A Relationship between Market Share Elasticities and Brand Switching Probabilities

Abstract

The authors derive a theoretical relationship between the aggregate market share elasticity matrix and the aggregate brand switching matrix on the basis of a logit model of heterogeneous consumers choosing among competing brands in a product class. Aggregate cross-elasticities are shown to be proportional (through a single scaling constant) to their corresponding aggregate row-conditional brand switching probabilities. Aggregate own-elasticities are shown to be proportional (through the negative of the same scaling constant) to one minus their corresponding aggregate row-conditional repeat purchase probabilities. An empirical analysis conducted on household scanner panel data in the liquid laundry detergent category shows that the theoretical correspondence holds as a very good approximation. An illustrative use of the relationship in estimating aggregate (store-level) models of market share indicates that the relationship helps improve predictive validity in a holdout period.