Approximate factor models with weaker loadings

By Jushan Bai, Serena Ng. Journal of Econometrics, 2021

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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 $\Lop\Lo/N^\alpha$ 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 $\alpha\in(0,1]$ 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.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/8469c0275b7ecdfb01e4b15b0b9d5ff0c34cc020