Identifying price discrimination when product menus are endogenous.

• Author: Cohen, Andrew

1. Introduction

   Many markets are characterized by competing firms, with each offering a menu of goods differing in a single dimension. Oftentimes these products are sold according to nonlinear price schedules; that is, the price per unit of quantity or quality may differ along a firm's product line. Nonlinear prices are consistent with second-degree price discrimination (or nonlinear pricing), but they are also consistent with production costs that vary across quantities or qualities. Without directly observing marginal costs, however, it is difficult to distinguish between the two explanations. Over the last several years, economists have attempted to document and characterize examples of second-degree price discrimination in markets with several firms. A pioneering article in this literature is Shepard (1991), who documents quality-based price discrimination in a seemingly competitive market (retail gasoline). Shepard's insight is to treat differences in product menus as a natural experiment whereby the cost of producing a given product variant is assumed to be independent of the other variants offered on the product menu. Under the price discrimination hypothesis, a good's price depends on its relative position in a firm's product line, whereas under cost-based pricing, (1) the price of a good is independent of the other goods in the product line; that is, under the price discrimination hypothesis, the prices of the same quantity of a good sold in two different outlets will differ depending on whether larger and/or smaller quantities of that good are sold at each outlet. One can use this logic to make statements such as "Prices are discriminatory because the unit price of a given package size of brand X increases/decreases by 5% with each larger/smaller package size that brand X offers in the same market." A well-known problem associated with using variation in product menus to test for price discrimination is that product menus are unlikely to be exogenous. The return to offering a longer product line is likely to be a function of the brand's attributes--such as a better horizontal location, higher product quality, or a more recognized brand name--as is the price of any given product on the firm's line. The econometrician, however, may not be able to directly observe all or some of these attributes. Therefore, one may observe cross-sectional price differentials (i.e., differences in the prices of products with identical observable characteristics) that are consistent with price discrimination even when prices are not discriminatory. For example, a brand with more desirable unobserved attributes may find it more profitable to offer additional product variants as well as to charge higher prices--whether it is price discriminating or not. An obvious solution (employed by Shepard, among others) is to control for differences across brands by including brand characteristics--either observable quality characteristics in cross-sectional settings or fixed effects when panel data are available--in the estimated pricing equation.

   This article makes several contributions to the empirical price discrimination literature. The first contribution is a negative result: When product menus may contain more than two products, any characterization of price discrimination that relies solely on variation in prices and product menus will be biased under a reasonable and minimal set of assumptions. The statement that "the unit price of a given package size of brand X falls by 5% with each larger package size that brand X offers in the same market" is based on comparisons across markets or time. These comparisons will be biased to the extent that unit-price discounts along the product menu are a function of unobserved brand-level characteristics. The second contribution of the article is to provide assumptions under which one may characterize price discrimination using changes in product menus over time. Under reasonable assumptions, using price changes rather than levels effectively differences out the confounding influence of the brand level unobservable on unit-price discounts. I employ a difference in differences approach that compares price changes for a particular product over time when (i) new variants have been added to a firm's product menu, (ii) existing variants have been removed from a firm's product menu, and (iii) no changes have been made to a firm's product menu.

   The empirical application to package sizes of paper towels provides an example of the issues discussed above. The relationship between price levels and product menus suggests that prices are discriminatory, with higher prices being associated with offering a greater quantity of larger sizes, when minimal controls for unobservable product attributes are used. When finer controls for unobserved product attributes (in the form of more specific fixed effects) are used, these effects go away and sometimes change sign. Using the difference in differences approach, however, I find evidence that when manufacturers introduce larger paper towel sizes, it allows them to increase the prices of smaller sizes. On the other hand, when manufacturers remove larger paper towel sizes from the product menu, prices are reasonably unchanged.

   The article is organized as follows. Section 2 discusses the paper towel industry and introduces the data used in the study. Section 3 reviews theoretical and empirical papers on second-degree price discrimination. Section 4 presents the econometric framework and empirical results using the testing strategy suggested by Shepard (1991) and used by others.

   Section 5 presents the econometric framework and empirical results for the test exploiting intertemporal changes in firms' product menus and prices. Section 6 concludes.

2. The Paper Towel Industry

   Most of the top paper towel brands sold during the study period, 1994-1998, belong to one of the following firms: Fort James Corporation (the result of an August 1997 merger of Fort Howard Corporation and James River Corporation); Georgia Pacific Corporation; Kimberly Clark Corporation (which merged with Scott Paper in July 1995); and Procter and Gamble. In addition to branded paper towels, private label (i.e., towels sold under the name of the grocery store) and generic paper towels comprise a substantial quantity (approximately one-fourth) of total paper towel sales.

   The sample used in this study comes from data compiled by Information Resources Incorporated (IRI). The data have been compiled for 64 cities over 20 quarters from 1994 through 1998. Each city/quarter combination represents a "market." For each product (i.e., brand/size combination), therefore, there are 1280 potential markets in which the good could have been sold. IRI's sample is collected from grocery stores with sales greater than $2 million per year. (2) A product corresponds to a brand and a package size, where size refers to the number of rolls contained in the package.

   Assumptions about Data-Generating Process

   I have made three general assumptions about the behavior of agents in the paper towel market for purposes of tractability and ease of exposition. These assumptions are standard in the industrial organization literature, but it is worth noting that violation of these assumptions could change the interpretation of the empirical exercise performed in the article. First, I have assumed that retail prices are the result of a data-generating process that is observationally equivalent to the practice of resale price maintenance by paper towel manufacturers. (3) This assumption is valid if one believes that retailers either apply constant markups (4) or manufacturers influence retail prices for their products. (5) Second, in addition to abstracting from the relationship between manufacturers and retailers, I also abstract from interbrand strategic behavior on the part of manufacturers; that is, I treat each brand as a local monopolist (similar to Shepard 1991; Manuszak 2001; and Nevo and Wolfram 2002). Finally, I have assumed that a brand's production costs associated with a particular package size may vary across sizes. For a particular package size, however, production costs are assumed constant over quantity produced and independent of the other sizes offered by a given brand; that is, it is assumed that there are no economies of scope or scale. (6)

   Summary Statistics

   Table 1 presents some summary statistics of the paper towel brands considered in this study. The first column presents the number of markets in which each brand is observed. Not all of the brands appear in each possible market. Some of the difference will be due to geographic differences (for example, Zee was offered mainly in the western part of the United States), and some will be due to differences over time (for example, Bounty Rinse and Reuse was introduced in the middle of the study period). The remainder of the table discusses the offering and pricing of different package sizes. I define package size to be given by the number of rolls contained in each package because this is likely to be the best proxy for transportation and storage costs. There are 11 different package sizes in the sample varying from 1 to 24 rolls. There is also some variation among the brands as to which sizes they offer; for example, Brawny is the only brand that offers 24-roll packages.

   An important stylized fact for this market is that the product menu for all of the paper towel brands in the sample always includes 1-roll packages. This limits the type of variation in product menus (to the larger sizes) that one might exploit to test the price discrimination hypothesis. Columns 2-8 of the table report the frequency with which different numbers of package sizes were offered by each brand in the sample. There is a fair amount of variation within and particularly between brands. The next two columns report the frequency with which each brand changed its product menu...