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) ÷ βr(j) + δiχj aipjt + Sijt                          (18)

where βb(j∙) represents a brand specific effect on utility capturing time invariant brand characteris-
tics,
βr(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
jt is the
price of product j at period t, and
Sijt 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 ÷ σaυijx where υβ is an unobserved consumer characteristic and σa 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
δi = δ ÷ σδυδ where υδ 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 Sijt 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

19



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