Agriculture

The most recent and complete agriculture model documentation is available on Pardee's website. Although the text in this interactive system is, for some IFs models, often significantly out of date, you may still find the basic description useful to you.

The IFs agriculture model tracks the supply and demand, including imports, exports, and prices, of three agricultural commodities: crops, meat, and fish. Crops have direct food, animal feed, and industrial uses. Meat and fish have only food use. The agriculture 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, as well as parameters such as the capital elasticity of substitution, 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 agriculture model also has important links to the population and health models, using population forecasts and providing forecasts of calorie availability.

Structure and Agent System: Agriculture

System/Subsystem	Agriculture
Organizing Structure	Partial market equilibrium
Stocks	Capital, labor, accumulated technology, agricultural commodities, land
Flows	Production, loss, consumption, trade, investment
Key Aggregate  Relationships  (illustrative, not comprehensive)	Production function with endogenous technological change  Price determination
Key Agent-Class Behavior  Relationships (illustrative, not comprehensive)	Household crop, meat, and fish consumption Industry crop use Livestock producers crop use

Dominant Relations: Agriculture

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 food supply chain), which is 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 tie to, and track 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.

Agriculture 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.

This section presents several block diagrams that provide an overview of the variables and dynamics of the agricultural model.

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.

Meat and Fish Production

Meat and fish production are represented far more simply than crop p

roduction. Meat production is simply the product of livestock herd size and the slaughter rate. 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 global catch and the regional share, both of which are specified exogenously. 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.

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. 

Meat and food demand 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 changes in response also to GDP per capita (increasing with income). 

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.

Industrial Crop Demand

Industrial crop 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 agricultural demand.  A maximum per capita demand parameter constrains the total and an exogenous multiplier allows users to alter the total.

Animal Feed Demand for Crops

The total feed demand for the livestock herd is dependent on the weight of the livestock herd and the per weight unit 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 the same exogenous crop demand parameter that modifies industrial crop demand.

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. 

The calculations of demand for meat and food crop determine the ultimate division of calorie sources (shown in other topics).  Calories from meat are connected to the demand for meat in tons, with adjustments for the conversion of meat to crop equivalents and then crop equivalents to calories. 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 from the demand for total calories.

Food Demand for Meat and Fish

Meat and fish demand are only for food. Fish demand is the simpler.  It is driven by changes in population, GDP per capita, and fish prices (the elasticity of demand for prices is currently hard-coded in the model and should be made a parameter).

The demand for meat also increases with population and GDP per capita, and falls with increasing meat prices. Additionally, it is also subject to a maximum level per capita.  Further it is subject to a constraint that the calories provided by meat cannot exceed an exogenously specified maximum share of total calorie demand; if it does upon first calculation, it is recalculated to be consistent with that share.  Finally, meat demand can be modified with a multiplier.

Food Demand for Crops

Food demand is driven by the demand for calories from crops, which is the residual of the total calorie demand and the demand for meat. A conversion factor translates calorie demand into food demand.  Crop prices and an elastici

ty affect the resultant food demand.  So too does a constraint on the maximum calories per capita and the size of the population.  Finally, the crop demand for food can be modified directly by an exogenous crop demand parameter.

Financial Constraint on Food Demand

Total food demand in million metric tons consists of the sum of meat demand and food 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 and meat demand are proportionately reduced.

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.

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.

Agricultural Equations

Overview

Briefly, each year the agriculture model begins by estimating the production of crops, meat, and fish. It then turns to the demand for these commodities, followed by trade. The model then looks at changes in stocks and potential shortages related to calorie availability. These 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.

This help section presents and discusses the equations that are central to each of these steps in the agricultural model. Along the way, it also presents information related to the actions in the pre-processor and first year of the agriculture model, which are important in setting the stage for the forecasts. <header><hgroup>

Agricultural Supply

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

Crop Production

Crop production (AGP_f=1) i is the product of yield and land devoted to crops (LD_l=1).

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We focus here on the determination of yield; the amount of land devoted to crops is addressed in the Land Dynamics section.

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 (Meadows, 1974), SARUM, (SARU, 1977), the Bariloche Model (Herrera, et al., 1976), and AGRIMOD (Levis, et al., 1977). 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.

In the first year of the model, yield (YL) is computed simply as the ratio of crop production (AGP_f=1) to cropland (LD_l=1). The determinations of the initial values of these variables are described elsewhere in this document. It is bound, however, to be no greater than 20 tons per hectare in any country.

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.

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).

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

cD is a scaling factor calculated in the first year of the model based upon the base year yield (YL), capital (KAG), and labor supply (LABS).  It 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.

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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.

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 (TECHGROAG).

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The algorithmic structure for computing the annual values of TECHGRO involves four elements:

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.  This element is assumed to decrease by half over100 years.

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.^[1]

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.

The degree to which crop production is approaching upper limits of potential; this again involves the saturation coefficient (SATK).

The algorithmic structure this is:

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The saturation coefficient 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.

