Babson College - Do Models of Vertical Strategic Interaction for National and Store Brands Meet the Market Test?

Formulating theoretical models inevitably requires various simplifications that assist in making analysis tractable and that facilitate deriving closed form solutions. Although the strategic insights gained from theoretical models of market phenomena are often valuable, testing the theoretical assumptions made in these models can aid in assessing the broader applicability of the conclusions drawn. This is particularly true in the channels area, where the focus of research to date has largely been theoretical in nature. Empirically examining the common assumptions used in the theoretical channels literature is the primary objective of our research.

Thus, we begin our article by developing a methodology to test these assumptions rigorously. In developing this methodology, we follow two of the most widely cited models in the literature on vertical channel interaction and private labels (Choi, 1991; Raju, Sethuraman. and Dhar, 1995) closely, expanding upon them where appropriate. More powerful "nested" tests arc developed and used wherever possible.

In this initial attempt to examine some of the assumptions made in previous theoretical research (e.g., Jeuland and Shugan, 1983; McGuire and Staelin, 1983; Choi. 1991; Raju, Sethuraman, and khan, 1995), we focus on a limited set of issues. First, we empirically examine the two most common vertical channel assumptions made theoretical models of retailer-manufacturer interaction: the Vertical Nash (VN) and Manufacturer Stackelberg (MS) models (Choi 1991). Under VN interaction, each manufacturer chooses its wholesale price conditional on both the retailer's margin on its own product and the observed retail price of the competing brand, whereas the retailer determines the margin of each brand conditional on the wholesale prices. Under MS interaction, each manufacturer chooses its wholesale price based on the retailer's best response function, conditional on the wholesale price of its competitor; the retailer determines the price of each product so as to maximize the total profit from both brands given the manufacturer's wholesale prices. Thus, each form of vertical interaction captures a very different form of competitive interaction across players within the channel.

Second, we relax the underlying assumption of strategic profit maximizing behavior by retailers to test for proportional mark-up as a "rule of thumb" pricing practice by retailers. Many theoretical and empirical models have assumed that retailers apply a proportional mark-up to manufacturer's wholesale prices to simplify the analysis. Although this assumption often makes analysis tractable, it necessarily implies that retailers do not act strategically in setting retail prices (since they "blindly" apply a mark-up rule to wholesale prices). Consequently, it seems important to test whether or not such an assumption "meets the market test" empirically.

Third, because most theoretical models in the literature on private labels and channels assume relatively simple linear demand structures, we examine how well linear demands characterize actual market behavior. In doing so, we first examine the assumptions made in two well-cited models and then we compare the general linear form to a flexible non-linear form, the LA/AIDS model.

The empirical analysis is conducted using data for six individual categories (milk, butter, bread, pasta, margarine, and instant coffee) across 59 local markets in 1991 and 1992. There are three main empirical findings. First, whereas the empirical results pertaining to vertical strategic interaction generally support the VN model of channel interaction, the results vary by category and by type of brand (national brand versus private label). For example, VN interaction is more common for private label brands, whereas vertical interaction for national brands is considerably more varied. This finding of cross-category and cross-brand variability in vertical strategic interaction is consistent with recent research by Putsis and Dhar (1998) that suggests that horizontal strategic interaction (HSI) also has a similar degree of variability. Second, we generally reject the use of proportional mark-up behavior by retailers, consistent with recent research by Karunakaran (2000). This suggests that while such assumptions may make models developed in the theoretical research in the channels area more tractable, they are not likely to be representative of actual market behavior. Finally, we reject linear demands in a favor of a more flexible nonlinear form. This suggests that theoretical work in this area should move to more flexible forms wherever possible.

More generally, while the nature of the vertical strategic interaction may be idiosyncratic m the category and brand, we find that demand form and the use of proportional mark-ups by retailers is not (indeed neither linear demands nor the use of proportional mark-ups can be supported empirically). These results are extremely important for interpreting the realworld applicability of conclusions drawn from theoretical models of channels behavior and of private label-national brand interaction. As a consequence, results from theoretical models that employ linear demands and the use of proportional mark-up by retailers should be viewed with caution. The relaxation of these assumptions should be a key feature of future theoretical research.

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