https://pardeewiki.du.edu//index.php?action=history&feed=atom&title=Social_Accounting_Matrix_%28SAM%29Social Accounting Matrix (SAM) - Revision history2026-04-26T04:50:13ZRevision history for this page on the wikiMediaWiki 1.43.6https://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8593&oldid=prevWikiadmin at 22:47, 2 October 20172017-10-02T22:47:16Z<p></p>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">See (Hughes and Hossain, 2003)<ref>Hughes, B. B., & Hossain, A. (2004). LONG-TERM SOCIOECONOMIC MODELING (WITH UNIVERSAL, GLOBALLY INTEGRATED SOCIAL ACCOUNTING MATRICES IN A GENERAL EQUILIBRIUM MODEL STRUCTURE) (Working Paper No. Working Paper 2004.05.07). Denver, CO: Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver. Retrieved from http://pardee.du.edu/long-term-socio-economic-modeling-universal-globally-integrated-social-accounting-matrices-sams</ref>&nbsp;for a more thorough explanation of the Social Accouting Matrix as implemented in the IFs model.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A SAM integrates a multi-sector input-output representation of an economy with the broader system of national accounts, also critically representing flows of funds among societal agents/institutions and the balance of payments with the outside world. [https://en.wikipedia.org/wiki/Richard_Stone Richard Stone] is the acknowledged father of social accounting matrices, which emerged from his participation in setting up the first systems of national accounts or SNA (see Pesaran and Harcourt 1999<ref>Pesaran, M. Hashem and G. C. Harcourt. 1999. Life and Work of John Richard Nicholas Stone. Available at http://www.econ.cam.ac.uk/faculty/pesaran/stone.pdf.</ref> on Stone’s work and Stone 1986<ref>Stone, Richard. 1986. "The Accounts of Society," Journal of Applied Econometrics 1, no. 1 (January): 5-28.</ref>). Many others have pushed the concepts and use of SAMs forward, including Pyatt (Pyatt and Round 1985<ref>Pyatt, G. and J.I. Round, eds. 1985. Social Accounting Matrices: A Basis for Planning. Washington, D.C.: The World Bank.</ref>) and Thorbecke (2001)<ref>Thorbecke, Erik. 2001. "The Social Accounting Matrix: Deterministic or Stochastic Concept?", paper prepared for a conference in honor of Graham Pyatt's retirement, at the Institute of Social Studies, The Hague, Netherlands (November 29 and 30). Available at http://people.cornell.edu/pages/et17/etpapers.html.</ref>. So, too, have many who have extended the use of SAMs into new frontiers. One such frontier is the additional representation of environmental inputs and outputs and the creation of what are coming to be known as social and environmental accounting matrices or SEAMs (see Pan 2000)<ref>Pan, Xiaoming. 2000 (January). "Social and Ecological Accounting Matrix: an Empirical Study for China," paper submitted for the Thirteenth International Conference on Input-Output Techniques, Macerata, Italy, August 21-25, 2000.</ref>. Another very productive extension is into the connection between SAMs and technological systems of a society (see Khan 1998<ref>Khan, Haider A. 1998. Technology, Development and Democracy. Northhampton, Mass: Edward Elgar Publishing Co.</ref>; Duchin 1999<ref>Duchin, Faye. 1998. Structural Economics: Measuring Change in Technology, Lifestyles, and the Environment. Washington, D.C.: Island Press.</ref>). It is fitting that the 1993 revision of the System of National Accounts by the United Nations began explicitly to move the SNA into the world of SAMs.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A SAM integrates a multi-sector input-output representation of an economy with the broader system of national accounts, also critically representing flows of funds among societal agents/institutions and the balance of payments with the outside world. [https://en.wikipedia.org/wiki/Richard_Stone Richard Stone] is the acknowledged father of social accounting matrices, which emerged from his participation in setting up the first systems of national accounts or SNA (see Pesaran and Harcourt 1999<ref>Pesaran, M. Hashem and G. C. Harcourt. 1999. Life and Work of John Richard Nicholas Stone. Available at http://www.econ.cam.ac.uk/faculty/pesaran/stone.pdf.</ref> on Stone’s work and Stone 1986<ref>Stone, Richard. 1986. "The Accounts of Society," Journal of Applied Econometrics 1, no. 1 (January): 5-28.