Approximately Parallel Trends: Event Study Inference under Trend Violations

When the data reject parallel trends, however, applied researchers commonly continue to interpret treatment effect estimates, provided the observed pre-trend violations are deemed sufficiently small. To rationalize this behavior, we recast difference-in-differences designs as relying solely on an approximate version of parallel trends, which allows parallel trends to fail in some realizations of the data. Our reformulation delivers new inference procedures that account for uncertainty about possible deviations from parallel trends.

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