Inference for Product Competition and Separable Demand
Adam N. Smith, Peter E. Rossi, and Greg M. Allenby
This paper presents a methodology for identifying groups of products that exhibit similar patterns in demand and responsiveness to changes in price using store-level sales data. We use the concept of economic separability as an identification condition for different product groups, and build a weakly separable model of aggregate demand. A common issue with separable demand models is that the partition of products into separable groups must be known a priori, which severely shrinks the set of admissible substitution patterns. This paper relaxes this assumption and allows the partition to be an estimated model parameter. We focus on estimating partitions within a log-linear demand system where weak separability induces equality restrictions on a subset of cross-price elasticity parameters.
An advantage of our approach is that we are able to find groups of separable products rather than just test whether a given set of groups is separable. Our method is applied to two aggregate, store-level data sets. We find evidence that the separable structure of demand can be markedly different than predefined category labels, which has implications for optimal category marketing strategies.
More details on Dr. Adam Smith can be found at: https://www.mgmt.ucl.ac.uk/people/adamsmith