Nonparametric Demand Estimation in the Presence of Unobserved Factors

In many applications of discrete choice modeling, there exist unobserved factors (UFs) driving the consumer demand that are not included in the model. Ignoring such UFs when fitting the choice model can produce biased parameter estimates and ultimately lead to incorrect policy decisions. At the same time, accounting for UFs during estimation is challenging since we typically have only partial or indirect information about them. Existing approaches such as the classical BLP estimator make strong parametric assumptions to deal with this challenge, and therefore can suffer from model misspecification issues. We propose a novel estimator for dealing with UFs in the mixtures of logit model that is {\em nonparametric}, i.e., does not impose any parametric assumptions on the mixing distribution or the underlying mechanism generating the UFs. We theoretically characterize the benefit of using our estimator over the BLP estimator. We then leverage the alternating minimization framework to design an efficient algorithm for implementing our proposed estimator and establish its sublinear convergence to a stationary point of the estimation problem. Using a simulation study, we demonstrate that our estimator is robust to different ground-truth settings, whereas the performance of the BLP estimator suffers significantly under model misspecification. Using real-world grocery sales transaction data, we show that accounting for product and store-level UFs can significantly improve the accuracy of predicting weekly demand at an individual product and store level, with an avg. 57% improvement across 12 product categories over a state-of-the-art benchmark that ignores UFs during estimation