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

This paper considers modelling 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 an unknown parameter, which is defined by assuming that a small proportion of the total factor loadings are important. Compared with the usual parameterized style, this exponential description of extent covers the case of small proportion of the total sections being cross-sectionally dependent. We established a 'moment' criterion to estimate the unknown 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 the unknown parameter. Due to the involvement of some unknown parameter, both joint and marginal estimators are constructed. This paper then establishes that the joint estimators of a pair of unknown parameters converge in distribution to bivariate normal. In the case where the other unknown parameter is being assumed to be known, an asymptotic distribution for an estimator of the original unknown parameter is also established, which naturally coincides with the joint asymptotic distribution for the case where the other unknown parameter 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 SP500 market are also reported to show the practical relevance of the proposed estimation theory.