Difference-in-differences estimation under non-parallel trends
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Date
2020
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Abstract
Classic difference-in-differences estimation relies on the validity of the "parallel
trends assumption" (PTA), which ensures that the evolution of the variable of interest in the
control group can be used to determine its counterfactual development in the treatment group
in the absence of treatment. The plausibility of the PTA is usually assessed by a test of the
null hypothesis that the difference between the means of both groups is constant over time
before the treatment. However, this procedure is problematic as failure to reject the null
hypothesis does not imply the absence of differences in time trends between both groups due
to low power to detect economically relevant differences. We provide three tests of equivalence
leading to a "common range" (CR) condition that replaces the PTA and which naturally reflects
differences between treatment and control. We combine the CR with standard confidence
intervals to capture both design and sampling uncertainty in the data and show that the
combined confidence intervals yield more reliable inference when the PTA is violated.