Seigniorage and Distortionary Taxation in a Model with Heterogeneous Agents and Idiosyncratic Uncertainty

In this paper we study the optimal monetary and fiscal policy mix in a model in which agents are subject to idiosyncratic uninsurable shocks to their labor productivity. We identify two main effects of anticipated inflation absent in representative agent frameworks. First, inflation stimulates saving for precautionary reasons. Hence, a higher level of anticipated inflation implies a higher capital stock in steady state, which translates into higher wages and lower taxes on labor income. This benefits poor, less productive agents. Second, inflation acts as a regressive consumption tax, which favors rich and productive agents. We calibrate our model economy to the U.S. economy and compute the optimal policy mix. We find that, for a utilitarian government, the Friedman rule is optimal even when we allow for the presence of heterogeneity and uninsurable idiosyncratic risk. Although the aggregate welfare costs of inflation are small, individual costs and benefits are large. Net winners from inflation are poor, less productive agents, while middle-class and rich households are always net losers.