</ref>). Many others have pushed the concepts and use of SAMs forward, including Pyatt (Pyatt and Round 1985<ref>Pyatt, G. and J.I. Round, eds. 1985. Social Accounting Matrices: A Basis for Planning. Washington, D.C.: The World Bank.</ref>) and Thorbecke (2001)<ref>Thorbecke, Erik. 2001. "The Social Accounting Matrix: Deterministic or Stochastic Concept?", paper prepared for a conference in honor of Graham Pyatt's retirement, at the Institute of Social Studies, The Hague, Netherlands (November 29 and 30). Available at http://people.cornell.edu/pages/et17/etpapers.html.</ref>. So, too, have many who have extended the use of SAMs into new frontiers. One such frontier is the additional representation of environmental inputs and outputs and the creation of what are coming to be known as social and environmental accounting matrices or SEAMs (see Pan 2000)<ref>Pan, Xiaoming. 2000 (January). "Social and Ecological Accounting Matrix: an Empirical Study for China," paper submitted for the Thirteenth International Conference on Input-Output Techniques, Macerata, Italy, August 21-25, 2000.</ref>. Another very productive extension is into the connection between SAMs and technological systems of a society (see Khan 1998<ref>Khan, Haider A. 1998. Technology, Development and Democracy. Northhampton, Mass: Edward Elgar Publishing Co.</ref>; Duchin 1999<ref>Duchin, Faye. 1998. Structural Economics: Measuring Change in Technology, Lifestyles, and the Environment. Washington, D.C.: Island Press.</ref>). It is fitting that the 1993 revision of the System of National Accounts by the United Nations began explicitly to move the SNA into the world of SAMs.</div></td></tr>
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</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8592&oldid=prevWikiadmin at 22:43, 2 October 20172017-10-02T22:43:40Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The estimated value then enters a convergence calculation that IFs uses in a number of instances. In the first year a ratio term (GovConR) was computed that represented the degree to which a country’s consumption/GDP differed from the estimated value. That ratio multiplies the estimated term in future years, allowing the function normally to increase consumption/GDP as GDP per capita rises. At the same time, such divergence from estimated functions is almost as often a matter of data inadequacy or of temporary factors for a country as it is of persistent idiosyncrasy. The convergence function allows the country/region’s value to converge towards the functional calculation over a period of time ('''&nbsp;''govfinconv''&nbsp;'''), usually quite long. Such convergence also helps avoid ceiling effects (e.g. government consumption as 100% of GDP) as GDP per capita rises.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The estimated value then enters a convergence calculation that IFs uses in a number of instances. In the first year a ratio term (GovConR) was computed that represented the degree to which a country’s consumption/GDP differed from the estimated value. That ratio multiplies the estimated term in future years, allowing the function normally to increase consumption/GDP as GDP per capita rises. At the same time, such divergence from estimated functions is almost as often a matter of data inadequacy or of temporary factors for a country as it is of persistent idiosyncrasy. The convergence function allows the country/region’s value to converge towards the functional calculation over a period of time ('''&nbsp;''govfinconv''&nbsp;'''), usually quite long. Such convergence also helps avoid ceiling effects (e.g. government consumption as 100% of GDP) as GDP per capita rises.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The second term in the equation below is called the Wagner term, after the discoverer of the long-term behavioral tendency for government consumption to rise as a share of GDP, even at <del style="font-weight: bold; text-decoration: none;">stabile </del>levels of GDP per capita. This is built into the consumption calculation through an exogenous parameter ('''<del style="font-weight: bold; text-decoration: none;">&nbsp;</del>''wagnerc''<del style="font-weight: bold; text-decoration: none;">&nbsp;</del>''') that is multiplied by the number of the forecast year (at the time of this writing the coefficient’s value was 0). The result of the convergence process and the multiplicative terms is divided by 100 and multiplied by a GDPBase term. The GDP base term could just be GDP. But relative price adjustments in countries can greatly affect government consumption—for instance, rising and falling relative oil prices can sharply affect government revenues and expenditures in oil-rich countries like those of the Gulf. Hence we arbitrarily add half of the difference between the GDP relative price adjusted value (GDPRPA) and the GDP to the base from which we compute GOVCON.