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 isomorhpic 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 in ation bias problem under Calvo contracts is significantly greater than under Rotemberg pricing, despite the fact that the for- mer typically exhibits far greater welfare costs of inflation. The rates of in inflation observed under this policy are non-trivial and suggest that the model can comfort- ably generate the rates of in ation at which the problematic issues highlighted in the trend in 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.