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Principal Components and Regularized Estimation of Factor Models

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  • Jushan Bai
  • Serena Ng

Abstract

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of shrinking the singular values of the common component and possibly reducing its rank. The method is used in the machine learning literature to recover low-rank matrices. We study the procedure from the perspective of estimating a minimum-rank approximate factor model. We show that the constrained factor estimates are biased but can be more efficient in terms of mean-squared errors. Rank consideration suggests a data-dependent penalty for selecting the number of factors. The new criterion is more conservative in cases when the nominal number of factors is inflated by the presence of weak factors or large measurement noise. The framework is extended to incorporate a priori linear constraints on the loadings. We provide asymptotic results that can be used to test economic hypotheses.

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  • Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1708.08137
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    References listed on IDEAS

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    Cited by:

    1. Wan, Runzhe & Li, Yingying & Lu, Wenbin & Song, Rui, 2024. "Mining the factor zoo: Estimation of latent factor models with sufficient proxies," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Lettau, Martin & Pelger, Markus, 2020. "Estimating latent asset-pricing factors," Journal of Econometrics, Elsevier, vol. 218(1), pages 1-31.
    3. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    4. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    5. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," DSSR Discussion Papers 96, Graduate School of Economics and Management, Tohoku University.
    6. Victor Chernozhukov & Christian Hansen & Yuan Liao & Yinchu Zhu, 2019. "Inference for heterogeneous effects using low-rank estimations," CeMMAP working papers CWP31/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Gu, Shihao & Kelly, Bryan & Xiu, Dacheng, 2021. "Autoencoder asset pricing models," Journal of Econometrics, Elsevier, vol. 222(1), pages 429-450.
    8. Philippe Goulet Coulombe, 2020. "Time-Varying Parameters as Ridge Regressions," Papers 2009.00401, arXiv.org, revised Nov 2024.
    9. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    10. Jiangtao Duan & Wei Gao & Hao Qu & Hon Keung Tony, 2019. "Subspace Clustering for Panel Data with Interactive Effects," Papers 1909.09928, arXiv.org, revised Feb 2021.
    11. Belloni, Alexandre & Chen, Mingli & Madrid Padilla, Oscar Hernan & Wang, Zixuan (Kevin), 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," The Warwick Economics Research Paper Series (TWERPS) 1230, University of Warwick, Department of Economics.

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