Nominal GDP targeting with heterogeneous labor supply

We study nominal GDP targeting as optimal monetary policy in a model with a credit market friction following Azariadis, Bullard, Singh and Suda (2018), henceforth ABSS. As in ABSS, the macroeconomy we study has considerable income inequality which gives rise to a large private sector credit market. Households participating in this market use non-state contingent nominal contracts (NSCNC). We extend the ABSS framework to allow for endogenous and heterogeneous household labor supply among credit market participant households. We show that nominal GDP targeting continues to characterize optimal monetary policy in this setting. Optimal monetary policy repairs the distortion caused by the credit market friction and so leaves heterogeneous households supplying their desired amount of labor, a type of "divine coincidence" result. We also analyze the incomplete markets equilibrium that exists when the monetary policymaker pursues a suboptimal policy, and show how an extension to more general preferences can limit the ability of the policymaker to provide full insurance to households in this setting