The Relationship Between Price Elasticities and Brand Switching Probabilities

The authors derive a theoretical relationship between the market share price elasticity matrix and the aggregate brand switching matrix using a logit model of individual consumer choice among competing brands. The elements of the market-level cross-price elasticity matrix are shown to be proportional (via a single scaling constant) to the corresponding elements of the market-level brand switching matrix (when expressed in row conditional form). Market-level own-price elasticities are shown to be proportional (via the negative of the same scaling constant) to one minus the corresponding diagonal elements of the row conditional switching matrix. The authors empirically assess this theoretical correspondence using scanner panel data for the liquid laundry detergent category. The own and cross-price elasticities based on the brand switching matrix are (1) predictive of aggregate market share variation due to price changes, and (2) outperform regression-based elasticity estimates in a hold-out time period._x000B_