Nested Pseudo-GMM Estimation of Demand for Differentiated Products

TL;DR

This paper introduces a fast, scalable nested pseudo-GMM algorithm for demand estimation in differentiated products models, significantly reducing computation time while maintaining accuracy, especially with large product sets.

Contribution

It develops a novel nested pseudo-GMM approach that simplifies the demand inversion step, enabling efficient estimation for large-scale differentiated products models.

Findings

Method is significantly faster than existing alternatives.

Efficiency gains increase with the number of products.

Applicable to empirical demand estimation with large product sets.

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.