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How do cohort saving decisions and demographic change shape the long-run capital stock, wages, and rates of return across generations?
The overlapping generations model originates with Samuelson (1958), who introduced fiat money in a two-period life-cycle setting, and Diamond (1965), who embedded capital accumulation into the same framework. Diamond's contribution was decisive: by letting young agents save through physical capital rather than paper money, he showed that a decentralized economy can accumulate too much or too little capital relative to the social optimum. The model became the canonical tool for intergenerational economics.
The core mechanism is life-cycle saving. Each cohort lives for two periods: young workers earn wages, consume some, and save the rest; old retirees consume their savings plus interest. Because generations overlap -- the old coexist with the young -- the capital stock in any period is exactly the saving of the previous young cohort divided across the current population. This link between cohort saving and aggregate capital is the engine of the model.
OLG is the workhorse for Social Security analysis, pension reform, demographic transition modeling, and public debt sustainability at institutions like the Congressional Budget Office, the IMF Fiscal Affairs department, and central bank long-run projection units. Auerbach and Kotlikoff (1987) scaled the two-period structure to a 55-period realistic life-cycle model that remains the template for applied fiscal policy analysis.
Key extensions include Blanchard's (1985) perpetual youth model with a constant probability of death (tractable for continuous-time analysis), Gertler (1999) with lifecycle workers and retirees in a New Keynesian setting, and Krueger and Ludwig (2007) on demographic transition effects. The stochastic OLG literature (Rios-Rull 1996, Conesa and Krueger 1999) adds idiosyncratic risk and incomplete markets, bridging toward the heterogeneous-agent tradition.
The model has two agent types alive at any date: young workers and old retirees. Young agents supply one unit of labor inelastically, earn the competitive wage, allocate income between current consumption and saving, and exit the labor market at the end of the period. Old agents receive the gross return on their savings, consume everything, and die. There is no bequest motive in the baseline Diamond specification.
A representative firm operates a Cobb-Douglas production technology, renting capital from the old (who own it through their savings) and hiring labor from the young. Competitive factor markets set the wage equal to the marginal product of labor and the rental rate equal to the marginal product of capital. The firm's problem is static -- it maximizes profits period by period with no intertemporal decisions.
The key equilibrium condition is the law of motion for capital: next-period capital per worker equals this period's saving per young worker divided by one plus the population growth rate. This single difference equation -- together with the young agent's optimal saving function and the firm's factor prices -- determines the entire dynamic path of the economy. The steady state is the fixed point of this map.
The Congressional Budget Office and the IMF Fiscal Affairs department use Auerbach-Kotlikoff-style OLG models to score Social Security and pension reforms. The OLG structure is essential because these policies redistribute across cohorts, and only an overlapping-generations framework can track who pays and who benefits. The CBO's long-term budget model is built on this foundation.
OLG is the standard framework for analyzing the macroeconomic effects of demographic transitions -- aging populations, declining fertility, immigration shocks. The Japan and EU aging literature (Krueger and Ludwig 2007, Attanasio et al. 2007) relies on multi-period OLG to project capital deepening, interest rate declines, and pension system sustainability decades ahead.
The model should not be used when the question is about business cycle dynamics at quarterly frequency, monetary policy transmission, or financial market frictions. The two-period abstraction is too coarse for short-run fluctuations, and the absence of nominal rigidities or financial intermediation makes the framework silent on central bank actions and credit cycles.
OLG is also the natural home for Ricardian equivalence failures. Because agents have finite lives and new cohorts arrive without inheriting the debts of the old, government bonds are net wealth in OLG -- a result that does not hold in the infinite-horizon Ramsey framework. This makes OLG indispensable for public debt analysis.
Rate at which young agents discount old-age utility, governing the saving rate out of wage income.
Output elasticity of capital in the Cobb-Douglas production function, pinning the wage and rental rate schedules.
Fraction of capital that depreciates each period; affects the gross return to saving.
Rate at which each new young cohort is larger than the previous one; dilutes per-worker capital.
Optimal saving of the young as a function of the current wage and the expected next-period return.
Ratio of the aggregate capital stock to the young labor force; the single state variable.
Competitive wage equal to the marginal product of labor; the young agent's sole income source.
Competitive rental rate equal to the marginal product of capital; determines the return on saving.
Each agent lives exactly two periods -- work when young, retire when old -- with no intra-period labor-leisure choice.
If violated: Multi-period life cycles (Auerbach-Kotlikoff 1987) are needed for realistic age-earnings profiles and retirement timing.
Old agents consume all wealth before dying; no intentional or accidental bequests link dynasties.
If violated: With bequests, dynasties become infinitely lived and the model converges to the Ramsey framework, eliminating dynamic inefficiency.
Young agents supply one unit of labor regardless of the wage; there is no labor-leisure margin.
If violated: Elastic labor supply introduces a second margin of adjustment and changes the mapping from wages to saving.
Agents correctly anticipate the future interest rate when making their saving decision.
If violated: Myopic or adaptive expectations alter the convergence path and can introduce additional instability.
Wages and rental rates equal marginal products; no market power, search frictions, or unions.
If violated: Imperfect competition introduces wedges between marginal products and factor payments, changing the saving-capital link.
The production function has unitary elasticity of substitution between capital and labor.
If violated: CES production changes the curvature of the factor price schedules and can alter the number and stability of steady states.