Optimal inflation and firms' productivity dynamics

Empirical data indicate that firms tend to have below-average productivity upon entry

and that they tend to experience post-entry productivity growth. I present a New Keynesian

model with growth in firm-specific productivity and firm turnover that captures these two

phenomena. The model predicts that the optimal rate of long-run inflation is positive and

equal to growth in firm-specific productivity. When linearized at positive optimal inflation,

the model is observationally equivalent to the basic New Keynesian model with homogenous

productivity linearized at zero inflation. Optimal stabilization policies are the same in both

models, and the Taylor principle ensures determinacy in either model.