Endogeneity of store attributes in heterogeneous store-level sales response models

Abstract

Retailing firms as a rule decide on store attributes (e.g., store size) considering an assessment of future sales of these stores. Typically, managers allocate better or more equipment to stores for which they expect higher sales. Models which ignore the fact that this behavior leads to endogeneity overestimate effects of these attributes. Managers, who base decisions on such models, loose profits by installing more (or more costly) equipment. The number of papers studying store-level sales response models accounting for endogeneity appears to be very limited. We consider potential endogeneity of store attributes in the sales response function by an instrumental variable approach. We also allow for heterogeneity across stores by assuming that store-level coefficients are generated by a finite mixture distribution. Models are estimated by a Markov chain Monte Carlo simulation technique which combines two Gibbs sampling algorithms. In the empirical study both heterogeneity and endogeneity turn out to influence estimates. For a cross section of more than 1,000 gas stations credible intervals of differences of coefficients are computed between models ignoring and models considering endogeneity. These intervals indicate that models which ignore endogeneity overestimate the effects of two store attributes on sales. We also discuss managerial implications of these endogeneity biases.