/faoinfo/agricult/agl/aglw/aquastat/water_res/index.htm].

| style="width: 406px; height: 341px;" |
Water resources

|-
| style="width:234px;height:222px;" |
SeriesLandUrban&Built

| style="width:142px;height:222px;" |
Land, urban and built-up areas

| style="width: 212px; height: 222px;" |
Loveland, T.R., Reed, B.C., J.F., Brown, J.F., Ohlen, D.O., Zhu, Z., Yang, L.  Merchant. J. 2000. Global Land Cover Characteristics Database  V 2.0. [http://edcdaac.usgs.gov/glcc/globdoc2_0.html http://edcdaac.usgs.gov/glcc/globdoc2_0.html]

| style="width: 406px; height: 222px;" |
LdUrbTbl

|-
| style="width:234px;height:40px;" |
SeriesAgBovineMeatProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Bovine Meat Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Meat production (AGP)

|-
| style="width:234px;height:40px;" |
SeriesAgCerealsEx

| style="width:142px;height:40px;" |
Cereal exports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgCerealsIm

| style="width:142px;height:40px;" |
Cereal imports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgCerealSupply

| style="width:142px;height:40px;" |
Cereal, domestic supply quantity

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgCerealWaste

| style="width:142px;height:40px;" |
FAO Cereal Waste

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgMeatEx

| style="width:142px;height:40px;" |
Meat exports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgMeatIm

| style="width:142px;height:40px;" |
Meat imports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgMeatOtherProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Meat (Other) Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Meat production (AGP)

|-
| style="width:234px;height:52px;" |
SeriesAgMuttonandGoatMeatProductionFAO

| style="width:142px;height:52px;" |
Total Domestic Mutton and Goat Meat Production (million metric tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Meat production (AGP)

|-
| style="width:234px;height:40px;" |
SeriesAgPigMeatProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Pigmeat Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Meat production (AGP)

|-
| style="width:234px;height:40px;" |
SeriesAgPoultryMeatProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Poultry Meat Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Meat production (AGP)

|-
| style="width:234px;height:40px;" |
SeriesAgPulsesEx

| style="width:142px;height:40px;" |
Pulse exports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgPulsesIm

| style="width:142px;height:40px;" |
Pulseimports

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgVegetableSupply

| style="width:142px;height:40px;" |
FAO Vegetable Supply

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAgVegetableWaste

| style="width:142px;height:40px;" |
FAO Vegetable Waste

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:52px;" |
SeriesAGCropCalPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total calories consumed from crops per capita per day (kcal/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
CLPC

|-
| style="width:234px;height:40px;" |
SeriesAGCropDomesticSupplyFAO

| style="width:142px;height:40px;" |
Domestic Supply Quantity of Crops (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAGCropExportsFAO

| style="width:142px;height:40px;" |
Total Crop Exports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:69px;" |
SeriesAGCropFatPerCapPerDayFAO

| style="width:142px;height:69px;" |
Total grams of fat consumed from crops per capita per day (g/capita/day).

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
GRAMSPC

|-
| style="width:234px;height:52px;" |
SeriesAGCropFoodSupplyPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total food supply per capita per day from crops (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
GRAMSPC

|-
| style="width:234px;height:40px;" |
SeriesAGCropImportsFAO

| style="width:142px;height:40px;" |
Total Crop Imports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAGCropProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Crop Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Crop production (AGP)

|-
| style="width:234px;height:52px;" |
SeriesAGCropProteinPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total protein consumption per capita per day from crops (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
PROTEINPC

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoFeedFAO

| style="width:142px;height:40px;" |
Total crop quantity used for feed (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FEDDEM

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoFoodFAO

| style="width:142px;height:40px;" |
Total crop quantity used for food (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FDEM

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoFoodManuFAO

| style="width:142px;height:40px;" |
Total crop quantity used for food manufacture (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FDEM

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoOtherUtilFAO

| style="width:142px;height:40px;" |
Total crop quantity used for other utilities (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
INDEM

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoSeedFAO

| style="width:142px;height:40px;" |
Total crops used for seeds (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FMDEM

|-
| style="width:234px;height:40px;" |
SeriesAGCroptoWasteFAO

| style="width:142px;height:40px;" |
Total crops that go to waste(tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
AGLOSSTRANS

|-
| style="width:234px;height:86px;" |
SeriesAGFishCalPerCapPerDayFAO

| style="width:142px;height:86px;" |
Total per capita per day caloric supplies derived from fish for human consumption (kcal/capita/day).

| style="width: 212px; height: 86px;" |
FAO

| style="width: 406px; height: 86px;" |
CLPC

|-
| style="width:234px;height:40px;" |
SeriesAGFishDomesticSupplyFAO

| style="width:142px;height:40px;" |
Domestic Supply Quantity of Fish  (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAGFishExportsFAO

| style="width:142px;height:40px;" |
Total Fish Exports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:69px;" |
SeriesAGFishFatPerCapPerDayFAO

| style="width:142px;height:69px;" |
Total grams of fat consumed from fish per capita per day (g/capita/day).

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
GRAMSPC

|-
| style="width:234px;height:52px;" |
SeriesAGFishFoodSupplyPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total food supply per capita per day from fish (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
GRAMSPC

|-
| style="width:234px;height:40px;" |
SeriesAGFishImportsFAO

| style="width:142px;height:40px;" |
Total Fish Imports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:52px;" |
SeriesAGFishProteinPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total protein consumption per capita per day from fish (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
PROTEINPC

|-
| style="width:234px;height:40px;" |
SeriesAGFishtoFeedFAO

| style="width:142px;height:40px;" |
Total fish quantity used for feed (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FEDDEM

|-
| style="width:234px;height:40px;" |
SeriesAGFishtoFoodFAO

| style="width:142px;height:40px;" |
Total fish quantity used for food (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FDEM

|-
| style="width:234px;height:40px;" |
SeriesAGFishtoOtherUtilFAO

| style="width:142px;height:40px;" |
Total fish quantity used for other utilities (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
INDEM

|-
| style="width:234px;height:40px;" |
SeriesAGFishtoSeedFAO

| style="width:142px;height:40px;" |
Total fish used for seeds i.e. reproduction (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FMDEM

|-
| style="width:234px;height:52px;" |
SeriesAGMeatCalPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total calories consumed from meat per capita per day (kcal/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
CLPC

|-
| style="width:234px;height:40px;" |
SeriesAGMeatDomesticSupplyFAO

| style="width:142px;height:40px;" |
Domestic Supply Quantity of Meat (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAGMeatExportsFAO

| style="width:142px;height:40px;" |
Total Meat Exports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:69px;" |
SeriesAGMeatFatPerCapPerDayFAO

| style="width:142px;height:69px;" |
Total grams of fat consumed from meat per capita per day (g/capita/day).

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
GRAMSPC

|-
| style="width:234px;height:52px;" |
SeriesAGMeatFoodSupplyPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total food supply per capita per day from meat (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
GRAMSPC

|-
| style="width:234px;height:40px;" |
SeriesAGMeatImportsFAO

| style="width:142px;height:40px;" |
Total Meat Imports (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Trade data

|-
| style="width:234px;height:40px;" |
SeriesAGMeatProductionFAO

| style="width:142px;height:40px;" |
Total Domestic Meat Production (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Meat production (AGP)

|-
| style="width:234px;height:52px;" |
SeriesAGMeatProteinPerCapPerDayFAO

| style="width:142px;height:52px;" |
Total protein consumption per capita per day from meat (g/capita/day).

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
PROTEINPC

|-
| style="width:234px;height:40px;" |
SeriesAGMeattoFeedFAO

| style="width:142px;height:40px;" |
Total meat quantity used for feed (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FEDDEM

|-
| style="width:234px;height:40px;" |
SeriesAGMeattoFoodFAO

| style="width:142px;height:40px;" |
Total meat quantity used for food (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FDEM

|-
| style="width:234px;height:52px;" |
SeriesAGMeattoFoodManuFAO

| style="width:142px;height:52px;" |
Total meat quantity used for food manufacture (tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
FDEM

|-
| style="width:234px;height:40px;" |
SeriesAGMeattoOtherUtilFAO

| style="width:142px;height:40px;" |
Total meat quantity used for other utilities (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
INDEM

|-
| style="width:234px;height:40px;" |
SeriesAGMeattoSeedFAO

| style="width:142px;height:40px;" |
Total meat used for seeds i.e. reproduction (tonnes)

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
FMDEM

|-
| style="width:234px;height:40px;" |
SeriesAGMeattoWasteFAO

| style="width:142px;height:40px;" |
Total meat that goes to waste (tonnes).

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
AGLOSSTRANS

|-
| style="width:234px;height:69px;" |
SeriesAgFishAquaProdOthersFSJ

| style="width:142px;height:69px;" |
Total Others Aquaculture Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Data from Fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdAqMammalsFSJ

| style="width:142px;height:69px;" |
Total Aquatic Mammals Catch Production (tonnes) from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Data from Fish stat j

|-
| style="width:234px;height:69px;" |
SeriesAgFishCatchProdOthersFSJ

| style="width:142px;height:69px;" |
Total Others Capture Production from FishstatJ

| style="width: 212px; height: 69px;" |
FAO  Global Aquaculture Production Quantity data

| style="width: 406px; height: 69px;" |
Data from Fish stat j

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarAqPlantsFAO

| style="width:142px;height:52px;" |
Total Aquatic Plants Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarBodyOilFAO

| style="width:142px;height:52px;" |
Total Body Oil Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarLiverOilFAO

| style="width:142px;height:52px;" |
Total Fish Liver Oil Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarMealFAO

| style="width:142px;height:52px;" |
Total Fish Meal Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishCalPerCapPerDayAqMammalsFAO

| style="width:142px;height:69px;" |
Total Aquatic Mammals used for Calories/capita/day (kcal/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
CLPC

|-
| style="width:234px;height:52px;" |
SeriesAgFishDomesticSupplyAqMammalsFAO

| style="width:142px;height:52px;" |
Domestic Supply of Aquatic Mammals (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportsAqMammalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Mammals Exports(Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayAqMammalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Mammals used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishFatPerCapPerDayCephalopodsFAO

| style="width:142px;height:69px;" |
Total Cephalopods Fish Quantity used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish consumed for Fat/cap/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Fish consumed for Fat/cap/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishFatPerCapPerDayMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish used for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishFatPerCapPerDayPelagicFAO

| style="width:142px;height:69px;" |
Total Pelagic Fish consumed for Fat/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:69px;" |
SeriesAgFishFoodSupplyPerCapPerDayAqMammalsFAO

| style="width:142px;height:69px;" |
Total Aquatic Mammals used for Food Supply/capita/day (g/capita/day)

| style="width: 212px; height: 69px;" |
FAO

| style="width: 406px; height: 69px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProdAqMammalsFAO

| style="width:142px;height:52px;" |
Production Quantity of Aquatic Mammals (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishProteinPerCapPerDayAqMammalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Mammals used for Protein/capita/day (g/capita/day)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarAqAnimalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Animals Stock Variation (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarCephalopodsFAO

| style="width:142px;height:52px;" |
Total Cephalopods Fish Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarCrustaceansFAO

| style="width:142px;height:52px;" |
Total Crustaceans Fish Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarDemersalFAO

| style="width:142px;height:52px;" |
Total Demersal Fish Stock VariationTonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarFreshwaterFAO

| style="width:142px;height:52px;" |
Total Freshwater Stock Variation (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarMarineFAO

| style="width:142px;height:52px;" |
Total Marine Fish Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarMolluscsFAO

| style="width:142px;height:52px;" |
Total Molluscs Fish Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishStockVarPelagicFAO

| style="width:142px;height:52px;" |
Total Pelagic Fish Stock Variations (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoFoodAqMammalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Mammals used for Food (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:52px;" |
SeriesAgFishtoOtherUtilAqMammalsFAO

| style="width:142px;height:52px;" |
Total Aquatic Mammals used for Other Utilities (Tonnes)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Read in all fish series from FAO Food Balance Sheets

|-
| style="width:234px;height:40px;" |
SeriesAgFishProdAquaInland

| style="width:142px;height:40px;" |
Fish,Production, Inland Aquaculture

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Data from Fish stat j

|-
| style="width:234px;height:40px;" |
SeriesAgFishProdAquaMarine

| style="width:142px;height:40px;" |
Fish, production, Marine Aquaculture

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Data from Fish stat j

|-
| style="width:234px;height:40px;" |
SeriesAgFishProdCatchInland

| style="width:142px;height:40px;" |
Fish, Production, Inland Catch

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Data from Fish stat j

|-
| style="width:234px;height:40px;" |
SeriesAgFishProdCatchMarine

| style="width:142px;height:40px;" |
Fish, Production, Marine Catch

| style="width: 212px; height: 40px;" |
FAO

| style="width: 406px; height: 40px;" |
Data from Fish stat j

|-
| style="width:234px;height:52px;" |
SeriesAgFishExportVal

| style="width:142px;height:52px;" |
Global Commodities Production and Trade Value of Fish Exports (USD)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Trade data

|-
| style="width:234px;height:52px;" |
SeriesAgFishImportVal

| style="width:142px;height:52px;" |
Global Commodities Production and Trade Value of Fish Imports (USD)

| style="width: 212px; height: 52px;" |
FAO

| style="width: 406px; height: 52px;" |
Trade data

|-
| style="width:234px;height:35px;" |
SeriesAgFishAquaOther

| style="width:142px;height:35px;" |
Aquaculture, other (plants, frogs, crocodiles, turtles)

| style="width: 212px; height: 35px;" |
FAO

| style="width: 406px; height: 35px;" |
Data from Fish stat j

|-
| style="width:234px;height:20px;" |
SeriesAgFishImpt

| style="width:142px;height:20px;" |
Fish, import value

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Trade data

|-
| style="width:234px;height:20px;" |
SeriesAidCerealDon

| style="width:142px;height:20px;" |
Cereal donations

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Trade data

|-
| style="width:234px;height:20px;" |
SeriesAidCerealRec

| style="width:142px;height:20px;" |
Cereal gifts/aid received

| style="width: 212px; height: 20px;" |
FAO

| style="width: 406px; height: 20px;" |
Trade data

|-
| style="width:234px;height:256px;" |
SeriesAgFishAquaInland

| style="width:142px;height:256px;" |
Aquaculture, inland

| style="width: 212px; height: 256px;" |
FAO, Aquaculture Quantities Dataset 1984-1997, Fishery Statistics Database downloadable with Fishstat-Plus software at: ([http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM]

| style="width: 406px; height: 256px;" |
Data from Fish stat j

|-
| style="width:234px;height:256px;" |
SeriesAgFishAquaMarine

| style="width:142px;height:256px;" |
Aquaculture, marine fish catch

| style="width: 212px; height: 256px;" |
FAO, Aquaculture Quantities Dataset 1984-1997, Fishery Statistics Database downloadable with Fishstat-Plus software at: ([http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM]

| style="width: 406px; height: 256px;" |
Data from Fish stat j

|-
| style="width:234px;height:256px;" |
SeriesAgFishAquaCatchTot

| style="width:142px;height:256px;" |
Fish production totals, aquaculture and capture

| style="width: 212px; height: 256px;" |
FAO, Aquaculture Quantities Dataset 1984-1997, Fishery Statistics Database downloadable with Fishstat-Plus software at: ([http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM]

| style="width: 406px; height: 256px;" |
Data from Fish stat j

|-
| style="width:234px;height:273px;" |
SeriesAgFishAquaTotal

| style="width:142px;height:273px;" |
Aquaculture, coastal and marine total fish production

| style="width: 212px; height: 273px;" |
Fishery Information, Data and Statistics Unit,  FAO. 2004. FISHSTAT Plus:  Version 2.3 (available on-line at [http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp]); Capture production 1950-2002 dataset. Rome: FAO

| style="width: 406px; height: 273px;" |
Data from Fish stat j

|-
| style="width:234px;height:256px;" |
SeriesAgFishExpt

| style="width:142px;height:256px;" |
Fish, export value

| style="width: 212px; height: 256px;" |
FAO, Aquaculture Quantities Dataset 1984-1997, Fishery Statistics Database downloadable with Fishstat-Plus software at: ([http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM]

| style="width: 406px; height: 256px;" |
Trade data

|-
| style="width:234px;height:273px;" |
SeriesAgFishInlandProd

| style="width:142px;height:273px;" |
Fish capture, inland

| style="width: 212px; height: 273px;" |
Fishery Information, Data and Statistics Unit,  FAO. 2004. FISHSTAT Plus:  Version 2.3 (available on-line at [http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp]); Capture production 1950-2002 dataset. Rome: FAO

| style="width: 406px; height: 273px;" |
Data from Fish stat j

|-
| style="width:234px;height:256px;" |
SeriesAgFish%Protein

| style="width:142px;height:256px;" |
Fish protein as percent of total supply

| style="width: 212px; height: 256px;" |
FAO, Aquaculture Quantities Dataset 1984-1997, Fishery Statistics Database downloadable with Fishstat-Plus software at: ([http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM http://www.fao.org/WAICENT/FAOINFO/FISHERY/statist/FISOFT/FISHPLUS.HTM])

| style="width: 406px; height: 256px;" |
PROTEINPC

|-
| style="width:234px;height:273px;" |
SeriesAgFishFreshwaterCatch

| style="width:142px;height:273px;" |
Freshwater fish catch

| style="width: 212px; height: 273px;" |
Fishery Information, Data and Statistics Unit,  FAO. 2004. FISHSTAT Plus:  Version 2.3 (available on-line at [http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp]); Capture production 1950-2002 dataset. Rome: FAO

| style="width: 406px; height: 273px;" |
Data from Fish stat j

|-
| style="width:234px;height:273px;" |
SeriesAgFishMarineCatch

| style="width:142px;height:273px;" |
Marine fish catch

| style="width: 212px; height: 273px;" |
Fishery Information, Data and Statistics Unit,  FAO. 2004. FISHSTAT Plus:  Version 2.3 (available on-line at [http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp http://www.fao.org/fi/statist/FISOFT/FISHPLUS.asp]); Capture production 1950-2002 dataset. Rome: FAO

| style="width: 406px; height: 273px;" |
Data from Fish stat j

|}

= Key variables in the agricultural model =

{| border="1" cellspacing="0" cellpadding="0" width="0" style="width:528px;"
|-
| style="width:110px;height:52px;" |
'''Name'''

| style="width:90px;height:52px;" |
'''Unit'''

| style="width:100px;height:52px;" |
'''Dimensionality'''

| style="width:106px;height:52px;" |
'''Description'''

| style="width:121px;height:52px;" |
'''Where Initialized*'''

|-
| style="width:110px;height:137px;" |
AGDEM

| style="width:90px;height:137px;" |
10^6 tons

| style="width:100px;height:137px;" |
country, food type

| style="width:106px;height:137px;" |
total agricultural demand/apparent consumption by food type

| style="width:121px;height:137px;" |
FY

|-
| style="width:110px;height:137px;" |
AGLOSSCONS

| style="width:90px;height:137px;" |
10^6 tons

| style="width:100px;height:137px;" |
country, food type

| style="width:106px;height:137px;" |
Consumption losses

| style="width:121px;height:137px;" |
FY

|-
| style="width:110px;height:137px;" |
AGLOSSPROD

| style="width:90px;height:137px;" |
10^6 tons

| style="width:100px;height:137px;" |
country, food type

| style="width:106px;height:137px;" |
Production losses

| style="width:121px;height:137px;" |
FY

|-
| style="width:110px;height:137px;" |
AGLOSSTRANS

| style="width:90px;height:137px;" |
10^6 tons

| style="width:100px;height:137px;" |
country, food type

| style="width:106px;height:137px;" |
Transmission and distribution losses

| style="width:121px;height:137px;" |
PP

|-
| style="width:110px;height:35px;" |
AGM

| style="width:90px;height:35px;" |
10^6 tons

| style="width:100px;height:35px;" |
country, food type

| style="width:106px;height:35px;" |
food imports

| style="width:121px;height:35px;" |
PP

|-
| style="width:110px;height:69px;" |
AGP

| style="width:90px;height:69px;" |
10^6 tons

| style="width:100px;height:69px;" |
food type

| style="width:106px;height:69px;" |
total food production by food type

| style="width:121px;height:69px;" |
PP for crops, FY for meat and fish

|-
| style="width:110px;height:69px;" |
AGPMILKAND EGGS

| style="width:90px;height:69px;" |
10^6 tons

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
Total non-meat animal products

| style="width:121px;height:69px;" |
PP

|-
| style="width:110px;height:35px;" |
AGX

| style="width:90px;height:35px;" |
10^6 tons

| style="width:100px;height:35px;" |
country, food type

| style="width:106px;height:35px;" |
food exports

| style="width:121px;height:35px;" |
PP

|-
| style="width:110px;height:86px;" |
AQUACUL

| style="width:90px;height:86px;" |
10^6 tons fish

| style="width:100px;height:86px;" |
country

| style="width:106px;height:86px;" |
total fish production in aquaculture

| style="width:121px;height:86px;" |
PP

|-
| style="width:110px;height:86px;" |
CDALF

| style="width:90px;height:86px;" |
dimensionless (0-1)

| style="width:100px;height:86px;" |
country

| style="width:106px;height:86px;" |
Cobb-Douglas alpha

| style="width:121px;height:86px;" |
FY (ECONOMY)

|-
| style="width:110px;height:52px;" |
CIVDM

| style="width:90px;height:52px;" |
dimensionless

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
civilian damage from war

| style="width:121px;height:52px;" |
FY (SOCIOPOL)

|-
| style="width:110px;height:52px;" |
CLAVAL

| style="width:90px;height:52px;" |
10^6 Calories/day

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
actual calorie availability

