Menu Costs and Markov Inflation: A Theoretical Revision with New Evidence

We revisit a foundational theoretical paper in the menu cost literature, Sheshinski and Weiss (1983), one of the few to treat stochastic inflation with persistent deviations from trend. In contrast to the original finding, we find that optimal pricing in this environment entails using different (s,S) bands in high-inflation and low-inflation states of the world. The low-inflation band is strictly contained within the high-inflation band. This revised solution has very different implications from the original one. Firms are generally risk-loving, not risk-averse, with respect to inflation. An increase in the variance of inflation increases price dispersion when inflation is high and decreases price dispersion when inflation is low. On an aggregate level, this optimal pricing would lead to bunching of prices and non-neutrality of money in the setting of Caplin and Spulber (1987). To test the main finding, we construct an establishment-level dataset from the months surrounding Mexico's Tequila crisis, in 1995. In the high-inflation state, price increases are larger and establishments allow their prices to vary more widely around their respective long-run mean relative prices. Cross-establishment price dispersion is lower, but this result seems due to decreased establishment heterogeneity rather than narrower (s,S) bands. Overall, the evidence suggests that establishments employ wider (s,S) bands in the high-inflation state.