Time-dependent pricing and New Keynesian Phillips curve

This paper explores what can be lost when assuming price adjustment is a time - independent (memoryless) process.I derive a generalized NKPC in an optinizing model with the non- constant hazard function and trend inflation. Memory emerges in the resulting Phillips curve through the presence of lagged inflation and lagged expectations. It nests the Calvo NKPC as a limitting case in the sense that the effect of both terms are canceled out by one another under the constant-hazard assumption. Furthermore, I find lagged inflation always has negative coefficients, thereby making it impossible to interpret inflation persistence as intrinsic to the model. The numerical evaluation shows that introducing trend inflation strengthens the effects of the increasing hazard function on the inflation dynamics . The model can jointly account for persistent dynamics of inflation and output, hump-shaped impulse responses of inflation to monetary shocks, and the fact that high trend inflation leads to more persistence in inflation but not for real variables.