Vertical Contracts between Manufacturers and Retailers: Inference with Limited Data

In this paper we compare different models of vertical contracting between manufacturers and retailers in the supermarket industry. 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 which set of margins is compatible with the margins obtained from direct estimates of cost and to select among non-nested competing models the one most consistent with the data. 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, nonlinear pricing and strategic behavior with respect to private label products. Using data on yogurt sold in several stores in a large urban area of the United States, we find that wholesale prices are close to marginal cost and that retailers have pricing vertical chain. This is consistent with non-linear pricing by the manufacturers or high bargaining power of the retailers.