Combining Prior Information and Data to Uncover the
Parameters from the Random Coefficient Discrete–
Choice Demand Model
Sergio Aquino DeSouza**
Abstract
Demand estimation in product-differentiated industries has been the central object in many studies in the
industrial organization field. Indeed, after pinning down the preference parameters it is possible to analyze
issues related to innovation, antitrust (mergers and divestitures), calculation of quality adjusted price-
indices and prediction of the competitive effect of entry and exit of products. However, uncovering
consumers’ preferences using aggregate data on product-differentiated markets imposes a serious
challenge: find instruments do deal with price endogeneity. Berry, Levinsohn, and Pakes (1995) propose a
GMM method based on instruments that are functions of the regressors (except price) to estimate general
Random Coefficients Discrete-Choice models. However, these instruments may prove to be in many
instances weakly correlated with the endogenous variable (price), leading to inference problems regarding
the estimation of the coefficient on price. The key contribution of this paper is to show how to incorporate
more prior information into the empirical strategy in order to avoid the need for such instruments. What I
propose in this work is to augment the researchers’ set of prior information. I use prior information on the
aggregate price elasticity to propose a two-stage methodology that is able to determine the parameters of a
particular class of Random Coefficients Discrete-Choice models. I show that, provided that the prior
information is valid, we can determine the demand parameters using only the exogenous regressors
(characteristics other than prices) as instruments, avoiding then the need to use potentially weak
instruments. Finally, for illustrative purposes, I apply this methodology to the ready-to-eat cereal industry
and simulate the entry of new products.
Keywords- Discrete-Choice; Demand, Mixed Logit
Resum