Overlapping generations model

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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 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.

Economic growth increase in production and consumption in an economy

Economic growth is the increase in the inflation-adjusted market value of the goods and services produced by an economy over time. It is conventionally measured as the percent rate of increase in real gross domestic product, or real GDP.

The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans. The Ramsey–Cass–Koopmans model differs from the Solow–Swan model in that the choice of consumption is explicitly microfounded at a point in time and so endogenizes the savings rate. As a result, unlike in the Solow–Swan model, the saving rate may not be constant along the transition to the long run steady state. Another implication of the model is that the outcome is Pareto optimal or Pareto efficient.


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, on the income per capita in the long-run, [1] (c) the determinates of economic growth in the course of human history, and (d) the factors that triggered the fertility transition.

Human capital is the stock of habits, knowledge, social and personality attributes embodied in the ability to perform labour so as to produce economic value.

Retirement point where a person ceases employment permanently

Retirement is the withdrawal from one's position or occupation or from one's active working life. A person may also semi-retire by reducing work hours.

In economics, resource allocation is the assignment of available resources to various uses. In the context of an entire economy, resources can be allocated by various means, such as markets or planning.


The construction of the OLG model was inspired by Irving Fisher's monograph The Theory of Interest. [2] 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. [3] In 1965, Peter Diamond [4]  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, [5] and the introduction of OLG models with endogenous fertility. [6] [7]

Irving Fisher American economist

Irving Fisher was an American economist, statistician, inventor, and Progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt deflation has been embraced by the post-Keynesian school. Joseph Schumpeter described him as "the greatest economist the United States has ever produced", an assessment later repeated by James Tobin and Milton Friedman.

Maurice Allais French economist

Maurice Félix Charles Allais was a French physicist and economist, the 1988 winner of the Nobel Memorial Prize in Economic Sciences "for his pioneering contributions to the theory of markets and efficient utilization of resources", for Maurice Allais contribution, along with John Hicks and Paul Samuelson, to neoclassical synthesis. They formalize the self-regulation of markets, that Keynes refuted, while reiterating some of his ideas.

Paul Samuelson American economist

Paul Anthony Samuelson was an American economist. The first American to win the Nobel Memorial Prize in Economic Sciences, the Swedish Royal Academies stated, when awarding the prize in 1970, that he "has done more than any other contemporary economist to raise the level of scientific analysis in economic theory". Economic historian Randall E. Parker has called him the "Father of Modern Economics", and The New York Times considered him to be the "foremost academic economist of the 20th century".

Books devoted to the use of the OLG model include Azariadis' Intertemporal Macroeconomics [8] and de la Croix and Michel's Theory of Economic Growth. [9]

Constantine Christos "Costas" Azariadis is a macroeconomist born in Athens, Greece. He has worked on numerous topics, such as labor markets, business cycles, and economic growth and development. Azariadis originated and developed implicit contract theory.

David de la Croix is a Belgian scholar and author in the field of economic growth and demographic economics. He is professor at the University of Louvain (UCLouvain).

Philippe Michel was a French mathematical economist.

The Pure-Exchange OLG Model

Generational Shifts in OLG Models OLG model- Generation.png
Generational Shifts in OLG Models

The most basic OLG model has the following characteristics: [10]

where is the rate of time preference.

The OLG Model with Production

The Basic One-Sector OLG Model

The pure-exchange OLG model was augmented with the introduction of an aggregate neoclassical production by Peter Diamond. [4]  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, [11] 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.

Peter Diamond Nobel prize in economics winner

Peter Arthur Diamond is an American economist known for his analysis of U.S. Social Security policy and his work as an advisor to the Advisory Council on Social Security in the late 1980s and 1990s. He was awarded the Nobel Memorial Prize in Economic Sciences in 2010, along with Dale T. Mortensen and Christopher A. Pissarides. He is an Institute Professor at the Massachusetts Institute of Technology. On June 6, 2011, he withdrew his nomination to serve on the Federal Reserve's board of governors, citing intractable Republican opposition for 14 months.

