Difference-in-Differences and Treatment x Pretest Interactions: A Critique of Dual-Centered ANCOVA

Abstract

This paper critically examines dual-centered ANCOVA, proposed by Lin and Larzelere (2020) and Larzelere and Lin (2025), which is claimed to accommodate a Treatment X Pretest interaction while preserving the difference-in-differences (DiD) estimate. We take issue with their claims on four grounds. First, DiD without an interaction term does not assume constant treatment effects; under the parallel trends assumption, it identifies the average treatment effect on the treated even when treatment effects vary across pretest scores. Second, ANCOVA requires correctly modeling the conditional expectation of the outcome in order to identify causal effects, whereas DiD does not, so the concern about omitting an interaction term applies to ANCOVA but not to DiD. Third, dual-centered ANCOVA is not a distinct ANCOVA-type method but merely a re-expression of DiD, sharing the same estimand and identification conditions. Fourth, the claimed innovation of presenting both estimates---the DiD estimate of the treatment effect and the ANCOVA estimate of the interaction term---within a single model offers little practical advantage, because obtaining correct standard errors requires a second analysis. Overall, we argue that dual-centered ANCOVA is based on a misunderstanding of what DiD assumes and is better understood as a re-expression of existing analytic methods rather than a methodological innovation.