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A method to evaluate the rank condition for CCE estimators

Ignace De Vos, Gerdie Everaert (UGent) and Vasilis Sarafidis
(2024) ECONOMETRIC REVIEWS. 43(2-4). p.123-155
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Abstract
We develop a binary classifier to evaluate whether the rank condition (RC) is satisfied or not for the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, rho. When this condition fails, the CCE estimator is inconsistent, in general. Despite its importance, to date this rank condition could not be verified. The difficulty lies in the fact that factor loadings are unobserved, such that rho cannot be directly determined. The key insight in this article is that rho can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. Thus, a binary classifier, constructed by comparing estimates of m and rho, correctly determines whether the RC is satisfied or not as (N,T)->infinity. We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability. The RC classifier reveals that the rank condition fails for a subperiod of the sample, in which case the estimated effect of bank size on profitability appears to be biased upwards.
Keywords
Common factors, common correlated effects approach, rank condition, NUMBER, TESTS, INFERENCE, MODELS, RISK, IMPACT, PANELS

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MLA
De Vos, Ignace, et al. “A Method to Evaluate the Rank Condition for CCE Estimators.” ECONOMETRIC REVIEWS, vol. 43, no. 2–4, 2024, pp. 123–55, doi:10.1080/07474938.2023.2292383.
APA
De Vos, I., Everaert, G., & Sarafidis, V. (2024). A method to evaluate the rank condition for CCE estimators. ECONOMETRIC REVIEWS, 43(2–4), 123–155. https://doi.org/10.1080/07474938.2023.2292383
Chicago author-date
De Vos, Ignace, Gerdie Everaert, and Vasilis Sarafidis. 2024. “A Method to Evaluate the Rank Condition for CCE Estimators.” ECONOMETRIC REVIEWS 43 (2–4): 123–55. https://doi.org/10.1080/07474938.2023.2292383.
Chicago author-date (all authors)
De Vos, Ignace, Gerdie Everaert, and Vasilis Sarafidis. 2024. “A Method to Evaluate the Rank Condition for CCE Estimators.” ECONOMETRIC REVIEWS 43 (2–4): 123–155. doi:10.1080/07474938.2023.2292383.
Vancouver
1.
De Vos I, Everaert G, Sarafidis V. A method to evaluate the rank condition for CCE estimators. ECONOMETRIC REVIEWS. 2024;43(2–4):123–55.
IEEE
[1]
I. De Vos, G. Everaert, and V. Sarafidis, “A method to evaluate the rank condition for CCE estimators,” ECONOMETRIC REVIEWS, vol. 43, no. 2–4, pp. 123–155, 2024.
@article{01HQTF95M12RTX03AYB29C7X24,
  abstract     = {{We develop a binary classifier to evaluate whether the rank condition (RC) is satisfied or not for the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, rho. When this condition fails, the CCE estimator is inconsistent, in general. Despite its importance, to date this rank condition could not be verified. The difficulty lies in the fact that factor loadings are unobserved, such that rho cannot be directly determined. The key insight in this article is that rho can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. Thus, a binary classifier, constructed by comparing estimates of m and rho, correctly determines whether the RC is satisfied or not as (N,T)->infinity. We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability. The RC classifier reveals that the rank condition fails for a subperiod of the sample, in which case the estimated effect of bank size on profitability appears to be biased upwards.}},
  author       = {{De Vos, Ignace and Everaert, Gerdie and  Sarafidis, Vasilis}},
  issn         = {{0747-4938}},
  journal      = {{ECONOMETRIC REVIEWS}},
  keywords     = {{Common factors,common correlated effects approach,rank condition,NUMBER,TESTS,INFERENCE,MODELS,RISK,IMPACT,PANELS}},
  language     = {{eng}},
  number       = {{2-4}},
  pages        = {{123--155}},
  title        = {{A method to evaluate the rank condition for CCE estimators}},
  url          = {{http://doi.org/10.1080/07474938.2023.2292383}},
  volume       = {{43}},
  year         = {{2024}},
}
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