Social Security in a Classical Growth Model

This paper develops a growth model with overlapping generations of workers who save for life-cycle reasons and Ricardian capitalists who save from a bequest motive. The population of workers accommodates growth,so that the rate of capital accumulation is endogenous and determines the growth of employment. Two regimes are possible, one in which workers’ saving dominates the long-run and a second in which the long-run equilibrium growth rate is determined completely by the capitalist saving function, sometimes called the Cambridge equation. The second regime exhibits a version of the Pasinetti Paradox: changes in workers’ saving affect the level, but not the growth rate, of capital in the long run. Applied to social security, this result implies that an unfunded system relying on payroll taxes reduces workers’ lifetime wealth and saving, creating level effects on the capital stock without affecting its long-run growth rate. These effects are mitigated by the presence of a reserve fund, various levels of which are examined. Calibrating the model to realistic parameter values for the U.S. facilitates an interpretation of the controversies over the percentage of the national wealth originating in life-cycle saving and the effects of social security on saving. The model is offered as an analytical framework for the review of current topics in fiscal policy, in particular identifying the social security reserve fund as a potential vehicle for generating capital accumulation and effecting a progressive redistribution of wealth.