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

49 Pages Posted: 21 Jul 2023 Last revised: 18 Feb 2024

See all articles by Amandeep Singh

Amandeep Singh

University of Washington - Michael G. Foster School of Business; University of Pennsylvania - The Wharton School

Ye Liu

University of Washington - Michael G. Foster School of Business

Hema Yoganarasimhan

University of Washington

Date Written: July 13, 2023

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.

Keywords: Choice Models, Demand Estimation, Permutation Invariance, Set Functions

Suggested Citation

Singh, Amandeep and Liu, Ye and Yoganarasimhan, Hema, Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets (July 13, 2023). Available at SSRN: https://ssrn.com/abstract=4508227 or http://dx.doi.org/10.2139/ssrn.4508227

Amandeep Singh

University of Washington - Michael G. Foster School of Business ( email )

Box 353200
Seattle, WA 98195-3200
United States

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

Ye Liu (Contact Author)

University of Washington - Michael G. Foster School of Business ( email )

Box 353200
Seattle, WA 98195-3200
United States

Hema Yoganarasimhan

University of Washington ( email )

481 Paccar Hall
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/hemay/

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