Variance Estimation in Matched Difference‐in‐Differences Designs

ABSTRACT

This paper studies variance estimation in difference‐in‐differences (DID) designs under covariate matching. While matching is widely used to improve covariate balance, it induces a dependence structure that complicates variance estimation. In particular, covariate‐based matching generates positive correlation within matched pairs, which reduces the variance of the DID estimator. Standard variance estimators fail to account for this design‐induced covariance and therefore yield systematically conservative standard errors. We characterize the asymptotic variance implied by the matched design and propose a projection‐based variance estimator to remove variation attributable to the matching covariates. Simulation results show that the proposed estimator achieves accurate coverage, whereas standard methods substantially overestimate uncertainty. An empirical application illustrates the practical implications for inference.