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

• URL: http://arxiv.org/abs/2307.07090v2
• Date: Tue, 20 Feb 2024 14:17:45 GMT
• Title: Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets
• Authors: Amandeep Singh, Ye Liu, and Hema Yoganarasimhan
• Abstract summary: We demonstrate how non-parametric estimators like neural nets can easily approximate choice functions. Our proposed functionals can flexibly capture underlying consumer behavior in a completely data-driven fashion. Our empirical analysis confirms that the estimator generates realistic and comparable own- and cross-price elasticities.
• Score: 5.8429701619765755
• License: http://creativecommons.org/licenses/by/4.0/
• 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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