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

Choice Modeling is at the core of many economics, operations, and marketing problems. 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 \cite{berry1995automobile}. 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.