Estimating Discrete Choice Demand Models with Sparse Market-Product Shocks

2025-01-04

AI Summary

This paper addresses estimation of the random-coefficients logit model for discrete choice with differentiated products under sparse market- and product-level demand shocks. We propose a novel nonparametric identification and Bayesian estimation approach that neither requires instrumental variables nor demand inversion. Our key contributions are: (i) the first nonparametric identification of the model under sparse shock assumptions; and (ii) explicit Bayesian modeling of shock sparsity via shrinkage priors—particularly the horseshoe prior—thereby fully circumventing the instrumental-variable dependency inherent in the BLP framework. Monte Carlo simulations demonstrate consistent identification and robust estimation performance. Empirical analysis of canonical datasets reveals substantial sparse demand shocks; relative to conventional IV-based estimation, our method delivers greater robustness and improved accuracy in counterfactual predictions.

Technology Category

Machine Learning: Bayesian LearningReasoning under Uncertainty: Relational Probabilistic ModelsKnowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsEconomics, Online Markets and Human Computation: The sharing economy

Abstract

We propose a new approach to estimating the random coefficient logit demand model for differentiated products when the vector of market-product level shocks is sparse. Assuming sparsity, we establish nonparametric identification of the distribution of random coefficients and demand shocks under mild conditions. Then we develop a Bayesian procedure, which exploits the sparsity structure using shrinkage priors, to conduct inference about the model parameters and counterfactual quantities. Comparing to the standard BLP (Berry, Levinsohn,&Pakes, 1995) method, our approach does not require demand inversion or instrumental variables (IVs), thus provides a compelling alternative when IVs are not available or their validity is questionable. Monte Carlo simulations validate our theoretical findings and demonstrate the effectiveness of our approach, while empirical applications reveal evidence of sparse demand shocks in well-known datasets.

Problem

• Estimates demand models with sparse market-product shocks
• Identifies random coefficients and demand shocks nonparametrically
• Provides IV-free alternative to standard BLP method

Innovation

• Sparse market-product shocks assumption
• Bayesian procedure with shrinkage priors
• No demand inversion or IVs required