Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets
CoRR(2023)
摘要
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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关键词
choice models,permutation invariance
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