Changes-in-Changes for Ordered Choice Models: Too Many "False Zeros"?

Abstract: In this paper, we develop a 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 or substance abuse, where too many "false zeros", or more broadly, underreporting are likely. We start by providing a characterization for parallel trends within a general threshold-crossing model. We then propose a partial and point identification framework for different distributional treatment effects when the outcome is subject to underreporting. 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.