New Keynesian analysis relies heavily on two workhorse models of nominal inertia – due to Calvo (1983) and Rotemberg (1982), respectively – to generate a meaningful role for monetary policy. These are often used interchangeably since they imply an isomorphic linearized Phillips curve and, if the steady-state is efficient, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in the benchmark New Keynesian model containing each form of price stickiness using global solution techniques. We find that, due to an offsetting endogenous impact on average markups, the inflation bias problem under Calvo contracts is often significantly greater than under Rotemberg pricing, despite the fact that the former typically exhibits far greater welfare costs of inflation. The nonlinearities inherent in the New Keynesian model are significant and the form of nominal inertia adopted is not innocuous
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