Relative price and inflation variability in a simple consumer search model

There is a large empirical literature on the effect of aggregate inflation on both price-level dispersion (relative price variability, RPV) and inflation rate dispersion (relative inflation variability, RIV) across goods or locations. Early empirical work of RIV has an explicit theoretical foundation in signal-extraction models. However, recent empirical work on RPV has produced results 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. We show that consumer search theory offers a potential explanation for these apparently contradictory observations.