Demand Estimation with High-dimensional Product Characteristics

Structural models of demand founded on the classic work of Berry, Levinsohn, and Pakes (1995) link variation in aggregate market shares for a product to the influence of product attributes on heterogeneous consumer tastes. We consider implementing these models in settings with complicated products where consumer preferences for product attributes are sparse, that is, where a small proportion of a high-dimensional product characteristics influence consumer tastes. We propose a multistep estimator to efficiently perform uniform inference. Our estimator employs a penalized pre-estimation model specification stage to consistently estimate nonlinear features of the BLP model. We then perform selection via a Triple-LASSO for explanatory controls, treatment Bayesian Model Comparison Advances in Econometrics, Volume 34, 301 323 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0731-9053/doi:10.1108/S0731-905320140000034020 301 (C ) E m ral d G rou p P ub lis hin g selection controls, and instrument selection. After selecting variables, we use an unpenalized GMM estimator for inference. Monte Carlo simulations verify the performance of these estimators.