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Estimation of BLP models with high-dimensional controls

Hua Jin

arXiv 2 May 2026 · Econometrics

arXiv:2605.01594 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

32
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Du… (2018) Double/debiased machine learning for treatment and structural parameters0.87462100%
2Belloni, Alexandre and Chernozhukov, Victor and Chetverikov, Denis a… (2018) High-dimensional econometrics and regularized GMM0.81142100%
3Backus, Matthew and Conlon, Christopher and Sinkinson, Michael (2021) Common ownership and competition in the ready-to-eat cereal industry0.73732100%
4Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian (2014) High-dimensional methods and inference on structural and treatment effects0.73732100%
5Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian (2014) Inference on treatment effects after selection among high-dimensional controls0.64441100%
6Gillen, Benjamin J and Montero, Sergio and Moon, Hyungsik Roger and… (2019) BLP-2LASSO for aggregate discrete choice models with rich covariates0.64441100%
7Berry, Steve and Linton, Oliver B and Pakes, Ariel (2004) Limit theorems for estimating the parameters of differentiated product demand systems0.64422100%
8Freyberger, Joachim (2015) Asymptotic theory for differentiated products demand models with many markets0.58531100%
9Newey, Whitney K and McFadden, Daniel (1994) Large sample estimation and hypothesis testing0.5115220%
10Wainwright, Martin J (2019) High-dimensional statistics: A non-asymptotic viewpoint0.5114225%

Showing the top 10 of 32 scored citations.