Determining the number of factors with potentially strong within-block correlations in error terms

ABSTRACT

We develop methods to estimate the number of factors when error terms have potentially strong correlations in the cross-sectional dimension. The information criteria proposed by Bai and Ng (2002 Bai, J., Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica 70:191–221.Crossref], Web of Science ®] , Google Scholar]) require the cross-sectional correlations between the error terms to be weak. Violation of this weak correlation assumption may lead to inconsistent estimates of the number of factors. We establish two data-dependent estimators that are consistent whether the error terms are weakly or strongly correlated in the cross-sectional dimension. To handle potentially strong cross-sectional correlations between the error terms, we use a block structure in which the within-block correlation may either be weak or strong, but the between-block correlation is limited. Our estimators allow imperfect knowledge and a moderate misspecification of the block structure. Monte-Carlo simulation results show that our estimators perform similarly to existing methods for cases in which the conventional weak correlation assumption is satisfied. When the error terms have a strong cross-sectional correlation, our estimators outperform the existing methods.