Approximate factor models with weaker loadings

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where Λ0′Λ0/Nα is positive definite in the limit when α=1, early work established convergen...

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Bibliographic Details
Published in:Journal of econometrics Vol. 235; no. 2; pp. 1893 - 1916
Main Authors: Bai, Jushan, Ng, Serena
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2023
Subjects:
econometrics
factor analysis
Factor augmented regressions
Low rank decomposition
Principal components
sample size
Weak factors
C31
C30
Low rank decomposition
Factor augmented regressions
Weak factors
Principal components
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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Summary:Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where Λ0′Λ0/Nα is positive definite in the limit when α=1, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when α∈(0,1] albeit at slower rates and under additional assumptions on the sample size. The results hold whether α is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2023.01.027