A BLP Demand Model of Product-Level Market Shares with Complementarity

Applied researchers most often estimate the demand for differentiated products assuming that at most one item can be purchased. Yet simultaneous multiple purchases are pervasive. Ignoring the interdependence among multiple purchases can lead to erroneous counterfactuals, in particular, because complementarities are ruled out. I consider the identification and estimation of a random coefficient discrete choice model of bundles, namely sets of products, when only product-level market shares are available. This last feature arises when only aggregate purchases of products, as opposed to individual purchases of bundles, are available, a very common phenomenon in practice. Following the classical approach with aggregate data, I consider a two-step method. First, using a novel inversion result in which demand can exhibit Hicksian complementarity, I recover the mean utilities of products from product-level market shares. Second, to infer the structural parameters from the mean utilities while dealing with price endogeneity, I use instrumental variables. I propose a practically useful GMM estimator whose implementation is straightforward, essentially as a standard BLP estimator. Finally, I estimate the demand for Ready-To-Eat (RTE) cereals and milk in the US. The demand estimates suggest that RTE cereals and milk are overall complementary and the synergy in consumption crucially depends on their characteristics. Ignoring such complementarities results in misleading counterfactuals.