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The second term in the equation below is called the Wagner term, after the discoverer of the long-term behavioral tendency for government consumption to rise as a share of GDP, even at <ins style="font-weight: bold; text-decoration: none;">stable </ins>levels of GDP per capita. This is built into the consumption calculation through an exogenous parameter ('''''wagnerc''''') that is multiplied by the number of the forecast year (at the time of this writing the coefficient’s value was 0). The result of the convergence process and the multiplicative terms is divided by 100 and multiplied by a GDPBase term. The GDP base term could just be GDP. But relative price adjustments in countries can greatly affect government consumption—for instance, rising and falling relative oil prices can sharply affect government revenues and expenditures in oil-rich countries like those of the Gulf. Hence we arbitrarily add half of the difference between the GDP relative price adjusted value (GDPRPA) and the GDP to the base from which we compute GOVCON.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>GOVCON_r=</math><math>(Converge(EstGovtConsum_r*GovConR_{r,t=1},EstGovtConsum_r,\mathbf{govfinconv})*</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>GOVCON_r=</math><math>(Converge(EstGovtConsum_r*GovConR_{r,t=1},EstGovtConsum_r,\mathbf{govfinconv})*</math></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>WagnerTerm*\mathbf{govexpm_r}*MulExp_{r,t-1})/100*GDPBase_r+WBFlowTerm_r+AidFlowTerm_r</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>WagnerTerm*\mathbf{govexpm_r}*MulExp_{r,t-1})/100*GDPBase_r+WBFlowTerm_r+AidFlowTerm_r</math></div></td></tr>
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</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8591&oldid=prevWikiadmin at 22:39, 2 October 20172017-10-02T22:39:53Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>ConsumHH_{r,h=1,t=1}=HHINC{r,h=1,t=1}*AveConsumptionR{r,h=1,t=1}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:<math>ConsumHH_{r,h=1,t=1}=HHINC{r,h=1,t=1}*AveConsumptionR{r,h=1,t=1}</math></div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>ConsumHH_{r,h=1,t=2}=C_{r,t=1}-ConsumHH_{r,h=1,t=1}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>ConsumHH_{r,h=1,t=2}=C_{r,t=1}-ConsumHH_{r,h=1,t=1}<ins style="font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
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</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8590&oldid=prevWikiadmin at 22:30, 2 October 20172017-10-02T22:30:48Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005<ref>Zhang, J., & Zhang, J. (2005). The Effect of Life Expectancy on Fertility, Saving, Schooling and Economic Growth: Theory and Evidence. The Scandinavian Journal of Economics, 107(1), 45–66.</ref>, Zhang and Zhang 2009<ref>Zhang, J., & Zhang, J. (2009). LONGEVITY, RETIREMENT, AND CAPITAL ACCUMULATION IN A RECURSIVE MODEL WITH AN APPLICATION TO MANDATORY RETIREMENT. Macroeconomic Dynamics, 13(3), 327–348. https://doi.org/10.1017/S1365100508080073</ref>, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005<ref>Zhang, J., & Zhang, J. (2005). The Effect of Life Expectancy on Fertility, Saving, Schooling and Economic Growth: Theory and Evidence. The Scandinavian Journal of Economics, 107(1), 45–66.</ref>, Zhang and Zhang 2009<ref>Zhang, J., & Zhang, J. (2009). LONGEVITY, RETIREMENT, AND CAPITAL ACCUMULATION IN A RECURSIVE MODEL WITH AN APPLICATION TO MANDATORY RETIREMENT. Macroeconomic Dynamics, 13(3), 327–348. https://doi.org/10.1017/S1365100508080073</ref>, Lee and Mason 2011<ins style="font-weight: bold; text-decoration: none;"><ref>Lee, Ronald D. and Andrew Mason, eds. 2011. Population Aging and the Generational Economy: A Global Perspective. Cheltenham, UK: Edward Elgar.</ref></ins>). