Optimal trend inflation, misallocation and the pass-through of labour costs to prices

We show that a sticky price model featuring firms' heterogeneity in terms of productivity and strategic complementarities in price setting delivers a strictly positive optimal inflation in steady state, differently from standard New Keynesian models. Due to strategic complementarities, more productive firms have higher markups in steady state. This leads to a misallocation distortion, as more productive firms produce too little compared to the social optimum. An increase of steady state inflation curbs the markups, especially those of the more productive firms, hence attenuating the inefficient dispersion of markups. At low levels of inflation, the gains from the reduction in misallocation outweigh the cost of inflation. Heterogeneity in productivity and strategic complementarities in price setting, the key ingredients of our model, imply that also firms' response to shocks is heterogenous: less productive firms transmit cost shocks to prices much more than more productive ones. To provide empirical support to our key mechanism we resort to a quasi-natural experiment occurred in Italy in late 2014, when a cut to social security contributions for all new open-ended contracts was announced. Consistently with our theory, we show that the pass-through of this shock to labour costs was much stronger for less productive firms.