Overlapping generations model: Difference between revisions

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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>

== The Pure-Exchangeexchange OLG Modelmodel ==

[[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 Modelmodel with Productionproduction ==

=== The Basic Oneone-Sectorsector OLG Modelmodel ===

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.

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*Labor and capital markets are perfectly competitive and the aggregate production technology is CRS, Y = F(K,L).

=== The Two-Sectorsector OLG Modelmodel ===

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|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 Modelmodel with Endogenousendogenous Fertilityfertility ===

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|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|doi=10.1257/aer.101.5.2003|pmid=25506082|pmc=4262154}}</ref>

== Dynamic Inefficiencyinefficiency ==

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 [[FirstFundamental Welfaretheorems Theoremof welfare economics|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}}

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* [[Karl Shell]]

* [[Macroeconomic model]]

* [[Fundamental theorems of welfare economics|first welfare theorem]]

* [[First Welfare Theorem]]

* [[Walrasian equilibrium]]