Estimating High-Dimensional Discrete Choice Model of Differentiated Products with Random Coefficients

Abstract

We propose an estimation procedure for discrete choice models of differentiated products with possibly high-dimensional product attributes. In our model, high-dimensional attributes can be determinants of both mean and variance of the indirect utility of a product. The key restriction in our model is that the high-dimensional attributes affect the variance of indirect utilities only through finitely many indices. In a framework of the random-coefficients logit model, we show a bound on the error rate of a $l_1$-regularized minimum distance estimator and prove the asymptotic linearity of the de-biased estimator.

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• ${\ell }_{\infty }$ Vector Contraction for Rademacher Complexity