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Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets

2023/07/13 by Amandeep Singh, Ye Liu, Singh, Amandeep +3
Business, Management and Accounting · Economics, Econometrics and Finance · #Consumer Market Behavior and Pricing #Digital Platforms and Economics #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Merger and Competition Analysis

paper · pdf · doi:10.48550/arxiv.2307.07090

openalex publication_date 2023/07/13 · openalex created_date 2023/07/18 · openalex updated_date 2026/07/28

Abstract

Choice modeling is at the core of understanding how changes to the competitive landscape affect consumer choices and reshape market equilibria. In this paper, we propose a fundamental characterization of choice functions that encompasses a wide variety of extant choice models. We demonstrate how non-parametric estimators like neural nets can easily approximate such functionals and overcome the curse of dimensionality that is inherent in the non-parametric estimation of choice functions. We demonstrate through extensive simulations that our proposed functionals can flexibly capture underlying consumer behavior in a completely data-driven fashion and outperform traditional parametric models. As demand settings often exhibit endogenous features, we extend our framework to incorporate estimation under endogenous features. Further, we also describe a formal inference procedure to construct valid confidence intervals on objects of interest like price elasticity. Finally, to assess the practical applicability of our estimator, we utilize a real-world dataset from S. Berry, Levinsohn, and Pakes (1995). Our empirical analysis confirms that the estimator generates realistic and comparable own- and cross-price elasticities that are consistent with the observations reported in the existing literature.

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