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Nested Pseudo-GMM Estimation of Demand for Differentiated Products

Victor Aguirregabiria, Hui Liu, Yao Luo

arXiv 4 Feb 2026 · Econometrics

arXiv:2602.05137 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose a fast algorithm for computing the GMM estimator in the BLP demand model (Berry, Levinsohn, and Pakes, 1995). Inspired by nested pseudo-likelihood methods for dynamic discrete choice models, our approach avoids repeatedly solving the inverse demand system by swapping the order of the GMM optimization and the fixed-point computation. We show that, by fixing consumer-level outside-option probabilities, BLP's market-share to mean-utility inversion becomes closed-form and, crucially, separable across products, yielding a nested pseudo-GMM algorithm with analytic gradients. The resulting estimator scales dramatically better with the number of products and is naturally suited for parallel and multithreaded implementation. In the inner loop, outside-option probabilities are treated as fixed objects while a pseudo-GMM criterion is minimized with respect to the structural parameters, substantially reducing computational cost. Monte Carlo simulations and an empirical application show that our method is significantly faster than the fastest existing alternatives, with efficiency gains that grow more than proportionally in the number of products.

Citation extraction

24
references
63
in-text mentions
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distinct cited
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main-text words

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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
1Lee and Seo (2015) A computationally fast estimator for random coefficients logit demand models using aggregate data1.000124100%
2Dubé, Fox, and Su (2012) Improving the numerical performance of static and dynamic aggregate discrete choice random coefficients demand estimation1.00094100%
3Berry, Levinsohn, and Pakes (1995) Automobile prices in market equilibrium1.00054100%
4Aguirregabiria and Mira (2002) Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models0.87452100%
5Aguirregabiria and Mira (2007) Sequential estimation of dynamic discrete games0.87452100%
6Conlon and Gortmaker (2020) Best practices for differentiated products demand estimation with pyblp0.81142100%
7Dearing and Blevins (2025) Efficient and convergent sequential pseudo-likelihood estimation of dynamic discrete games0.64422100%
8Lin, Tang, and Xiao (2024) Endogeneity in games with incomplete information: Us cellphone service deployment0.64422100%
9Berry (1994) Estimating discrete-choice models of product differentiation0.58531100%
10Aguirregabiria and Guiton (2023) Decentralized decision-making in retail chains: Evidence from inventory management0.51121100%

Showing the top 10 of 24 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Sequential algorithm for structural estimations with equilibrium constraints0.40511