Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data

In this paper, different models of vertical relationships between manufacturers and retailers in the supermarket industry are compared. Demand estimates are used to compute price-cost margins for retailers and manufacturers under different supply models when wholesale prices are not observed. The purpose is to identify the set of margins compatible with the margins obtained from estimates of cost and to select the model most consistent with the data among non-nested competing models. The models considered are (1) a simple linear pricing model; (2) a vertically integrated model; and (3) a variety of alternative (strategic) supply scenarios that allow for collusion, non-linear pricing, and strategic behaviour with respect to private label products. Using data on yogurt sold in several stores in a large urban area of the U.S. the results imply that wholesale prices are close to marginal cost and that retailers have pricing power in the vertical chain. This is consistent with non-linear pricing by the manufacturers or high bargaining power of the retailers.