| style="width:121px;height:52px;" |
PP (DATAAGRI)

|-
| style="width:110px;height:69px;" |
CLD

| style="width:90px;height:69px;" |
thousand $/hectare

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
cost of land development

| style="width:121px;height:69px;" |
FY

|-
| style="width:110px;height:69px;" |
CLPC

| style="width:90px;height:69px;" |
calories

| style="width:100px;height:69px;" |
country, food type

| style="width:106px;height:69px;" |
Calories per capita per day

| style="width:121px;height:69px;" |
PP

|-
| style="width:110px;height:137px;" |
CO2PER

| style="width:90px;height:137px;" |
Percent

| style="width:100px;height:137px;" |
none

| style="width:106px;height:137px;" |
CO2, percentage increase in atmosphere, pre-industrial base

| style="width:121px;height:137px;" |
FY (ENVIRONMENT)

|-
| style="width:110px;height:69px;" |
CS

| style="width:90px;height:69px;" |
billion $

| style="width:100px;height:69px;" |
country, economic sector

| style="width:106px;height:69px;" |
value of HH consumption

| style="width:121px;height:69px;" |
PP (DATAECON)

|-
| style="width:110px;height:120px;" |
CULTREG

| style="width:90px;height:120px;" |
Index

| style="width:100px;height:120px;" |
country

| style="width:106px;height:120px;" |
Culutrual region: CULTREG 6 includes India, Nepal, Mauritius

| style="width:121px;height:120px;" |
PP (DataValues)

|-
| style="width:110px;height:103px;" |
ENVYLCHG

| style="width:90px;height:103px;" |
Percent

| style="width:100px;height:103px;" |
country

| style="width:106px;height:103px;" |
annual change in agricultural yield due to climate change

| style="width:121px;height:103px;" |
FY (ENVIRONMENT)

|-
| style="width:110px;height:86px;" |
FDEM

| style="width:90px;height:86px;" |
10^6 tons

| style="width:100px;height:86px;" |
country

| style="width:106px;height:86px;" |
food production going directly to food

| style="width:121px;height:86px;" |
PP

|-
| style="width:110px;height:69px;" |
FEDDEM

| style="width:90px;height:69px;" |
10^6 tons

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
food production going to livestock

| style="width:121px;height:69px;" |
PP

|-
| style="width:110px;height:69px;" |
FISH

| style="width:90px;height:69px;" |
10^6 tons fish

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
total fish production

| style="width:121px;height:69px;" |
FY

|-
| style="width:110px;height:52px;" |
FMDEM

| style="width:90px;height:52px;" |
10^6 tons

| style="width:100px;height:52px;" |
country,food type

| style="width:106px;height:52px;" |
food production going to food manufacturing

| style="width:121px;height:52px;" |
PP

|-
| style="width:110px;height:120px;" |
FPRI

| style="width:90px;height:120px;" |
Base 100

| style="width:100px;height:120px;" |
country, food type

| style="width:106px;height:120px;" |
country specific food price by food type (all 100 in base year)

| style="width:121px;height:120px;" |
FY

|-
| style="width:110px;height:52px;" |
FPROFITR

| style="width:90px;height:52px;" |
dimensionless

| style="width:100px;height:52px;" |
country, food type

| style="width:106px;height:52px;" |
food profit ratio to initial year

| style="width:121px;height:52px;" |
FY

|-
| style="width:110px;height:52px;" |
FSTOCK

| style="width:90px;height:52px;" |
10^6 tons

| style="width:100px;height:52px;" |
country, food type

| style="width:106px;height:52px;" |
food stocks, by food type

| style="width:121px;height:52px;" |
FY

|-
| style="width:110px;height:52px;" |
GRAMSPC

| style="width:90px;height:52px;" |
grams

| style="width:100px;height:52px;" |
country, food type

| style="width:106px;height:52px;" |
Food supply per capita per day in grams

| style="width:121px;height:52px;" |
PP

|-
| style="width:110px;height:52px;" |
I

| style="width:90px;height:52px;" |
billion$

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
total investment

| style="width:121px;height:52px;" |
FY (ECONOMY)

|-
| style="width:110px;height:86px;" |
IALK

| style="width:90px;height:86px;" |
ratio (fraction)

| style="width:100px;height:86px;" |
country

| style="width:106px;height:86px;" |
investment in agriculture, land share

| style="width:121px;height:86px;" |
PP

|-
| style="width:110px;height:69px;" |
IDS

| style="width:90px;height:69px;" |
billion$

| style="width:100px;height:69px;" |
country, economic sector

| style="width:106px;height:69px;" |
investment by economic sector

| style="width:121px;height:69px;" |
FY (ECONOMY)

|-
| style="width:110px;height:137px;" |
INDEM

| style="width:90px;height:137px;" |
10^6 tons crops

| style="width:100px;height:137px;" |
country

| style="width:106px;height:137px;" |
industrial crop demand (crop production going directly to industry)

| style="width:121px;height:137px;" |
PP

|-
| style="width:110px;height:52px;" |
KAG

| style="width:90px;height:52px;" |
billion$

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
value of agricultural capital

| style="width:121px;height:52px;" |
FY

|-
| style="width:110px;height:52px;" |
LABS

| style="width:90px;height:52px;" |
million people

| style="width:100px;height:52px;" |
country, economic sector

| style="width:106px;height:52px;" |
labor supply

| style="width:121px;height:52px;" |
FY (ECONOMY)

|-
| style="width:110px;height:52px;" |
landarablepot

| style="width:90px;height:52px;" |
10^6 ha

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
potential arable land

| style="width:121px;height:52px;" |
PP

|-
| style="width:110px;height:35px;" |
LD

| style="width:90px;height:35px;" |
10^6 ha

| style="width:100px;height:35px;" |
country, land type

| style="width:106px;height:35px;" |
Amount of land

| style="width:121px;height:35px;" |
PP

|-
| style="width:110px;height:52px;" |
LVHERD

| style="width:90px;height:52px;" |
10^6 tons meat

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
Size of livestock herd

| style="width:121px;height:52px;" |
PP

|-
| style="width:110px;height:52px;" |
MFPRATE

| style="width:90px;height:52px;" |
dimensionless

| style="width:100px;height:52px;" |
country, economic sector

| style="width:106px;height:52px;" |
multifactor productivity rate

| style="width:121px;height:52px;" |
FY (ECONOMY)

|-
| style="width:110px;height:52px;" |
MS

| style="width:90px;height:52px;" |
billion $

| style="width:100px;height:52px;" |
country, economic sector

| style="width:106px;height:52px;" |
value of imports

| style="width:121px;height:52px;" |
PP (DATAECON)

|-
| style="width:110px;height:52px;" |
PROTEINPC

| style="width:90px;height:52px;" |
per capita per day

| style="width:100px;height:52px;" |
country, food type

| style="width:106px;height:52px;" |
Proteins per capita per day

| style="width:121px;height:52px;" |
PP

|-
| style="width:110px;height:69px;" |
TGRYL

| style="width:90px;height:69px;" |
growth rate in decimal form

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
target growth rate in yield

| style="width:121px;height:69px;" |
FY

|-
| style="width:110px;height:103px;" |
WAP

| style="width:90px;height:103px;" |
Base 100

| style="width:100px;height:103px;" |
food type

| style="width:106px;height:103px;" |
global food price by food type (all 100 in base year)

| style="width:121px;height:103px;" |
?

|-
| style="width:110px;height:86px;" |
WAPRO

| style="width:90px;height:86px;" |
10^6 tons

| style="width:100px;height:86px;" |
food type

| style="width:106px;height:86px;" |
world agricultural production

| style="width:121px;height:86px;" |
FY

|-
| style="width:110px;height:52px;" |
WATUSE

| style="width:90px;height:52px;" |
cubic km

| style="width:100px;height:52px;" |
country

| style="width:106px;height:52px;" |
water usage, annual

| style="width:121px;height:52px;" |
FY

|-
| style="width:110px;height:69px;" |
WATUSEPC

| style="width:90px;height:69px;" |
cubic km/10^6 persons

| style="width:100px;height:69px;" |
country

| style="width:106px;height:69px;" |
water usage per capita, annual

| style="width:121px;height:69px;" |
PP

|-
| style="width:110px;height:103px;" |
WEP

| style="width:90px;height:103px;" |
Base 100

| style="width:100px;height:103px;" |
none

| style="width:106px;height:103px;" |
World Energy Price per Barrel Oil Equivalent (Base 100)

| style="width:121px;height:103px;" |
FY (ENERGY)

|-
| style="width:110px;height:35px;" |
WFORST

| style="width:90px;height:35px;" |
10^6 ha forest land

| style="width:100px;height:35px;" |
none

| style="width:106px;height:35px;" |
world forest area

| style="width:121px;height:35px;" |
FY

|-
| style="width:110px;height:35px;" |
WGDP

| style="width:90px;height:35px;" |
billion $

| style="width:100px;height:35px;" |
none

| style="width:106px;height:35px;" |
global GDP

| style="width:121px;height:35px;" |
FY

|-
| style="width:110px;height:52px;" |
WSTK

| style="width:90px;height:52px;" |
10^6 tons

| style="width:100px;height:52px;" |
food type

| style="width:106px;height:52px;" |
world agricultural stocks

| style="width:121px;height:52px;" |
FY

|-
| style="width:110px;height:52px;" |
XS

| style="width:90px;height:52px;" |
billion $

| style="width:100px;height:52px;" |
country, economic sector

| style="width:106px;height:52px;" |
value of exports

| style="width:121px;height:52px;" |
PP (DATAECON)

|-
| style="width:110px;height:86px;" |
YL

| style="width:90px;height:86px;" |
10^6 tons crops/10^6 ha crop land

| style="width:100px;height:86px;" |
country

| style="width:106px;height:86px;" |
productivity of crop land in terms of crops

| style="width:121px;height:86px;" |
FY

|-
| style="width:110px;height:69px;" |
ZS

| style="width:90px;height:69px;" |
billion $

| style="width:100px;height:69px;" |
country, economic sector

| style="width:106px;height:69px;" |
value of gross production

| style="width:121px;height:69px;" |
PP (DATAECON)

|}

= Key User controllable parameters in the IFs agricultural model =

{| border="1" cellspacing="0" cellpadding="0" width="0" style="width:388px;"
|-
| style="width:132px;height:34px;" |
'''Name'''

| style="width:64px;height:34px;" |
'''Unit'''

| style="width:64px;height:34px;" |
'''Dimensionality'''

| style="width:64px;height:34px;" |
'''Description'''

| style="width:64px;height:34px;" |
'''Default Value'''

|-
| style="width:132px;height:85px;" |
Agconv

| style="width:64px;height:85px;" |
years

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
agricultural demand convergence time to function

| style="width:64px;height:85px;" |
75

|-
| style="width:132px;height:85px;" |
Aginvm

| style="width:64px;height:85px;" |
Multiplier Base 1

| style="width:64px;height:85px;" |
year, country

| style="width:64px;height:85px;" |
multiplier on investment in agriculture

| style="width:64px;height:85px;" |
1

|-
| style="width:132px;height:102px;" |
aglossconsperc

| style="width:64px;height:102px;" |
percentage

| style="width:64px;height:102px;" |
year, country, food type (crop, meat, fish)

| style="width:64px;height:102px;" |
waste rate of agricultural consumption

| style="width:64px;height:102px;" |
'''10'''

|-
| style="width:132px;height:136px;" |
aglossprodperc

| style="width:64px;height:136px;" |
percentage

| style="width:64px;height:136px;" |
year, country, food type (crop, meat, aquaculture, fish catch)

| style="width:64px;height:136px;" |
loss rate at point of production

| style="width:64px;height:136px;" |
'''10'''

|-
| style="width:132px;height:102px;" |
aglosstransm

| style="width:64px;height:102px;" |
Multiplier Base 1

| style="width:64px;height:102px;" |
year, country, food type (crop, meat, fish)

| style="width:64px;height:102px;" |
loss rate from producer to consumer, multiplier

| style="width:64px;height:102px;" |
'''1'''

|-
| style="width:132px;height:170px;" |
Agon

| style="width:64px;height:170px;" |
switch (0-1)

| style="width:64px;height:170px;" |
year

| style="width:64px;height:170px;" |
switch to turn off or on linkages between ag module and other modules; default is on

| style="width:64px;height:170px;" |
1

|-
| style="width:132px;height:85px;" |
aquaculconv

| style="width:64px;height:85px;" |
years

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
time over which aquaculture growth falls to 0

| style="width:64px;height:85px;" |
50

|-
| style="width:132px;height:51px;" |
Aquaculgr

| style="width:64px;height:51px;" |
growth rate in percent

| style="width:64px;height:51px;" |
year, country

| style="width:64px;height:51px;" |
aquaculture growth rate, initial

| style="width:64px;height:51px;" |
3.5

|-
| style="width:132px;height:102px;" |
Aquaculm

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year, country

| style="width:64px;height:102px;" |
multiplier on aquaculture production

| style="width:64px;height:102px;" |
1

|-
| style="width:132px;height:203px;" |
Calmax

| style="width:64px;height:203px;" |
Calories/person/day

| style="width:64px;height:203px;" |
year

| style="width:64px;height:203px;" |
maximum kilocalories needed per day per person.  This value should be a biologically-determined number that you will not normally change over time.

| style="width:64px;height:203px;" |
3800

|-
| style="width:132px;height:374px;" |
Calmeatm

| style="width:64px;height:374px;" |
dimensionless (0-1)

| style="width:64px;height:374px;" |
year

| style="width:64px;height:374px;" |
the maximum portion of calories that will come from meat.  The model increases the portion of calories taken in the form of meat with income up to this level (a value between 0 and 1). 

| style="width:64px;height:374px;" |
0.7

|-
| style="width:132px;height:51px;" |
clpcm

| style="width:64px;height:51px;" |
Multiplier Base1

| style="width:64px;height:51px;" |
year,country

| style="width:64px;height:51px;" |
Per capita calorie multiplier

| style="width:64px;height:51px;" |
1

|-
| style="width:132px;height:68px;" |
Dkl

| style="width:64px;height:68px;" |
depreciation rate in decimal form

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
depreciation rate of investment in land

| style="width:64px;height:68px;" |
0.01

|-
| style="width:132px;height:546px;" |
Dstl

| style="width:64px;height:546px;" |
dimensionless (0-1)

| style="width:64px;height:546px;" |
year

| style="width:64px;height:546px;" |
Desired stock (inventory) level in the economy.  It is in proportional terms so that 0.1 represents a 10% target stock level (of a base that usually includes annual production and may include demand, exports, or imports).  There is little reason for most users to want to change this parameter.

| style="width:64px;height:546px;" |
0.1

|-
| style="width:132px;height:153px;" |
Elagind

| style="width:64px;height:153px;" |
dimensionless

| style="width:64px;height:153px;" |
year

| style="width:64px;height:153px;" |
elasticity of industrial (incl. energy) use of crops with energy price

| style="width:64px;height:153px;" |
0.2

|-
| style="width:132px;height:85px;" |
elagmpr1

| style="width:64px;height:85px;" |
 

| style="width:64px;height:85px;" |
 

| style="width:64px;height:85px;" |
elasticity of agricultural imports to prices

| style="width:64px;height:85px;" |
 

|-
| style="width:132px;height:102px;" |
elagmpr2

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
elasticity of agricultural imports to change in prices

| style="width:64px;height:102px;" |
 

|-
| style="width:132px;height:85px;" |
elagxpr1

| style="width:64px;height:85px;" |
 

| style="width:64px;height:85px;" |
 

| style="width:64px;height:85px;" |
elasticity of agricultural exports to prices

| style="width:64px;height:85px;" |
 

|-
| style="width:132px;height:102px;" |
elagxpri2

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
elasticity of agricultural exports to change in prices

| style="width:64px;height:102px;" |
 

|-
| style="width:132px;height:85px;" |
Elascd

| style="width:64px;height:85px;" |
dimensionless

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
elasticity of crop food demand to prices

| style="width:64px;height:85px;" |
-0.15

|-
| style="width:132px;height:68px;" |
Elasfd

| style="width:64px;height:68px;" |
dimensionless

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
elasticity of fish demand to prices

| style="width:64px;height:68px;" |
-0.3

|-
| style="width:132px;height:68px;" |
Elasmd

| style="width:64px;height:68px;" |
dimensionless

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
elasticity of meat demand to prices

| style="width:64px;height:68px;" |
-0.3

|-
| style="width:132px;height:68px;" |
elfdpr1

| style="width:64px;height:68px;" |
dimensionless

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
elasticity of yield to stocks/inventories

| style="width:64px;height:68px;" |
-0.5

|-
| style="width:132px;height:102px;" |
elfdpr2

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
elasticity of yield to changes in stocks/inventories

| style="width:64px;height:102px;" |
-1

|-
| style="width:132px;height:102px;" |
Elglinpr

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
elasticity of livestock grazing intensity to prices

| style="width:64px;height:102px;" |
0.5

|-
| style="width:132px;height:85px;" |
eliasp1

| style="width:64px;height:85px;" |
dimensionless

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
elasticity of ag investment in land to return

| style="width:64px;height:85px;" |
0.2

|-
| style="width:132px;height:102px;" |
eliasp2

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
elasticity of ag investment in land to change in return

| style="width:64px;height:102px;" |
0.4

|-
| style="width:132px;height:68px;" |
elinag1

| style="width:64px;height:68px;" |
dimensionless

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
elasticity of ag investment to profit

| style="width:64px;height:68px;" |
0.15

|-
| style="width:132px;height:102px;" |
elinag2

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
elasticity of ag investment to change in profit

| style="width:64px;height:102px;" |
0.3

|-
| style="width:132px;height:102px;" |
ellvhpr1

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
 

| style="width:64px;height:102px;" |
elasticity of livestock herd size to stock level

| style="width:64px;height:102px;" |
 

|-
| style="width:132px;height:136px;" |
ellvhpr2

| style="width:64px;height:136px;" |
 

| style="width:64px;height:136px;" |
 

| style="width:64px;height:136px;" |
elasticity of livestock herd size to changes in stock level

| style="width:64px;height:136px;" |
 

|-
| style="width:132px;height:34px;" |
envco2fert

| style="width:64px;height:34px;" |
No unit

| style="width:64px;height:34px;" |
No unit

| style="width:64px;height:34px;" |
Crop CO2 sensitivity

| style="width:64px;height:34px;" |
0.1365

|-
| style="width:132px;height:85px;" |
envylchgadd

| style="width:64px;height:85px;" |
percentage

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
additive factor for effect of climate on yield

| style="width:64px;height:85px;" |
0

|-
| style="width:132px;height:68px;" |
envylchgm

| style="width:64px;height:68px;" |
Multiplier Base 1

| style="width:64px;height:68px;" |
year, country

| style="width:64px;height:68px;" |
multiplier on effect of climate on yield

| style="width:64px;height:68px;" |
1

|-
| style="width:132px;height:68px;" |
feddemm

| style="width:64px;height:68px;" |
Multiplier Base 1

| style="width:64px;height:68px;" |
year,country

| style="width:64px;height:68px;" |
Livestock feed demand multiplier

| style="width:64px;height:68px;" |
1

|-
| style="width:132px;height:34px;" |
fishcatchm

| style="width:64px;height:34px;" |
Multiplier Base 1

| style="width:64px;height:34px;" |
year, country

| style="width:64px;height:34px;" |
fish catch multiplier

| style="width:64px;height:34px;" |
1

|-
| style="width:132px;height:34px;" |
Forest

| style="width:64px;height:34px;" |
Multiplier Base 1

| style="width:64px;height:34px;" |
year, country

| style="width:64px;height:34px;" |
forest land multiplier

| style="width:64px;height:34px;" |
1

|-
| style="width:132px;height:85px;" |
fpricr1

| style="width:64px;height:85px;" |
dimensionless

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
food prices, response to stock level

| style="width:64px;height:85px;" |
-0.3

|-
| style="width:132px;height:102px;" |
fpricr2

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
food prices, response to change in stock level

| style="width:64px;height:102px;" |
-0.6

|-
| style="width:132px;height:85px;" |
Fprihw

| style="width:64px;height:85px;" |
ratio

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
food prices (inertial delay) in change

| style="width:64px;height:85px;" |
0.8

|-
| style="width:132px;height:85px;" |
fprimt1

| style="width:64px;height:85px;" |
dimensionless

| style="width:64px;height:85px;" |
year

| style="width:64px;height:85px;" |
fish prices, response to stock level

| style="width:64px;height:85px;" |
-0.3

|-
| style="width:132px;height:102px;" |
fprimt2

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
fish prices, response to change in stock level

| style="width:64px;height:102px;" |
-0.6

|-
| style="width:132px;height:68px;" |
indemm

| style="width:64px;height:68px;" |
Multiplier Base 1

| style="width:64px;height:68px;" |
year,country

| style="width:64px;height:68px;" |
Industrial agricultural demand multiplier

| style="width:64px;height:68px;" |
1

|-
| style="width:132px;height:102px;" |
Ldcropm

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year, country

| style="width:64px;height:102px;" |
multiplier on land to be developed for cropland

| style="width:64px;height:102px;" |
1

|-
| style="width:132px;height:102px;" |
Ldwf

| style="width:64px;height:102px;" |
hectares/person

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
land withdrawal factor with population growth

| style="width:64px;height:102px;" |
0.05

|-
| style="width:132px;height:102px;" |
Livhdpro

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
livestock herd productivity with grain feeding

| style="width:64px;height:102px;" |
0.5

|-
| style="width:132px;height:51px;" |
Lks

| style="width:64px;height:51px;" |
years

| style="width:64px;height:51px;" |
country, economic sector

| style="width:64px;height:51px;" |
lifetime of capital

| style="width:64px;height:51px;" |
30

|-
| style="width:132px;height:119px;" |
Lvcf

| style="width:64px;height:119px;" |
tons crops/tons meat

| style="width:64px;height:119px;" |
year

| style="width:64px;height:119px;" |
global livestock to calorie conversion factor, compared to crops

| style="width:64px;height:119px;" |
2

|-
| style="width:132px;height:136px;" |
malelimprecisesw

| style="width:64px;height:136px;" |
switch (0-1)

| style="width:64px;height:136px;" |
year,country

| style="width:64px;height:136px;" |
elimination of hunger for only the undernoursihed population

| style="width:64px;height:136px;" |
0

|-
| style="width:132px;height:102px;" |
malnelimstartyr

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
year,country

| style="width:64px;height:102px;" |
start year for an elimination of hunger scenario

| style="width:64px;height:102px;" |
0

|-
| style="width:132px;height:102px;" |
malnelimtargetyr

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
year,country

| style="width:64px;height:102px;" |
Target year for an elimination of hunger scenario

| style="width:64px;height:102px;" |
0

|-
| style="width:132px;height:546px;" |
Meatmax

| style="width:64px;height:546px;" |
tons meat/person/yr

| style="width:64px;height:546px;" |
year

| style="width:64px;height:546px;" |
The maximum meat consumption per person, in tons per person per year.  This parameter is only used to restrict meat consumption calculations in the initial year, in case of unreasonable data.  If you wish to introduce scenarios around dietary patterns (for instance, to reduce meat consumption), use the parameter calmeatm.

