We document the presence of both small and large price changes in individual price records from the CPI in France and the US. After correcting for measurement error and cross-section heterogeneity, the size-distribution of price changes has a positive excess kurtosis. We propose an analytical menu cost model that encompasses several classic models, as We show that the ratio of kurtosis to the frequency of price changes is a sufficient statistics for the real effects of monetary policy in a large class of models.
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Álvarez et al. (2014) studied this question.