From market shares to consumer types: duality in diferentiated product demand estimation

A widely applied method for differentiated product demand estimation, introduced by Berry, Levinsohn and Pakes in 1995, is founded on matching observed and theoretical market shares of products. In this paper, we allow for discrete consumer tastes and derive an equivalent matching occurring in the consumer type space. The equivalence between the two formulations expresses a duality between market shares and consumer types. In applications where a large number of products and a small number of consumer types is natural, the dual formulation introduced in this paper is computationally more efficient than the primal. Indeed, simulation exercises show that the dual method can be significantly faster.