Semiparametric Estimation of Brand Choice Behavior

Methodist University for their comments and suggestions, and Ulrich Doraszelski for his research assistance in the programming of the simulations. Matzkin gratefully acknowledges the support of NSF through grant #SBR-9410182. Abstract In the existing marketing literature, there does not seem to be a widely accepted answer to the question: do consumers react differently to a reduction in price and to an increase in the deal discount, when purchasing brands in a given product category. Previous studies that have attempted to address this issue have used different data sets and have also assumed that price and discount have a linear effect on a brand's indirect utility. We investigate the effects of price and deals on household choices of different brands in several product categories. Rather than impose a specific parametric form on the indirect utility function, we estimate the response surface relating brand choices to the effects of these variables using semiparametric methods. We relax the linearity assumption typically imposed on the effects of the price and deal variables in the indirect utility function by allowing the effects of these variables to be captured by an arbitrary function. This specification allows for a general pattern of interaction effects between these variables to influence the systematic component of utility. Consistent with the recent literature on estimating brand choice models with panel data, we account for heterogeneity in brand preferences across consumers. Besides the semiparametric approach we also provide results obtained from a fully nonparametric specification in which we leave the distribution of the stochastic components of brand utilities unspecified (in addition to the effects of price and deals). This way, we abstract from specific parametric choice models such as logit, probit, etc. Hence, we avoid misspecification in both the systematic as well as the random components of utility. The proposed specification enables us to investigate the following questions. (a) Is the linearity assumption imposed on the systematic component of utility appropriate for available scanner panel data? (b) Do households display differential response to regular price and to deals? (c) What is the nature of interaction effects between price and deals, if any? (d) Does heterogeneity continue to play an important role after accounting for potential nonlinear price and deal effects? (e) Is it critical to relax the linearity assumption on the systematic component, or the parametric assumption on the stochastic component of brand utility in a brand choice model? To generalize our …