Trend Inflation and Firms Price-Setting: Rotemberg vs. Calvo

We compare two widely used pricing assumptions in the New-Keynesian literature: the Calvo and Rotemberg price-setting mechanisms. We show that, once trend in?ation is taken into account, the two models are very different. i) The long-run relationship between inflation and output is positive in the Rotemberg model and negative in the Calvo model. ii) The log-linearized NKPCs are very different and the dynamics of the two models differs even to a first order approximation. iii) Positive trend inflation enlarges the determinacy region in the Rotemberg model, while it shrinks the determinacy region in the Calvo model. iv) The responses of output and inflation to a positive technology shock are amplified by trend inflation in Calvo, while they are damped in Rotemberg. v) The two models imply a different non-linear adjustment after a disinflation.