Difference-in-differences with an ordinal dependent variable : assessing the impact of the London bombings on the safety perceptions of Muslims

In this paper, we propose a methodology for estimating treatment effects when using difference-in-differences with an ordinal dependent variable. Specifically, we derive an expression for the Average Treatment Effect on the Treated in terms of changes in response probabilities. An advantage of taking this approach is the ability to assess any distributional effects of exposure to treatment. We use the proposed estimator to evaluate the impact of the London bombings on the safety perceptions of Muslims, with our results highlighting a shift from moderately low to very high safety concerns among younger Muslims in the aftermath of the bombings.