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.