Optimal Monetary Policy with Heterogeneous Agents

Abstract

Incomplete markets models with heterogeneous agents are increasingly used for policy analysis. We propose a novel methodology for solving fully dynamic optimal policy problems in models of this kind, both under discretion and commitment. We illustrate our methodology by studying optimal monetary policy in an incomplete-markets model with non-contingent nominal assets and costly inflation. Under discretion, an inflationary bias arises from the central bank’s attempt to redistribute wealth towards debtor households, which have a higher marginal utility of net wealth. Under commitment, this inflationary force is countered over time by the incentive to prevent expectations of future inflation from being priced into new bond issuances; under certain conditions, long run inflation is zero as both effects cancel out asymptotically. For a plausible calibration, we find that the optimal commitment features first-order initial inflation followed by a gradual decline towards its (near zero) long-run value. Welfare losses from discretionary policy are first-order in magnitude, affecting both debtors and creditors.