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The OLG model is the natural framework for: (a) the study of life-cycle behavior (investment in human capital, work and 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, (c) the determinates of economic growth in the course of human history, and (d) the factors that triggered the fertility transition.
OLG models allow us to look at intergenerational redistribution and systems.<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}}</ref>
== 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 D.|last2=Brown|first2=Donald J.|last3=Burkinshaw|first3=Owen|date=April 1988|publisher=Springer-Verlag|isbn=3-540-52866-0|edition=1990 student|___location=Berlin|pages=xii+284|chapter=5 The overlapping generations model (pp. 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=}}</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}}</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|publisher=|volume=90|issue=4|pages=806-828|via=}}</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>
[[File:OLG model- Generation.png|thumb|Generational Shifts in OLG Models]]
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:where <math> \beta </math> is the rate of time preference.
== The OLG Model with Production ==
=== The Basic One-Sector OLG Model ===
One important aspect of the OLG model is that the steady state equilibrium need not be efficient, in contrast to general equilibrium models where the [[First Welfare Theorem]] guarantees Pareto efficiency. Because there are an infinite number of agents in the economy (summing over future time), the total value of resources is infinite, so Pareto improvements can be made by transferring resources from each young generation to the current old generation. Not every equilibrium is inefficient; the efficiency of an equilibrium is strongly linked to the interest rate and the [[Cass Criterion]] gives [[necessary and sufficient condition]]s for when an OLG competitive equilibrium allocation is inefficient.<ref name="Cass72">{{cite journal | last1 = Cass| first1 = David | authorlink=David Cass| year=1972 |title= On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization | journal =[[Journal of Economic Theory]] | volume = 4| pages = 200–223 | doi = 10.1016/0022-0531(72)90149-4 | issue = 2}}</ref>▼
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.
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}}▼
A third 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"/>▼
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=}}</ref>[[File:OLG Model - Diamond.png|thumb|Convergence of OLG Economy to Steady State]]
▲===Diamond OLG Model===
The economy has the following characteristics:<ref>{{cite book|title=OLG Model|last=Carrol|first=Christopher
▲The economy has the following characteristics:<ref>{{cite book|last=Carrol|first=Christopher|title=OLG Model}}</ref>
*Two generations are alive at any point in time, the young (age 1) and old (age 2).
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*Labor and capital markets are perfectly competitive and the aggregate production technology is CRS, Y = F(K,L).
In Diamond's version of the model, individuals tend to save more than is socially optimal, leading to dynamic inefficiency. Subsequent work has investigated whether dynamic inefficiency is a characteristic in some economies<ref name="Mankiw89">{{cite news
=== 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=}}</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 in 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=}}</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=}}</ref>
== Dynamic Efficiency ==
▲One important aspect of the OLG model is that the steady state equilibrium need not be efficient, in contrast to general equilibrium models where the [[First Welfare Theorem]] guarantees Pareto efficiency. Because there are an infinite number of agents in the economy (summing over future time), the total value of resources is infinite, so Pareto improvements can be made by transferring resources from each young generation to the current old generation. Not every equilibrium is inefficient; the efficiency of an equilibrium is strongly linked to the interest rate and the [[Cass Criterion]] gives [[necessary and sufficient condition]]s for when an OLG competitive equilibrium allocation is inefficient.<ref name="Cass72">{{cite journal | last1 = Cass| first1 = David | authorlink=David Cass| year=1972 |title= On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization | journal =[[Journal of Economic Theory]] | volume = 4| pages = 200–223 | doi = 10.1016/0022-0531(72)90149-4 | issue = 2}}</ref>
▲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}}
▲A third 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"/>
==See also==
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