The results show that the price coefficient has the correct sign. In the case of the random
coefficient logit model, the price coefficient has a distribution with mean equal to 20.33 and standard
deviation σa equal to 6.42 which means that only 0.07% of the distribution of the coefficient ai
has the wrong sign. The mean taste of the mineral characteristic is positive which means that
consumers like mineral waters. Only 17.6% do not like it. In the multinomial or random coefficient
logit model, the parameter τ of the control term 77j∙t (obtained from a first stage price regression
shown in appendix 7.3) is significantly positive showing that, on one hand, some correlation existed
between prices and unobserved product characteristics included in the error term Sijt and these
unobserved characteristics would enter positively in the utility function. We would expect that
product advertising increases the consumer utility and is also positively correlated with price,
giving an interpretation to this control function approach as in Petrin and Train (2010).
Finally, once we obtained our structural demand estimates, we can compute price elasticities of
demand for these differentiated products. Table 3 presents the different average elasticities obtained
with the estimates of the random-coefficients logit model. Although the data are more recent and
the demand model more flexible and estimated on individual data, we obtain that mineral waters
are more sensitive to price variation than spring waters as in Bonnet and Dubois (2010).
Average Own-price Elasticities (Ejk)
Mean (Std. Dev.)
All -5.80 (1.68)
Mineral water -6.70 (0.63)
Spring water -3.09 (0.63)
Table 3 : Estimated Elasticities under Random Coefficients Logit
5.2 Estimation of Price-Cost Margins and Non Nested Tests
Once one has estimated the demand parameters, we can use the formulas obtained in section 3
to compute the price-cost margins at the retailer and manufacturer levels, for all products, under
the various classes of models considered. Under some models, wholesale, retail or total margins are
not identified without additional restrictions that we will thus impose. Empirically, we are able to
solve the minimization problem (23) using the additional restriction (22).
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