This paper provides new insight into the relationship between inflation and the setting of individual prices by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation. When the annual rate of inflation is low (below 10%–15%), the frequency of price changes comoves weakly with inflation because movements in the frequency of price decreases and increases partly offset each other. In contrast, the average magnitude of price changes correlates strongly with inflation because it is sensitive to movements in the relative shares of price increases and decreases. When inflation rises beyond 10%–15%, few price decreases are observed and both the frequency and average magnitude are important determinants of inflation. I show that a menu-cost model with idiosyncratic technology shocks predicts the average frequency and magnitude of price changes well over a range of inflation similar to that experienced by Mexico.

Coibion, Gorodnichenko, and Hong (2015) argue that the CPI underestimates the deceleration in consumer prices during economic downturns because the index fails to account for the reallocation of consumer spending from high-price to low-price stores. We show that their conclusion hinges on some nonstandard methodological choices, including an aggressive censoring of price adjustments and a treatment for missing observations that can leave out some of the price variation. Under our preferred methodology, the regression results no longer indicate that greater store switching during downturns is a statistically or economically significant phenomenon.