Estimating a Multinomial Probit Model of Brand Choice Using the Method of Simulated Moments

The multinomial probit model of brand choice is theoretically appealing for marketing applications as it is free from the "independence of irrelevant alternatives" property of the multinomial logit model. However, difficulties in estimation have restricted its widespread use in marketing. This paper presents an application of the method of simulated moments, a new methodology that enables easy estimation of probit models with a large number of alternatives in the choice set. We describe the theoretical development of the technique and using pseudo-simulated data, conduct numerical experiments to compare the method with existing techniques for estimating probit models. Using the scanner panel data on the purchases of catsup, we provide an empirical application of the method of simulated moments to the estimation of the parameters of a multinomial probit model. Estimating the covariance structure associated with the underlying latent variable probit model enables us to identify broad patterns of similarities across alternatives. It also enables us to derive a pairwise similarity matrix across choice alternatives which when input into a multidimensional scaling routine provides us with a graphical representation of competitive structure in the catsup market. For completeness, we compare the substantive implications for the effects of marketing variables obtained from the multinomial probit model with those obtained from models in the extant marketing literature.