Distribution Regression for Partially Observed Discrete, Ordered Outcomes—The Case of Adolescent Substance Abuse

This paper studies Distribution Regression (DR) for ordered and discrete outcomes that are only partially observed due to misreporting. Such outcomes frequently occur in self‐reported surveys eliciting socially undesirable, illegal or stigmatised behaviours like substance abuse, domestic violence or anti‐social behaviour. We demonstrate that DR can offer a flexible way to study the distribution of these outcomes. Specifically, we analyse the asymptotic properties of the DR estimator and derive simultaneous confidence bands for unconditional ‘survival’ probabilities generated by that estimator as well as for counterfactual functionals thereof. The method is illustrated by examining possibly underreported lifetime marijuana consumption behaviour among US high‐school students. We find significant, positive differences across some consumption frequencies in lifetime marijuana use between students residing in states with and without recreational marijuana laws.