In this presentation is developed a structural nonlinear equilibrium model to characterize sales and prices in the 2014 new car market in France. As is now popular in empirical industrial organization (e.g. Einav and Levin, 2010), consumers are assumed to maximize utility when choosing among a discrete set of products (including an outside good). Aggregate demands and market shares are derived from this microeconomic framework. Berry et al. (1995, 2004) detailed how the workhorse mixed logit discrete choice model can be implemented when only market shares are available. Fosgerau and de Palma (2016) recently proposed a generalized framework for demand analysis using market shares.
Several authors (e.g. Zenetti and Otter (2014)) pointed out that it is more informative to use directly aggregate finite purchase counts when available. It is here the case. Their probability distribution is characterized by parameters that model market shares of the different types of cars. It is here assumed that market shares take the form of mixtures of error component logit probabilities. The error component structure captures unobserved car attributes. It offers enough flexibility and practicability to generate realistic correlation patterns across choice alternatives.
On the supply side is assumed a Nash-Bertrand competition in price for multi-product car manufacturers. Optimal prices are characterized as nonlinear functions of market shares and marginal production costs. Up to additional, yet standard, assumptions about distribution of unobservables on the supply side (marginal cost equation) and how they are correlated with unobservable car attributes that affect demand, it can contentedly be combined with aggregate purchase counts to derive the analytical formulation of the joint distribution of sales and prices.
As contrary to sole demand analysis where price endogeneity is solved by a purely descriptive and auxiliary regression model (or other IV techniques), the proposed econometric specification explicitly models the sources of price endogeneity in equilibrium formation, namely simultaneity and unobserved correlation in the error terms.
The approach is applied using data for the new car market in France. Market is made of about 1500 car alternatives produced by around 30 manufacturers in year 2014. Sensitivity to the definition of the no-purchase option is discussed. Heterogeneity of consumers is modeled by accounting for income distribution in the population.
Bayesian inference is carried out to estimate posterior distributions of parameters. Choice of prior distributions is discussed. The NUTS sampler is used (Hofman and Gelman, 2014) in a Hamiltonian MCMC setting (Neal, 2011) with an additional data augmentation step (Albert and Chib, 1993).
The estimates are used to derive distributions of willingness-to-pay for car attributes, own and cross-price elasticities, and price-cost margins. Some merger simulations are also proposed.