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where

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

ylexp 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 (YL_r,t=1) and the multiple of an external user-controlled parameter (ylmax ) and an adjustment factor (YLMaxM).

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where

ylmax is a country-specific parameter 

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

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where

DevWeight_r is the GDPPCP_r/30, with a maximum value of 1

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

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 (tgryli_r).^[2]   This latter target growth rate in yield is set in the first year and is a function of current crop demand (AGDEM), expected crop demand (etdem), and a target growth rate in cropland.

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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

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

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.

In this second stage, the recomputed yield (YL) is multiplied by a stock adjustment factor.

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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 (AGDEM_f=1) and crop production (AGP_f=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.

In the third stage. IFs considers the potential effects of a changing climate on crop yields. This is separated into two parts: the direct effect of atmospheric carbon dioxide concentrations and the effects of changes in temperature and precipitation.

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.

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where

envco2fert is a global, user-controllable parameter

CO2PPM_t=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).  Together, these result in the following equation: 

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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 50 tons per hectare.

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[file:///C:/Users/Ara/Desktop/Agricultural%20Documentation%20v19_AG.docx#_ftnref1 [1]] 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 .

[file:///C:/Users/Ara/Desktop/Agricultural%20Documentation%20v19_AG.docx#_ftnref1 [2]] There is also an adjustment whereby ylmaxgr  is reduced for countries with syl>5, falling to a value of 0.01 when syl>=8.

Meat Production

Meat production, in metric tons, is given as the multiple of the herd size (LVHERD) and the slaughter rate (slr ). The latter is a global parameter.

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The dynamics of the livestock herd are described in the Livestock Dynamics section.

Fish Production

The production of fish has two components, wild catch and aquaculture. Total global wild fish catch (ofscth ), and each region's share in it (rfssh_r ) are exogenous parameters that can be set by the user.

The amount of aquaculture (AQUACUL) in the first year is provided by historical data; these values 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 . Finally, users can change the amount of aquaculture production, by country, with the multiplier aquaculm .

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where

aquaculgr_r,t declines from aquaculgr_r,t=1 to 0 over aquaculconv years

Total fish production (FISH) is given as:

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Production Losses

Some food production will never make it to markets, but will be lost in the field or in distribution systems to pests, spoilage, etc. For crops, an initial estimate of the loss in the first year, LOSSI, is given as a function of GDP per capita using a table function that captures the tendency of loss to decrease with higher income levels (see figure below). This is reset to 0 in the pre-processor if the estimate of cereal production in the first ye

ar is zero. If the loss seems too high, specifically if it is greater than or equal to 0.9 - cereal exports/cereal production, then the loss for crops is recomputed as the maximum of 0.05 and 0.9 – cereal exports/cereal production. The estimate of loss in the first year for meatis assumed to be one-half of the initial estimate for crops; no losses are assumed for fish. In future years, for crops and meat, the loss is calculated as the loss in the first year multiplied by the ratio of the loss estimated from the table function above using current GDP per capita to GDP per capita in the first year; therefore, as GDP per capita increases relative to the first year, loss decreases.  A common loss multiplier (lossm ) is also available, allowing users to adjust crop and meat losses.  Finally, losses are bound between 0 and 0.8.  At present, fish loss remains constant at 0 for all years.

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Agricultural Demand

IFs computes demand for three agricultural categories—crops, meat, and fish.  Total human food demand (for both crops and meat) is 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 changes in response also to GDP per capita (increasing in income).  The calculation sequence of human food demand in IFs thus begins with determination of calorie demand, determines how much of that is satisfied by the typically increasing share from meat (bounding that share with reasonable upper limits), and how much remains to be satisfied from crops.  At this point IFs does not track calories from fish. Once the remaining needed calories from crops are determined, the physical demand for crops in million metric tons can also be determined. 

Crop demand also involves demand for industrial use and animal feed.  Total crop demand is the sum of those two demands and that for food crops.

Initial Agricultural Demands

A common process across categories is used to estimate initial values for the first years. It relies upon the first year values of production, imports, exports, and losses, all of which are generated in the pre-processor and discussed elsewhere in this document, to compute an apparent level of demand or consumption. The reason for this is that demand data are much less available for food and agriculture than are production and trade data. An initial estimate of demand in each category is given as the sum of post-loss production and imports minus exports:

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An initial portion of this first estimate of demand is set aside for the purposes of satisfying the need for growth in food stocks as underlying total food demand and supply change (using initial economic growth as a proxy for that annual stock growth). See also the section on stocks.  That adjusted demand then becomes the basis, along with production, for an estimate of food stocks.

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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

igdpr is the initial growth rate in GDP

Given the resulting initial model year value for food stocks, it is then possible to calculate a more precise increment of stock change needed and add that back into the demand.

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Total Calorie Demand (and the Share from Meat)

In the first year of the model, a predicted level of calories per capita (CalPerCap) is estimated as an increasing function of average income.^[1]   This is bound from above by an assumed maximum value, given by the global parameter calmax .