Estimation of Structural Breaks in Large Panels with Cross-Sectional Dependence

This paper considers modeling and detecting structure breaks associated with cross-sectional dependence for large dimensional panel data models, which are popular in many fields including economics and finance. We propose a dynamic factor structure to measure the degree of cross-sectional dependence. The extent of such cross-sectional dependence is parameterized as alpha0 which is defined by assuming that only a proportion of the total N factor loadings are important. Compared with the parameterized style alpha0, this exponential description of extent covers the case of small proportion of the total sections being cross-sectionally dependent. We establish a 'moment' criterion to estimate alpha0 based on the covariance of cross-sectional averages at different time lags. By taking into account the fact that the serial dependence of common factors is stronger than that of idiosyncratic components, the proposed criterion is able to capture weak cross-sectional dependence that is reflected on relatively small values of alpha0. Due to the involvement of some unknown parameter kappa0, both joint and marginal estimators are constructed. This paper then establishes that the joint estimators of (alpha0, kappa0) converge in distribution to bivariate normal. In the case where kappa0 is being assumed to be known, an asymptotic distribution for an estimator of alpha0 is also established, which naturally coincides with the joint asymptotic distribution for the case where kappa0 is assumed to be known. Simulation results show the finite-sample effectiveness of the proposed method. Empirical applications to cross-country macro-variables and stock returns in S&P500 market are also reported to show the practical relevance of the proposed estimation theory