Identification and Estimation of Demand for Bundles

Abstract

We present novel identification and estimation results for a mixed logit model of demand for bundles with endogenous prices given bundle-level market shares. Our approach hinges on an affine relationship between the utilities of single products and of bundles, on an essential real analytic property of the mixed logit model, and on the existence of exogenous cost shifters. We propose a new demand inverse in the presence of complementarity that enables to concentrate out of the likelihood function the (potentially numerous) market-product specific average utilities, substantially alleviating the challenge of dimensionality inherent in estimation. To illustrate the use of our methods, we estimate demand and supply in the US ready-to-eat cereal industry, where the proposed MLE reduces the numerical search from approximately 12000 to 130 parameters. Our estimates suggest that ignoring Hicksian complementarity among different products often purchased in bundles may result in misleading demand estimates and counterfactuals.