Debiased Difference-in-Differences Estimation and Inference of Causal Effects Under Adaptive Controls

Differences (DiD) method is a widely used empirical strategy for identifying causal effects when randomized experiments are infeasible. By comparing outcome trends between treated and untreated units before and after an intervention, DiD isolates treatment effects while controlling confounders exhibiting parallel temporal trends. However, as adaptive experiments and data-driven decision systems become increasingly prevalent in managerial and operational settings, the validity of standard DiD methods is challenged when data collection depends on past outcomes. This paper studies the problem of estimating and conducting inference on causal effects within the DiD framework when data are adaptively collected under policy control. We make three main contributions. First, we develop a general debiasing method that converts the bias of standard DiD estimators under adaptive data collection into additional variance. Second, we provide finite-sample bounds on the bias and variance of the proposed estimator and establish the asymptotic validity of the resulting confidence intervals. Third, we demonstrate the practical relevance of our approach through dynamic pricing examples, showing that our estimator achieves a minimax-optimal trade-off between estimation accuracy and policy regret. Together, these results offer a robust framework for applying DiD methods in sequential decision-making environments, extending their applicability to modern adaptive data settings where classical assumptions no longer hold.