Semiparametric Discrete Choice Models for Bundles

We propose new identification and estimation approaches to semiparametric discrete choice models for bundles in both cross-sectional and panel data settings. The random utility functions of these models take the usual parametric form, while no distributional assumption is imposed on the stochastic disturbances. Our proposed methods permit certain forms of heteroskedasticity and arbitrary correlation in the disturbances across choices. Our identification approach is matching-based; it matches observed covariates across agents for the cross-sectional case, and over time for the panel data case. For the cross-sectional model, we propose a kernel-weighted rank procedure and establish N-asymptotic normality of the resulting estimators. We show the validity of the nonparametric bootstrap for the inference. For the panel data model, we propose localized maximum score type estimators which have a non-standard asymptotic distribution. We show that the numerical bootstrap developed by Hong and Li (2020) is a valid inference method for our panel data estimators. Monte Carlo experiments demonstrate that our proposed estimation and inference procedures perform adequately in finite samples.