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Approximate factor models with weaker loadings
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DOI：10.1016/j.jeconom.2023.01.027.png)
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Abstract
En 中文
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 A0 & PRIME; A0/N & alpha; is positive definite in the limit when & alpha; = 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 & alpha; & ISIN; (0, 1] albeit at slower rates and under additional assumptions on the sample size. The results hold whether & alpha; 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. & COPY; 2023 Elsevier B.V. All rights reserved.
Keywords:
Principal components
Low rank decomposition
Weak factors
Factor augmented regressions
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