Firm Heterogeneity, Capital Misallocation and Optimal Monetary Policy

We analyze monetary policy in a New Keynesian model with heterogeneous firms and financial frictions. Firms differ in their productivity and net worth and face collateral constraints that cause capital misallocation. TFP endogenously depends on the time-varying distribution of firms. Although a reduction in real rates increases misallocation in partial equilibrium, general-equilibrium effects overturn this result: a monetary expansion increases the investment of high-productivity firms relatively more than that of low-productivity ones, crowding out the latter and increasing TFP. We provide empirical evidence based on Spanish granular data supporting this mechanism. This has important implications for optimal monetary policy. We show how a central bank without pre-commitments engineers an unexpected monetary expansion to increase TFP in the medium run. In the event of a cost-push shock, the central bank leans with the wind to increase demand and reduce misallocation