Inference for Product Competition and Separable Demand
Adam N. Smith, Peter E. Rossi, Greg M. Allenby
Marketing Science · 2019 · Volume 38 · Issue 4
Abstract
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 the basis for establishing similarity between products 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. We develop a methodology that allows the partition to be an estimated model parameter. In particular, we specify a log-linear demand system in which 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 inconsistent with category labels, which has implications for optimal category marketing strategies.
Keywords
price elasticities, category demand, dimension reduction, random partition models, Bayesian inference
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