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8589&oldid=prevWikiadmin at 22:23, 2 October 20172017-10-02T22:23:19Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005<ref>Zhang, J., & Zhang, J. (2005). The Effect of Life Expectancy on Fertility, Saving, Schooling and Economic Growth: Theory and Evidence. The Scandinavian Journal of Economics, 107(1), 45–66.</ref>, Zhang and Zhang 2009, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005<ref>Zhang, J., & Zhang, J. (2005). The Effect of Life Expectancy on Fertility, Saving, Schooling and Economic Growth: Theory and Evidence. The Scandinavian Journal of Economics, 107(1), 45–66.</ref>, Zhang and Zhang 2009<ins style="font-weight: bold; text-decoration: none;"><ref>Zhang, J., & Zhang, J. (2009). LONGEVITY, RETIREMENT, AND CAPITAL ACCUMULATION IN A RECURSIVE MODEL WITH AN APPLICATION TO MANDATORY RETIREMENT. Macroeconomic Dynamics, 13(3), 327–348. https://doi.org/10.1017/S1365100508080073</ref></ins>, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8588&oldid=prevWikiadmin at 22:21, 2 October 20172017-10-02T22:21:50Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:21, 2 October 2017</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005, Zhang and Zhang 2009, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005<ins style="font-weight: bold; text-decoration: none;"><ref>Zhang, J., & Zhang, J. (2005). The Effect of Life Expectancy on Fertility, Saving, Schooling and Economic Growth: Theory and Evidence. The Scandinavian Journal of Economics, 107(1), 45–66.</ref></ins>, Zhang and Zhang 2009, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8587&oldid=prevWikiadmin at 22:08, 2 October 20172017-10-02T22:08:05Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:08, 2 October 2017</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== The Impact of Age Structure on Consumption ====</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976) sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005, Zhang and Zhang 2009, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Modigliani (1976)<ins style="font-weight: bold; text-decoration: none;"><ref>Modigliani, Franco. 1976. “Life-cycle, individual thrift, and the wealth of nations,” American Economic Review, 76(3), 297–313.</ref> </ins>sketched the pattern of life-cycle savings and consumption and many others have followed (e.g. Lee and Miller 1992, Zhang and Zhang 2005, Zhang and Zhang 2009, Lee and Mason 2011). Consumption as a portion of income tends to be lowest during the peak working years and higher for the young and the old and/or retired.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Drawing especially on Lee and Mason (2011) we structured a relationship between marginal propensity to consume and age (the percentage portion of additional household income that would typically be consumed at different ages). We use that to differentiate consumption demands or needs of the population prior to working years (CPREWORK), during working years (CWORKING) and in retirement (CRETIRE). The function is used to compute an estimate of the percentage of additional income that each of the three groups consumes (YouthCon, WorkerCon, and PensionCon).</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8586&oldid=prevWikiadmin at 21:59, 2 October 20172017-10-02T21:59:35Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>CalcInfraBudgetDemand_r=\Sigma_{infct}infrainvnewpubshrm_{r,infct}*INFRAINVESTNEW_{r,infct}+\Sigma_{infct}infrainvmaintpubshrm_{r,infct}*INFRAINVESTMAINT_{r,infct}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>CalcInfraBudgetDemand_r=\Sigma_{infct}infrainvnewpubshrm_{r,infct}*INFRAINVESTNEW_{r,infct}+<ins style="font-weight: bold; text-decoration: none;"></math><math></ins>\Sigma_{infct}infrainvmaintpubshrm_{r,infct}*INFRAINVESTMAINT_{r,infct}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the equations above, infct stands for the index number of various infrastructure types included in the IFs model, for example, road, electricity, water connections etc.; INFRAINVESTNEW and INFRAINVESTMAINT are total costs of new construction and maintenance respectively and infrainvnewpubshrm and infrainvmaintpubshem are shares of the costs borne by the government.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the equations above, infct stands for the index number of various infrastructure types included in the IFs model, for example, road, electricity, water connections etc.; INFRAINVESTNEW and INFRAINVESTMAINT are total costs of new construction and maintenance respectively and infrainvnewpubshrm and infrainvmaintpubshem are shares of the costs borne by the government.</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8585&oldid=prevWikiadmin at 21:58, 2 October 20172017-10-02T21:58:28Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:58, 2 October 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l220">Line 220:</td>
