A Weighted Regression Approach to Break-Point Detection in Panel Data

Referee: [theoretical results on limiting distribution under weak dependence] The derivation that the limiting null distribution is independent of bandwidth under weak cross-sectional dependence (abstract and the main theoretical section) appears to rest on the weighted cross-sectional means converging at rates that dominate bandwidth-induced variability in the long-run variance estimator. The manuscript should state explicit rate conditions relating the weight sequence, panel dimensions (N,T), and the strength of cross-sectional dependence; without them the claimed bandwidth-free property may fail in some regimes even when dependence is weak.

Authors: We agree that the bandwidth independence of the limiting null distribution under weak cross-sectional dependence relies on the weighted cross-sectional means converging at a rate that dominates the variability induced by the bandwidth in the long-run variance estimator. While the manuscript derives the results for general regression weights under the maintained weak-dependence assumption, we acknowledge that the rate conditions linking the weight sequence, N, T, and the dependence strength are not stated explicitly. In the revised version we will add a remark immediately after the main theorem that supplies these conditions. Concretely, we will require that the weights satisfy max_i |w_{i,N}| = o(N^{-1/2}) and sum_i w_{i,N}^2 = o(b_T^{-1}), where b_T denotes the bandwidth, together with the standard weak-dependence restriction that the cross-sectional covariances are summable at a rate ensuring consistency of the long-run variance estimator. These additions will make the domain of validity of the bandwidth-free result transparent while leaving the core theorems unchanged. revision: yes