The Optimal Inflation Rate and the Sources of Productivity Growth

We consider a sticky price economy with exogenous firm entry and exit, featuring three sources of productivity growth: (1) general TFP increases affecting all firms, (2) a learning effect causing firms to become more productive with age, and (3) a cohort effect that causes newly entering firms to expand the technology frontier. Aggregating the model with heterogeneous firms in closed form, we show that the welfare optimal steady state inflation rate is generally different from zero. The optimal inflation rate increases with the strength of the learning effect, decreases with the strength of the cohort effect and is independent of the strength of the TFP effect. In the absence of firm turnover, the optimal inflation rate jumps discontinuously and is zero at all times. To the extent that aggregate growth is increasingly driven by productivity gains of newly entering firms, the model thus suggests lower inflation rates to be optimal. We provide some empirical evidence in this regard.