A Weighted Regression Approach to Break-Point Detection in Panel Data
Charl Pretorius, Heinrich Roodt
TL;DR
The paper develops a class of change-point tests for high-dimensional panel data by exploiting cross-sectional averages of squared CUSUM statistics and a regression-based estimator of the mean long-run variance. It derives the limit null distribution under weak and strong cross-sectional dependence, offers multiple weighting schemes (OLS, WLS, and τ-based) with explicit limit kernels, and proves consistency under alternatives. An improved estimator for the long-run variance is proposed to mitigate power loss when breaks are present, along with a neighborhood-consistency result. The methodology is extended to dependent panels via a common-factor model and is validated through extensive simulations using a bootstrap approach for critical values, showing favorable finite-sample performance and higher power than existing methods.
Abstract
New procedures for detecting a change in the cross-sectional mean of panel data are proposed. The procedures rely on estimating nuisance parameters using certain cross-sectional means across panels using a weighted least squares regression. In the case of weak cross-sectional dependence between panels, we show how test statistics can be constructed to have a limit null distribution not depending on any choice of bandwidths typically needed to estimate the long-run variances of the panel errors. The theoretical assertions are derived for general choices of the regression weights, and it is shown that consistent test procedures can be obtained from the proposed process. The theoretical results are extended to the case where strong cross-sectional dependence exist between panels. The paper concludes with a numerical study illustrating the behavior of several special cases of the test procedure in finite samples.