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

to the standard logit model, the random-coefficients logit model imposes very few restrictions on
the demand own and cross-price elasticities. This flexibility makes it the most appropriate model
to get consistent estimates of the demand parameters required in the computation of the price-cost
margins.

As in Bonnet and Dubois (2010), we use a random coefficient logit model but allow a more
flexible specification of random utility with more heterogeneity of preferences and estimate the
demand on individual purchase choices instead of aggregate data (we also use more recent data
using the year 2006 instead of 1998-2000).

The basic specification of the direct utility function of a consumer i buying product j at t is

Uijt = βb[j) ÷ β_r(j) + ^δi^χj — aipj_t + Sij_t                          ⁽¹⁸⁾

where β_b(_j∙) represents a brand specific effect on utility capturing time invariant brand characteris-
tics, β_r(j) represents a retailer specific effect capturing time invariant retailer characteristics, Xj is
a dummy variable which is equal to 1 if the product j is a mineral water and 0 otherwise, p_j∙_t is the
price of product j at period t, and Sij_t is a separable additive random shock to utility. The random
coefficient α_i represents the unobserved marginal disutility of price for consumer i. We assume
that α_i = a ÷ σ^aυij^x where υβ is an unobserved consumer characteristic and σ^a characterizes how
consumer marginal disutility of price deviates form the mean disutility of price a with this unob-
served characteristic. We also assume that consumers have different tastes for the mineral water
versus spring water characteristic. Hence, we write δ_i = δ ÷ σ^δυ^δ where υ^δ represents unobserved
consumer characteristic and δ the mean taste for that product characteristic.

The model is completed by the inclusion of an outside good, denoted good zero, allowing
consumer i not to buy one of the J marketed products. The mean utility of the outside good
is normalized to zero implying that the consumer indirect utility of choosing the outside good is
^Ui0t = ^siθt.

Then, doing the usual parametric assumption on Sij_t would allow to write a closed form solution
for the probability for a consumer i to buy a product j at a given period. However, more than the

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