Identification and estimation of a large factor model with structural instability

This paper tackles the identification and estimation of a high dimensional factor model with unknown number of latent factors and a single break in the number of factors and/or factor loadings occurring at unknown common date. First, we propose a least squares estimator of the change point based on the second moments of estimated pseudo factors and show that the estimation error of the proposed estimator is Op(1). We also show that the proposed estimator has some degree of robustness to misspecification of the number of pseudo factors. With the estimated change point plugged in, consistency of the estimated number of pre and post-break factors and convergence rate of the estimated pre and post-break factor space are then established under fairly general assumptions. The finite sample performance of our estimators is investigated using Monte Carlo experiments

Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model

This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.), (JBFK). This is done under the alternative hypotheses of weak and strong factors. By weak factors, we mean that the Euclidean norm of the vector of the factor loadings is O(1). By strong factors, we mean that the Euclidean norm of the vector of factor loadings is , where n is the number of individuals in the panel. To derive the limiting distribution of JBFK under the alternative, we first derive the limiting distribution of its raw data counterpart. Our results show that, when the factor is strong, the test statistic diverges in probability to infinity as fast as Op(nT). However, when the factor is weak, its limiting distribution is a rightward mean shift of the limit distribution under the null. Second, we derive the asymptotic behavior of the difference between JBFK and its raw data counterpart. Our results show that when the factor is strong, this difference is as large as Op(n). In contrast, when the factor is weak, this difference converges in probability to a constant. Taken together, these results imply that when the factor is strong, JBFK is consistent, but when the factor is weak, JBFK is inconsistent even though its asymptotic power is nontrivial

Structural changes in heterogeneous panels with endogenous regressors

This paper extends Pesaran's (Econometrica, 2006, 74, 967–1012) common correlated effects (CCE) by allowing for endogenous regressors in large heterogeneous panels with unknown common structural changes in slopes and error factor structure. Since endogenous regressors and structural breaks are often encountered in empirical studies with large panels, this extension makes Pesaran's CCE approach empirically more appealing. In addition to allowing for slope heterogeneity and cross‐sectional dependence, we find that Pesaran's CCE approach is also valid when dealing with unobservable factors in the presence of endogenous regressors and structural changes in slopes and error factor loadings. This is supported by Monte Carlo experiments

Structural changes in heterogeneous panels with endogenous regressors

This paper extends Pesaran's (Econometrica, 2006, 74, 967–1012) common correlated effects (CCE) by allowing for endogenous regressors in large heterogeneous panels with unknown common structural changes in slopes and error factor structure. Since endogenous regressors and structural breaks are often encountered in empirical studies with large panels, this extension makes Pesaran's CCE approach empirically more appealing. In addition to allowing for slope heterogeneity and cross‐sectional dependence, we find that Pesaran's CCE approach is also valid when dealing with unobservable factors in the presence of endogenous regressors and structural changes in slopes and error factor loadings. This is supported by Monte Carlo experiments