The Four Equation New Keynesian Model

Abstract

This paper develops a New Keynesian model featuring financial intermediation, short- and long-term bonds, credit shocks, and scope for unconventional monetary policy. The log-linearized model reduces to four key equations -- a Phillips curve, an IS equation, and policy rules for the short-term nominal interest rate and the central bank's long bond portfolio (QE). The four equation model collapses to the standard three equation New Keynesian model under a simple parameter restriction. Credit shocks and QE appear in both the IS and Phillips curves. In equilibrium, optimal monetary policy entails adjusting the short-term interest rate to offset natural rate shocks, but using QE to offset credit market disruptions. Such policies can be supported by implementable rules in which the short-term interest rate reacts strongly to inflation and the central bank's bond portfolio reacts strongly to the output gap. The ability of the central bank to engage in QE significantly mitigates the costs of a binding zero lower bound.