Valid Inference After Control Selection in Difference-in-Differences

Takahiro Hoshino and Ryoya Nakano

Papers from arXiv.org

Abstract: We develop the first empirically implementable selective-inference framework for difference-in-differences with controls selected by pre-treatment fit. We construct confidence intervals for the average treatment effect on the treated (ATT), incorporating that selection and estimating the unknown full covariance from the same observations. Counterexamples establish undercoverage from Roth's fixed-comparison pretest adjustment and direct Gaussian-score application of Andrews--Kitagawa--McCloskey to this selection, despite parallel trends for every candidate. Retaining the actual polynomial or piecewise-polynomial event, we establish uniform validity at perfect fit and population ties, endpoint equivalence with known-covariance inference, and unequal-sample guarantees. We accommodate staggered adoption, reused observations, and fitting-rule choice. In police-deployment and minimum-wage reanalyses, we find changes in significance and economically relevant effect ranges while retaining the selected comparison. For a smooth randomized test, we obtain higher-order accuracy through stabilized joint mean--covariance correction preserving normal-sampling baseline rejection probabilities. Researchers should disclose selection rules alongside ATT uncertainty.

Date: 2026-10, Revised 2026-10
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