Logit Price Dynamics

Abstract

We propose a near-rational model of retail price adjustment consistent with microeconomic and macroeconomic evidence on price dynamics. Our framework is based on the idea that avoiding errors in decision making is costly. Given our assumed cost function for error avoidance, the timing of firms’ price adjustments is determined by a weighted binary logit, and the prices they choose are determined by a multinomial logit. We build this behavior into a DSGE model, estimate the decision cost function by matching microdata, and simulate aggregate dynamics using a tractable algorithm for heterogeneous-agent models. Both errors in the prices firms set, and errors in the timing of these adjustments, are relevant for our results. Errors of the first type help make our model consistent with some puzzling observations from microdata, such as the coexistence of large and small price changes, the behavior of adjustment hazards, and the relative variability of prices and costs. Errors of the second type increase the real effects of monetary shocks, by reducing the correlation between the value of price adjustment and the probability of adjustment, (i.e., by reducing the/selection effect»). Allowing for both types of errors also helps reproduce the effects of trend inflation on price adjustment behavior. Our model of error-prone pricing in many ways resembles a stochastic menu cost (SMC) model, but it has less free parameters than most SMC models have, and unlike those models, it does not require the implausible assumption of i.i.d. adjustment costs. Our derivation of a weighted logit from control costs goers an alternative justification for the adjustment hazard derived by Woodford (2008). Our assumption that costs are related to entropy is similar to the framework of Sims (2003) and the subsequent/rational inattention» literature. However, our setup has the major technical advantage that a firm’s idiosyncratic state variable is simply its price level and productivity, whereas under rational inattention a firm’s idiosyncratic state is its prior (which is generally an infinite-dimensional object).

Keywords: nominal rigidity, logit equilibrium, state-dependent pricing, near rationality, information-constrained pricing

JEL Classification: E31, D81, C72