| style="width:64px;height:546px;" |
0.12

|-
| style="width:132px;height:459px;" |
Mhw

| style="width:64px;height:459px;" |
dimensionless

| style="width:64px;height:459px;" |
year

| style="width:64px;height:459px;" |
iMport propensity, historical (inertial) delay in change.  Values near 1.0 imply very rapid adjustment and values near 0 imply little or no adjustment.  Significant changes in this parameter could destabilize model behavior.

| style="width:64px;height:459px;" |
0.5

|-
| style="width:132px;height:102px;" |
Ofscth

| style="width:64px;height:102px;" |
10^6 tons fish

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
total global non-aquaculture fish production

| style="width:64px;height:102px;" |
80

|-
| style="width:132px;height:493px;" |
Protecm

| style="width:64px;height:493px;" |
Multiplier Base 1

| style="width:64px;height:493px;" |
year, country

| style="width:64px;height:493px;" |
Trade protection multiplier.  A multiplier on the price of imported goods, unit-less, by region.  A value of 1 implies no change, while higher values proportionately increase the prices of imported goods and lower values decrease them.

| style="width:64px;height:493px;" |
1

|-
| style="width:132px;height:34px;" |
Slr

| style="width:64px;height:34px;" |
fraction (0-1)

| style="width:64px;height:34px;" |
year

| style="width:64px;height:34px;" |
slaughter rate

| style="width:64px;height:34px;" |
0.7

|-
| style="width:132px;height:68px;" |
Tgrld

| style="width:64px;height:68px;" |
growth rate in decimal form

| style="width:64px;height:68px;" |
country

| style="width:64px;height:68px;" |
target growth in cultivated land

| style="width:64px;height:68px;" |
0.1

|-
| style="width:132px;height:408px;" |
Xhw

| style="width:64px;height:408px;" |
dimensionless

| style="width:64px;height:408px;" |
year

| style="width:64px;height:408px;" |
eXport propensity, inertial delay in change.  This parameter computes a moving average of export propensity.  A value of 0.7 would weight the historical or moving average by 0.7 and the newly computed value by 1-0.7 or 0.3.

| style="width:64px;height:408px;" |
0.7

|-
| style="width:132px;height:102px;" |
Ylexp

| style="width:64px;height:102px;" |
dimensionless

| style="width:64px;height:102px;" |
year

| style="width:64px;height:102px;" |
yield, exponent controlling saturation speed

| style="width:64px;height:102px;" |
0.5

|-
| style="width:132px;height:68px;" |
Ylhw

| style="width:64px;height:68px;" |
ratio

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
yield, inertial delay in change

| style="width:64px;height:68px;" |
0.2

|-
| style="width:132px;height:34px;" |
Ylm

| style="width:64px;height:34px;" |
Multiplier Base 1

| style="width:64px;height:34px;" |
year, country

| style="width:64px;height:34px;" |
yield multiplier

| style="width:64px;height:34px;" |
1

|-
| style="width:132px;height:68px;" |
Ylmax

| style="width:64px;height:68px;" |
10^6 tons crops/10^6 ha crop land

| style="width:64px;height:68px;" |
year, country

| style="width:64px;height:68px;" |
crop yield, maximum

| style="width:64px;height:68px;" |
15

|-
| style="width:132px;height:68px;" |
Ylmaxgr

| style="width:64px;height:68px;" |
growth rate in decimal form

| style="width:64px;height:68px;" |
year

| style="width:64px;height:68px;" |
maximum growth in yield

| style="width:64px;height:68px;" |
0.075

|}

= References and Bibliography =

<references />

Socio-Political

2026-08-24T15:12:29Z

Megan.Livengood:

Please cite as: Hughes, Barry B., and José R. Solórzano. 2014. "IFs Governance and Socio-Cultural Model Documentation ." Working paper 2014.03.05.a. Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <https://pardee.du.edu/wiki/Socio-Political>

Further information on this topic is provided in two dedicated chapters for [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_13 The Global Sociopolitical System] and [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_12 Domestic Sociopolitical Systems], which offers additional context, analysis, and supporting information.

A substantial portion of the socio-political model of IFs is scattered throughout the other models. There are "policy handles" or intervention points throughout those models. For instance, in the population model, multipliers on the total fertility rate can reflect policy decisions (although they can also reflect the model user's judgment concerning social changes in the country or region, independent of policy). Patterns of regulation, subsidy, tax incidence, and provision of state services are so diffuse and complicated that we resort to looking at their aggregate consequences through various "policy handles" rather than trying to represent them explicitly.

For more information on this module, please use the links below or read more at [[Socio-Political#Socio-political_Equations|Socio-Political Equations Overview]].

= Structure and Agent System: Socio-Political =

{| class="tableGrid" style="width:100%;" cellspacing="0" cellpadding="5" border="1"
|-
| style="width: 50%" | <div>'''System/Subsystem'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Socio-political</div>
|-
| style="text-align: left" | <div>'''Organizing Structure'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Social fabric</div>
|-
| style="text-align: left" | <div>'''Stocks'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Levels of human well-being and institutional development (human and social capital)</div><div> </div><div>Cultural structures</div>
|-
| style="text-align: left" valign="center" | <div>'''Flows'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Social expenditures</div><div> </div><div>Value change</div>
|-
| style="text-align: left" | <div>'''Key Aggregate ''' '''Relationships '''</div><div>(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Growth in literacy and human development;</div><div> </div><div>Democratic development, state failure</div>
|-
| style="text-align: left" valign="center" | <div style="text-align: left">'''Key Agent-Class Behavior ''' '''Relationships'''</div><div style="text-align: left">(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Government efforts to develop human capital through spending on health, education, R&D</div>
|}

Unlike the use of cohort-component structures in demographics and of markets and social accounting matrices for economics, there is no standard organizing structure that is widely used for representing socio-political systems. In the context of the TERRA project, IFs developed a multi-component approach to structure that might be called the "social fabric" (a la Robert Pestel).

Although representation of agent-class behavior would be of special interest in a socio-political module, most relationships in IFs remain at the level of aggregate specifications.

= Dominant Relations: Socio-political =

== Domestic Socio-Political Change: Dominant Relations ==

Social and political change occurs on three dimensions (social characteristics or individual life conditions, values, socio-political institutions and process). Although GDP per capita is strongly correlated with all dimensions of change, it might be more appropriate to conceptualize a syndrome or complex of developmental change than to portray an economically-driven process.<ref>here is the first reference</ref>

For causal diagram see [[Socio-Political#Socio-political_Flow_Charts|Socio-Political Flow Charts Overview]].

For equations see, for example, [[Socio-Political#Socio-political_Equations|Socio-Political Equations Overview]].

== Key dynamics are directly linked to the dominant relations ==

*The model computes some key social characteristics/life conditions, including life expectancy and fertility rates in the demographic model, but the user can affect them via multipliers (mortm, tfrm). Literacy rate is an endogenous function of education spending, which the user can influence (via gdsm).
*The model computes value or cultural change on three dimensions: traditional versus secular-rational, survival versus self-expression, and modernism versus postmodernism, which the user can affect via additive factors (tradsrateadd, survseadd, matpostradd).
*Freedom, democracy (the POLITY measure), autocracy, economic freedom, and the status of women are all computed endogenously but can all be shifted by the user via multipliers (freedomm, democm, autocm, econfreem, gemm)

== Domestic Socio-Political Change: Selected Added Value ==

The larger socio-political model provides representation and control over government spending on education, health, the military, R&D, foreign aid, and a residual category. Military spending is linked to interstate politics, both as a driver of threat and as a result of action-and-reaction based arms spending. The sub-model provides aggregated indicators of the physical quality of life and the human development index.

= Socio-political Flow Charts =

=== Overview ===

[[File:SP1.gif|frame|center|Visual representation of the social and political module]]

The social and political module represents a complex of interacting structures and processes. These include:

*The various social characteristics or life conditions of individuals
*Human values, beliefs, and orientations’
*Social and political structures, informal as well as formal
*Social and political processes, both domestic and international

Cultural foundations frame all of these components. And all of the components interact closely with human demographic and economic systems.

The socio-political elements of IFs are among the most dynamically evolving aspects of the overall modeling system. Much, but not everything in the above figure has been fully represented yet within IFs; the figure indicates direction of development and shows implemented elements in italics.

For more, please read the links below.

== Social Characteristics: Life Conditions ==

Individuals are the foundations of society. Many social indicators are actually aggregated indicators of their condition. The Human Development Index (HDI) is a widely-used summary measure of that life condition, based on life expectancy, educational attainment, and GDP per capita.

[[File:Sp2.gif|frame|center|Visual representation of life conditions]]

== Physical Quality of Life (PQLI) ==

The Overseas Development Council (then under the leadership of Jim Grant) developed and publicized a measure of (physical) quality of life (the PQLI) many years ago. It combines literarcy rate, infant mortality rate, and life expectancy, using scales from the lowest to the highest values in the global system. It weights the three scales equally. The literacy rate is, in turn, a function of the per capita spending levels on education, estimated cross-sectionally. In many respects the PQLI was a predecessor of the [[Socio-Political#Social_Characteristics:_Life_Conditions|human development index (HDI)]].[[File:Sp3.gif|frame|center|Visual representation of Physical Quality of Life (PQLI)]]

Based on country/region-specific Physical Quality of Life, it is possible to compute world quality of life (WPQLI) and the North-South gap in quality of life (NSPQLI). Given country-specific literacy rates, it is also possible to compute world literacy (WLIT).

== Income Distribution ==

Income distribution is represented by the share of national income earned by the poorest 20 percent of the population. That share is obtained from data whenever possible, but is estimated from a cross-sectional relationship when necessary and changed over time by that relationship (the values tend, however, to be very stable both in the real world and in the model). Because initial conditions of variables affected by income share, such as fertility and mortality rates, already reflect existing income distributions, it is only the changes in that distribution relative to the expected value that the model uses in such relationships. A parameter (incshrm) is available to change income share and thus affect those variables influenced by it.

[[File:Sp4.gif|frame|center|Visual representation of income distribution]]

== Social Characteristics: Networking ==

Being electronically networked is an increasingly important aspect of human life condition. The number of networked persons (NUMNWP) is a function primarily of the growth rate in that number (NUMNWPGR). It is ultimately constrained, however, by the size of the population and by the number of connections and organizational memberships that people can have (numnwplim). The growth in networked person number slows as it approaches the ultimate limit. The model user can affect the growth pattern via a multiplier on the growth rate (numnwpgrm).

This approach was added to IFs during the TERRA project and draws on the thinking of Tom Tesch and Pol Descamps.

[[File:NetworkedPersons2.gif|frame|center|Visual representation of networking.]]

== Social Values and Cultural Evolution ==

IFs computes change in three cultural dimensions identified by the World Values Survey (Inglehart 1997). Those are dimensions of materialism/post-materialism, survival/self-expression, and traditional/secular-rational values.

Inglehart has identified large cultural regions that have substantially different patterns on these value dimensions and IFs represents those regions, using them to compute shifts in value patterns specific to them.

Levels on the three cultural dimensions are predicted not only for the country/regional populations as a whole, but in each of 6 age cohorts. Not shown in the flow chart is the option, controlled by the parameter "wvsagesw," of computing country/region change over time in the three dimensions by functions for each cohort (value of wvsagesw = 1) or by computing change only in the first cohort and then advancting that through time (value of wvsagesw = 2).

The model uses country-specific data from the World Values Survey project to compute a variety of parameters in the first year by cultural region (English-speaking, Orthodox, Islamic, etc.). The key parameters for the model user are the three country/region-specific additive factors on each value/cultural dimension (matpostradd, etc.).

Finally, the model contains data on the size (percentage of population) of the two largest ethnic/cultural groupings. At this point these parameters have no forward linkages to other variables in the model.

[[File:Sp6.gif|frame|center|Visual representation of social values and cultural evolution]]

== Social Organization and Change ==

The sociopolitical module computes change in freedom (political and economic) and the status of women. For freedom it uses both the measure of the Freedom House and the combined measure for democracy (building on democracy and autocracy) of the POLITY project. It also computes a measure of economic freedom and of gender equality.[[File:Sp7.gif|frame|center|Visual representation of change in freedom and the status of women]]

== Social Organization: Stability/State Failure ==

The State Failure project has analyzed the propensity for different types of state failures within countries, including those associated with revolution, ethnic conflict, genocide-politicide, and abrupt regime change (using categories and data pioneered by Ted Robert Gurr. Upon the advice of Gurr, IFs groups the first three as internal war and the last as political instability.

IFs uses the same primary variables (infant mortality, democracy, and trade openness) as the State Failure project to drive forecasts of the probability of individual events of state failure, of ongoing episodes of it, and of the magnitude of episodes. In addition, it allows the use in the formulation of GDP per capita and years of education. Many other linkages have been and can be explored, including cultural regions.

[[File:Sp8.gif|frame|center|Visual representation of stability/state failure]]

== Government Spending ==

The economic submodel provides total government spending. Government spending by category begins as a simple product of total government consumption and fractional shares by spending category.

Spending by type (military, health, education, research and development, other, and foreign aid) is largely specified exogenously, building on the initial conditions for each country/region. In addition, an action-reaction (arms-race) dynamic can be established in military spending if the action-reaction switch is turned on. After adjustments to foreign aid and military spending, spending in all categories is re-normalized to equal total governmental spending.

Educational spending is further broken out of total educational spending. The user can shift the spending across three educational levels (primary, secondary, and tertiary) through the use of an educational multiplier.[[File:Gs1.gif|frame|center|Visual representation of government spending]]

See also the specifications of [[Economics#Firm_Accounts|detailed final demand]] and of [[Economics#International_Finance|international finance]].

== Drug Demand ==

The UNODC drug report finds that illicit drug use is concentrated amongst the youth, notably young males living in an urban environment. The UNODC report also finds a pronounced gender gap in relation to illicit drug consumption. Gender equality and empowerment seems to act as a key driver when it comes to determining drug consumption. For example, in the United States, characterized by a small gender gap, female drug use is about two thirds that of males, whereas in some other countries, including India and Indonesia, female drug use is as low as one tenth that of males, though there is a risk that female drug use may be underreported.

In addition, we have also found poverty, inequality and government health expenditure as drivers of specific types of drug prevalence. Policy options with respect to drug prevalence are represented in the model using multipliers which can be used to simulate an increase or decrease in drug prevalence. The table below lists the driving variables for each of the drug types.

{| border="1" align="center" cellspacing="1" cellpadding="1" style="width: 444px;"
|-
| '''Drug Type'''
| '''Driving Variables'''
| style="width: 166px;" | '''Driving Variables in IFS'''
|-
|
Amphetamines

| Youth Bulge, Gender Inequalities
| style="width: 166px;" | YTHBULGE, GEM
|-
| Cocaine
| Consumption levels, Gender Empowerment Measure and Income Inequality
| style="width: 166px;" | (C/POP), GEM, GINIDOM
|-
| Opiates
| Poverty, Youth Bulge and Urban Population
| style="width: 166px;" | INCOMELT310LN, YTHBULGE, POPURBAN
|-
| Prescription Opiods
| Health Expenditure
| style="width: 166px;" | HLEXPEND
|}

The figure below shows a diagrammatic representation of the drug demand model in IFs,

[[File:DrugModelFinalKBN.jpg|frame|center|500x600px|Drug Demand in IFs]]

== Violence ==

Mortality from conflict is driven using the probability of internal war (SFINTLWARALL). Mortality from homicides and violence against women and children are driven using the youthbulge (YTHBULGE) and the GINI co-efficient (GINIDOM).   Police violence deaths are driven by homicides(SVDTHSOTHERINTERPERSON) and the Corruption index in IFs (GOVCORRUPT). Finally, mortality from self-harm is calculated using mental health deaths (which are calculated in the health model) and deaths of women and children (SVDTHSWOMENANDCHILDREN). There are user controllable parameters available in the model to increase the death rates ('''''svmulm''''') and the total number of deaths ('''''svdthsadd''''') for each of the categories of violence. Finally, the homicide index(HOMICIDEINDEX) is calculated using each of the death rates mentioned above excluding self-harm. The homicide index itself is used in computing a conflict component of the security index in IFs (GOVINDSECUR).

The figure below shows a visual representation of the violence model in IFs.

[[File:ViolenceModelFinal.jpg|frame|center|500x600px|Violence model in IFs]]

= Socio-political Equations =

=== Overview ===

A substantial portion of the policy model of IFs is scattered throughout the other models. There are "policy handles" or intervention points throughout those models. For instance, in the population model, multipliers on the total fertility rate can reflect policy decisions (although they can also reflect the model user's judgment concerning social changes in the country or region, independent of policy). Similarly, in the energy model, the multiplier on energy demand can represent conservation policy. Similarly, the ultimate energy resource base and the rate of resource discovery remain uncertain in part because they are subject to a wide range of government interventions - multipliers can introduce assumptions about such interventions. In the economic module, the level of trade protection is very clearly a policy parameter as is the multiplier on the tax rate. Patterns of regulation, subsidy, tax incidence, and provision of state services are so diffuse and complicated that we resort to looking at their aggregate consequences through various "policy handles" rather than trying to represent them explicitly.

IFs contains other categories of sociol-political activity, however, that it represents in more integrated fashion in the sociopolitical module as a four-dimensional social fabric: social characteristics/life condition, values, social structures (formal and informal), and social processes.

For help understanding the equations see [[Understand_IFs#Equation_Notation|Notation]].

== Socio-political Equations: Life Conditions ==

Literacy changes from the initial level for the region because of a multiplier (LITM).

:<math>LIT_{\gamma}=\mathbf{LIT}^{t=1}_{\gamma}*LITM_{\gamma}</math>

The function upon which the literacy multiplier is based represents the cross sectional relationship globally between educational expenditures per capita (EDEX) from the government submodel and literacy rate (LIT). Rather than imposing the typical literacy rate on a region (and thereby being inconsistent with initial empirical values), the literacy multiplier is the ratio of typical literacy at current expenditure levels to the normal literacy level at initial expenditure levels. This formulation predates the development of an educational module that calculates the numbers of those with a primary education (one common definition of literacy). As that module is refined, we will likely derive literacy dynamics from it.

:<math>LITM=\frac{AnalFunc(EDEX)}{AnalFunc(\mathbf{EDEX}^{t=1})}</math>

Educational expenditures (and thus implicitly literacy and labor efficiency) are tied back to the economic model via the economic production function.

Given life expectancy, literacy, and infant mortality levels from the mortality distribution, it is possible to compute the Physical Quality of Life Index (PQLI) that the Overseas Development Council developed (ODC, 1977: 147#154). This measure averages the three quality of life indicators, first normalizing each indicator so that it ranges from zero to 100. The normaliza"tion is not needed for literacy; for life expectancy it converts the range of approximately 28 (LIFEXPMIN) to 80 (LIFEXPMAX) years into 0 to 100; for infant mortality it converts the range of approximately 229 per thousand (INFMORMAX) to 9 per thousand (INFMORMIN) into 0 to 100.

:<math>PQLI_{\gamma}=\frac{LIT_{\gamma}+\frac{LIFEXP_{\gamma}-\mathbf{lifexpmin}}{LifExpMax-\mathbf{lifexpmin}}*100+\frac{\mathbf{infmormax}-MORDST_{\gamma,c-1}}{\mathbf{infmormax}-InfMorMin}*100}{300}</math>

where

:<math>LifExpMax=Max(LIFEXP^t_{\gamma})</math>

:<math>InfMorMin=Min(INFMOR^t_{\gamma})</math>

For most users, the United Nations Development Program’s human development index (HDI) has replaced the PQLI as an integrated measure of life condition. It is a simple average of three sub-indices for life expectancy, education, and GDP per capita (using purchasing power parity). The life expectancy sub-index is the same as was used for the PQLI. The literacy sub-index is again the literacy rate. The GDP per capita index is a logged form that runs from a minimum of 100 to a maximum of $40,000 per capita. The measure in IFs differs slightly from the HDI version, because it does not put educational enrollment rates into a broader educational index with literacy; that will be changed as the educational model of IFs is better tested.

