We document three new empirical facts: (i) monetary policy shocks increase the markup dispersion across firms, (ii) they increase the relative markup of firms with stickier prices, and (iii) firms with stickier prices have higher markups. This is consis- tent with a New Keynesian model in which price rigidity is heterogeneous across firms. In the model, firms with more rigid prices optimally set higher markups and their markups increase by more after monetary policy shocks. The consequent increase in markup dispersion explains a negative aggregate TFP response. In a calibrated model, monetary policy shocks generate substantial fluctuations in aggregate productivity.