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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| Vydané v: | Journal of econometrics Ročník 235; číslo 2; s. 1893 - 1916 |
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| Jazyk: | English |
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Elsevier B.V
01.08.2023
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| ISSN: | 0304-4076, 1872-6895 |
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| 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. |
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| AbstractList | 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. |
| Author | Bai, Jushan Ng, Serena |
| Author_xml | – sequence: 1 givenname: Jushan surname: Bai fullname: Bai, Jushan email: jb3064@columbia.edu organization: Columbia University, 420 W. 118 St. MC 3308, New York, NY 10027, United States of America – sequence: 2 givenname: Serena surname: Ng fullname: Ng, Serena email: serena.ng@columbia.edu organization: Columbia University and NBER, 420 W. 118 St. MC 3308, New York, NY 10027, United States of America |
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| Cites_doi | 10.1007/BF02294464 10.1016/j.jeconom.2008.08.011 10.1016/j.jeconom.2013.03.007 10.1002/jae.2476 10.1016/j.jeconom.2012.01.034 10.2307/1912275 10.1080/07350015.2021.2008405 10.3386/w6702 10.1016/j.jeconom.2019.04.021 10.1198/016214502388618960 10.1017/S0266466615000328 10.1111/1468-0262.00273 10.1016/j.jeconom.2019.08.012 10.1162/003465300559037 10.1016/j.jeconom.2021.04.006 10.1111/1468-0262.00392 |
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