:<math>HDI_{\gamma}=\frac{LifeExpInd_{\gamma}+LitInd+GDPInd}{3}</math>

where

:<math>LifeExpInd=\frac{LIFEXP_{\gamma}-LIFEXPMIN}{LIFEXPMAX-LIFEXPMIN}</math>

:<math>LitInd=LIT_{\gamma}/100</math>

:<math>GDPInd=\frac{Log(GDPPCP_{\gamma}*1000)-Log(100)}{Log(40000)-Log(100)}</math>

Although the HDI is a wonderful measure for looking at past and current life conditions, it has some limitations when looking at the longer-term future. Specifically, the fixed upper limits for life expectancy and GDP per capita are likely to be exceeded by many countries before the end of the 21st century. IFs has therefore introduced a floating version of the HDI, in which the maximums for those two index components are calculated from the maximum performance of any state in the system in each forecast year.

:<math>HDIFLOAT_{\gamma}=\frac{LifeExpInd_{\gamma}+LitInd+GDPInd}{3}</math>

where

:<math>LifeExpInd=\frac{LIFEXP_{\gamma}-LIFEXPMIN}{HDILIFEMAXFLOAT-LIFEXPMIN}</math>

:<math>LitInd=LIT_{\gamma}/100</math>

:<math>GDPInd=\frac{Log(GDPPCP_{\gamma}*1000)-Log(100)}{Log(GDPPCPMAX)-Log(100)}</math>

The floating measure, in turn, has some limitations because it introduces relative attainment into the equation rather than absolute attainment. IFs therefore uses still a third version of the HDI, one that allows the users to specify probable upper limits for life expectancy and GDPPC in the twenty-first century. Those enter into a fixed calculation of which the normal HDI could be considered a special case.

:<math>HDI21stFIX_{\gamma}=\frac{LifeExpInd_{\gamma}+LitInd+GDPInd}{3}</math>

where

:<math>HDILIFEMAX21=\mathbf{hdilifemaxf}</math>

:<math>LifeExpInd=\frac{LIFEXP_{\gamma}-LIFEXPMIN}{HDILIFEMAX21-LIFEXPMIN}</math>

:<math>LitInd=LIT_{\gamma}/100</math>

:<math>Log(GDPPCP21)=Log(\mathbf{hdigdppcmax}*1000)</math>

:<math>GDPInd=\frac{Log(GDPPCP_{\gamma}*1000)-Log(100)}{Log(GDPPCP21)-Log(100)}</math>

It is useful to compute several additional global indicators, a world physical quality of life index (WPQLI), a world life expectancy (WLIFE), a world literacy rate (WLIT), and a North#South gap index or ratio of quality of life in the "developed -D" regions to the "less developed-L" regions (NSPQLI).

:<math>WPQLI=\frac{\sum^RPQLI_{\gamma}*POP_{\gamma}}{WPOP}</math>

:<math>WLIFE=\frac{\sum^RLIFEXP_{\gamma}*POP_{\gamma}}{WPOP}</math>

:<math>WLIT=\frac{\sum^RLIT_{\gamma}*POP_{\gamma}}{WPOP}</math>

:<math>NSPQLI=\frac{\frac{\sum^DPQLI_{\gamma}*POP_{\gamma}}{\sum^DPOP_{\gamma}}}{\frac{\sum^LPQLI_{\gamma}*POP_{\gamma}}{\sum^LPOP_{\gamma}}}</math>

== Socio-political Equations: Income Distribution ==

The income share of the poorest 20 percent of the population (INCSHR) depends on the GDP per capita at PPP (GDPPCP) and on an exogenous income share multiplier (incshrm).

:<math>INCSHR^t_{\gamma}=INCSHR^t_{\gamma}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}*\mathbf{incshrm_{\gamma}}</math>

The introduction of different household types into the social accounting matrix structure of IFs made possible the computation of a more sophisticated measure of income distribution tied directly to the model’s computation of household income (HHINC) and household size (HHPOP) by type. A domestic Gini value (GINIDOM) is calculated from a function that uses the normal Lorenz curve foundation for Gini indices. Because that function can calculate values that are quite different from the empirical initial values, a ratio of the empirical value to the initial computed value (GINIDOMRI) is used for scaling purposes. The model’s formulation of the relative household income levels of different household types, and therefore the calculation of a domestic GINI based on those income levels, are in early versions and are still rather crude.

:<math>GINIDOM^t_{\gamma}=GINIFUN(HHINC_{R,S},HHPOP_{R,S})*GINIDomRI^{t-1}_{\gamma}</math>

where

:<math>GINIDomRI^{t-1}_{\gamma}=\frac{GINIDOM^{t-1}_{\gamma}}{GINIFUN(HHINC^{{\gamma}-1}_{R,S},HHPOP^{t-1}_{R,S})}</math>

One value of a domestic Gini calculation is that it, in turn, makes possible the calculation of the percentage of population living on less than one dollar per day (INCOMELT1) or two dollars per day (INCOMELT2). Functions were estimated linking GDP per capita at purchasing power (GDPPCP) and the Gini index to those percentages. Again, IFs uses initial conditions for scaling purposes.

:<math>INCOMELT1^t_{\gamma}=AnalFunc(GDPPCP_{\gamma},GINIDOM_{\gamma})*INCOMELT1RI^{t-1}_{\gamma}</math>

where

:<math>INCOMELT1RI^{t-1}_{\gamma}=\frac{\mathbf{INCOMELT1}^{t-1}{\gamma}}{AnalFunc(GDPPCP^{\gamma-1}_{\gamma},GINIDOM^{t-1}_{\gamma})}</math>

:<math>INCOMELT2^t_{\gamma}=AnalFunc(GDPPCP_{\gamma},GINIDOM_{\gamma})*INCOMELT2RI^{t-1}_{\gamma}</math>

where

:<math>INCOMELT2RI^{t-1}_{\gamma}=\frac{INCOMELT2^{t-1}_{\gamma}}{AnalFunc(GDPPCP^{\gamma-1}_{\gamma},GINIDOM^{t-1}_{\gamma})}</math>

IFs also calculates a global Gini index across all countries/regions in the model, again using the standard Lorenz curve approach to areas of inequality and equality. It does not yet take into account intra-regional income differentials, but the foundation is now in place to do so.

:<math>GINI^t_{\gamma}=GINIFUN(GDP_R,POP_R)</math>

The user interface of IFs now uses the same Lorenz-curve approach to allow the user to calculate a specialized-display GINI for any variable that can be represented across all countries/regions of the model.

== Social Equations Networking ==

The focal point of this portion of the model is on the computation of the total number of networked persons (NUMNWP). The rate of growth in that number (NUMNWPGR) is subject to several forces. The initial value of that rate is set in the data preprocessor of the model from empirical data. When no data are available for a country or region, the rate is set at a level determined via a cross-sectional relationship between GDP per capita (PPP) and portion of population networked.

:<math>NUMNWP_{\gamma}=NUMNWP^{t-1}_{\gamma}*(1+NumNwGR^t_{\gamma})</math>

where

:<math>NumNwGR^t_{\gamma}=NUMNWPGR^{t-1}_{\gamma}*(\frac{nwplm-NUMNWP^{t-1}_{\gamma}}{nwplm-NUMNWP^{t-1}_{\gamma}})^2*numnwpgrm</math>

:<math>nwplm=numnwplim*POP_{\gamma}</math>

Over time the growth rate of networked persons is subject to a saturating function, as the actual number of networked persons approaches a limit. The limit is set by an exogenous multiplier (numnwplim) on total population; networked persons can exceed total population because of multiple affiliations of individuals (households, NGOs, companies). The user of the model can accelerate or de-accelerate the process of networking via a multiplier on the growth rate (numnwpgrm).

Although of interest in its own right, the number of networked persons is also carried forward in the model to the production function of the economy.

== Socio-political Equations: Values ==

IFs computes change in three cultural dimensions identified by the World Values Survey [[Introduction_to_IFs#IFs_Bibliography|(Inglehart 1997)]]. Those are dimensions of materialism/post-materialism (MATPOSTR), survival/self-expression (SURVSE), and traditional/secular-rational values (TRADSRAT). On each dimension the process for calculation is somewhat more complicated than for freedom or gender empowerment, however, because the dynamics for change in the cultural dimensions involves the aging of population cohorts. IFs uses the six population cohorts of the World Values Survey (1= 18-24; 2=25-34; 3=35-44; 4=45-54; 5=55-64; 6=65+). It calculates change in the value orientation of the youngest cohort (c=1) from change in GDP per capita at PPP (GDPPCP), but then maintains that value orientation for the cohort and all others as they age. Analysis of different functional forms led to use of an exponential form with GDP per capita for materialism/postmaterialism and to use of logarithmic forms for the two other cultural dimensions (both of which can take on negative values).

:<math>MATPOSTR_{\gamma,c-1}=\mathbf{MATPOSTR}^{t-1}_{\gamma,c-1}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}+\mathbf{CultShMP}^t_{\gamma-cultural}+\mathbf{matpostradd}^t_{\gamma}</math>

where

:<math>\mathbf{CultShMP}^t_{\gamma-cultural}=F(\mathbf{MATPOSTR}^{t-1}_{\gamma,c-1},AnalFunc(GDPPCP^{t-1}_{\gamma})</math>

:<math>SURVSE_{\gamma,c-1}=\mathbf{SURVSE}^{t-1}_{\gamma,c-1}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}+\mathbf{CultShSE}^t_{\gamma-cultural}+\mathbf{survseadd}^t_{\gamma}</math>

where

:<math>CultShSE^t_{\gamma-cultural}=F(\mathbf{SURVSE}^{t-1}_{\gamma,c-1}, AnalFunc(GDPPCP^{t-1}_{\gamma})</math>

:<math>TRADSRAT_{\gamma,c-1}=\mathbf{TRADSRAT}^{t-1}_{\gamma,c-1}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}+\mathbf{CultShTS}^t_{\gamma-cultural}+\mathbf{tradsratadd}^t_{\gamma}</math>

where

:<math>\mathbf{CultShTS}^t_{\gamma-cultural}=F(\mathbf{TRADSRAT}^{t-1}_{\gamma,c-1},AnalFunc(GDPPCP^{t-1}_{\gamma})</math>

The user can influence values on each of the cultural dimensions via two parameters. The first is a cultural shift factor (e.g. CultSHMP) that affects all of the IFs countries/regions in a given cultural region as defined by the World Value Survey. Those factors have initial values assigned to them from empirical analysis of how the regions differ on the cultural dimensions (determined by the pre-processor of raw country data in IFs), but the user can change those further, as desired. The second parameter is an additive factor specific to individual IFs countries/regions (e.g. matpostradd). The default values for the additive factors are zero.

Some users of IFs may not wish to assume that aging cohorts carry their value orientations forward in time, but rather want to compute the cultural orientation of cohorts directly from cross-sectional relationships. Those relationships have been calculated for each cohort to make such an approach possible. The parameter (wvsagesw) controls the dynamics associated with the value orientation of cohorts in the model. The standard value for it is 2, which results in the "aging" of value orientations. Any other value for wvsagesw (the WVS aging switch) will result in use of the cohort-specific functions with GDP per capita.

Regardless of which approach to value-change dynamics is used, IFs calculates the value orientation for a total region/country as a population cohort-weighted average.

IFs uses an approach that is similar to the one for literacy in order to estimate the future of another measure created by the United Nations Development Program, one called the Gender Equity Measure (GEM). The closer the values of that measure approach "1", the closer women are to men in political and social power.

:<math>GEM_{\gamma}=GEM^{t-1}_{\gamma}*\frac{AnalFunc(GDPPC_{\gamma})}{AnalFunc(GDPPC^{t-1}_{\gamma})}</math>

== Socio-political Equations: Structures or Institutions ==

IFs endogenizes level of freedom (FREEDOM), based on the Freedom House measures, by linking change from initial conditions to GDP per capita at purchasing power parity in an analytic function. For discussion of the relationship between GDP and democracy, see [[Introduction_to_IFs#IFs_Bibliography|Londregran and Poole (1996)]] and [[Introduction_to_IFs#IFs_Bibliography|Przeworski and Limongi (1997)]]. The latter view it as a probabilistic relationship in which there are a variety of reasons (often external pressure) at all levels of economic development for the conversion of dictatorships to democracies and in which the conversion of democracies to dictatorships occurs commonly at low but not high levels of development. That pattern creates a positive correlation between economic development and democratic government. A multiplier in freedom level (freedomm) increases or decreases the level of freedom.

:<math>FREEDOM_{\gamma}=FREEDOM^{t-1}_{\gamma}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(\mathbf{GDPPCP}^{t-1}_{\gamma})}*\mathbf{freedomm}_{\gamma}</math>

The Economic Freedom Institute (with leadership from the Fraser Institute; see Gwartney and Lawson with Samida, 2000) have also introduced a measure of economic freedom. IFs represents that in similar fashion.

:<math>ECONFREE_{\gamma}=ECONFREE^{t-1}_{\gamma}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}*\mathbf{econfreem}_{\gamma}</math>

The POLITY project provides an alternative to the freedom house measure of freedom or democracy level. In fact, it provides multiple variables related to political system. IFs EARLIER included formations of two of those, democracy (DEMOC) and autocracy (AUTOC). They worked in completely analogous fashion.

:<math>DEMOC_{\gamma}=DEMOC^{t-1}_{\gamma}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}*\mathbf{democm}_{\gamma}</math>

:<math>AUTOC_{\gamma}=AUTOC^{t-1}_{\gamma}*\frac{AnalFunc(GDPPCP_{\gamma})}{AnalFunc(GDPPCP^{t-1}_{\gamma})}*\mathbf{autocm}_{\gamma}</math>

More recently, IFs has (1) combined the two Polity project measures into a single one as is often done with the Polity measures, setting POLITYDEMOC equal to democracy – autocracy + 10, a measure that runs from 0 to 20; (2) introduced a more complicated, multi-level forecast for the new measure.

Specifically, the project identified three levels of analysis for factors that affect democratic change: domestic, regional, and systemic. At each of the three levels there are multiple factors that can affect democracy within states. At the domestic level we can identify two categories of factors in particular:

*GDP per capita. This variable correlates highly with almost all measures of social condition; GDP provides the resources for democratization and other social change.
*values/culture. Values clearly do differ across countries and regions of the world and almost certainly affect propensity to democratize.

At the regional level (or, more accurately, the "swing-states" level) we can also identify three prospective drivers:

*world average effects. It is possible that the world average exerts a pull-effect on states around the world (for instance, increasingly globalization could lead to homogenization of a wide variety of social structures around the world).
*swing states effects. Some states within regions quite probably affect/lead others (obviously the former Soviet Union was a prime example of such a swing state within its sphere of influence, but there is reason to believe in lesser and less coercive effects elsewhere).
*regional average. States within a region possibly affect each other more generally, such that "swing states" are moved by regional patterns and not simply movers of them.

At the system level we identify three:

*systemic leadership impetus. It is often suggested that the United States and other developed countries can affect democratization in less developed countries, either positively or negatively
*snowballing of democracy (Huntington 1991). The wave character of democratization suggests that there may be an internal dynamic, a self-reinforcing positive feedback loop, of the process globally, partially independent of other forces that act on the process. Such a conclusion is consistent with the fact that idea spread and global regime development influence many types of social change (Hughes 2001)
*miscellaneous other forces. Historic analysis would identify world war, economic depression, and other factors to explain the global pattern of democratization, especially the surge or retreat of waves.

A project document prepared for the CIA’s Strategic Assessment Group (SAG) analyzed historic data and, in cooperation with David Epstein and Larry Diamond, fit an approach to it that cut across these three levels (see Hughes 2002: 59-74 for elaboration and documentation of the empirical work). The empirical work is not documented again here. The work did not find significant and consistent regional level effects, however, and the regional variables are therefore normally turned off.

The resulting formulation uses the domestic level as an initial base calculation because it is the empirically strongest piece, and later adds (optionally) the regional level effects and the systemic effects. The base calculation is further tied to the actual empirical levels in the initial year of the run, with the impact of the driving variables being felt only in change of those levels. An ‘expected" democracy level (DEMOCEXP) is computed using an analytic function that uses GDP per capita at purchasing power parity (GDPPCP) and the World Value Survey’s survival and self-expression dimension (SURVSE). These were found quite powerful in their level of correlation with democracy and the WVS dimension, interestingly, carries a cultural component into the formulation. The user can further modify this basic formulation with an exogenous multiplier (democm).

:<math>DEMOCPOLITYBase^t_{\gamma}=\mathbf{DEMOCPOLITY}^{t-1}_{\gamma}*\frac{DEMOCEXP^t_{\gamma}}{DEMOCEXP^{t-1}_{\gamma}}*\mathbf{democm}^t_{\gamma}</math>

where

:<math>DEMOCEXP^t_{\gamma}=AnalFunc(GDPPCP^t_{\gamma},SURVSE^t_{\gamma})</math>

It is also useful to have a separate calculation of the empirically strongest piece of the formulation, namely the domestic effects, but without any adjustment to the initial empirical values. The expected democracy variable (DEMOCEXP) carries that. It can be compared with the fully computed values to see the degree to which there may be tension in countries between democracy levels that GDP per capita and values would predict, on the one hand, and those that are in the initial data. The greatest tension levels tend to be in the Middle Eastern countries, where decmocracy is considerably below "expected" levels.

The initial conditions of democracy in countries carry a considerable amount of idiosyncratic, country-specific influence, much of which can be expected to erode over time. Therefore a revised base level is computed that converges over time from the base component with the empirical initial condition built in to the value expected purely on the base of the analytic formulation. The user can control the rate of convergence with a parameter that specifies the years over which convergence occurs (polconv) and, in fact, basically shut off convergence by sitting the years very high.

:if <math>\mathbf{sweffects}=1</math>

:then <math>SwingEffects^t_{\gamma}=timeadj*\mathbf{swingstsdem}_{\gamma-Swinger,p-1}*(WDemoc^{t-1}-DEMOCPOLITY^{t-1}_{\gamma-Swingee})+timeadj*\mathbf{swingstsdem}_{\gamma-Swinger,p-2}*(DEMOCPOLITY^{t-1}_{\gamma-Swinger}-DEMOCPOLITY^{t-1}_{\gamma-Swingee})+timeadj*\mathbf{swingstsdem}_{\gamma-Swinger,p-3}*(RgDemoc-DEMOCPOLITY^{t-1}_{\gamma-Swingee})</math>

where

:<math>timeadj=.2</math>

:<math>WDemoc^{t-1}=\frac{\sum^RDEMOCPOLITY^{t-1}_{\gamma}}{R}</math>

else

:<math>SwingEffects^t_{\gamma}=0</math>

On top of the country-specific calculation sits the (optional) regional or swing state effect calculation (SwingEffects), turned on by setting the swing states parameter (swseffects) to 1. The swing effects term has three components. The first is a world effect, whereby the democracy level in any given state (the "swingee") is affected by the world average level, with a parameter of impact (swingstdem) and a time adjustment (timeadj) . The second is a regionally powerful state factor, the regional "swinger" effect, with similar parameters. The third is a swing effect based on the average level of democracy in the region (RgDemoc).

David Epstein of Columbia University did extensive estimation of the parameters (the adjustment parameter on each term is 0.2). Unfortunately, the levels of significance were inconsistent across swing states and regions. Moreover, the term with the largest impact is the global term, already represented somewhat redundantly in the democracy wave effects. Hence, these swing effects are normally turned off and are available for optional use.

Also on top of the country-level effects sits the effect of global waves (DemGlobalEffects). Those depend on the amplitude of waves (DEMOCWAVE) relative to their initial condition and on a multiplier (EffectMul) that translates the amplitude into effects on states in the system. Because democracy and democratic wave literature often suggests that the countries in the middle of the democracy range are most susceptible to movements in the level of democracy, the analytic function enhances the affect in the middle range and dampens it at the high and low ends.

:<math>DemGlobalEffect^t_{\gamma}=(DEMOCWAVE^t-\mathbf{democwave^{t-1}})*EffectMul_{\gamma}</math>

where

:<math>MDemocPolity^{t-1}_{\gamma}=MovingAverage(DEMOCPOLITY^{t-1}_{\gamma})</math>

:<math>EffectMul_{\gamma}=AnalFunc(MDemocPolity^{t-1}_{\gamma})</math>

The democratic wave amplitude is a level that shifts over time (DemocWaveShift) with a normal maximum amplitude (democwvmax) and wave length (democwvlen), both specified exogenously, with the wave shift controlled by a endogenous parameter of wave direction that shifts with the wave length (DEMOCWVDIR). The normal wave amplitude can be affected also by impetus towards or away from democracy by a systemic leader (DemocImpLead), assumed to be the exogenously specified impetus from the United States (democimpus) compared to the normal impetus level from the U.S. (democimpusn) and the net impetus from other countries/forces (democimpoth).

:<math>DEMOCWAVE^t=DEMOCWAVE^{t-1}+DemocImpLead+\mathbf{democimpoth}+DemocWaveShift</math>

where

:<math>DemocImpLead=\frac{(\mathbf{democimpus-democimpusn)*eldemocimp}}{\mathbf{democwvlen}}</math>

:<math>DemocWaveShift=\mathbf{\frac{democwvmax}{demowvlen}}*DEMOCWVDIR</math>

Given both the global and regional/swing-state effects, it is possible to add these to the basic country calculation for the final computation of the level of democracy using the Polity scale. The size of the swing effects is constrained by an external parameter (swseffmax).

