Generalized Difference-in-Differences for Ordered Choice Models: Too Many "False Zeros"?

In this paper, we develop a generalized Difference-in-Differences model for discrete, ordered outcomes, building upon elements from a continuous Changes-in-Changes model. We focus on outcomes derived from self-reported survey data eliciting socially undesirable, illegal, or stigmatized behaviors like tax evasion, substance abuse, or domestic violence, where too many "false zeros", or more broadly, underreporting are likely. We provide characterizations for distributional parallel trends, a concept central to our approach, within a general threshold-crossing model framework. In cases where outcomes are assumed to be reported correctly, we propose a framework for identifying and estimating treatment effects across the entire distribution. This framework is then extended to modeling underreported outcomes, allowing the reporting decision to depend on treatment status. A simulation study documents the finite sample performance of the estimators. Applying our methodology, we investigate the impact of recreational marijuana legalization for adults in several U.S. states on the short-term consumption behavior of 8th-grade high-school students. The results indicate small, but significant increases in consumption probabilities at each level. These effects are further amplified upon accounting for misreporting.