Social Security, the Supply of Labor, and Capital Accumulation

The Social Security system has played an important role in the economic life of American families. It not only provides security for the elderly, but is a device for automatic stabilization, a method of income redistribution, as well as an important factor affecting capital accumulation and the supply of labor. The purpose of this paper is to analyze the long-run effects of the Social Security system in a growing economy. The model employed here extends and generalizes the neoclassical life cycle growth models of Peter A. Diamond and Paul A. Samuelson by explicitly allowing for an endogenous retirement decision and bequest motive. I consider an economy in which the population grows at a constant rate. Each individual lives for two periods. In the first period, he works full time, earning an income of w and paying a Social Security tax of T. In the second period, he works a fraction of time and then retires, receiving from the government a pension of z. He is to choose a consumption path, a retirement age, and an amount of bequest so as to maximize his lifetime utility. From these individual decisions and the assumption that the government budget is balanced each period, we derive the aggregate capital and labor supply functions and analyze the effects of changes in Social Security on capital accumulation and the equilibrium wage and interest rates. The present model is similar to that of Martin S. Feldstein in that retirement decisions are assumed endogenous. The main difference is that his is a partial equilibrium analysis while the model presented here is a general equilibrium model capable of analyzing long-run effects. I show that the short-run effects of Social Security depend primarily on the elasticities of the demand and supply of labor, and its long-run effects are influenced as well by the elasticities of savings and bequest. It is further shown that an appropriate Social Security system can increase the long-run well-being of the economy by causing the rate of return on capital to converge to the Golden Rule level. If, however, the tax and pension levels are tied to the individual workingretirement decisions, the system causes distortions in the labor market. Because of this distortional effect, the optimal Social Security does not necessarily lead to the Golden Rule.