:<math>DEMOCPOLITY^t_{\gamma}=DEMOCPOLITYBaseRev^t_{\gamma}+SwingEffect^t_{\gamma}+DemGlobalEffects^t_{\gamma}</math>

== Socio-political Equations: Stability/State Failure ==

The State Failure project has analyzed the propensity for different types of state failures within countries, including those associated with revolution, ethnic conflict, genocide-politicide, and abrupt regime change (using categories and data pioneered by Ted Robert Gurr. Upon the advice of Gurr, IFs groups the first three as internal war and the last as political instability.

The extensive database of the project includes many measures of failure. IFs has variables representing three measures in each of the two categories, corresponding to the probability of the first year of a failure event (SFINSTABY1 and SFINTLWARY1), the probability of the first year or a continuing year (SFINSTABALL and SFINTLWARALL), and the magnitude of a first year or continuing event (SFINSTABMAG and SFINTLWARMAG).

Using data from the State Failure project, formulations were estimated for each variable using up to five independent variables that exist in the IFs model: democracy as measured on the Polity scale (DEMOCPOLITY), infant mortality (INFMOR) relative to the global average (WINFMOR), trade openness as indicated by exports (X) plus imports (M) as a percentage of GDP, GDP per capita at purchasing power parity (GDPPCP), and the average number of years of education of the population at least 25 years old (EDYRSAG25). The first three of these terms were used because of the state failure project findings of their importance and the last two were introduced because they were found to have very considerable predictive power with historic data.

The IFs project developed an analytic function capability for functions with multiple independent variables that allows the user to change the parameters of the function freely within the modeling system. The default values seldom draw upon more than 2-3 of the independent variables, because of the high correlation among many of them. Those interested in the empirical analysis should look to a project document (Hughes 2002) prepared for the CIA’s Strategic Assessment Group (SAG), or to the model for the default values.

One additional formulation issue grows out of the fact that the initial values predicted for countries or regions by the six estimated equations are almost invariably somewhat different, and sometimes quite different than the empirical rate of failure. There may well be additional variables, some perhaps country-specific, that determine the empirical experience, and it is somewhat unfortunate to lose that information. Therefore the model computes three different forecasts of the six variables, depending on the user’s specification of a state failure history use parameter (sfusehist). If the value is 0, forecasts are based on predictive equations only. The equation below illustrates the formulation and that for the other five state failure variables varies with estimation. The analytic function obviously handles various formulations including linear and logarithmic.

:if <math>\mathbf{sfusehist}=0</math> then (no history)

:<math>SFINSTABALL^t_{\gamma}=PredictedTerm^t_{\gamma}</math>

where

:<math>PredictedTerm^t_{\gamma}=ANALFUN(GDPPCP^t_{\gamma},DemocTerm^t,InfMorTerm^t,TradeTerm^t,Educ25Term^t)</math>

:<math>DemocTerm=DemoPolity_{\gamma}</math>

:<math>InfMorTerm=\frac{INFMOR_{\gamma}}{WINFMOR}</math>

:<math>TradeTerm=\frac{X_{\gamma}+M_{\gamma}}{GDP}*100</math>

:<math>Educ25Term=EDYRSAG25_{\gamma}</math>

If the value of the sfusehist parameter is 1, the historical values determine the initial level for forecasting, and the predictive functions are used to change that level over time. Again the equation is illustrative.

:if <math>\mathbf{sfusehist}=1</math> then (use history)

:<math>SFINSTABALL^t_{\gamma}=\frac{PredictedTerm^t_f}{PredictedTerm^{t-1}_f}*\mathbf{SFINSTABALL}^{t-1}_{\gamma}</math>

where

:<math>PredictedTerm=ANALFUN(GDPPCP^t_{\gamma},DemocTerm^t,InfMorTerm^t,TradeTerm^t,Educ25Term^t)</math>

:<math>DemocTerm=DemoPolity_{\gamma}</math>

:<math>InfMorTerm=\frac{INFMOR_{\gamma}}{WINFMOR}</math>

:<math>TradeTerm=\frac{X_{\gamma}+M_{\gamma}}{GDP}*100</math>

:<math>Educ25Term=EDYRSAG25_{\gamma}</math>

If the value of the sfusehist parameter is 2, the historical values determine the initial level for forecasting, the predictive functions are used to change the level over time, and the forecast values converge over time to the predictive ones, gradually eliminating the influence of the country-specific empirical base. That is, the second formulation above converges linearly towards the first over years specified by a parameter (polconv), using the CONVERGE function of IFs.

:if <math>\mathbf{sfusehist}=3</math> then (converge)

:<math>SFINSTABALLBase^t_{\gamma}=\frac{PredictedTerm^t_f}{PredictedTerm^{t-1}_f}*\mathbf{SFINSTABALL}^{t-1}_{\gamma}</math>

:<math>SFINSTABALL^t_{\gamma}=ConvergeOverTime(SFINSTABALLBase^t_{\gamma},PredictedTerm^t_f,\mathbf{polconv})</math>

where

:<math>PredictedTerm=ANALFUN(GDPPCP^t_{\gamma},DemocTerm^t,InfMorTerm^t,TradeTerm^t,Educ25Term^t)</math>

:<math>DemocTerm=DemoPolity_{\gamma}</math>

:<math>InfMorTerm=\frac{INFMOR_{\gamma}}{WINFMOR}</math>

:<math>TradeTerm=\frac{X_{\gamma}+M_{\gamma}}{GDP}*100</math>

:<math>Educ25Term=EDYRSAG25_{\gamma}</math>

== Probability of state failure from different causes ==

The variables represent the probability of failure with respect to distinct conceptual groups of drivers.

*SFDEM (demography)
*SFECONDEV (economic/development)
*SFGOV (governance)
*SFIMBAL (structural imbalances)

=== Input variables needed to compute the probabilities ===

{| border="1" cellspacing="1" cellpadding="1" width="0" style="width:576px;" align="center"
|-
! nowrap="nowrap" style="width: 150px; height: 35px;" scope="col" |
Drivers

! nowrap="nowrap" style="width: 72px; height: 35px;" scope="col" |
Coeff.

! nowrap="nowrap" style="width: 138px; height: 35px;" scope="col" |
Units

! nowrap="nowrap" style="width: 84px; height: 35px;" scope="col" |
Transformation

! style="width: 132px; height: 35px;" scope="col" |
Other specification

|-
| nowrap="nowrap" style="width:150px;height:19px;" |
'''Demography'''

| nowrap="nowrap" style="width:72px;height:19px;" |
| nowrap="nowrap" style="width:138px;height:19px;" |
| nowrap="nowrap" style="width:84px;height:19px;" |
| nowrap="nowrap" style="width:132px;height:19px;" |
 

|-
| nowrap="nowrap" style="width:150px;height:2px;" |
Infant mortality

| nowrap="nowrap" style="width:72px;height:2px;" |
0.77919

| nowrap="nowrap" style="width:138px;height:2px;" |
Deaths/1000 Births

| nowrap="nowrap" style="width:84px;height:2px;" |
Ln

| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:2px;" |
population

| nowrap="nowrap" style="width:72px;height:2px;" |
0.30204

| nowrap="nowrap" style="width:138px;height:2px;" |
Millions

| nowrap="nowrap" style="width:84px;height:2px;" |
Ln

| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:2px;" |
Population growth

| nowrap="nowrap" style="width:72px;height:2px;" |
0.07767

| nowrap="nowrap" style="width:138px;height:2px;" |
Percent

| nowrap="nowrap" style="width:84px;height:2px;" |
| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:2px;" |
Youth bulge (15-29/15+)

| nowrap="nowrap" style="width:72px;height:2px;" |
0.0077

| nowrap="nowrap" style="width:138px;height:2px;" |
Percent

| nowrap="nowrap" style="width:84px;height:2px;" |
| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:2px;" |
Net migration

| nowrap="nowrap" style="width:72px;height:2px;" |
-0.29432

| nowrap="nowrap" style="width:138px;height:2px;" |
Millions

| nowrap="nowrap" style="width:84px;height:2px;" |
| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:2px;" |
_cons

| nowrap="nowrap" style="width:72px;height:2px;" |
-8.23582

| nowrap="nowrap" style="width:138px;height:2px;" |
-

| nowrap="nowrap" style="width:84px;height:2px;" |
| nowrap="nowrap" style="width:132px;height:2px;" |
|-
| nowrap="nowrap" style="width:150px;height:19px;" |
'''Economic/Development'''

| nowrap="nowrap" style="width:72px;height:19px;" |
 

| nowrap="nowrap" style="width:138px;height:19px;" |
 

| nowrap="nowrap" style="width:84px;height:19px;" |
 

| nowrap="nowrap" style="width:132px;height:19px;" |
 

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
GDP/cap

| nowrap="nowrap" style="width:72px;height:10px;" |
-0.30591

| nowrap="nowrap" style="width:138px;height:10px;" |
Thousands (2011 PPP)

| nowrap="nowrap" style="width:84px;height:10px;" |
Ln

| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:10px;" |
GDP/cap (log) growth

| nowrap="nowrap" style="width:72px;height:10px;" |
-0.06393

| nowrap="nowrap" style="width:138px;height:10px;" |
Percent

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:10px;" |
Life expectancy

| nowrap="nowrap" style="width:72px;height:10px;" |
-0.02537

| nowrap="nowrap" style="width:138px;height:10px;" |
Years

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:10px;" |
_cons

| nowrap="nowrap" style="width:72px;height:10px;" |
-2.06558

| nowrap="nowrap" style="width:138px;height:10px;" |
-

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:19px;" |
'''Governance'''

| nowrap="nowrap" style="width:72px;height:19px;" |
 

| nowrap="nowrap" style="width:138px;height:19px;" |
 

| nowrap="nowrap" style="width:84px;height:19px;" |
 

| nowrap="nowrap" style="width:132px;height:19px;" |
 

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
Polity

| nowrap="nowrap" style="width:72px;height:10px;" |
0.03273

| nowrap="nowrap" style="width:138px;height:10px;" |
-10 to 10

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:10px;" |
Polity^2

| nowrap="nowrap" style="width:72px;height:10px;" |
-0.02155

| nowrap="nowrap" style="width:138px;height:10px;" |
Polity2

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:10px;" |
_cons

| nowrap="nowrap" style="width:72px;height:10px;" |
-2.89726

| nowrap="nowrap" style="width:138px;height:10px;" |
-

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|-
| nowrap="nowrap" style="width:150px;height:19px;" |
'''Structural Imbalances'''

| nowrap="nowrap" style="width:72px;height:19px;" |
 

| nowrap="nowrap" style="width:138px;height:19px;" |
 

| nowrap="nowrap" style="width:84px;height:19px;" |
 

| nowrap="nowrap" style="width:132px;height:19px;" |
 

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
polity v GDP/cap

| nowrap="nowrap" style="width:72px;height:10px;" |
0.04735

| nowrap="nowrap" style="width:138px;height:10px;" |
[Polity - Expected]

| nowrap="nowrap" style="width:84px;height:10px;" |
Ln(GDP/cap)

| nowrap="nowrap" style="width:132px;height:10px;" |
Pooled

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
Life Exp. v GDP/cap

| nowrap="nowrap" style="width:72px;height:10px;" |
-0.0558

| nowrap="nowrap" style="width:138px;height:10px;" |
[Life Exp. - Expected]

| nowrap="nowrap" style="width:84px;height:10px;" |
Ln(GDP/cap)

| nowrap="nowrap" style="width:132px;height:10px;" |
Partial Pool (re)

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
Youth Bulge v Polity

| nowrap="nowrap" style="width:72px;height:10px;" |
0.0131

| nowrap="nowrap" style="width:138px;height:10px;" |
[Yth Blg % - Expected]

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
Based on year 2013

|-
| nowrap="nowrap" style="width:150px;height:10px;" |
_cons

| nowrap="nowrap" style="width:72px;height:10px;" |
-4.23404

| nowrap="nowrap" style="width:138px;height:10px;" |
-

| nowrap="nowrap" style="width:84px;height:10px;" |
| nowrap="nowrap" style="width:132px;height:10px;" |
|}

Formulation for the probabilities is below, where β0 is the constant, β1…k are the parameters listed above, and X1…k are the driver values

== Economic Inequality and Political Conflict ==

IFs does not yet include this important relationship. See Lichbach (1989) and Moore, Lindstrom, and O’Regan (1996) for analyses of how difficult this relationship is to specify. One critical problem is conceptualization of political conflict, political repression, political instability, political violence, political protest, etc. There are clearly many interacting, but separate dimensions for consideration. As Lichbach (1989: 448) says, "robust EI-PC laws have not been discovered."

== Drug Model Equations ==

We use linear regressions for each of the variables described above. We fit this linear equation to logistic curves to derive the final prevalence rate. The methodology used here is similar to what is used in the water and sanitation model in the International Futures tool to compute access to water and sanitation.<ref>Rothman, D.S. and Irfan M.T, IFs infrastructure model documentation, Working Paper 2013.07.22, Josef Korbel School of International Studies, University of Denver, Denver CO. https://pardee.du.edu/ifs-infrastructure-model-documentation</ref> 

The values are computed using the equations given below,

:<math>DRUGUSECOCAINE_{R}=(0.040239 * \frac{C_{R}}{POP_{R}}) + (1.966652 * GEM_{R}) + (0.476489* GINIDOM_{R}) - 8.7474</math>

:<math>DRUGUSEAMPHETAMINE_{R}=(3.522315 * YTHBULGE_{R}) + (2.495262* GEM_{R})-7.801985</math>

:<math>DRUGUSEOPIATES_{R}=(-.1.946209* LN(100 * \frac{INCOMELT310LN _{R}}{ POP_{R}}) + </math>
::::::::::::<math>(4.236404* YTHBULGE_{R}) + (.7277734 * LN(100 * \frac{POPURBAN _{R}}{ POP_{R}}) - 8.601204</math>

:<math>DRUGUSEPRESCRIPTOPIOID_{R}=(.2469778 * 100 * \frac{HLEXPEND_{R}} {GDP_{R}})-7.063833</math>

Where,

*C is the amount of household consumption in billion USD
*POP is the population
*YTHBULGE is the youth bulge (Population aged between 15-29 years as a percent of the total population)
*INCOMELT310LN is the number of people living in poverty (earning less than USD 3.10 per day.
*POPURBAN is the number of people living in urban areas.
*HLEXPEND is the amount of health spending (private and public)
*GDP is the gross domestic product

=== Pre-Processor and first year ===

The values for drug prevalence are initialized using illicit drug demand data from the UNODC. However, data availability from this source is low. Appendix II shows the data coverage across countries from the UNODC. Therefore, filling holes for the first year where no data is available is crucial. There are three options available to the user when filling holes. They are,
<ol style="list-style-type:lower-alpha;">
<li>'''Using IHME equations to fill holes-  '''The institute for health and metric evaluation also provides data on drug prevalence and this source has much higher coverage (184 countries from 1990 to 2016). However, this data pertains to treatment of drug prevalence. We developed regression equations to estimate levels of illicit drug use from the IHME drug prevalence data set. Appendix III describes these regression equations in detail.  </li>
<li>'''Using forecast year equations - '''This method uses the forecast year equations to derive the drug prevalence value for the first year of the model.</li>
<li>'''Using regional averages from the UNODC- '''Alternatively, we can also use regional averages for illicit drug prevalence to fill in holes for individual countries.  </li>
</ol>

The user can choose the initialization method using the parameter '''''druginitsw'''''. By default the model will choose the first option i.e. using IHME equations to fill in holes for the first year of the model.

=== Forecast Years ===

==== Computing Drug Demand Using the Bottom Up Approach ====

In the forecast years, logistic regressions are used to first estimate the drug prevalence rates. The equations for amphetamines are shown below,

:<math>z_{amphetamines}=(3.522315 * YTHBULGE_{R} )+ (2.495262* GEM_{R} )-7.801985</math>

:<math>z_{cocaine}=(.040239 * \frac{C_{R}}{POP_{R}} + (1.96421* GEM_{R} )+(.0476489* GINIDOM_{(R)})-8.7474</math>

:<math>z_{opiates}=(.7277734 * LN(POPURBAN_{R} ))+ (.42364* YTHBULGE_{R} )+(-.1946*LN(INCOMELT190LN_{R} ))-7.801985</math>

:<math>z_{presopioid}=(.2469778 * HLEXPEND_{R})-7.06</math>

This value is then used to compute the prevalence rate for each of the four drug types as follows,

:<math>DRUGUSEAMPHETAMINE_{R}=100*\frac{e^{(z_{amphetamines} )}}{1+e^{(z_{amphetamines}) }}</math>

:<math>DRUGUSECOCAINE_{R}=100*\frac{e^{(z_{cocaine} )}}{1+e^{(z_{cocaine}) }}</math>

:<math>DRUGUSEOPIATES_{R}=100*\frac{e^{(z_{opiates} )}}{1+e^{(z_{opiates}) }}</math>

:<math>DRUGUSEPRESCRIPTOPIOID_{R}=100*\frac{e^{(z_{presopioid} )}}{1+e^{(z_{presopioid}) }}</math>

The above values are then adjusted for the shift factor, multipliers and a cap on the maximum possible value

:<math>DRUGUSEAMPHETAMINE_{R}=AMIN(DRUGUSEAMPHETAMINE_{R}+DrugShift_{R} ),2.3)*druguseamphetaminem_{R}</math>

:<math>DRUGUSECOCAINE_{R}=AMIN(DRUGUSECOCAINE_{R}+DrugShift_{R} ),2.3)*drugusecocainem_{R}</math>

:<math>DRUGUSEOPIATES_{R}=AMIN(DRUGUSEOPIATES_{R}+DrugShift_{R} ),2.3)*druguseopiatesm_{R}</math>

:<math>DRUGUSEPRESCRIPTOPIOID_{R}=AMIN(DRUGUSEPRESCRIPTOPIOID_{R}+DrugShift_{R} ),2.3)*druguseprescriptopioidm_{R}</math>

Where,

'''DrugShift''' is the shift factor computed in the first year of the model which is used to chain the forecast values to the historical values from the data

2.3 is the cap on drug prevalence for amphetamines. <ref>These caps have been chosen on the basis of the highest historical global prevalence rates</ref>

'''AMIN''' is the function used to get the minimum value of drug prevalence and the cap (2.3). Since prevalence of drug usage tends to be slow moving over time, we have also capped the rate of growth of the prevalence rate for all four drug types. The growth rate in the drug prevalence rate is capped at 5 percent for every country for every year. However, this growth rate is not applicable when the parameters on drug prevalence rate are activated by a user.

Finally, total drug use is computed as the average of the four drug types divided by a '''drugusepolyindex''' parameter which is set to 1.2. This is done to account for users who use multiple drugs.

=== Adjusting Drug Use Using the Top Down Approach ===

The paragraph above described the computation of drug prevalence using the bottom up approach (i.e. drug prevalence is computed for each drug type individually and this is used to compute total drug demand). However, another approach to computing drug demand would be to compute total drug demand first and distribute that across drug types (i.e. a top down approach). The model computes total drug demand using this top down approach and then converges the drug demand computed through the bottom up approach to the same

The top down model uses youth bulge and household consumption as the two main drivers.

Total drug demand is calculated as,

:<math>z_{druguseest}=(1.245 * YTHBULGE_{R} )+ (.508* \frac{C_{R}}{POP_{R}})-3.498</math>

:<math>DruguseEst_{R}=100*\frac{(e^{(z_{druguseest} )}}{1+e^{(z_{druguseest} )}}</math>

The total drug use from the bottom up approach is converged to the above value over a period of 100 years. Note that there is a restriction on the year growth and decline rate of total drug use of 2%.

== Violence Model Equations ==

=== Pre-processor and first year ===

In the pre-processor, each of the violence variables are initialized using death rate data from the Institute for Health and Metric Evaluation (IHME). Please note that we only forecast mortality and the model currently does not have a representation of the prevalence of violence.

For the conflict deaths, instead of using the latest data point for initialization, we use a weighted average of conflict deaths from the previous 10 years which is then divided by two to generate a more realistic number for the initialization.

Where no data is available for any particular type of violence, we use the forecast equations to fill in holes for the first year of the model.

In the first year of the model, we need to make sure that the total deaths from violence matches the total deaths from intentional injuries in the health model. Hence we normalize the total violence deaths to the total intentional injuries deaths. Please note that this normalization is optional (i.e. the user can activate a switch '''''svvionormsw'''''). The normalization will also be activated in the event the user turns on the forward linkage switch from the violence model to the health model '''''svtohlsw'''''.

For the normalization we first calculate the total deaths from intentional injuries in the health model. This term is called the AdjustedViolenceTerm. Now, we calculate the total deaths from the violence model and call this tem SVTerm. The deaths from the violence model are now normalized to the deaths from the health model using the equations below. (The below equation is used for normalizing conflict deaths. Similar equations are used for the other types of violence),

:<math>SVDTHSCONFLICT_{R}=((AdjustedViolenceTerm_{R}*(SVDTHSCONFLICT_{R}*POP_{R}/SVTerm_{R})/POP_{R})*100000</math>

Where,

POP is the total population

Shift factors are then calculated in the first year to chain the forecast values to the historical data.

=== Forecast Years ===

In the forecast years estimated values are calculated using forecast equations for each type of violence. The forecast equations have been explained in Table 1 below. Each of the types of violence are calculated using this estimated value and the respective shift factor calculated in the first year of the model and the multipliers on the death rates are applied.

