A comparison of semiparametric and heterogeneous store sales models for optimal category pricing

Abstract

Category management requires sales response models helping to simultaneously estimate marketing mix effects for all brands of a product category. We, therefore, develop a general heterogeneity seemingly unrelated regression (SUR) model accommodating correlations between sales across brands. This model contains a latent class SUR model, the well-known hierarchical Bayesian SUR model and the homogeneous SUR model as special cases. We further propose a hierarchical Bayesian semiparametric SUR model based on Bayesian P-splines which comprises a homogeneous semiparametric SUR model as nested version. The results of an empirical application with store-level scanner data indicate that the flexible SUR approaches of modeling price response clearly outperform the various parametric (homogeneous and heterogeneous) SUR approaches with respect to not only predictive validity but also total expected category profits. In particular, functional flexibility turns out to be the primary driver for improving the predictive performance of a store sales model as heterogeneity pays off only once functional flexibility has been accounted for. Furthermore, since both flexible SUR models perform nearly equally well with respect to expected category profits, a uniform pricing strategy which is much less complex to implement than micromarketing can be recommended for our data.