Social Sciences Brown Bag Seminar
Structural demand estimation characterizes the market share of a product competing for heterogeneous consumers based on its attributes, its endogenous price, and the attributes of alternative products. Researchers estimating models of demand begin by specifying which product attributes affect consumer utility, a model selection exercise that may affect counterfactual inference. In a parallel to the literature on hypothesis testing in high-dimensional linear models, we find that common approaches to model selection distort counterfactual inference. We characterize model sparsity in the random-coefficients model and introduce a new penalty that operationalizes the LASSO in this context. We also propose a hybrid model selection algorithm that chooses not only those variables that explain market share, but also those that have significant influence on endogenous prices and counterfactuals of interest. Post-selection estimation in the hybrid model generates counterfactual statistics with well-behaved asymptotic distributions that satisfy the conditions for bootstrap validity.