Tianqi Li

Job market paper

Demand Estimation with High-Dimensional Consumer Demographics

Random-coefficient multinomial logit models are widely applied to study discrete choices in economics. By assuming random coefficients for each individual, the models can account for unobserved individual heterogeneity and suggest more realistic substitution patterns, compared to standard logit models. In this paper, I find that random coefficients become undetectable (i.e., estimated variances are zero) even if they exist, as many observed individual covariates are incorporated. Having zero estimates of variances not only yields bias in estimating other parameters but also raises the concern of parameters on boundary. To address these issues, I propose l1-regularized maximum likelihood estimation for simultaneous covariate selection, and develop a debiased machine learning estimator to correct regularization bias while accounting for parameter constraints, such as non-negativity of variance. I derive non-asymptotic probability bounds for the regularized estimator and limiting distributions for the debiased estimator. Finally, I validate the estimators with thorough Monte Carlo simulations, and illustrate the impacts of high-dimensional covariates in an application to soft-drink markets in North Carolina.