Approximate factor models with weaker loadings

Jushan Bai and Serena Ng

Journal of Econometrics, 2023, vol. 235, issue 2, 1893-1916

Abstract: 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.

Keywords: Principal components; Low rank decomposition; Weak factors; Factor augmented regressions (search for similar items in EconPapers)
JEL-codes: C30 C31 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Working Paper: Approximate Factor Models with Weaker Loadings (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:2:p:1893-1916

DOI: 10.1016/j.jeconom.2023.01.027

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