The equations used are as follows,

:<math>SVDTHSCONFLICT_{R}=((ConflictEst)_{R}+ConflictShift_{R})*svmulm_{R,2} </math>

:<math>SVDTHSOTHERINTERPERSON_{R}=(HomicideEst_{R}+HomicideShift_{R})*svmulm_{R,5} </math>

:<math>SVDTHSWOMENCHILDREN_{R}=(WomenandChilEst_{R}+WomenandChilShift_{R})*svmulm_{R,4} </math>

:<math>SVDTHSPOLICS_{R}=(PoliceEst_{R}+ PoliceShift_{R})*svmulm_{R,3} </math>

:<math>SVDTHSSELFHARM_{R}=(SelfHarmEst_{R}+ SelfHarmShift_{R})*svmulm_{R,1} </math>

Where,

ConflictEst, HomicideEst, WomenandChilEst, PoliceEst and SelfHarmEst are the estimated level of deaths calculated using the forecast equations.

ConflictShift, HomicideShift, WomenandChilShift, PoliceShift and SelfHarmShift are the shift factors calculated in the first year of the model.

{| border="1" cellspacing="0" cellpadding="0" width="0" style="width:694px;" align="center"
|+ Functions used to compute estimates in the forecast years in the violence model
|-
| nowrap="nowrap" style="width:32px;height:20px;" |
'''No'''

| nowrap="nowrap" style="width:284px;height:20px;" |
'''Function'''

| nowrap="nowrap" style="width:71px;height:20px;" |
'''R-Squared'''

| nowrap="nowrap" style="width:158px;height:20px;" |
'''Independent variable'''

| nowrap="nowrap" style="width:82px;height:20px;" |
'''Co-efficient'''

| nowrap="nowrap" style="width:70px;height:20px;" |
'''Constant'''

|-
| nowrap="nowrap" style="width:32px;height:20px;" |
1

| nowrap="nowrap" style="width:284px;height:20px;" |
Conflict deaths computation

| style="width:71px;height:20px;" |
0.5885

| nowrap="nowrap" style="width:158px;height:20px;" |
Internal War magnitude

| style="width:82px;height:20px;" |
.5501

| style="width:70px;height:20px;" |
.0991

|-
| nowrap="nowrap" rowspan="2" style="width:32px;height:20px;" |
2

| nowrap="nowrap" style="width:284px;height:20px;" |
Police violence deaths computation

| style="width:71px;height:20px;" |
0.1447

| nowrap="nowrap" style="width:158px;height:20px;" |
Log of homicides

| style="width:82px;height:20px;" |
.25879

| style="width:70px;height:20px;" |
-3.3145

|-
| nowrap="nowrap" style="width:284px;height:20px;" |
Police violence deaths computation

| style="width:71px;height:20px;" |
0.1447

| nowrap="nowrap" style="width:158px;height:20px;" |
Log of corruption

| nowrap="nowrap" style="width:82px;height:20px;" |
0.28308

| style="width:70px;height:20px;" |
-3.3145

|-
| nowrap="nowrap" rowspan="2" style="width:32px;height:20px;" |
3

| nowrap="nowrap" style="width:284px;height:20px;" |
Interpersonal Violence Deaths computation

| style="width:71px;height:20px;" |
0.21

| nowrap="nowrap" style="width:158px;height:20px;" |
Youthbulge

| style="width:82px;height:20px;" |
1.04344

| style="width:70px;height:20px;" |
-10.5462

|-
| nowrap="nowrap" style="width:284px;height:20px;" |
Interpersonal Violence Deaths computation

| style="width:71px;height:20px;" |
0.21

| nowrap="nowrap" style="width:158px;height:20px;" |
GINI

| style="width:82px;height:20px;" |
2.4341

| style="width:70px;height:20px;" |
-10.5462

|}

After this, the total number of deaths are calculated for each category. For this purpose, we first calculate the total populations for adult males, women and children from the population model as '''AdultMaleTerm''', '''WomenTerm''' and '''ChildrenTerm''' respectively. Next, we calculate the total number of deaths for each of the categories and apply the additive parameters on total deaths ('''''svdthsadd''''') as follows,

:<math>SVDTHSOTHERINTERTOT_{R}=(SVDTHSOTHERINTERPERSON_{R}/100000)*AdultMaleTerm)+svdthsadd_{R,5}</math>

:<math>SVDTHSPOLICSTOT_{R}=(SVDTHSPOLICS_{R}/100000)*POP_{R})+svdthsadd_{R,3}</math>

:<math>SVDTHSWOMENANDCHILTOT_{R}=(SVDTHSWOMENANDCHILDREN_{R}/100000)*(WomenTerm_{R}+ChildrenTerm_{R}))+svdthsadd_{R,3}</math>

:<math>SVDTHSCONFLICTTOT_{R}=(SVDTHSCONFLICT_{R}/100000)*POP_{R})+svdthsadd_{R,2}</math>

:<math>SVDTHSSELFHARMTOT_{R}=(SVDTHSSELFHARM_{R}/100000)*POP_{R})+svdthsadd_{R,1}</math>

After this stage, we calculate the total deaths from societal violence as a simple sum of each of the above categories,

:<math>SVDTHSSOCIETALVIOLENCETOT_{R}=(SVDTHSCONFLICTTOT_{R}+SVDTHSOTHERINTERTOT_{R}+SVDTHSPOLICSTOT_{R}</math>

<math>+SVDTHSWOMENANDCHILTOT_{R}+SVDTHSSELFHARMTOT_{R})+ svdthsadd_{R,6}</math>

Because we have applied additive parameters above, we perform a recalculation of the total death rates using the total number of deaths from each category of violence.

We now calculate the total death rate from societal violence,

:<math>SOCIETALVIOLENCEDEATHS_{R}=(SVDTHSSOCIETALVIOLENCETOT_{R}/POP_{R} )*100000</math>

Finally, the homicide index is calculated using each of the above except self-harm. The contribution of each term to the homicide index can be changed using the parameter '''''svindexm'''''. Each term is set to a value of 1 in the Base Case.

== Policy Equations: Government Expenditures ==

The fiscal model of IFs is quite simple and builds on the computation of government consumption (GOVCON) in the economic model.

IFs expenditures fall into six categories: military, health, education, research and development, other, and foreign aid. IFs divides total government consumption (GOVCON) into these five destination sectors (GDS) with a vector of government spending coefficients (GK) based on initial conditions. The user can change that default pattern of government spending over time with a multiplier parameter (gdsm). The model normalizes the allocation to assure that the money spent is no more or less than total government consumption.

The last category of spending complicates the allocation of spending to destination categories. It is traditional not to think of foreign aid in terms of its percentage of the governmental budget (as we often think of defense or educational expenditures), but to think of it in terms of a percentage of the GDP. For instance, the United Nations has called for foreign aid spending equal to 0.7% (earlier 1.0%) of GDP of donor countries. Moreover, for some governments, foreign aid is not an expenditure, but a receipt and an addition to government revenues.

Therefore IFs actually calculates foreign aid expenditures and receipts first and fixes those amounts (see the [[Socio-Political#Policy_Equations:_Foreign_Aid|foreign aid equations]]). It then allocates the amount of government spending that remains in the coffers of aid donors (or the augmented amount available to aid recipients) among the other categories, normalizing the allocation to the sum of the coefficients in those other categories.

:<math>GDS^t_{\gamma,g}=GOVCON_{\gamma}*GK^{t-1}_{\gamma,g}*\mathbf{gdsm}_{\gamma,g}</math>

where

:<math>GK^{t-1}_{\gamma,g}=\frac{\mathbf{GDS}^{t-1}_{\gamma,g}}{\mathbf{GOVCON}^{t-1}_{\gamma}}</math>

There are several forward linkages of government spending that are important. A mortality multiplier (MORTMG) is computed for the demographic model, using changes in health spending from the initial year and a parameter of the impact of that spending (elashc).

:<math>MORTMG_{\gamma}=1-(\frac{GDS_{\gamma,g=health}}{GDP_{\gamma}}-\frac{\mathbf{GDS}^{t=1}_{\gamma,g=health}}{\mathbf{GDP}^{t=1}_{\gamma}})*\mathbf{elashc}</math>

Three of the forward linkages carry information on spending to the calculation of multifactor productivity in the economic production function, for additive rather than multiplicative use. One variable tracks change in education spending (CNGEDUC), modified by an elasticity of education on MFP (elmfped) and carries it forward. Another tracks changes in health spending (CNGHLTH) using a parameter (elmfphl). The third tracks changes in R&D spending with a parameter of impact (elmfprd). In each case there is a lag involved because of computational sequence.

:<math>CNGEDUC^{t-1}_{\gamma}=(\frac{GDS_{\gamma,g=educ}}{GDP_{\gamma}}-\frac{\mathbf{GDS}^{t=1}_{\gamma,g=educ}}{\mathbf{GDP}^{t=1}_{\gamma}})*\mathbf{elmfped}</math>

:<math>CNGHLTH^{t-1}_{\gamma}=(\frac{GDS_{\gamma,g=health}}{GDP_{\gamma}}-\frac{\mathbf{GDS}^{t=1}_{\gamma,g=health}}{\mathbf{GDP}^{t=1}_{\gamma}})*\mathbf{elmfphl}</math>

:<math>CNGRAND^{t-1}_{\gamma}=(\frac{GDS_{\gamma,g=R\&D}}{GDP_{\gamma}}-\frac{\mathbf{GDS}^{t=1}_{\gamma,g=R\&D}}{\mathbf{GDP}^{t=1}_{\gamma}})*\mathbf{elmfprd}</math>

Because essentially of an older variable form for the education term that is still used in the agricultural model’s production function, the first of the three terms is transferred to that older variable (LEFMG).

:<math>LEFMG^{t-1}_{\gamma}=CNGEDUC^{t-1}_{\gamma}</math>

== Policy Equations: Foreign Aid ==

IFs uses a "pool" approach to aid (AID) rather than indicating bilateral flows from particular donors to particular recipients. That is, all aid from all donors flows into the pool and then all recipients draw proportions of the pool.

IFs uses the aid value parameter (AIDDON) to calculate the aid (AID) from donors and AIDREC to calculate the targeted aid to recipients. The pool of aid donations determines the actual total level of interstate aid flows, however, and is allocated among potential recipients according to the proportions targeted for each.

:<math>AID_{\gamma}=\frac{GDP*(\mathbf{aidrec}_{\gamma}-\mathbf{aiddon}_{\gamma})}{100}</math>

Aid outflows are negative and the total aid pool given (AIDP) is the sum of the negative flows, while the total desired aid of recipients (AIDR) is the sum of positive flows.

:<math>AIDP=\sum^R-AID_{\gamma}</math> if <math>AID_{\gamma}<1</math>

:<math>AIDR=\sum^RAID_{\gamma}</math> if <math>AID_{\gamma}>1</math>

A recomputation of aid for recipients distributes the aid pool across their demands.

:<math>AID=AIDP*\frac{AID_{\gamma}}{AIDR}</math> if <math>AID_{\gamma}>1</math>
: 

= References =

<references /><references />

Environment

2026-08-20T22:16:52Z

Megan.Livengood:

Please cite as: Hughes, Barry B. 2016. "IFs Environment Model Documentation." Working paper 2016.03.21. Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <https://pardee.du.edu/wiki/Environment>

Further information on this topic is provided in a [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_11 dedicated chapter], which offers additional context, analysis, and supporting information.

Most of the environmental elements of the model are included within other modules, such as [[Economics|Economy]] and [[Agriculture|Agriculture]]. Please see those modules for more information, or click through the links below to learn more about how the IFs model can help environment-related analysis. 

= Structure and Agent System: Environment =

{| class="tableGrid" style="width:100%;" cellspacing="0" cellpadding="5" border="1"
|-
| style="width: 50%" | <div>'''System/Subsystem'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Environment (e.g. CO2, water)</div>
|-
| style="text-align: left" | <div>'''Organizing Structure'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Systemic Accounting</div>
|-
| style="text-align: left" | <div>'''Stocks'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Atmospheric carbon</div><div> </div><div>Oceanic carbon</div><div> </div><div>Forest area</div><div> </div><div>Renewable water resources</div>
|-
| style="text-align: left" valign="center" | <div>'''Flows'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Annual Emissions</div><div> </div><div>Water Use</div>
|-
| style="text-align: left" | <div>'''Key Aggregate ''' '''Relationships '''</div><div>(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Oceanic absorption of CO2</div><div> </div><div>Global temperatures with CO2</div>
|-
| style="text-align: left" valign="center" | <div style="text-align: left">'''Key Agent-Class Behavior ''' '''Relationships'''</div><div style="text-align: left">(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Governments and environmental policies regarding emissions</div><div> </div><div>Farmers and water use with agriculture </div>
|}

= Dominant Relations: Environment =

== Environment: Dominant Relations ==

Atmospheric carbon dioxide is function of emissions from fossil fuel burning. Water use is primarily a function of agricultural sector size (and therefore on irrigation). Forest area is dependent upon the rate of conversion of forest to crop land and grazing area.

For a causal diagram see [[Environment#Environment_Flow_Charts|Environment Flow Charts Overview]].

For equations see [[Environment#Environment_Equations|Environment Equations Overview]].

== Key dynamics are directly linked to the dominant relations ==

The energy submodel determines fossil fuel use, and the agricultural model determines agricultural sector size and land conversion patterns. See those models for discussion of dominant patterns and of control parameters.

== Environment: Selected Added Value ==

The larger environmental model provides a more extended model of carbon dioxide, including oceanic absorption rates and possible impact of build-up on global temperature and agricultural patterns.

= Environment Flow Charts =

=== Overview ===

Among the most important elements of the "environmental submodel," which is imbedded in the other portions of the model, is the calculation of atmospheric carbon dioxide levels and global warming.

[[File:Envt1.gif|frame|center|Visual representation of environment submodule]]

For detail, see the equations on [[Environment#Greenhouse_Effect_and_Climate_Change|Greenhouse Effect and Climate Change]].

To look at deforestation, look at the way in which [[Agriculture#Agricultural_Production|Agricultural Production]] leads to changing land use. 

= Environment Equations =

=== Overview ===

Many environmental computations take place within the economic module. This is true for topics, such as:

== Greenhouse Effect and Climate Change ==

The beginning point for examining the greenhouse effect is calculation of the percentage increase in atmospheric carbon dioxide (C02PER). This figure is a percentage of the pre#industrial CO2 level, not of the total atmosphere. The model first calculates annual increase in atmospheric carbon from energy use (CARANN) and adds it to a cumulative tracking of carbon (SACARB). That increase depends on global production (WENP) in the fossil fuel categories (oil, gas and coal). The coefficients representing tons of carbon generated per barrel of oil equivalent burned (CARFUELn) multiply those fossil fuel totals (coefficients calculated from the IPCC 1995 report). The oceans and other sinks annually absorb an exogenously specified amount of atmospheric carbon (CARABR) and that retards the accumulation. Deforestation (or reforestation) has an impact via another parameter (CARFORST), the value of which was calculated using deforestation estimates from Vital Signs (Brown, Flavin, and Kane, 1996) and figures for the contribution of deforestation to CO2 emissions from the IPCC. The ultimate value was taken from [[Introduction_to_IFs#IFs_Bibliography|Mori and Takahaashi (1997: 6)]]. For an understanding of this process and data underlying the parameters see the report of the [[Introduction_to_IFs#IFs_Bibliography|Intergovernmental Panel on Climate Change (IPCC)]] and [[Introduction_to_IFs#IFs_Bibliography|Flavin (1996)]]. See also [[Introduction_to_IFs#IFs_Bibliography|Repetto and Austin (1997)]] for an outstanding analysis of models used to investigate climate protection.

:<math>CARANN=WENP_{e-1}*\mathbf{carfuel1}+WENP_{e-2}*\mathbf{carfuel2}+WENP_{e-3}*\mathbf{carfuel3}</math>

:<math>SACARB=SACARB^{t-1}+CARANN+(WFORST^{t-1}-WFORST)*\mathbf{carforst-carabr}</math>

where

:<math>SACARB^{t-1}=\mathbf{carinit}</math>

The percentage increase in atmospheric carbon relative to pre-industrial levels (CO2PER) depends on the accumulated atmospheric level of carbon (billion tons) and the pre-industrial level of carbon in the atmosphere by weight (CARPREIN).

:<math>CO2PER=\frac{SACARB-\mathbf{carprein}}{\mathbf{carprein}}*100</math>

We can calculate the atmospheric level of carbon dioxide in parts per million (CO2PPM) from these figures, if we know the pre-industrial level of carbon dioxide in parts per million (CO2PREIN).

:<math>CO2PPM=\mathbf{co2prein}+\mathbf{co2prein}*\frac{CO2PER}{100}</math>

We can use a table function to determine the average world temperature (WTEMP) in Centigrade from the atmospheric carbon dioxide level in parts per million (based on figures provided by the IPCC).

:<math>WTEMP=\mathbf{A}nalFunc(CO2PPM)</math>

Finally, we must compute the increase to overall energy prices (CarTaxEnPriAdd) that carbon taxes cause, because total energy demand will respond to the total price. The increase will depend on the carbon tax per fossil fuel and the production level of fossil fuels in the overall pattern of energy production.

:<math>CarTaxEnPriAdd_r=\frac{\sum^3_{e-1}ENP_{r,e}-\mathbf{carfuel_e}*carbtax_r}{\sum^3_{e-1}ENP_{r,e}}</math>

== Water ==

IFs calculates the water use per capita (WATUSEPC) and the total water use (WATUSE) for each model region. The biggest water use for most countries is agricultural (on a global basis 65% of freshwater use, according to Postel, 1996: 13). IFs uses a table function that relates change in per capita use to change in agricultural production per capita.

:<math>WATUSEPC_r=WATUSEPC^{t-1}_r*\frac{\mathbf{TF}(\frac{AGP_{r,f-1}}{POP_{\gamma}})}{\mathbf{TF}(\frac{AGP^{t-1}_{r,f-1}}{POP^{t-1}_{\gamma}})}</math>

:<math>WATUSE_r=WATUSEPC_r*\frac{POP_r}{1000}</math>

== Advanced Sustainability Analysis ==

The Advanced Sustainability Analysis (ASA) is a framework developed by the Finland Futures Research Centre (FFRC), and the partial implementation in IFs was in cooperation with the FFRC within the TERRA project. For further information on ASA see: Kaivo-oja, Jari, Jyrki Luukhanen, and Pentti Malaski (2002). "'Methodology for the Analysis of Critical Industrial Ecology Trends: an Advanced Sustainability Analysis of the Finnish Economy' " Turku, Finland: Finland Futures Research Centre.

The ASA builds on resource use or emissions calculations such as those for annual carbon emissions. The implementation in IFs represents four different environmental impact areas:

#Fossil fuel use
#Carbon emissions
#Deforestation
#Water use

The raw values for each environmental impact are put into the ASA raw value matrix (ASARAW), drawing upon variables from elsewhere in IFs.

:<math>ASARAW_{\gamma,1}=ENP_{\gamma,e-oL}+ENP_{\gamma,e-gas}+ENP_{\gamma,e-coal}</math>

:<math>ASARAW_{\gamma,2}=CARANN_{\gamma}</math>

:<math>ASARAW_{\gamma,3}=FOREST^{t-1}_{\gamma}-LD^t_{\gamma,l-Forest}</math>

:<math>ASARAW_{\gamma,4}=WATUSE_{\gamma}</math>

Within each area there are four environmental impact views, including the raw impact view shown above. The views are:

#Raw values of impact (e.g. ASARAW, 2 for raw carbon emissions)
#Impact per unit of GDP (e.g. ASAGDP, 2 for carbon emissions per unit of GDP)
#Impact per unit of population (e.g. ASAPOP, 2 for carbon emissions per unit of POP)
#Impact per member of the labor force (e.g. ASALAB, 2 for carbon emissions per unit of LAB)

The equations below illustrate those for views, using carbon emissions. The other three sets for the other three impact areas would be completely parallel.

:<math>ASARAW_{\gamma,2}=CARANN_{\gamma}</math>

:<math>ASAGDP_{\gamma,2}=\frac{CARANN_{\gamma}*1000}{GDP_{\gamma}}</math>

:<math>ASAPOP_{\gamma,2}=\frac{CARANN_{\gamma}*1000}{POP_{\gamma}}</math>

:<math>ASALAB_{\gamma,2}=\frac{CARANN_{\gamma}*1000}{LAB_{\gamma}}</math>

In addition, there are calculations within each view of dematerialization over time. Dematerializations are calculated within each impact area (a) relative to raw impact (ASARAWDMAT), to GDP (ASAGDPDMAT), to population (ASAGDPDPOP), and to labor (ASAGDPDMAT)

:<math>ASARAWDMAT_{\gamma,\alpha}=\frac{ASARAW^t_{\gamma,\alpha}-ASARAW^{t-1}_{\gamma,\alpha}}{ASARAW^{t-1}_{\gamma,\alpha}}</math>

:<math>ASAGDPDMAT_{\gamma,\alpha}=\frac{ASAGDP^t_{\gamma,\alpha}-ASAGDP^{t-1}_{\gamma,\alpha}}{ASAGDP^{t-1}_{\gamma,\alpha}}</math>

:<math>ASAPOPDMAT_{\gamma,\alpha}=\frac{ASAPOPDMAT^t_{\gamma,\alpha}-ASAPOPDMAT^{t-1}_{\gamma,\alpha}}{ASAPOPDMAT^{t-1}_{\gamma,\alpha}}</math>

:<math>ASALABDMAT_{\gamma,\alpha}=\frac{ASALAB^t_{\gamma,\alpha}-ASALAB^{t-1}_{\gamma,\alpha}}{ASALAB^{t-1}_{\gamma,\alpha}}</math>

Gross rebounds are also calculated for the ASA system. They are basically the raw impact times the growth in either GDP, population, or labor.

