🤖 AI Summary
This study addresses the inferential failure of two-way fixed effects M-estimators in unbalanced panels, which arises from incidental parameter bias and feedback bias. Within an asymptotic framework where both cross-sectional and time dimensions grow jointly, the paper proposes a debiased estimation method that accommodates missing observations without requiring prior knowledge of regressor predeterminedness or the selection mechanism. The approach is the first to simultaneously handle two sources of feedback bias—those stemming from predetermined regressors in the outcome equation and from a predetermined selection mechanism—without relying on assumptions about their predetermined structure. It remains valid under deterministic, stochastic, or mixed missingness mechanisms. Theoretical analysis shows that while the uncorrected estimator is asymptotically normal yet biased, the proposed debiased estimator effectively eliminates this bias, thereby enabling valid statistical inference.
📝 Abstract
We derive the asymptotic properties of two-way fixed effects M-estimators with missing observations in an asymptotic framework in which the numbers of cross-sectional units and time periods grow jointly. We allow the selection process to be deterministic (conditional on the unobserved effects and initial conditions), stochastic, or mixed, and we impose only a conditional mean restriction. The uncorrected estimators are asymptotically normal but not centered at zero, suffering from incidental parameter and feedback biases. Feedback bias can be induced by predetermined regressors in the outcome equation and by a predetermined selection process. We propose debiased estimators that handle both sources without requiring knowledge of which regressors or selection components are predetermined.