The Distribution of the Size of Price Changes

Abstract

Different theories of price stickiness have distinct implications on the number of modes in the distribution of price changes. We formally test for the number of modes in the price change distribution of 36 supermarkets, spanning 22 countries and 5 continents. We present results for three modality tests: the two best-known tests in the statistical literature, Hartigan's Dip and Silverman's Bandwidth, and a test designed in this paper, called the Proportional Mass test (PM). Three main results are uncovered. First, when the traditional tests are used, unimodality is rejected in about 90 percent of the retailers. When we used the PM test, which reduces the impact of smaller modes in the distribution and can be applied to test for modality around zero percent, we still reject unimodality in two thirds of the supermarkets. Second, category-level heterogeneity can account for about half of the PM test's rejections of unimodality. Finally, a simulation of the model in Alvarez, Lippi, and Paciello (2010) shows that the data is consistent a combination of both time and state-dependent pricing behaviors.