In this paper, we develop a framework for estimating market share and price reaction equations in an attempt to understand the nature of competitive interaction in the market for private label and branded grocery products. Specifically, we employ a Linear Approximate Almost Ideal Demand System (LA/AIDS, Deaton and Muellbauer 1980a), and specify the price reaction equations derived under the LA/AIDS demand specification. This enables us to consistently estimate shareprice relationships, accounting for demand-side and competitive reactions simultaneously. The incorporation of LA/AIDS demands into a structural equation framework represents an important departure from previous demand specifications in competitive analysis. In addition to its rigorous foundation in utility theory, LA/AIDS demands are especially flexible for demand-side estimation, provide consistent reaction functions on the supply side, and have particularly nice aggregation properties. In order to test the relative contribution of employing a flexible LA/AIDS functional form on the demand-side, and in a preliminary attempt to assess manufacturer-retailer interaction on the supply side, we compare our general framework (LA/AIDS demands with retailers following a proportional markup rule) to two alternative models of manufacturer-retailer interaction: Chois (1991) Manufacturer-Stackelberg (M-S) model under linear demands, as well as Shubik demands under Stackelberg conduct (Raju, Sethuraman and Dhar 1995a, 1995b). We first apply the proposed LA/AIDS framework to a sample pooled across 125 categories and 54 geographic markets in an attempt to produce result that generalize across the entire sample. We then estimate all three models using data on seven individual categories: bread, milk, pasta, yogurt, instant coffee, butter and margarine. We conclude that the LA/AIDS demand specification is preferred to the alternative linear demand specifications. Further, the empirical findings support our premise that consumer response to price and promotion decisions (demand) and the factors influencing firm pricing behavior (supply) jointly determine observed market prices and market shares. Most importantly, our specification with LA/AIDS demands produced excellent overall fits, as well as reasonable demand and price response elasticities.
