Overlapping generations model: Difference between revisions

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{{For|the topic in population genetics|Overlapping generations}}

An '''overlapping generations (OLG) model''', abbreviatedis toone '''OLGof model''',the isdominating aframeworks typeof analysis in the study of representativemacroeconomic agentdynamics and [[economics|economic]] modelgrowth. inIn whichcontrast, to the  [[AgentRamsey–Cass–Koopmans (economics)model|agentsRamsey–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. As it models explicitly the different periods of life, - such as schooling, working or retirement periods --, it is the natural framework to study the allocation of resources

across the different generations.

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.

== 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}}:

The concept of an OLG model was inspired by [[Irving Fisher]]'s monograph ''The Theory of Interest''.<ref name="ABB29">{{harvtxt|Aliprantis|Brown|Burkinshaw|1988|p=229}}:<p>{{cite book|last1=Aliprantis |first1=Charalambos&nbsp;D.|authorlink1=Charalambos D. Aliprantis| last2=Brown|first2=Donald&nbsp;J.|last3=Burkinshaw|first3=Owen|title=Existence and optimality of competitive equilibria|chapter=5 The overlapping generations model (pp.&nbsp;229–271)|publisher=Springer-Verlag|___location=Berlin|date=April 1988|edition=1990 student|pages=xii+284|isbn=3-540-52866-0|mr=1075992}}</ref> Notable improvements were published by [[Maurice Allais]] in 1947, [[Paul Samuelson]] in 1958, and [[Peter Diamond]] in 1965. 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>

{{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=3-540-52866-0|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=}}</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" /> and the introduction of OLG models with endogenous fertility.<ref>{{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>{{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>

The concept of an OLG model was inspired by [[Irving Fisher]]'s monograph ''The Theory of Interest''.<ref name="ABB29">{{harvtxt|Aliprantis|Brown|Burkinshaw|1988|p=229}}:<p>{{cite book|last1=Aliprantis |first1=Charalambos&nbsp;D.|authorlink1=Charalambos D. Aliprantis| last2=Brown|first2=Donald&nbsp;J.|last3=Burkinshaw|first3=Owen|title=Existence and optimality of competitive equilibria|chapter=5 The overlapping generations model (pp.&nbsp;229–271)|publisher=Springer-Verlag|___location=Berlin|date=April 1988|edition=1990 student|pages=xii+284|isbn=3-540-52866-0|mr=1075992}}</ref> Notable improvements were published by [[Maurice Allais]] in 1947, [[Paul Samuelson]] in 1958, and [[Peter Diamond]] in 1965. 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>

==Basic model==

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==Production==

A OLG model with an aggregate neoclassical production was constructed by [[Peter Diamond]].<ref name="Diamond65"/> A two-sector OLG model was developed 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| pages = 1351–1386 | jstor=2951525 | issue = 6 }}</ref>

Unlike the [[Ramsey–Cass–Koopmans model]] the steady state level of capital need not be unique.<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| pages = 360–375 | doi = 10.1016/0022-0531(89)90088-4 | issue = 2 }}</ref> Moreover, as demonstrated by Diamond (1965), the steady-state level of the capital labor ratio need not be efficient which is termed as "[[dynamic efficiency|dynamic inefficiency]]".