Testing the Theory: Vertical Strategic Interaction and Demand Functional Form

Formulating theoretical models inevitably requires various simplifications that assist in making analysis tractable and that facilitate deriving closed form solutions. While the strategic insights gained from theoretical models of market phenomena are often quite 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. In an 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 Dhar 1995), we focus on a limited set of issues. First, we empirically examine the vertical channel assumptions made in two well-cited models of retailer-manufacturer interaction: a) the Choi (1991) Manufacturer-Stackelberg (MS) model, and b) the Raju, Sethuraman and Dhar (1995) Stackelberg model addressing store brands. Specifically, empirical tests are developed for Manufacturer Stackelberg conduct and the use of proportional mark-up rules within the channel. Second, since each of these models assume relatively simple linear demand structures, we examine how well linear demands characterize actual market behavior by comparing them 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. The empirical results generally support the assumptions of proportional mark-up behavior by retailers and Manufacturer Stackelberg conduct (Choi 1991) within the channel. While this lends support to the assumptions made in a number of theoretical models addressing channel behavior, we reject linear demands in a favor of a more flexible non-linear form. When combined with the analytical work of Lee and Staelin (1997), this suggests that additional theoretical and empirical work is needed in order to fully understand the implications of using a linear demand specification.