Optimal trend inflation

We present a sticky-price model incorporating heterogeneous firms and systematic firm-level productivity trends. Aggregating the model in closed form, we show that it delivers radically different predictions for the optimal inflation rate than canonical sticky price models featuring homogenous firms: (1) the optimal steady-state inflation rate generically differs from zero and (2) inflation optimally responds to productivity disturbances. Using micro data from the US Census Bureau to estimate the inflation-relevant productivity trends at the firm level, we find that the optimal US inflation rate is positive. It was slightly above 2 percent in the year 1986, but continuously declined thereafter, reaching about 1 percent in the year 2013.