🤖 AI Summary
This study addresses the challenge of demand estimation in differentiated product markets when the dimensionality of product characteristics exceeds the number of observations, a setting where the classical Berry–Levinsohn–Pakes (1995) model struggles. The authors extend the BLP framework by incorporating high-dimensional control variables and employing Neyman-orthogonal estimation combined with machine learning techniques—such as Lasso—to handle high-dimensional nuisance parameters. Under approximate sparsity conditions, the proposed approach ensures √T-asymptotic normality for key parameters of interest, such as price coefficients, even when nuisance parameters converge at slower rates. Monte Carlo simulations demonstrate that the method yields accurate and robust estimates of price effects in finite samples under high-dimensional settings, substantially broadening the applicability of the BLP model.
📝 Abstract
This study proposes a framework for estimating demand in differentiated product markets with high dimensional product characteristics, building upon the seminal Berry, Levinsohn, and Pakes (1995) model, using market level data. We allow for a very large set of potential product characteristics, where the number of characteristics may exceed the number of market observations. Our contributions are twofold. First, we establish a general estimation theory for BLP models featuring high-dimensional nuisance parameters. We propose a Neyman orthogonal estimator specifically adapted to this framework, utilizing machine learning techniques, such as Lasso, to construct nuisance parameter estimators that are plugged into the Neyman orthogonal estimator. This approach offers a significant advantage: it achieves $\sqrt{T}$-asymptotic normality for parameters of interest--such as the price coefficient and price heterogeneity--even when nuisance parameters are estimated at slower rates due to their high dimensionality. Second, we apply this theory to a specialized BLP model under approximate sparsity, developing an estimation strategy for the high-dimensional nuisance parameters. The approximate sparsity condition posits that nuisance parameters can be controlled, up to a small approximation error, by a small and unknown subset of variables. In an economic context, this implies that while products have a vast array of characteristics, consumers focus on only a small subset of these due to bounded rationality. This condition makes the recovery of parameters of interest feasible by enabling nuisance parameter estimators to converge at the required rates. The practical performance of the method is evaluated through comprehensive Monte Carlo simulations, which demonstrate its efficacy in finite samples.