Comment on Relative Price Variability and Inflation in Reinganum's Consumer Search Model

There is now a large empirical literature on the effect of the aggregate inflation rate on (i) the dispersion of prices across goods or locations (relative price variability, or RPV) and (ii) the dispersion of inflation rates across goods or locations (relative inflation variability, or RIV). In the early part of this literature, empirical modelling is explicitly based on theoretical macroeconomic models incorporating signal extraction problems. However, more recent empirical research is less directly connected to theory, and several authors report results that are inconsistent with signal extraction models. In particular, while RIV is increasing in the absolute value of inflation shocks, RPV is a negative monotonic function of inflation shocks. In this paper, we show that such a result is predicted by consumer search models in the style of Reinganum (1979). A proper understanding of the dynamics of price dispersion in 21st century economies will require a renewed interest in the theoretical foundations of empirical models.