Nested Pseudo-GMM Estimation of Demand for Differentiated Products

Victor Aguirregabiria (), Hui Liu and Yao Luo

Working Papers from University of Toronto, Department of Economics

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–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. We provide MATLAB and Julia code to facilitate implementation.

Keywords: Random Coefficients Logit; Sufficient Statistics; Market Share Inversion; Newton-Kantorovich Iteration; Asymptotic Properties; LCBO (search for similar items in EconPapers)
JEL-codes: C23 C25 C51 C61 D12 L11 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2026-02-04
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.economics.utoronto.ca/public/workingPapers/tecipa-819.pdf Main Text (application/pdf)

Related works:
Working Paper: Nested Pseudo-GMM Estimation of Demand for Differentiated Products (2026)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tor:tecipa:tecipa-819

Access Statistics for this paper

More papers in Working Papers from University of Toronto, Department of Economics 150 St. George Street, Toronto, Ontario.
Bibliographic data for series maintained by RePEc Maintainer ().