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 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.
We are grateful to David Brownstone, Martin Burda, Garland Durham, Jeremy Fox, Stefan Holderlein, Ivan Jeliazkov, Dale Poirier, Guillame Weisang, Frank Windmeijer, and seminar participants at the Advances in Econometrics Conference on Bayesian Model Comparison and the California Institute of Technology for helpful comments. We owe special thanks to Alexander Charles Smith for important insights early in developing the project.
Gillen, B.J., Shum, M. and Moon, H.R. (2014), "Demand Estimation with High-Dimensional Product Characteristics", Bayesian Model Comparison (Advances in Econometrics, Vol. 34), Emerald Group Publishing Limited, Bingley, pp. 301-323. https://doi.org/10.1108/S0731-905320140000034020
Emerald Group Publishing Limited
Copyright © 2014 Emerald Group Publishing Limited