Overlapping Generations Model

Definition

The overlapping generations (OLG) model is a dynamic general equilibrium framework in which the economy is populated by cohorts born at different dates, each living for a finite number of periods and interacting in goods and asset markets with members of other cohorts simultaneously alive. Introduced by Samuelson (1958) and Diamond (1965), OLG is the standard macroeconomic tool for analyzing phenomena that hinge on the life-cycle motive for saving — retirement preparation, intergenerational transfers, Social Security, and the macroeconomic effects of population aging — because it captures how a population's age structure shapes aggregate saving, capital accumulation, and interest rates.

Key Ideas

Life-cycle saving as the aggregate engine: In OLG, workers save during their working years and dissave in retirement. The capital stock in any period equals the savings of currently working cohorts. Population age structure therefore directly determines the capital-to-labor ratio, and demographic shifts translate mechanically into changes in aggregate saving, investment, and interest rates.
Intergenerational redistribution: Unlike infinitely-lived representative agent models, OLG contains distinct generations that can be made better or worse off by policy without triggering Ricardian equivalence. A pay-as-you-go (PAYG) pension system transfers resources from young workers to current retirees; whether this raises or lowers welfare depends on whether the economy is dynamically efficient (interest rate above population growth rate) — in an efficient economy, PAYG destroys capital and reduces steady-state welfare.
PAYG vs. funded systems: Under PAYG, pension benefits are financed by current workers' contributions; the implicit return is the wage bill growth rate (labor force growth + productivity growth). Under a funded system, each cohort saves for its own retirement and earns the market return on capital. When the capital return exceeds the wage bill growth rate (the Samuelson-Diamond condition), funded systems dominate PAYG in steady-state. The transition from PAYG to funded involves a "double burden" on the transitional generation (funds current retirees + saves for own retirement), making even a welfare-improving reform potentially politically infeasible.
Demographic shocks and capital flows: In a closed OLG economy, population aging (falling birth rates or rising longevity) reduces the size of working cohorts relative to retirees, lowers aggregate saving, raises consumption, and pushes up interest rates. In an open multi-country OLG, countries with older populations export capital to younger countries where labor is abundant and returns are higher. The demographic transition is thus a driver of international capital flows — aging Organisation for Economic Co-operation and Development (OECD) economies are expected to become net capital exporters to developing economies during the 2010–2050 window. See Börsch-Supan and Ludwig 2005 — Aging, Pension Reform, and Capital Flows A Multi-Country Simulation Model.
Calibrated simulation vs. analytical results: Modern OLG models are typically solved numerically with many overlapping cohorts (50–80 periods of life), calibrated to match aggregate moments (capital-output ratio, labor shares, saving rates) and demographic projections. Analytical results exist only for simplified two-period versions. Simulation results are sensitive to calibration assumptions, especially the intertemporal elasticity of substitution and the discount rate.
Social Security as intergenerational insurance: OLG models rationalize Social Security not only as a forced saving device but as insurance against idiosyncratic longevity risk (annuity markets may be thin) and earnings risk that cannot be contracted before birth. From this perspective, PAYG may be efficient even when the capital return exceeds wage growth, if it provides insurance that markets cannot.

How It Works

In the two-period Diamond (1965) version: agents work and save in period 1, retire and consume savings in period 2. Capital in period $t$ is supplied by the young generation's savings: $K_{t+1} = s(w_t, r_{t+1}) \cdot N_t$ , where $w_t$ is the wage, $r_{t+1}$ is the return on capital next period, $N_t$ is the size of the young cohort. Firms use capital and labor to produce output with a neoclassical production function. Equilibrium conditions: $w_t = f(k_t) - k_t f'(k_t)$ and $r_t = f'(k_t)$ where $k_t = K_t/N_t$ is capital per worker. Population growth rate $n$ determines steady-state capital: $k^* : s(w(k^*), r(k^*)) = (1+n)k^*$ . PAYG introduces a social security tax $\tau$ on the young, paying benefit $b = \tau(1+n)$ to the old — reducing private savings and the steady-state capital stock.

Multi-period calibrated models (Auerbach and Kotlikoff 1987; Börsch-Supan and Ludwig 2005) replace the two-period structure with 60–80 cohorts of varying size (matching observed demographic projections), add uncertain lifetimes and bequests, and solve numerically for the transition path between policy regimes.

Why It Matters

Social Security reform analysis: The OLG framework is the primary tool for assessing whether moving from PAYG to funded Social Security increases welfare and aggregate capital formation. It reveals the distributional conflict: transition-generation workers bear the double burden, so reform is almost always Pareto-inferior in the short run even if it improves steady-state welfare.
Demographic transition macroeconomics: OLG models are the standard framework for quantifying how falling birth rates and rising longevity affect national saving rates, interest rates, and trade balances. The aging-capital-flows prediction — that OECD countries will export capital to emerging markets as their populations age — is an OLG result with potentially large implications for international finance.
Evaluation of pension system design: Comparative analysis of defined benefit vs. defined contribution, PAYG vs. funded, and various hybrid systems requires an OLG framework because the welfare effects depend critically on the full path of interest rates and wages for all living cohorts, not just current ones.

Open Questions

How much of the predicted aging-driven capital outflows has actually materialized? The evidence is mixed — demographic models predict more capital export from aging countries than the data show (the Lucas paradox and institutional quality barriers may dominate).
Does the welfare result favoring funded systems survive with realistic labor market frictions (involuntary unemployment, imperfect annuity markets)?
How should OLG models incorporate within-cohort heterogeneity in health, income, and mortality, given that Social Security's progressivity affects the distributional analysis in ways that representative-cohort models miss? See Social Security Progressivity.