Bracketing Bounds for Differences-in-Differences

• In Event: Causal Inference for Time-Series Data

Abstract

The method of differences-in-differences (DID) is widely used in political science. With DID 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 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. We also develop new form of falsification test to probe the key assumption that is necessary for DID to provide consistent estimates of the treatment effect. We apply this new method to a study on the effect of voter identification laws on turnout. Specifically, we focus on voter identification laws in Georgia and Indiana.

Author

• Luke Keele, University of Pennsylvania