Inference for Product Competition and Separable Demand

59 Pages Posted: 1 Nov 2016 Last revised: 22 Feb 2020

See all articles by Adam N. Smith

Adam N. Smith

University College London - UCL School of Management

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management

Greg M. Allenby

Ohio State University (OSU) - Department of Marketing and Logistics

Date Written: November 29, 2018

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 which 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, price promotions, random partition models, Bayesian inference

Suggested Citation

Smith, Adam N. and Rossi, Peter E. and Allenby, Greg M., Inference for Product Competition and Separable Demand (November 29, 2018). Available at SSRN: https://ssrn.com/abstract=2861986 or http://dx.doi.org/10.2139/ssrn.2861986

Adam N. Smith (Contact Author)

University College London - UCL School of Management

One Canada Square
London, E14 5AA
United Kingdom

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States
773-294-8616 (Phone)

Greg M. Allenby

Ohio State University (OSU) - Department of Marketing and Logistics ( email )

Fisher Hall 524
2100 Neil Ave
Columbus, OH 43210
United States

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