Journal Article Education and Economic Growth Get access Sheng Cheng Hu Sheng Cheng Hu Purdue University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 3, October 1976, Pages 509–518, https://doi.org/10.2307/2297229 Published: 01 October 1976 Article history Received: 01 January 1974 Accepted: 01 December 1975 Published: 01 October 1976

[This paper constructs a life-cycle model of the consumer's allocation process in which the capital market is imperfect and the consumption bundle at each instant includes both durable and nondurable goods. The nondurables are instantaneously consumed at the moment of purchase, while the durable good is accumulated and yields a flow of services over its lifetime. The durable investment is assumed to be irreversible. The consumer's optimal allocation program is shown to vary between the periods of borrowing and lending with each phase defining a different relationship between consumption and the "truncated" permanent income.]

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.

We have constructed a simple two-sector model of the demand for housing and corporate capital. An increase in the inflation rate, with and with- out an increase in the risk premium on equities, was then simulated with a number of model variants. The model and simulation experiments illustrate both the tax bias in favor of housing (its initial average real user cost was 3 percentage points less than that for corporate capital) and the manner in which inflation magnifies it (the difference rises to 5 percentage points without an exogenous increase in real house prices and 4 percentage points with an exogenous increase). The existence of a capital-market constraint offsets the increase in the bias against corporate capital, but it introduces a sharp, inefficient reallocation of housing from less wealthy, constrained households to wealthy households who do not have gains on mortgages and are not financially const rained. Widespread usage of innovative housing finance instruments would overcome this reallocation but at the expense of corporate capital. Only a reduction in inflation or in the taxation of income from business capital will solve the problem of inefficient allocation of capital. The simulation results are also able to provide an explanation for the failure of nominal interest rates to rise by a multiple of an increase in the inflation rate in a world with taxes. When the inflation rate alone was increased, the ratio of the increases in the risk-free and inflation rates was 1.32. An increase in the risk premium on equities, in conjunction with the increase in inflation, lowered the simulated ratio to 1.10, introduction of a supply price elasticity of 4 and an exogenous increase in the real house price reduced the ratio to 1.03, and incorporation of the credit-market. constraint reduced the ratio to 0.95.