Optimal Government Debt Policy in the Overlapping Generations Model with Idiosyncratic Capital Return Risk

In this paper, we study the two-period overlapping generations model in which individuals are subject to idiosyncratic risks and study the optimal provision of government debt. In our model, individuals are ex ante homogeneous, and hold risky capital and safe government bonds in the first period. They are subject to idiosyncratic capital return risk in the second period. It is well-known that in deterministic overlapping generations models, when government debt is provided to maximize steady state welfare, the interest rate (r) is equal to the economic growth rate (g). However, in our model with idiosyncratic risks, the risk-free rate is less than the economic growth rate in the optimal steady state. This implies that even when the rollover of government debt is sustainable, increases in debt may reduce welfare. When the return on capital accumulation is risky, the level of safe assets the individuals hold is inefficiently high. Setting the risk-free rate below the economic growth rate reduces demand for government bonds and enhances capital accumulation, which is welfare-improving.