The Inflation Bias under Calvo and Rotemberg Pricing

New Keynesian models rely heavily on two workhorse models of nominal inertia - price contracts of random duration (Calvo, 1983) and price adjustment costs (Rotemberg, 1982) - to generate a meaningful role for monetary policy. These alternative descriptions of price stickiness are often used interchangeably since, to a first order of approximation they imply an isomorphic Phillips curve and, if the steady-state is efficient, identical objectives for the policy maker and as a result in an LQ framework, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in bench-mark New Keynesian models containing each form of price stickiness. Using global solution techniques we find that the inflation bias problem under Calvo contracts is significantly greater than under Rotemberg pricing, despite the fact that the former typically significant exhibits far greater welfare costs of inflation. The rates of inflation observed under this policy are non-trivial and suggest that the model can comfortably generate the rates of inflation at which the problematic issues highlighted in the trend inflation literature emerge, as well as the movements in trend inflation emphasized in empirical studies of the evolution of inflation. Finally, we consider the response to cost push shocks across both models and find these can also be significantly different. The choice of which form of nominal inertia to adopt is not innocuous.