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The difference-in-differences (DID) design is widely used in observationalstudies to estimate the causal effect of a treatment when repeated observationsover time are available. Yet, almost all existing methods assume linearity inthe potential outcome (parallel trends assumption) and target the additiveeffect. In social science research, however, many outcomes of interest aremeasured on an ordinal scale. This makes the linearity assumption inappropriatebecause the difference between two ordinal potential outcomes is not welldefined. In this paper, I propose a method to draw causal inferences forordinal outcomes under the DID design. Unlike existing methods, the proposedmethod utilizes the latent variable framework to handle the non-numeric natureof the outcome, enabling identification and estimation of causal effects basedon the assumption on the quantile of the latent continuous variable. The paperalso proposes an equivalence-based test to assess the plausibility of the keyidentification assumption when additional pre-treatment periods are available.The proposed method is applied to a study estimating the causal effect of massshootings on the public's support for gun control. I find little evidence for auniform shift toward pro-gun control policies as found in the previous study,but find that the effect is concentrated on left-leaning respondents whoexperienced the shooting for the first time in more than a decade.

Difference-in-Differences for Ordinal Outcomes: Application to the Effect of Mass Shootings on Attitudes toward Gun Control