The Distribution of the Size of Price Changes
NBER Working Paper No. 16760
Different theories of price stickiness have distinct implications on the properties of the distribution of price changes. One of those characteristics is the number of modes in the distribution. We formally test for the number of modes in the price change distribution of 32 supermarkets, spanning 23 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 Bandwith, 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, the unimodality around zero is rejected in about 90 percent of the establishments. When we used the PM test, which is more conservative than the first two, we still reject unimodality in two thirds of the supermarkets. There is significant heterogeneity across countries: the US, UK, and Uruguay are the most "unimodal" while the other countries in the sample exhibit significant bi-modality. Second, if we center the PM test on the largest mode – as opposed to zero – we have few rejections of unimodality. Finally, the rejection of unimodality changes through time and with the level of inflation. In countries where there is large inflation the distribution is unimodal around a positive value. In some countries where inflation drops over time – as it happened during the recent financial recession – unimodality at zero starts to disappear again. These results offer new stylized facts that theoretical models of price stickiness need to match. We perform a simple simulation exercise at the end using the model by Alvarez, Lippi, and Paciello (2010) and applying our PM test of unimodality to the model’s distributions.
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