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Overlapping Generations Model

Overlapping Generations Model


Like other economic models, an overlapping generations model (or as it is widely known, an OLG model) is a simplified theoretical representation of complicated economic processes through a set of identities and equations that describe the behavior of various agents interacting with each other. The most distinguishing feature of an OLG model lies in the way it captures the changing behavior of consumers over different phases of their lives. Since consumers in an OLG model are modeled as individuals who live for n periods (n 2), people born in n different periods (or n different generations) coexist in any given period t. While consumers die at the end of n periods, reproduction assures that there will be an infinite succession of consumers, each living for n periods.

At the beginning of their economically active lives, individuals are endowed with a labor power that they can sell to firms (and may have goods or assets they inherit from the previous generation). They work when young and spend part of their labor and asset earnings on present consumption, saving the rest for financing their consumption when they are old. Thus, their old-age consumption is financed through savings they made while they were young and any returns to assets they acquired by using those savings. In other words, individuals must spread their income from the wages they earn by supplying their labor power to firms and the return on their assets over their lifetime such that they can continue to consume even after they are too old to work (or after they retire).

Consumers just starting their economic lives make their decisions on how much to spend on consumption and how much to save within each period ahead of them so as to maximize their lifetime utility. Profit-maximizing firms produce an output by employing labor supplied by young workers and capital supplied through their savings invested in physical capital. In essence, capital is part of the current output set aside to be used in production of the next periods output. Thus, the more individuals save for future consumption, the higher the expansion in the capital stock and, hence, the higher the rate of economic growth will be. As such, OLG models extend standard growth models by relating capital accumulation to savings that young adults make out of their earnings for the purpose of financing their old-age consumption. Within this framework, the long-run equilibrium (or the steady state) will be reached after the growth rate of the total capital stock in the economy has become equal to the population growth rate (or equivalently, after capital stock per worker has stopped changing over time).

Suggested first by French economist Maurice Allais in 1947, the concept of an OLG model was further developed in a 1958 article by Paul A. Samuelson (Samuelson and Allais won the 1970 and 1988 Nobel prizes in economics, respectively). While Peter A. Diamond also made a significant contribution to the OLG modeling literature through a 1965 article, the growth of this literature remained slow until the mid-1980s. The growing concerns over the upcoming burden of the retirement of baby boomers born in the 1940s and the 1950s on social security systems of industrial countries starting from the 1980s led to the realization that extending previous OLG models to incorporate social security was relatively easy, as they realistically captured the changing consumption and savings behavior of individuals before and after retirement. This development has revived interest in OLG models and attracted the attention of economists to the long-term economic effects of demographic developments.

In addition to purely theoretical models, a book by Alan Auerbach and Laurence Kotlikoff published in 1987 popularized the use of numerical solutions to large-scale OLG models with several generations in studying issues related to social security and the evolution of fiscal policy in different countries with different demographic structures. Numerous applied models were constructed thereafter to investigate the implications of changes in age profiles of populations for labor supply, savings, and fiscal balances, as surveyed by David Miles (1999). The realism of applied models has increased with the introduction of additional production sectors that produce distinct goods by employing capital and labor. (Elaborate theoretical grounds for two-sector OLG models that allow the consumption goods to be distinguished from investment goods were laid out in an article by Oded Galor published in 1992.)

Theoretical as well as applied OLG models have since proved particularly popular in analyzing the long-term economic consequences of the gradual aging of nations, a demographic process characterized by the increasing population share of the elderly due to declining fertility rates and increasing life expectancies during a countrys demographic transition. As demographic projections pointed to the continuation of this trend in the decades ahead, modeling of demographics within the OLG framework became increasingly realistic. (According to the United Nations, the worlds population, standing at less than 7 billion in 2006, will reach 9.3 billion by 2050. The number of people aged sixty or over is projected to more than double to nearly 2 billion during the same period. Furthermore, the elderly population itself is aging, with the eighty-plus age group making up the fastest-growing segment of the population.)