<td colspan="2" class="diff-lineno">Line 220:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The larger of the two numbers indicates the total pressure in the system for transfers to households.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The larger of the two numbers indicates the total pressure in the system for transfers to households.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>GOVHHTRN_r=AMAX(GovHHTrnTop_r,GovHHTrnTotalBottom_r)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>GOVHHTRN_r=AMAX(GovHHTrnTop_r,GovHHTrnTotalBottom_r)<ins style="font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Given these total transfers, there are further steps required to finalize the division into pension and welfare transfers and to divide each of those into transfers to skilled and unskilled households. The first step is an interim division of the total into pension and welfare categories using the bottom-up calculations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Given these total transfers, there are further steps required to finalize the division into pension and welfare transfers and to divide each of those into transfers to skilled and unskilled households. The first step is an interim division of the total into pension and welfare categories using the bottom-up calculations.</div></td></tr>
</table>Wikiadminhttps://pardeewiki.du.edu//index.php?title=Social_Accounting_Matrix_(SAM)&diff=8584&oldid=prevWikiadmin at 21:57, 2 October 20172017-10-02T21:57:25Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:57, 2 October 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l202">Line 202:</td>
<td colspan="2" class="diff-lineno">Line 202:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Consistent with the bottom-up logic, that initial calculation is compared with a calculation that is built up from an estimate of the financial needs/demands of retired population. That second estimate looks at the size of the retired population, and multiplies that by per capita pension benefits in the first year, adjusted for the increase in GDP per capita. Given changing and often decreasing retirement ages, the retired population is a sum of those over age 65 and a term called RetirementPopAdj, which is computed to take into account an exogenous retirement age ('''&nbsp;''labretagem''&nbsp;'''). The larger of the analytically determined initial estimate and the retirement-population based numbers indicates the total pressure in the system for public pensions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Consistent with the bottom-up logic, that initial calculation is compared with a calculation that is built up from an estimate of the financial needs/demands of retired population. That second estimate looks at the size of the retired population, and multiplies that by per capita pension benefits in the first year, adjusted for the increase in GDP per capita. Given changing and often decreasing retirement ages, the retired population is a sum of those over age 65 and a term called RetirementPopAdj, which is computed to take into account an exogenous retirement age ('''&nbsp;''labretagem''&nbsp;'''). The larger of the analytically determined initial estimate and the retirement-population based numbers indicates the total pressure in the system for public pensions.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>GovHHTrnPenBottom_r=AMAX(GovtPensions_r,(PopGT65_r+RetirementPopAdj_r)*GovHHPenPC_{r,t=1}*\frac{GDPRPAPC_{R,T}}{GDPRPAPC_{r,t=1}}MulExp_{r,t-1}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>GovHHTrnPenBottom_r=AMAX(GovtPensions_r,<ins style="font-weight: bold; text-decoration: none;"></math><math></ins>(PopGT65_r+RetirementPopAdj_r)*GovHHPenPC_{r,t=1}*\frac{GDPRPAPC_{R,T}}{GDPRPAPC_{r,t=1}}MulExp_{r,t-1}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where</div></td></tr>
</table>Wikiadmin