The misallocation costs associated with different aggregate inflation rates can be estimated from micro price data via a set of sufficient statistics. We show that this works for a broad class of price-setting models and in the presence of unobserved product-level heterogeneity in pricing frictions and flexible prices. Applying the sufficient statistics approach to the micro price data underlying the U.K. consumer price index, we find large misallocation costs: aggregate productivity falls by about 1% if aggregate inflation is 8 percentage points above or below its optimal rate of 1.8%. Our findings provide important lessons for the calibration of sticky-price models: standard calibration targets can be uninformative about the sufficient statistics characterizing misallocation costs. To correctly capture these costs, models should be directly calibrated to the sufficient statistics that we uncover.
 

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