A Discrete–Continuous Model for Multicategory Purchase Behavior of Households

Abstract

This article provides an integrated utility-maximizing framework for households’ multicategory purchase incidence, brand choice, and purchase quantity decisions. On a store visit, households maximize utility across several categories subject to an overall budget constraint. Then, they choose to purchase a subset of categories, in which they select a specific brand and an associated quantity level. Under their assumptions for the stochastic terms in the specification, the authors obtain closed-form expressions for the household demands, the marginal and joint purchase incidence, and the brand choice probabilities along with conditional purchase quantities. The authors show that the modeling framework accounts for both coincidence and complementarity/ substitutability across categories. In addition, it accounts for unobserved heterogeneity in the estimation. Thus, the three key features of multicategory models proposed in the literature are all reflected in the framework. The authors provide an empirical application of the methodology using four categories from the Stanford market basket data—laundry detergent, fabric softener, toilette tissue, and paper towel. The results indicate that, in general, cross-category effects, as measured by the cross-category price elasticities between brands in the categories, are small, and they arise mostly through consumers’ joint purchase incidence decisions rather than at the purchase quantity decision conditional on brand choice. This finding indicates that the effects of coincidence are larger than the effects of complementarity in these data.