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. [12]

Convergence of OLG Economy to Steady State OLG Model - Diamond.png
Convergence of OLG Economy to Steady State

The economy has the following characteristics: [13]

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. [5] 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, [14] 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, [6] (b) the contribution of the rise in the return to human capital and the decline in fertility to the transition from stagnation to growth, [7] [15] and (c) the importance of population adjustment to technological progress for the emergence of the Malthusian trap. [16]

Dynamic Inefficiency

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 conditions for when an OLG competitive equilibrium allocation is inefficient. [17]

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. [4] 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 ]

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 [18] and whether government programs to transfer wealth from young to poor do reduce dynamic inefficiency[ citation needed ].

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. [10]

See also

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  1. Imrohoroglu, Selahattin; Imrohoroglu, Ayse; Joines, Douglas (1999). "Social Security in an Overlapping Generations Economy with Land". Review of Economic Dynamics. 2 (3): 638–665. doi:10.1006/redy.1999.0066.
  2. Aliprantis, Brown & Burkinshaw (1988 , p. 229): Aliprantis, Charalambos D.; Brown, Donald J.; Burkinshaw, Owen (April 1988). "5 The overlapping generations model (pp. 229–271)". Existence and optimality of competitive equilibria (1990 student ed.). Berlin: Springer-Verlag. pp. xii+284. ISBN   978-3-540-52866-1. MR   1075992.
  3. Samuelson, Paul A. (1958). "An exact consumption-loan model of interest with or without the social contrivance of money". Journal of Political Economy. 66 (6): 467–482. doi:10.1086/258100.
  4. 1 2 3 Diamond, Peter (1965). "National debt in a neoclassical growth model". American Economic Review . 55 (5): 1126–1150.
  5. 1 2 Galor, Oded (1992). "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System". Econometrica . 60 (6): 1351–1386. doi:10.2307/2951525. JSTOR   2951525.
  6. 1 2 Galor, Oded; Weil, David N. (1996). "The gender gap, fertility, and growth". American Economic Review. 86 (3): 374–387.
  7. 1 2 Galor, Oded; Weil, David N. (2000). "Population, technology, and growth: From Malthusian stagnation to the demographic transition and beyond". American Economic Review. 90 (4): 806–828. CiteSeerX . doi:10.1257/aer.90.4.806.
  8. "Wiley: Intertemporal Macroeconomics - Costas Azariadis". eu.wiley.com. Retrieved 2015-10-24.
  9. "A Theory of Economic Growth - 9780521001151 - Cambridge University Press". www.cambridge.org. Retrieved 2015-10-24.
  10. 1 2 Lars Ljungqvist; Thomas J. Sargent (1 September 2004). Recursive Macroeconomic Theory. MIT Press. pp. 264–267. ISBN   978-0-262-12274-0.
  11. Galor, Oded; Ryder, Harl E. (1989). "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital". Journal of Economic Theory . 49 (2): 360–375. doi:10.1016/0022-0531(89)90088-4.
  12. Galor, Oded (1996). "Convergence? Inferences from theoretical models" (PDF). The Economic Journal. 106 (437): 1056–1069. doi:10.2307/2235378. JSTOR   2235378.
  13. Carrol, Christopher. OLG Model.
  14. Uzawa, Hirofumi (1964). "Optimal growth in a two-sector model of capital accumulation". The Review of Economic Studies. 31 (1): 1–24. doi:10.2307/2295932. JSTOR   2295932.
  15. Galor, Oded; Moav, Omer (2002). "Natural selection and the origin of economic growth". The Quarterly Journal of Economics. 117 (4): 1133–1191. CiteSeerX . doi:10.1162/003355302320935007.
  16. Ashraf, Quamrul; Galor, Oded (2011). "Dynamics and stagnation in the Malthusian epoch". American Economic Review. 101 (5): 2003–2041. doi:10.1257/aer.101.5.2003. PMC   4262154 . PMID   25506082.
  17. Cass, David (1972). "On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization". Journal of Economic Theory . 4 (2): 200–223. doi:10.1016/0022-0531(72)90149-4.
  18. N. Gregory Mankiw; Lawrence H. Summers; Richard J. Zeckhauser (1 May 1989). "Assessing Dynamic Efficiency: Theory and Evidence". Review of Economic Studies . 56 (1). pp. 1–19. doi:10.2307/2297746.

Further reading