:<math>ASAGDPGRRB_{\gamma,1}=ASAGDP_{\gamma,\alpha}*(GDP^t_{\gamma}-GDP^{t-1}_{\gamma})/1000</math>

:<math>ASAPOPGRRB_{\gamma,1}=ASAPOP_{\gamma,\alpha}*(POP^t_{\gamma}-POP^{t-1}_{\gamma})/1000</math>

:<math>ASALABGRRB_{\gamma,1}=ASALAB_{\gamma,\alpha}*(LAB^t_{\gamma}-LAB^{t-1}_{\gamma})/1000</math>

Finally, there are three measures of cumulative change created for the display system, once for each of the GDP, population, and labor bases of the system.

:<math>ASAGDPCUMCHG_{\gamma}=\frac{GDP^t_{\gamma}-GDP^{t-1}_{\gamma}}{GDP^{t-1}_{\gamma}}*100</math>

:<math>ASAPOPCUMCHG_{\gamma}=\frac{POP^t_{\gamma}-POP^{t-1}_{\gamma}}{POP^{t-1}_{\gamma}}*100</math>

:<math>ASALABCUMCHG_{\gamma}=\frac{LAB^t_{\gamma}-LAB^{t-1}_{\gamma}}{LAB^{t-1}_{\gamma}}*100</math>

It is recommended that the model user look at the specialized display for ASA in order to see the variables of the ASA system most easily.

Equations on deforestation, however, exist in the agricultural model. See [[Agriculture#Changes_in_Urban_Land_from_Income_and_Population_Changes|Agricultural Land Use Dynamics]].

Energy

2026-08-20T22:13:09Z

Megan.Livengood:

Population

2026-08-20T22:02:47Z

Megan.Livengood:

Please cite as: Hughes, Barry B. 2014. "IFs Population Model Documentation." Working paper 2014.03.05.b. Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <https://pardee.du.edu/wiki/Population>

Further information on this topic is provided in a [https://link.springer.com/chapter/10.1007/978-3-032-22084-4_6 dedicated chapter], which offers additional context, analysis, and supporting information.

The population sub-model of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980)<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>, but has changed much over time. In particular, José Solórzano and Randall Kuhn have made many contributions to its development.

The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts: one for infants, 20 of five-year size, and one for all individuals of age 100 or older. A major advantage of five-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.

Because extensions of life expectancy are occurring steadily and there is at least the possibility of substantial breakthroughs, the IFs project has also created the option of extending the number of cohorts from 22 up to as many as 42 (allowing separate representation of age categories up to 200+). The capability is normally turned off, but instructions for turning on extended aging can be found [[Population#Demographic_Flow_Charts|here]].

= Structure and Agent System: Demographic =

{| class="tableGrid" style="width:100%;" cellspacing="0" cellpadding="5" border="1"
|-
| style="width: 50%" | <div>'''System/Subsystem''' </div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Demographic</div>
|-
| style="text-align: left" | <div>'''Organizing Structure'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Cohort-component</div>
|-
| style="text-align: left" | <div>'''Stocks'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Population by age-sex</div>
|-
| style="text-align: left" | <div>'''Flows'''</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Birth, death, migration</div>
|-
| style="text-align: left" | <div>'''Key Aggregate ''' '''Relationships '''</div><div>(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" | <div>Life expectancy (from health model)</div>
|-
| style="text-align: left" | <div style="text-align: left">'''Key Agent-Class Behavioral ''' '''Relationships'''</div><div style="text-align: left">(illustrative, not comprehensive)</div>
| style="text-align: left; padding-left: 10px" align="center" |
Household fertility and migration

|}

Humans as individuals within households interact in larger demographic systems or structures. The computer model should represent the behavior of such households, such as decisions to have children or to emigrate. And it should represent the larger demographic structures that incorporate the decisions of millions of such households. A typical approach to representing such demographic systems is through age-sex cohort distributions (see the figure below showing an example from the model). IFs also uses fertility and mortality distributions by age and sex and tracks migration across countries.[[File:Pop1.png|frame|center|Population pyramid for India (2010).]]

Demographers have widely accepted the representation of demographic systems and the development of demographic models with cohort-component structures. In fact, the United Nations, the U.S. Census Bureau, and the International Institute for Applied Systems Analysis (IIASA), pre-eminent demographic forecasting institutions, all use cohort-component modeling (O’Neill and Balk 2001)<ref>O’Neill, B. C., & Balk, D. (2001). World population futures (Vol. 56). Population Reference Bureau. Retrieved from http://auth.prb.org/Source/ACFAC56.pdf</ref>.

= Dominant Relations: Population =

 The dominant population (POP) equation is a simple addition of births (BIRTHS) at the bottom of the cohort distribution, subtraction of deaths (DEATHS) from each population cohort, and advance of people to the next cohort over time.

The following key dynamics are directly linked to the Dominant Relations:

*Births are primarily a function of the total fertility rate (TFR), which in the longer term responds especially to education level of the adult population. The model user has direct control over TFR with a multiplier ('''''tfrm'' '''), but also much control for low fertility countries with a parameter specifying long-term stabilization level and lower boundary for fertility ('''''tfrmin'' '''). There is also a secular trend reduction in fertility (controlled by '''''ttfrr'' ''').
*Deaths are primarily a function of life expectancy (LIFEXP), itself computed within the IFs health model where, like fertility, it responds in the long run to adult education and also to GDP per capita and technology change. The model user has direct control over all deaths with a mortality multiplier ('''''mortm'' ''') and over those specific to a cause of health with an alternative multiplier ('''''hlmortm'' '''). There is also a secular trend reduction in mortality (controlled by '''''tmortr'' ''').

The larger demographic model in combination with the health model provides representation of and control over migration; the fertility impact of infant mortality and contraception use rates; and the mortality impact of many factors including undernutrition, smoking rates, and indoor air pollution from open burning of solid fuels.

= Demographic Flow Charts =

=== Overview ===

The demographic model represents the population of each geographic unit in terms of 22 cohorts (infants, five-year intervals up to age 99, and those aged 100 and older), separately for females and males. An age distribution records the population in each cohort and sex category. The sum across all cohorts in the age distribution and both sexes is the total population. A fertility distribution determines births, which are added to the bottom of the age distribution, while a mortality distribution determines deaths, which are subtracted from the appropriate cohort of the age distribution.

Those who might like to turn on the extension of age-cohort representation, to as many as 42, can do so by making changes in the IFsInit table of the IFsInit.mdb file.  Specifically, the  NCohorts field can be changed to as many cohorts as 42 and the NAges field can be changed up to 200.  Registering these changes requires a rebuild of the Base Case (see documentation of Extended Features).

The population model is central to many broader dynamics of IFs. Two key feedback loops drive its own dynamics. The first is a positive feedback loop around fertility, linking population and births (causing population to drive exponentially upward if nothing else changes), while the second is a negative loop around mortality, linking population and deaths (causing population to decline). This second loop actually runs through the health model of IFs where deaths are computed (switching the control parameter '''''hlmodelsw'' ''' from 1 to 0 would, however, cause the model to revert to an earlier formulation in which life expectancy was computed as function of GDP per capita and controlled the death rate and deaths; it would turn off the health model's impact).  A Malthusian variation of the negative feedback loop involving deaths may be of interest to those who believe that food supplies do or will play an important role in population dynamics (as they clearly do in countries with very low nutritional levels) by raising mortality rates, especially of children. See the topic on nutrition.  Whether population rises or falls depends on the relative strength of those two loops.

The easiest and most often used scenario handles for the population model are a multiplier on the total fertility rate (the number of children borne by an average woman in a lifetime), namely '''''tfrm'' ''', a multiplier on the total mortality rate, '''''mortm'' ''', and a multiplier on mortality by cause, '''''hlmortm'' '''.[[File:Pop2.png|frame|right|Population sub-module overview.]]

A large number of indicators are calculated in IFs from the age distribution:

*the median age of the country's population (POPMEDAGE)
*population aged 15 to 65 (POP15TO65)
*population above age 65 (POPGT65)
*population below age 15 (POPLE15)
*population pre working age (POPPREWORK), controlled by the parameter specifying the work starting age ('''''workageentry'' ''')
*population post working age (POPRETIRED), controlled by the parameter specifying the retirement age ('''''workageretire''''')
*population within the working years (POPWORKING)
*the potential support ratio, or the population from 15 to 64 over that above 65 (POTSUPRAT)
*an indicator of the youth bulge or the population from 15 to 29 as a portion of that 15 and above (YTHBULGE)

In addition there are a number of indicators calculated from the size of country populations:

*the growth rate of population (POPR)
*the world population (WPOP)
*growth in the world population (WPOPR)

More description is available on the dynamics around fertility and mortality as well as several specialized topics on topics such as nutrition levels and migration.

== Fertility Detail ==

The central indicator of fertility is the total fertility rate (TFR), the number of children that the average woman will bear throughout her life. Fertility generally decreases in the long run as deep or distal drivers such as GDP per capita (from the economic model) or formal years of education of adults (EDYRSAG15 from the education model) increase; our own analysis suggested the use of education years, a result that Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref> reinforced.

In addition there are more proximate drivers, some of which can change more rapidly than GDP per capita or education levels and thereby affect fertility rate.  We represent two, namely infant mortality rates (INFMOR) and contraception usage (CONTRUSE).  The health model of IFs determines infant mortality rates.  Sudden change in those do not, however, immediately affect fertility rates and we smooth changes in rates so as to introduce an approximately 10-year lag, consistent again with the findings of Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref>. Based on cross-sectional analysis the population model of IFs forecasts the percentage of population using modern contraception as a function of GDP per capita at purchasing power parity (GDPPCP).  We found, however, that there was additional growth over time and the parameter for time-related usage growth ('''''tconr'' ''') controls that. The user can also change contraception use via an exogenous multiplier ('''''contrusm'' ''').[[File:Fertility.png|frame|right|Overview of fertility in population sub-module.]]

Although those three distal and proximate drivers substantially determine the forecasts of fertility rate, there are several additional elements that influence it.  First, we calculate the historical growth rate of TFR (TFRgr) and use that internal variable in the first few years so as to maintain an inertial pattern of change in TFR consistent with history; we phase out that inertial element in favor of endogenously computed factors over a 10-year period.  Second, we have used another time dependent parameter ('''''ttfrr'' ''') to allow  introduction of  somewhat faster or slower growth rates in TFR.  Mostly we have used that as a tuning parameter to adjust our long-term global population forecasts to be more consistent with those of others such as the UN Population Division or the International Institute of Applied Systems Analysis.  Normally that parameter is very small or zero.  Third, we provide the user with a direct multiplier on the fertility rate ('''''tfrm'' ''').  And finally, not knowing what the long-term minimum fertility rate might be in a world where for many countries rates have fallen very substantially below replacement rates, we provide such a minimum ('''''tfrmin'' ''').  Since some countries are below most expected minimums and therefore below common values of that parameter, we phase that minimum in over time with a convergence parameter ('''''tfrconv'' '''), which serves double duty by also marking the number of years of convergence of TFR itself to the values that the function with distal and proximate drivers produces. 

== Mortality Detail ==

The current default representation of mortality and life expectancy in IFs relies entirely on the health model so please see its documentation.  That model computes deaths by age and sex and uses those to compute total deaths (DEATHS) as well deaths by category of cause (DEATHCAT).  It also computes life expectancy (LIFEXP) and infant mortality (INFMOR), variables of importance to the population model.  Two parameters in the health model allow multiplicative intervention with respect to total deaths ('''''mortm'' ''') and those by cause ('''''hlmortm'' ''').[[File:Mortality detail.png|frame|right|Overview of mortality in population sub-module.]]

There is, however, a legacy representation of mortality in IFs (available if the health model is switched off with '''''hlmodelsw'' '''=0) that reverses that logic and uses the model's calculation of an initial estimate of life expectancy to drive mortality by age and sex (not cause). Life expectancy normally increases and mortality normally decreases as GDP per capita rises (see the economic model) or as the income share of the poorest 20% of the population increases. In the legacy representation, the initial calculation of life expectancy is imposed on an initial mortality distribution that provides a country-specific age and sex profile of mortality.

A number factors then further affect and alter the mortality distribution in the legacy mortality structure. These include deaths related to warfare (CIVDM), to AIDS, and possibly to starvation (via infant mortality, because it is primarily the very young who are at risk). In addition, the user of the model may introduce greater or lesser mortality via a mortality multiplier.

At the same time, however, increases in life expectancy shift the mortality distribution from its initial condition towards an ultimate life (survivor) table as life expectancy approaches that built into the ultimate life table (approximately 85 in the 1998 revision of the UN population tables).

Once the mortality distribution adjustments are made and deaths can be computed from it, the life expectancy is recomputed.

[[File:Mortdetail.png|frame|center|Visual representation of mortality distribution]]

== Nutrition ==

As noted in the overview of demographics, there is an element of mortality calculations that has historically captured considerable attention from many of those interested in long-term population forecasting, going back to at least Malthus's elaboration of the negative feedback loop linking undernutrition or starvation to higher death rates.  Donella Meadows, et al. (1972) popularized this in their discussion of ''The Limits to Growth.<ref>Meadows, Donella H., Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. 1972. The Limits to Growth. New York: Universe Books.</ref>''

In the current default representation of the model, with the health model turned on, that health model computes the rate of undernutrition among children (MALNCHP), the resultant total numbers of children undernourished (MALNCHIL), and the deaths associated with undernutrition.  Undernutrition in the health model is a function of calories, but also of access to improved sanitation and clean water.  Health interventions, including those to reduce diarrhea, can supplement greater access to calories to reduce the undernutrition and associated mortality.

In the legacy version of the population model there is a cruder and more overtly Malthusian representation.  A comparison of calories available with those needed can generate starvation deaths. Historical and contemporary data do not exist, however, to support calculation of starvation (the deaths of those who are severely malnourished are normally attributed to various diseases that prey on them, such as diarrhea among children).  For this reason and because of the considerably greater sophistication of the health model, we recommend leaving the health model engaged.[[File:Nutrition detail.png|frame|center|526x432px|Overview of nutrition in population sub-module.]]

== Migration ==

Although for most countries it is less important in determining population growth patterns than are fertility and mortality rate, migration is extremely important for some, such as those in the Arabian/Persian Gulf region.  Because long-term migration is, however, very difficult to forecast, we rely on exogenous scenarios of migration rate ('''''migrater'' ''') to drive forecasts in IFs.  Users can also affect global migration patterns with a multiplier on global rates ('''''wmigrm''''').   On a global basis immigration and emigration are required to balance, and the number of migrants (MIGRANTS) in IFs is balanced, resulting in a computation also of an endogenous migration rate (MIGRATE).

Although data on age and sex of migrants are poor and certainly vary considerably by countries by origin and target, a general representation of the portion of migrants who are male ('''''malemigr''''' ) is set as a parameter. In addition, the migration rate by age is represented by an internal parameter set, ''migratebyage'' , read from a file and not available for users to change via the model interface.  As rules of thumb, most migrants are male and disproportionately young adults. [[File:Migration.png|frame|center|Overview of migration in population sub-module.]]

The net of foreign-born population within a country relative to the size of a country’s diaspora abroad (POPFOREIGN) represents the accumulation of the net inflows of migrants over time.  That population size and the level of GDP per capita determine the net extent of remittances sent or received from abroad.

== Urbanization ==

 IFs does not represent urban and rural populations by age and sex, but does forecast the division in total.  The key driving variable in early model years, internal to the model, is the growth rate of the urban population.  Because that variable is initialized with historical data, it initially introduces an inertial element into the forecast.  But over time the rate of growth in urban population increases or decreases more and more in response to the gap between the actual portion of population that is urban and an expected urbanization rate based on a function driven by GDP per capita at purchasing power parity (GDPPCP).   The growth rate also responds, however, to approaching very high levels of urban population (POPURBAN) as a percentage of the total by slowing down.  Because the model dynamics are built around urban population, rural population (POPRURAL) is essentially a residual. [[File:Urbanization.png|frame|center|Overview of urbanization in population sub-module.]]

There is no parametric control over the growth of urban population in part because the model does not contain any significant forward linkages of urban population size or portion

= Demographic Equations =

=== Overview ===

The population submodel of IFs uses the cohort component analysis approach of many population models, including the studies done by the United Nations (United Nations, 1956<ref>United Nations, Department of Economic and Social Affairs. 1956. Methods of Population Projections by Sex and Age. New York: United Nations, ST/SOA Series A.</ref> and 1977). The structure of the IFs population model drew initially on the World Integrated Model (WIM) or the second generation Mesarovic-Pestel Model (Hughes, 1980<ref>Hughes, Barry B. 1980. World Modeling. Lexington, Mass: Lexington Books.</ref>), but has changed much over time.

The approach relies upon age, fertility, and mortality distributions for each country/region with 22 cohorts - one for infants, 20 of 5-year size, and one for all individuals of age 100 or older. A major advantage of 5-year cohorts is that data sources generally present demographic data in that form. Ideally, however, the cohort size should correspond to the model time step so as to avoid "numerical diffusion," the propagation of change from a five-year cohort to an adjoining cohort in a single year. To prevent such numerical diffusion, IFs actually runs an age distribution with 100 single-year cohorts and advances that over time, collapsing to 22 cohorts only for the calculations of births and deaths.

For help understanding the equations see [[Understand_IFs#Equation_Notation|Equation Notation]].

== Age Distribution ==

The basic structure of the population model is very simple, even if the implementation becomes more complex. The core of the model is fundamentally an accounting system around the age-sex distribution (AGEDST) with 5-year age categories—and an elaboration of that into single year categories (FAGDST)—in which people age over time, with births added into the bottom age category each year and deaths subtracted from the appropriate age and sex category.  The key to long-term dynamics lies primarily within change in the fertility and mortality distributions, with migration playing a secondary role for most countries.

A 5-year cohort fertility distribution (FERDST) multiplies the age distribution (AGEDST) to produce births (BIRTHS). The total fertility rate (TFR), or total number of births expected to a woman during her lifetime, modifies the fertility distribution over time. The fertility distribution itself moves from the initial empirical, country-specific pattern to an ultimate fertility distribution (ULTIMATEFERTILITY) as GDP per capita (PPP) moves towards a specified level (currently $45,000). The ultimate fertility distribution is exogenous to the model in a file and not available for the user to change via the model's interface. We will see the computation of TFR in our discussion of fertility.

:<math>BIRTHS_{r,p} = \sum^C AGEDST_{r,c,p} * FERDST_{r,c} * \dfrac{TFR_r}{TFR_{r,t=1}}</math>

''where''

:<math>FERDST_{r,c} = F(FERDST_{r,c},ULTIMATEFERTILITY_c,GDPPCP_r45)</math>

In the above equation and other documentation of the population model: 

:r=region/country

:c=age category

:p=sex (because s is used elsewhere in the model for economic sector)

:d=cause of death

Deaths (DEATHS) are computed in the health model of IFs, see the documentation of that model.  They are the sum of age, sex, and cause-of-death specific mortality forecasts. Life expectancy (LIFEXP) is also computed in the health model.

There is, however, a legacy model of mortality and deaths that now is very rarely used but can be activated by changing the ''hlmodelsw'' parameter from 1 to 0.  The legacy calculation of deaths parallels that of births in that it relies on a product of the age distribution with a mortality distribution (MORDST). As with fertility, the mortality distribution itself moves from the initial empirical, country-specific pattern to an ultimate mortality distribution as life expectancy moves towards a specified level (currently 85 years).  In the legacy model, life expectancy is computed from the mortality distribution.

Most of the model uses the 5-year age categories of the age distribution (AGEDST).  But 5-year categories can introduce a significant problem when we advance the model over time.  Specifically, it can lead to diffusion of births or deaths too quickly up the distribution (for instance, if a surge of births entered the bottom 5-year category one year, 1/5 of those could potentially move up to the next category the following year already, because a model that only used 5-year categories would not recognize their recent arrival in the category). 

Hence in the first year of the model, we spread the 5-year categories that come to us from UN data into a 1-year or annual age distribution (FAGEDST) using a spline function and use that annual distribution for our accounting dynamics across time. One-fifth of deaths in each 5-year category reduce the appropriate annual age category and those in each age category advance to the next year (all surviving infants advance to age 1). We also add one-fifth of net migration by 5-year category into each underlying single-year category. Births enter the infant category of the age distribution.

Once the full age distribution has been advanced for the next year, it can also be collapsed back into the 5-year cohorts of the age distribution (AGEDST), which is used for the calculations of births and deaths in the next year and for display in the model. The population (POP) is a sum across this distribution.

== Fertility ==

Change in fertility centers on the current value of the total fertility rate (TFR).  IFs determines the TFR and then imposes that on the cohort-specific fertility distribution (FERDST) of the region/country.

IFs uses three key variables to drive TFR forecasts over time.  One of those accounts for the change that typically accompanies long-term development and social evolution. The two principal candidates to represent such change in the long term across all IFs models are GDP per capita at purchasing power parity (GDPPCP) and the years of formal education attained by adults (EDYRSAG15).  Our own analysis and that by Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref> both suggest that the latter is the stronger predictor for TFR.  Frequently in IFs we find (Hughes 2001)<ref>Hughes, Barry B. 2001. "Global Social Transformation: The Sweet Spot, the Steady Slog, and the Systemic Shift,” Economic Development and Cultural Change 49, No. 2 (January 2001): 423-458.</ref> that the relationship between one of those two deep distal drivers and any specific element of social change is logarithmic (that is, social change happens especially rapidly at lower levels of income and education and then saturates) and this is the case in this instance also.  You can see the approximate form of that relationship by examining a scattergram of TFR as a function of EDYRSAG15 in the initial model year or you can look at the multivariate relationship that IFs actually uses (in Scenario Analysis/Change Selected Functions).

