Overlapping generations model: Difference between revisions

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The '''overlapping generations (OLG) model''' is one of the dominating frameworks of analysis in the study of macroeconomic dynamics and economic growth. In contrast, to the  [[Ramsey–Cass–Koopmans model|Ramsey–Cass–Koopmans neoclassical growth model]] in which individuals are infinitely-lived, in the OLG model individuals live a finite length of time, long enough to overlap with at least one period of another agent's life.

The OLG model is the natural framework for the study of: (a) the life-cycle behavior (investment in human capital, work and saving for retirement), (b) the implications of the allocation of resources across the generations, such as [[Social security|Social Security]], on the income per capita in the long-run,<ref>{{cite journal|last1=Imrohoroglu|first1=Selahattin|last2=Imrohoroglu|first2=Ayse|last3=Joines|first3=Douglas|year=1999|title=Social Security in an Overlapping Generations Economy with Land|journal=Review of Economic Dynamics|volume=2|issue=3|pages=638–665|doi=10.1006/redy.1999.0066}}</ref> (c) the determinates of economic growth in the course of human history, and (d) the factors that triggered the fertility transition.

== History ==

The construction of the OLG model was inspired by [[Irving Fisher]]'s monograph ''The Theory of Interest''.<ref name="ABB29">{{harvtxt|Aliprantis|Brown|Burkinshaw|1988|p=229}}:

{{cite book|title=Existence and optimality of competitive equilibria|last1=Aliprantis|first1=Charalambos&nbsp;D.|last2=Brown|first2=Donald&nbsp;J.|last3=Burkinshaw|first3=Owen|date=April 1988|publisher=Springer-Verlag|isbn=978-3-540-52866-1|edition=1990 student|___location=Berlin|pages=xii+284|chapter=5 The overlapping generations model (pp.&nbsp;229–271)|mr=1075992|authorlink1=Charalambos D. Aliprantis}}</ref> It was first formulated in 1947, in the context of a pure-exchange economy, by [[Maurice Allais]], and more rigorously by [[Paul Samuelson]] in 1958.<ref>{{Cite journal|last=Samuelson|first=Paul A.|date=1958|title=An exact consumption-loan model of interest with or without the social contrivance of money|url=|journal=Journal of Political Economy|volume=66|issue=6|pages=467–482|via=|doi=10.1086/258100}}</ref> In 1965, [[Peter Diamond]]<ref name="Diamond65" /> incorporated an aggregate neoclassical production into the model. This OLG model with production was further augmented with the development of the two-sector OLG model by [[Oded Galor]],<ref name=":0">{{cite journal|last1=Galor|first1=Oded|authorlink=Oded Galor|year=1992|title=A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System|journal=[[Econometrica]]|volume=60|issue=6|pages=1351–1386|jstor=2951525|doi=10.2307/2951525}}</ref> and the introduction of OLG models with endogenous fertility.<ref name=":1">{{Cite journal|last=Galor|first=Oded|last2=Weil|first2=David N.|date=1996|title=The gender gap, fertility, and growth|url=|journal=American Economic Review|volume=86|issue=3|pages=374–387|via=}}</ref><ref name=":2">{{Cite journal|last=Galor|first=Oded|last2=Weil|first2=David N.|date=2000|title=Population, technology, and growth: From Malthusian stagnation to the demographic transition and beyond|url=|journal=American Economic Review|volume=90|issue=4|pages=806–828|via=|doi=10.1257/aer.90.4.806|citeseerx=10.1.1.195.5342}}</ref>

Books devoted to the use of the OLG model include [[Costas Azariadis|Azariadis]]' Intertemporal Macroeconomics<ref>{{Cite web|title = Wiley: Intertemporal Macroeconomics - Costas Azariadis|url = http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1557863660.html|website = eu.wiley.com|accessdate = 2015-10-24}}</ref> and [[David de la Croix|de la Croix]] and [[Philippe Michel (economist)|Michel]]'s Theory of Economic Growth.<ref>{{Cite web|title = A Theory of Economic Growth - 9780521001151 - Cambridge University Press|url = https://www.cambridge.org/asia/catalogue/catalogue.asp?isbn=9780521001151|website = www.cambridge.org|accessdate = 2015-10-24}}</ref>

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The pure-exchange OLG model was augmented with the introduction of an aggregate neoclassical production by [[Peter Diamond]].<ref name="Diamond65" />  In contrast, to Ramsey–Cass–Koopmans neoclassical growth model in which individuals are infinitely-lived and the economy is characterized by a unique steady-state equilibrium, as was established by Oded Galor and Harl Ryder,<ref>{{cite journal|last1=Galor|first1=Oded|authorlink=Oded Galor|last2=Ryder|first2=Harl E.|year=1989|title=Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital|journal=[[Journal of Economic Theory]]|volume=49|issue=2|pages=360–375|doi=10.1016/0022-0531(89)90088-4}}</ref> the OLG economy may be characterized by multiple steady-state equilibria, and initial conditions may therefore affect the long-run evolution of the long-run level of income per capita.

Since initial conditions in the OLG model may affect economic growth in long-run, the model was useful for the exploration of the convergence hypothesis.<ref>{{Cite journal|last=Galor|first=Oded|date=1996|title=Convergence? Inferences from theoretical models|url=|journal=The Economic Journal|volume=106|issue=437|pages=1056–1069|via=|doi=10.2307/2235378|jstor=2235378}}</ref>[[File:OLG Model - Diamond.png|thumb|Convergence of OLG Economy to Steady State]]

The economy has the following characteristics:<ref>{{cite book|title=OLG Model|last=Carrol|first=Christopher}}</ref>

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=== The Two-Sector OLG Model ===

The one-sector OLG model was further augmented with the introduction of a two-sector OLG model by [[Oded Galor]].<ref name=":0" /> The two-sector model provides a framework of analysis for the study of the sectoral adjustments to aggregate shocks and implications of international trade for the dynamics of comparative advantage. In contrast to the Uzawa two-sector neoclassical growth model,<ref>{{Cite journal|last=Uzawa|first=Hirofumi|date=1964|title=Optimal growth in a two-sector model of capital accumulation|url=|journal=The Review of Economic Studies|volume=31|issue=1|pages=1–24|via=|doi=10.2307/2295932|jstor=2295932}}</ref> the two-sector OLG model may be characterized by multiple steady-state equilibria, and initial conditions may therefore affect the long-run position of an economy.

=== The OLG Model with Endogenous Fertility ===

Oded Galor and his co-authors develop OLG models where population growth is endogenously determined to explore: (a) the importance the narrowing of the gender wage gap for the fertility decline,<ref name=":1" /> (b) the contribution of the rise in the return to human capital and the decline in fertility to the transition from stagnation to growth,<ref name=":2" /><ref>{{Cite journal|last=Galor|first=Oded|last2=Moav|first2=Omer|date=2002|title=Natural selection and the origin of economic growth|url=|journal=The Quarterly Journal of Economics|volume=117|issue=4|pages=1133–1191|via=|doi=10.1162/003355302320935007}}</ref> and (c) the importance of population adjustment to technological progress for the emergence of the [[Malthusian trap]].<ref>{{Cite journal|last=Ashraf|first=Quamrul|last2=Galor|first2=Oded|date=2011|title=Dynamics and stagnation in the Malthusian epoch|url=|journal=American Economic Review|volume=101|issue=5|pages=2003–2041|via=|doi=10.1257/aer.101.5.2003|pmid=25506082|pmc=4262154}}</ref>

== Dynamic Inefficiency ==