Non Linear Contracting and Endogenous Buyer Power between Manufacturers and Retailers: Empirical Evidence on Food Retailing in France

chase. We use the information on all bottles of water purchased. For the purpose of estimation of
our structural models, we will consider the purchases in the seven most important retailers which
represent 70.9% of the total purchases of the sample. We take into account the most important
brands, that is : five national brands of mineral water, one national brand of spring water, one
retailer private label brand of mineral water and one retailer private label spring water. The pur-
chases of these eight brands represent 69.3% of the purchases of the seven retailers. The national
brands are produced by three different manufacturers : Danone, Nestlé and Castel. We consider
all other non-alcoholic refreshing drinks as the outside good.

We consider eight brands sold in seven retailer chains, which gives 56 differentiated products.
For each of these products, we compute an average price for each month using all observed purchases
by households during the month. These prices are in euros per liter. Table 1 presents some first
descriptive statistics on some of the main variables used.

Table 1 : Summary Statistics

We also use data from the French National Institute for Statistics and Economic Studies (IN-
SEE) allowing to characterize supply side cost shifters in this industry with the plastic price, a
wage salary index, and diesel oil prices.

3 Competition and Vertical Relationships Between Manu-
facturers and Retailers

We now introduce an oligopoly model with vertical relationships. As in Rey and Vergé (2004)
and Bonnet and Dubois (2010), we consider linear pricing and two part tariffs contracts but allow
also retailers to benefit from some endogenous buyer power when facing manufacturers’ offers.

Let’s introduce the model considering R retailers and F multi-brand manufacturers. We denote
J the number of differentiated products defined by the couple brand-retailer among which J' are

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