From Market Shares to Consumer Types: Duality in Differentiated Product Demand Estimation

This paper develops a dual formulation for differentiated product demand estimation in models based on the Berry-Levinsohn-Pakes (BLP) framework. Rather than matching observed and theoretical product market shares, the proposed approach matches distributions in the consumer type space, establishing a duality between market shares and consumer types. The method is especially useful in applications with many products but relatively few consumer types, where the dual formulation substantially improves computational efficiency. Simulation exercises demonstrate that the approach can significantly accelerate estimation relative to the standard primal formulation.