Relative Price Dispersion: Evidence and Theory

Abstract

Relative price dispersion is defined as persistent differences in the price that retailers set for the same good relative to the price they set for their other goods. Using a large-scale dataset on prices in the US retail market, we document that relative price dispersion accounts for about 30% of the variance of prices for the same good, in the same market, during the same week. Using a search-theoretic model of the retail market, we show that relative price dispersion can be rationalized as the equilibrium consequence of a pricing strategy used by sellers to discriminate between high-valuation buyers who need to make all of their purchases in one store, and low-valuation buyers who are able to purchase different items in different stores.

Equilibrium price dispersion across and within stores

“…For instance, if sellers post prices ((  )   ), we find that the overall standard deviation of prices is 23%, the across store variance is 56% of the overall variance, and the within store variance is 44%. These numbers are very close to those found by Kaplan and Menzio (2015), which shows that our simple model has the potential to match some of the key empirical facts about price dispersion.…”

“…Naturally, it would be interesting to estimate our model using the econometric techniques developed by Hong and Shum (2006) and Moraga-Gonzales and Wildenbeest (2009). Also, it would be useful to intergrate our model with the multiproduct model of Kaplan et al (2015) to build a unified framework for studying pricing in the retail market.…”

“…To formalize the above argument, consider an equilibrium in which the marginal price 5 Indeed, the results in Subsection 3.4 are used by Kaplan et al (2015) in the context of a model of multiproduct retailing. Lester et al (2015) develop similar arguments to solve for the equilibrium distribution of multiple screening contracts in the context of a model of the asset market.…”

Self-confirming Price Dispersion in Monetary Economies

“…Our work complements the existing literature on price dispersion in non-monetary models. In order to generate price dispersion, such models often need to assume some form of heterogeneity such as in outside options (as in Albrecht and Axell (1984)), in search opportunities (as in Lester (2011), Menzio and Trachter (2018), or Kaplan et al (2016)), or in seller size (as in Menzio and Trachter (2015)). In contrast, all the buyers and sellers in our model are identical in every respect, and price dispersion is entirely self-confirming.…”

The (Q,S,s) pricing rule: a quantitative analysis

“…where = ( + )= . Note that this is the price distribution that would emerge in an Next, consider the stationarity condition (13), which is a di¤erential equation for the price distribution F over the interval (S; Q). Using the fact that F is given by (16) and 17, we can solve (13) with respect to the new price distribution G and …nd…”