Precautionary price stickiness

This paper proposes a model in which retail prices are sticky even though firms can always change their prices at zero cost. Instead of imposing a "menu cost", we assume that more precise decisions are more costly. In equilibrium, firms optimally make some errors in price-setting, thus economizing on managerial time. Both the time cost of choice, and the resulting risk of errors, give firms an incentive to leave their prices unchanged until they perceive a sufficiently large deviation from the optimal price. We show that pricing errors help explain several "puzzles" from microdata: (1) small and large price changes coexist; (2) the probability of price adjustment is largely independent of the time since last adjustment; (3) the size of the adjustment is largely independent of the time since last adjustment; (4) extreme prices are younger than prices near the center of the distribution; (5) the coefficient of variation of prices is greater than that of costs; (6) the standard deviation of price adjustments is largely independent of the inflation rate, and the fraction of price increases converges slowly towards 100% as inflation rises. However, on the macroeconomic side, pricing errors do little to explain the real effects of monetary shocks. Since firms making sufficiently large errors always choose to adjust, a nominal shock generates a strong, inflationary "selection effect". Thus, like Golosov and Lucas (2007), we find that money shocks are almost neutral, but our model fits microdata better than their specification does.