Bracketing in the Comparative Interrupted Time-Series Design to Address Concerns About History Interacting with Group: Evaluating Missouri’s Handgun Purchaser Law

• Activity Number: 145 - Causal Inference
• Type: Invited
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Raiden Hasegawa and Daniel Webster and Dylan Small*
• Companies: University of Pennsylvania and Johns Hopkins University and University of Pennsylvania
• Keywords: causal inference; difference-in-difference; quasi-experiment; gun policy

Abstract

In the comparative interrupted time-series design (also called the method of difference-in-differences), the change in outcome in a group exposed to treatment in the periods before and after the exposure is compared to the change in outcome in a control group not exposed to treatment in either period. The standard difference-in-difference estimator for a comparative interrupted time-series design will be biased for estimating the causal effect of the treatment if there is an interaction between history in the after period and the groups, e.g., there is a historical event besides the start of the treatment in the after period that benefits the treated group more than the control group. We present a bracketing method for bounding the effect of an interaction between history and the groups that arises from a time-invariant unmeasured confounder having a different effect in the after period than the before period. The method is applied to a study of the effect of the repeal of Missouri’s permit-to-purchase handgun law on its firearm homicide rate.