This paper develops a tractable stochastic overlapping generations model to analyze the equilibrium equity premium and growth rate of the capital stock in the presence of a defined-benefit Social Security system. If the Social Security Trust Fund increases the share of its portfolio held in risky capital, the equilibrium equity premium falls in the following period and along a constant growth path. This change in the portfolio of the Social Security Trust Fund will increase the growth rate of capital in the following period, and, if a certain sufficient condition is satisfied, will increase the growth rate of the capital stock along a constant growth path. Calibration of the model indicates that it can match the historical average equity premium and the historical average growth rate of the capital stock using plausible values of the preference parameters. In addition, the sufficient condition for the growth rate of the capital stock to increase along a constant growth path is satisfied. Quantitatively, the effects on the riskless interest rate and the growth rate of capital are small.
Published as Andrew B. Abel. "The Social Security Trust Fund, the Riskless Interest Rate, and Capital Accumulation," in John Y. Campbell and Martin Feldstein, editors, "Risk Aspects of Investment-Based Social Security Reform" University of Chicago Press (2001)