Overlapping generations model: Difference between revisions

Revision as of 13:39, 21 October 2019

Revision as of 18:32, 11 December 2019

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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 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|citeseerx=10.1.1.199.2634}}</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 ==

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Another attribute of OLG type models is that it is possible that '[[over saving]]' can occur when [[capital accumulation]] is added to the model—a situation which could be improved upon by a social planner by forcing households to draw down their capital stocks.<ref name="Diamond65">{{cite journal | last1 = Diamond| first1 = Peter | authorlink=Peter Diamond| year=1965 |title= National debt in a neoclassical growth model | journal =[[American Economic Review]] | volume = 55| pages = 1126–1150 | issue = 5}}</ref> However, certain restrictions on the underlying technology of production and consumer tastes can ensure that the steady state level of saving corresponds to the [[Golden Rule savings rate]] of the [[Solow growth model]] and thus guarantee intertemporal efficiency. Along the same lines, most empirical research on the subject has noted that oversaving does not seem to be a major problem in the real world.{{Citation needed|date=May 2012}}

In Diamond's version of the model, individuals tend to save more than is socially optimal, leading to [[Dynamic efficiency|dynamic inefficiency]]. Subsequent work has investigated whether dynamic inefficiency is a characteristic in some economies<ref name="Mankiw89">{{cite news|title=Assessing Dynamic Efficiency: Theory and Evidence|author1=N. Gregory Mankiw|date=1 May 1989|journal=[[Review of Economic Studies]]|author2=Lawrence H. Summers|issue=1|volume=56|pages=1–19|doi=10.2307/2297746|author3=Richard J. Zeckhauser|jstor=2297746}}</ref> and whether government programs to transfer wealth from young to poor do reduce dynamic inefficiency{{Citation needed|date=November 2014}}.

Another fundamental contribution of OLG models is that they justify existence of money as a medium of exchange. A system of expectations exists as an equilibrium in which each new young generation accepts money from the previous old generation in exchange for consumption. They do this because they expect to be able to use that money to purchase consumption when they are the old generation.<ref name="LjungqvistSargent2004" />