We prove that the ratio of kurtosis to the frequency of price changes is a sufficient statistic for the real effects of monetary shocks, measured by the cumulated output response following the shock. The sufficient statistic result holds in a large class of models which includes Taylor (1980); Calvo (1983); Reis (2006); Golosov and Lucas (2007); Nakamura and Steinsson (2010); Midrigan (2011); and Alvarez and Lippi (2014). Several models in this class are able to account for the positive excess kurtosis of the size distribution of price changes that appears in the data. We review empirical measures of kurtosis and frequency and conclude that a model that successfully matches the microevidence on kurtosis and frequency produces real effects that are about four times larger than in the Golosov-Lucas model, and about 30 percent below those of the Calvo model. We discuss the robustness of our results to changes in the setup, including small inflation and leptokurtic cost shocks.