Bootstrap Inference under General Two-way Clustering with Serially and Spatially Dependent Common Effects

TL;DR

This paper introduces a bootstrap inference method for linear regression models with two-way clustered data, accommodating complex dependence structures and providing uniform validity across multiple regimes.

Contribution

It proposes a data-driven regime classifier and a projection-based wild bootstrap that adaptively achieves valid inference under various dependence regimes in two-way clustering.

Findings

The method is uniformly valid across four feasible regimes.

Monte Carlo simulations show high accuracy and flexibility.

Addresses serial and spatial dependence in two-way clustering.

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.