🤖 AI Summary
This study addresses the inconsistency and lack of uniform validity in inference for two-way clustered linear regression, which arise from heterogeneous score components and infeasible asymptotic regimes. To resolve these issues, the paper develops a unified, feasible inference framework encompassing four distinct asymptotic mechanisms. It innovatively integrates mechanism adaptivity with flexible modeling of spatial dependence along the first dimension and serial dependence along the second. For the first time in the two-way clustering literature, a data-driven mechanism classifier and a projection-based wild bootstrap procedure are introduced. Theoretical analysis establishes four impossibility results concerning consistency and distinguishability, while Monte Carlo simulations demonstrate that the proposed method achieves both high precision and strong adaptability under complex clustering structures, thereby enabling uniformly valid inference across asymptotic regimes.
📝 Abstract
This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two non-Gaussian. We establish four impossibility results: heterogeneous score components preclude uniform consistency; uniform consistency also fails in one non-Gaussian (infeasible) regime; the infeasible regime is not uniformly distinguishable from a feasible one; and uniform validity over all feasible regimes rules out uniform conservativeness over the infeasible regime.
To address the feasible regimes, we propose a data-driven regime classifier and a projection-based wild bootstrap procedure. The procedure delivers uniformly valid inference across the four feasible regimes while allowing serial dependence along the second clustering dimension and spatial dependence along the first. This combination of regime adaptivity and flexible dependence is new to the two-way clustering literature. Monte Carlo simulations confirm the accuracy and flexibility of the proposed methods in settings with complex clustering structures.