Despite variations in its timing and speed across countries, this demographic transition is expected to have important implications not only for future balances of the social security system and the time paths of age-specific public expenditures such as education and health care in a country, but also for the evolution of the supply of labor and capital. In most of the industrial countries where demographic transition started earlier than developing countries, the population shares of people older than the retirement age have already reached critical levels that signal financial trouble for publicly managed retirement systems. Likewise, the declining share of working-age population in these countries raises concern about contractions in domestic labor supply. Furthermore, because the elderly tend to spend more and save less, industrial countries are also expected to face changes in the ratio of savings to consumption in their national income, as well as in the composition of consumption.

These demographically induced developments are certain to affect not only investment and growth patterns of industrial economies but also the global allocation of resources by creating incentives for migration and by affecting the patterns of international trade and capital flows. They must, thus, have implications also for developing countries, even though these countries own demographic transition processes lag behind industrial nations. The growing awareness of this situation prompted renewed interest in the OLG works of the early 1980s, such as the articles by Joel Fried and Willem Buiter studying issues related to trade or capital flows between nations. Oded Galor and Shoukang Lin made important contributions to the theoretical analysis of international trade using OLG models. Such authors as Andrew Mountford and Emily Cremers showed in different articles that dynamic trade equilibrium in an OLG framework may not always imply welfare gains for trading partners, contrary to predictions of static trade models. In a particularly interesting 2001 article based on results from an applied OLG model developed to study trade between a middle-income country at the beginning of its demographic transition and a group of high-income countries with aging populations, Turalay Kenc and Serdar Sayan showed that trade and capital flows serve as a channel for the middle-income country to import the effects of population aging in its trade partners ahead of time.

SEE ALSO Insurance; Macroeconomics


Auerbach, Alan J., and Laurence J. Kotlikoff. 1987. Dynamic Fiscal Policy. New York: Cambridge University Press.

Buiter, Willem H. 1981. Time Preference and International Lending and Borrowing in an Overlapping-Generations Model. Journal of Political Economy 89 (4): 769797.

Cremers, Emily T. 2005. Intergenerational Welfare and Trade. Macroeconomic Dynamics 9: 585611.

Diamond, Peter A. 1965. National Debt in a Neoclassical Growth Model. American Economic Review 55 (5): 11261150.

Fried, Joel. 1980. The Intergenerational Distribution of the Gains from Technical Change and from International Trade. Canadian Journal of Economics 13 (1): 6581.

Galor, Oded. 1992. A Two-Sector Overlapping Generations Model: Global Characterization of the Dynamical System. Econometrica 60: 13511386.

Galor, Oded, and Shoukang Lin. 1997. Dynamic Foundations for the Factor Endowment Model of International Trade. In Dynamics, Economic Growth, and International Trade, eds. Bjarne S. Jensen and Kar-yiu Wong, 151168. Ann Arbor: University of Michigan Press.

Jelassi, Mehdi, and Serdar Sayan. 2005. Implications of Unequal Rates of Population Growth for Trade: An Overlapping Generations-General Equilibrium Analysis within the Heckscher-Ohlin Framework. METU Studies in Development 32: 391408.

Kenc, Turalay, and Serdar Sayan. 2001. Demographic Shock Transmission from Large to Small Countries: An Overlapping Generations CGE Analysis. Journal of Policy Modeling 23 (6): 677702.

Miles, David. 1999. Modelling the Impact of Demographic Change upon the Economy. Economic Journal 109: 136.

Mountford, Andrew. 1998. Trade, Convergence, and Overtaking. Journal of International Economics 46: 167182.

Samuelson, Paul A. 1958. An Exact Consumption-Loan Interest Model of Interest with and without the Social Contrivance of Money. Journal of Political Economy 66 (6): 467482.

Sayan, Serdar. 2005. Heckscher-Ohlin Revisited: Implications of Differential Population Dynamics for Trade within an Overlapping Generations Framework. Journal of Economic Dynamics and Control 29 (9): 14711493.

Tosun, Mehmet S. 2003. Population Aging and Economic Growth: Political Economy and Open Economy Effects. Economics Letters 81 (3): 291296.

Serdar Sayan

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