A RELATIONSHIP BETWEEN MARKET SHARE ELASTICITIES AND BRAND SWITCHING PROBABILITIES

The authors derive a theoretical relationship between the aggregate ma rket share elasticity matrix and the aggregate brand switching matrix on the basis of a legit model of heterogeneous consumers choosing amon g competing brands in a product class. Aggregate cross-elasticities ar e shown to be proportional (through a single scaling constant) to thei r corresponding aggregate row-conditional brand switching probabilitie s. Aggregate own-elasticities are shown to be proportional (through th e negative of the same scaling constant) to one minus their correspond ing aggregate row-conditional repeat purchase probabilities. An empiri cal analysis conducted on household scanner panel data in the liquid l aundry detergent category shows that the theoretical correspondence ho lds as a very good approximation. An illustrative use of the relations hip in estimating aggregate (store-level) models of market share indic ates that the relationship helps improve predictive validity in a hold out period.