In addition to long-term development and the deep or distal variables associated with it, societies are subject to short-term factors, most of which are in turn influenced heavily over time by the distal variables.  These more proximate variables do, however, exhibit patterns of change that are at least somewhat independent of the distal drivers and more dependent on societal choices and policies.  In the case of fertility change, two such variables often identified to be important are the rate of mortality, often infant mortality in particular (INFMORT), and the rate of use of modern contraception (CONTRUSE).

:<math>TFR_r = TFR_{r,t-1}* F(ln(EDYRSAG15_{r,p=total}),LagInfMor_r,CONTRUSE_r) * \mathbf{tfrm_r} * (1+(t-1) * \mathbf{ttfrr})</math>

In the equation we have used a lagged form of infant mortality.  The lag uses 10 percent of the new value for infant mortality and 90 percent of lagged (therefore actually moving average) value; the proportions are subject to change, but were chosen to capture roughly the 10-year lag to peak effect identified by Angeles (2010)<ref>Angeles, Luis. 2010. "Demographic Transitions: Analyzing the Effects of Mortality on Fertility", Journal of Population Economics 23: 99-120. DOI 10.1007/s00148-009-0255-6.</ref>. When such a moving average is initiated with the value of the first year of the model run, rather than with a value computed over an historical period preceding that first year, it gives rise to a pattern of slow change in initial years (values of early years tend to be very close to those of the initial value) and then accelerating change over time up to about the 10th year.  We therefore phase in the effect of the moving average, also over 10 years.

The additional term involving the parameter ''ttfrr'' is used to represent time change that is independent of the relationship estimated via cross-sectional analysis with recent data. There has been a global ideational change with respect to fertility that the term can represent; in addition, it can be a tuning parameter and normally the value is very low in IFs.  Finally in the equation above, the user can adjust a multiplier parameter ''(tfrm)''  from its default value of 1 so as to force higher or lower fertility.

There are also, however, three important algorithmic elements that wrap this equation in more extensive model code.  First, we compute in the model preprocessor the historical growth rate of TFR (TFRgr) and use that to help drive year-to-year change in TFR.  In fact, in the first year the change in TFR is fully driven by that internal variable, but attention to it is phased out over 10 years.  Second, we have captured in the first year of the model forecast the difference between TFR from the function and TFR from the data.  This difference or shift could be viewed as a country-specific fixed effect dependent on variables such as historical paths and cultural factors. We choose, however, to phase it out over a fairly long period of time specified by the parameter ''tfrconv'' .  Often in IFs the reduction of such shift factors is done over a half century or more, and, at the time of this writing, the parameter's value was 100.  Third, total fertility rate is unlikely to shift indefinitely toward zero. In fact, it requires a value of about 2.1 simply to maintain a steady population (unless life expectancies are growing). TFR is therefore bound by a minimum that responds to a global parameter (tfrmin). The equation below represents that long-term bound which is again phased in over a very long period of time and algorithmically raises the fertility of countries below the minimum. 

:<math>TFR_r = AMAX(TFR_r,\mathbf{tfrmin})</math>

The use of modern contraceptives (CONTRUSE) is itself a function of a key distal driver, in this case GDP per capita at purchasing power parity (GDPPCP).The reader may wish to use the model to look also at a scattergram of CONTRUSE against GDPPCP in the initial year. The "actual" level of contraception use depends not only on GDPPCP, but on an exogenous multiplier (''contrusm)'' , and on a temporal (t) upward drift in contraception use related to ideational change again, as well as related technological innovation and diffusion (controlled by ''tconr)'' .

:<math>CONTRUSE_r = F(GDPPCP_r) * \mathbf{contrusm_r} + t * \mathbf{tconr}</math>

Once we have computed the total fertility rate (TFR), the number of births in a given year is a simple function of the fertility distribution and the TFR.

If advances in health very substantially affect life expectancy, they may also affect fertility patterns.  Parameters in IFs allow control of the onset age of fertility (''hltfrageinit'' ), the peak age of it (''hltfragepeak'' ), the age of menopause (''hltfragestop'' ), and the rate of decline from peak to menopause (''hltfragehalflife'' ).  If child-bearing age were greatly extended, it would necessarily lead at some point to a change not only in the peak age of child-bearing, but also the rate of child-bearing at that age (''hltfrpeaklevel'' ), changed from current patterns at a rate controlled in the model by a final fertility parameter (''hltfrconv'' ).

== Mortality: Life Expectancy and Infant Mortality ==

The health model calculates the mortality distribution by country/region, age category, sex, and cause of death (modmordstdet).  This distribution allows the specification of key variables in the population model, including life expectancy (LIFEXP) and infant mortality (INFMOR).  Life Expectancy is computed as a mean average number of years of life given the survival rates in each age group. First we find total mortality by country/region (r), age (c) and gender (p) by adding all 15 types of mortality (d) using modmordstdet  (c,a,g,t). (Note with respect to model code: we actually combine the gender and mortality type subscript into one, with the odd type values representing males and the even type values for females). 

Second we find the average years lived (nax), within the age group, by those who die (per Coale and Demeny 1983<ref>Coale, Ansley and Paul Demeny with Barbara Vaughan. 1983. Regional Model Life Tables and Stable Populations. New York: Academic Press.</ref>, using parameters that came from the arithmetic mean of the separate male and female parameters shown in Preston, Heuveline, and Guillot 2001<ref>Preston, Samuel H., Patrick Heuveline, and Michel Guillot. 2001. Demography: Measuring and Modeling Population Processes. Oxford: Blackwell Publishing.</ref>):

:Infants with mortality >= 0.107 = 0.34 years

:Infants with mortality < 0.107 = 0.049 + 2.742 * (mortality)

:Children 1-4 where infant mortality >= 0.107 = 1.356 years

:Children 1-4 where infant mortality < 0.107 = 1.587 - 2.167 * (infant mortality)

:Everybody else lives 2.5 years (out of 5 possible years).

Third we compute the probability of death (nqx) for each country (c), group age (a), and gender (g) (this is the probability of dying between ages x and x + N, which is period a):

:<math>nqx_{r,c,p}=\frac{N_{c}*TotalMortality_{r,c,p}}{1+(N_{c}-nax_{r,c,p})*TotalMortality_{r,c,p}}</math>

where N is the number of years in the age category  (1 for infants, 4 for children 1-4, and 5 for everybody else), and nax is the number of years lived by those who died, described in the previous step. We're assuming nqx = 1 when we reach our maximum age category (100+ in general).

Fourth we start adding years for each age category (a) in the following way:

:<math>LifeEx_{r,p}=LifeEx_{r,p}+(lx_{r,c,p}*(1-nqx_{r,c,p})*N_{c})+(lx_{r,c,p}*nqx_{r,c,p}*nax_{r,c,p})</math>

Where the first term added to life expectancy is the total number of years (N) lived by those who survive this age category (1 - nqx) given they have survived all previous ages (lx). The second term is the number of years (nax) lived by those who die in this age category (nqx) given they have survived all previous ages (lx).

The probability of surviving until age a is computed as:

:<math>lx_{r,c,p}=lx_{r,c-1,p}*(1-nqx_{r,c-1,p})</math>

where lx at birth is 1.

Infant Mortality is simply calculated as the sum of all our 15 mortality types from internal variable modmordstdet but only for age 0 (infants).

== Mortality: The Legacy Formulation ==

 In the legacy population model (should the use of the health model ever be turned off) an initial value of life expectancy  (LIFEXP) is computed first and used to determine the mortality distribution (mordst, dimensioned by region, age cohort, and sex).   Adjustments are made to the mortality distribution by a number of factors and then life expectancy is recomputed. 

The initial calculation of life expectancy is based on long-term development, namely GDP per capita at purchasing power parity (GDPPCP).  The logarithmic function is modified by an additive term related to the extent of government spending on health (GDS), although that term is very minor in the calculation.

:<math>LIFEXP_{r,p}=F(ln(GDPPCP_{r}))+F(GDS_{r,g=health})</math>

The calculation of life expectancy is wrapped in a substantial algorithmic structure.  For instance, should the formulation suggest decrease in life expectancy over time, the decrease is smoothed via use of a moving average. The impact of government spending is also limited algorithmically.

We impose this initial calculation of life expectancy on the mortality distribution (with the movement towards an ultimate life table that is discussed in connection with the overall logic of the age distribution), by calculating a mortality factor (MFACTOR) that, when applied to all cohorts of the mortality distribution would generate the calculated life expectancy. The multiplier is computed so that the cumulative mortality to the age of life expectancy will ultimately be 0.5.

:<math>MFACTOR_{r}=\frac{0.5}{\Sigma_{c=1}^{LIFEXP}MORDST_{r,c,p}}</math>

We then further modify the mortality distribution and therefore the life expectancy (which we will need to recompute below) by the specification of several additional mortality factors. These include three of the four horsemen of the apocalypse, which tend to have a more immediate, shorter-term impact: starvation deaths, plague or in this case AIDS deaths (AIDSDTHS), and war deaths (using the civilian damage variable, CIVDM, calculated in the social-political module). We build starvation deaths in a recalculated infant mortality (INFMOR), because the youngest are most vulnerable to calorie shortages.

The additional mortality factors also include a parameter that reflects a time-related shift in mortality from medical advance (''tmortr'' ); long-term development (as reflected by GDP per capita) does not capture this additional influence on mortality. Finally, it includes a multiplier on mortality (''mortm'' ) that the user can set as desired to introduce further factors into a scenario.

In the second stage of mortality calculation we compute deaths by cohort.

:<math>DEATHS_{r,c=1,p}=\sum^{G}AGEDST_{r,c=1,p}*(MORDST_{r,c>1,p}+CIVDM_{r}+CLSF_{r}+AIDSDTHSCOH_{r,c,p})*\mathbf{mortm}_{r}*(1+(t-1)*\mathbf{tmortr})</math>

:<math>DEATHS_{r,c>1,p}=\sum^{G}AGEDST_{r,c>1,p}*(MORDST_{r,c>1,p}+CIVDM_{r}+AIDSDTHSCOH_{r})*MFACTOR_{r}*\mathbf{mortm}_{r}*(1+(t-1)*\mathbf{tmortr})</math>

''where''

:<math>AIDSTHSCOH_{r,c,p}=AIDSDEATHS_{r}*\mathbf{maleageportion}*\mathbf{aidsdeathbyage_{c,p}}</math>

The computation of civilian war damage/deaths (CIVDM) is shown in the international political module.

One of the factors above that affects infant deaths is a calorie starvation factor (CLSF). It depends on the ratio of calories available (CLAVAL) from the agricultural model to the calories needed (CLNEED). Details are available with the discussion of the legacy approach to nutrition/malnutrition.

We can now recompute the actual infant mortality, based on the actual infant deaths: 

:<math>INFMOR_{r}=DEATHS_{r,c=1,p}</math>

Finally, we recompute life expectancy based on the entire patterns of deaths across age categories. 

:<math>LIFEXP_{r}=F(DEATHS_{r,c,p})</math>

== Malnutrition: The Legacy Formulation ==

The health model has replaced the legacy formulation for child malnutrition rate or percent of population (MALNCHP) with a representation tied not just to calorie availability but also to access to safe water and sanitation. See documentation on that relationship.  This section documents the earlier and simpler formulation tied only to calories per capita.

In the legacy model IFs has estimated a relationship between calorie availability per capita (CLPC) and the percentage of children (MALNCHP) between the ages of 0-5 who are malnourished. In some countries, notably India, Bangladesh, and Nepal, initial values for this percentage are far from the value predicted by the analytical function representing this relationship. IFs assumes that outliers will converge towards the table function relationship over time (as controlled by the conversion parameter, ''polconv'' ).

IFs uses that relationship to update the percentage malnourished over time and to compute the actual number of malnourished children (MALNCHIL) in population cohorts 1 (infants) and 2 (0-4 years of age).

:<math>MALNCH_{r}=F(CLPC_{r},\mathbf{polconv})</math>

:<math>MALNCHIL_r=(AGEDST_{r,c=1,p}+AGEDST_{r,c=2,p})*MALNCH_r/100</math>

Relatively few models attempt to close the loop between food availability and mortality. (See, for example, Meadows, et. al., 1974<ref>Meadows, Dennis L. et al. 1974. Dynamics of Growth in a Finite World. Cambridge, Mass: Wright-Allen Press.</ref> and Mesarovic and Pestel, 1974<ref>Mesarovic, Mihajlo D. and Eduard Pestel. 1974. Mankind at the Turning Point. New York: E.P. Dutton & Co.</ref>). IFs does so, while recognizing that little is actually known about the linkage. IFs treats calories as the basis for severe malnutrition- or starvation-related deaths. Regional calorie need (CLNEED) is computed by a sum across the age distribution (AGEDST), considering age specific calorie requirements (CLAGE) and an exogenous factor'' (clnf'' ) with which the user can introduce regional variation in needs (or assumptions of regional differences in ability to respond to calorie shortages). 

:<math>CLNEED_{r}=\sum^{C}\sum^{G}AGEDST_{r,c,p}*\mathbf{clage}_{c}*\mathbf{clnf}_{r}</math>

:<math>CLSF_{r}=(1-\frac{CLAVAL_{r}}{CLNEED_{r}})^\mathbf{clexp}</math>

Once the calorie-based starvation factor (CLSF) is computed, with admitted arbitrariness in specification, it is possible to compute actual starvation death levels (SDEATH) in the youngest two cohorts,

:<math>SDEATH_{r}=\sum^{G}\sum_{c=1,2}agedst_{r,c,p}*CLSF_{r}</math>

== HIV/AIDS Mortality: The Legacy Formulation ==

In the legacy version of the population model, mortality from HIV/AIDs was treated separately from other mortality, which was related largely to income growth and increasing life expectancy.  HIV/AIDS was seen to be a special plague-like disease with a likely rise and fall in coming years that should be represented additionally to other mortality.  The HIV/AIDS formulation is still in the legacy code and would be activated if the health model switch (''hlmodelsw'' ) were turned off.  But normally HIV/AIDS is represented (with fundamentally the same logic) in the health model and those with interest should look at that documentation.

== Migration ==

Migration is treated with a pooled approach, which means that the model does not determine the flows between any two countries, but rather the net inward migration (MIGRANTS) to each country, making sure that new inflows and outflows balance globally. It is driven by an exogenous parameter (''migrater'' ), which we derive from the migration forecasts of other organizations such as the UN Population Division or the International Institute of Applied Systems Analysis, specifying the net percentage of the population migrating each year (negative values indicate immigration and positive values indicate emigration).  The user can increase or decrease global migration as a whole with a world migration multiplier, ''wmigrm'' . The first step is to swap the parameter values into an internal model calculation of the migration rate (MIGRATE).

:<math>MIGRATE_{r}=\mathbf{migrater}_{r}*\mathbf{wmigrm}</math>

The full global set of migration rates is unlikely, however, to provide a balanced global total of immigrants and emigrants. The next step is thus to calculate those totals, even though they are likely to be unequal.

:if <math>MIGRATE_{r}>0</math> then <math>SUMIM=\sum^{R}MIGRATE_{r}*POP_{r}</math>

:if <math>MIGRATE_{r}\le{0}</math> then <math>SUMEM=\sum^{R}MIGRATE_{r}*POP_{r}</math>

After calculation of the world sums of immigrants and emigrants, the total world migration is assumed to be the average of the two. Then that total world migration is imposed on net immigrant and net emigrant regions through normalization. 

:<math>WORLDIMEM=\frac{SUMIM+SUMEX}{2}</math>

:if <math>MIGRATE_{r}>0</math> then <math>MIGRANTS_{r}=\frac{MIGRATE_{r}*POP_{r}*WORLDIMEM}{SUMIM}</math>

:if <math>MIGRATE_{r}\le{0}</math> then <math>MIGRANTS_{r}=\frac{MIGRATE_{r}*POP_{r}*WORLDIMEM}{SUMEM}</math>

Although the above equation assures that the global sum of migrants will be zero (immigration equals emigration), it is important to recompute the actual migration rate, so that it represents the true inflow or outflow of migrants after that balancing. Note that the computed migration rates (MIGRATE) will almost certainly be a bit different from the input parameter (migrater).

:<math>MIGRATE_{r}=\frac{MIGRANTS_{r}}{POP_{r}}</math>

The migration specification in IFs is, as indicated above, basically exogenous.  Different series can be pulled from IFsHistSeries.mdb to drive it.  The active series is determined by specification within IFsInit.mdb, Table IFsInit, variables MigrantsTbl and MigrationRateTbl.    For instance, those two variables have values of SeriesForecastNetMigrationUNPD and SeriesForecastNetMigrationRateUNPD to pull in the migration data from the UN Population Division.

== Urbanization ==

 The size of urban population (POPURBAN) in the very near future is probably best forecast by using a growth rate (POPURBGR) computed initially from historic data, but gradually coming to represent the dynamic growth rate of urbanization calculated by the model. The growth rate applied to past urban population provides an initial estimate of urban population each year (PopUrbanGro).

In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%. Moreover, there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population. Thus, a function estimated cross-sectionally against GDP per capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP per capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. 

:<math>POPURBAN_{r}=ConvergeOverTime(PopUrbanGro,PopUrbanTar)</math>

''where''

:<math>PopUrbanGro=POPURBAN_{r,t-1}*(1+POPURBGR_{r,t-1})</math>

''and''

:<math>PopUrbanPor=AnalFunc(GDPPCP_{r})</math>

:<math>PopUrbanTar=POP_{r}*PopUrbanPor</math> with algorithmic modifications for smooth behavior over time and as saturation is approached.

Once the urban population has been updated in each time cycle, it is possible to compute the actual growth rate (POPURBGR), which will then be the starting point for growing urban population (PopUrbanGro) in the next time cycle.

:<math>POPURBGR_{r}=(\frac{POPURBAN_{r}}{POPURBAN_{r,t-1}}-1)*100</math>

== Household Size ==

 Household size (HHSIZE) is a function of the portion of the population that is of pre-work-force-entry age (POPREWORK); the bigger that population that has not begun to work is as portion of the population, the larger is household size.  

:<math>HHSIZE_{r}=\frac{1}{F(\frac{POPPREWORK_{r}}{POP_{r}})}+HHSizeShift_{r}</math>

Internal to the model the denominator of this equation is referred to as the household intensity, which falls as the pre-work age term rises.  Thus the household size rises with the pre-work age term.

There is an additive shift factor calculated in the first year of the model run to assure a match of the calculated and empirical values; that shift factor decays to zero over 100 years.

== Demographic Indicators ==

 Among the indicators computed in the population submodel of IFs are the crude birth rate (CBR) and crude death rate (CDR).

:<math>CBR_r=\frac{BIRTHS_r}{POP_r}*1000</math>

:<math>CDR_r=\frac{DEATHS_r}{POP_r}*1000</math>

Population growth rate (POPR) follows easily from crude death and birth rates.

:<math>POPR_r=\frac{CBR_r-CDR_r}{1000}</math>

Regional population (POP) is simply a sum across age cohorts. 

:<math>POP_r=\sum^CAGEDST_{r,c}</math>

For information and use elsewhere in the model, three computations of sub-portions of the population by age are made (POPLE15, POP15TO65, and POPGT65). [Note: each one of these is slightly misnamed.]

:<math>POPLE15_r=\sum^{14}_0AGEDST_{r,c}</math>

:<math>POP15to65_r=\sum^{64}_{15}AGEDST_{r,c}</math>

:<math>POPGT65_r=\sum^{Oldest}_{65}AGEDST_{r,c}</math>

More recently the IFs model has recognized that the working life span is not uniformly from 15 to 65 across countries or time and has designated country/region specific parameters for age of work entry (''workageentry'' ) and retirement (''workaageretire'' ).   These are used to compute POPPREWORK, POPWORKING, and POPRETIRED.  They also allow the computation of a potential support ratio for the retired population (POTSUPRAT), which is the ratio of those of working population to those of retirement age.

:<math>POTSUPRAT_r=\frac{POPWORKING_r}{POPRETIRED_r}</math>

Another useful indicator is the youth bulge (YTHBULGE), defined as the ratio of the population between ages 15-29 to that aged 15 and above. In general, a ratio of more than 0.4 and especially 0.5 suggests a particularly youthful society and may indicate potential for social instability.

:<math>YTHBULGE_r=\frac{\sum^{29}_{15}AGEDST_{r,c}}{\sum^{Oldest}_{15}AGEDST_{r,c}}</math>

Median age (POPMEDAGE) is another useful indicator and the age distribution (fagedst) can be used to determine that age at which there are equal numbers of people older and younger.

World population (WPOP) and world population growth rate (WPOPR) are simple functions across countries/regions.

:<math>WPOP=\sum^RPOP_r</math>

:<math>WPOPR=\frac{\sum^RPOP_r*POPR_r}{WPOP}</math>

== Data Used ==

 Our data for the population model come from the United Nations Population Division revisions of data and forecasts, released every second year.  We take population by age and sex from that source, as well as historical series for life expectancy, total fertility rate, and infant mortality.  We also pull in their migration data.

Often they present their data values in 5 year categories (1950-1955, . . . , 2095-2099).  To obtain values at specific 5-year intervals, such as 1960 or 2010, we average the values for the two 5-year categories that bracket that year.  To estimate annual values for all years from such categories, for instance for migration numbers, we used a Sprague algorithm to spread the 5 year data (1950-1955, . . . , 2095-2099). With respect to migration, to obtain net migration rates we divided their annualized numbers by annual population data'''.'''

= References  =

<references />

Agriculture

2026-08-20T22:00:48Z

Megan.Livengood: