A Structured Covariance Probit Demand Model

This paper introduces a heterogeneous agent discrete choice probit demand model with a structural interpretation of product choice covariance designed to overcome two hurdles in discrete choice demand modeling. One hurdle is the curse of dimensionality implicit in covariance probit demand models and the other hurdle is the independence of irrelevant alternatives (IIA) implicit in logit demand models. The structured covariance probit exploits the fact that choice models rely on utility differences to achieve identification. The utility difference structure implied by the additive random utility model is imposed on the covariance matrix and requires just one parameter in addition to those specified in the deterministic component of consumer utility. As an additional advantage the structured covariance probit is a better out-of-sample predictor because it allows covariance to change according to characteristics of the market. To estimate the model the paper develops a Bayesian estimation approach. The model also incorporates a Dirichlet process prior over normally distributed consumer segment clusters to flexibly model demand heterogeneity. The new model is evaluated relative to the widely used heterogeneous consumer logit demand model. Sampling experiments confirm that the model performs well under misspecification. An empirical analysis demonstrates that the new probit model captures realistic unrestricted switching behavior whereas its logit counterpart exhibits restrictiveness inconsistent with the utility theory on which the model is based.