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Efficient Estimation Of Factor Models

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  • Choi, In

Abstract

This paper considers the factor model X = Λ F + e . Assuming a normal distribution for the idiosyncratic error e conditional on the factors { F }, conditional maximum likelihood estimators of the factor and factor-loading spaces are derived. These estimators are called generalized principal component estimators (GPCEs) without the normality assumption. This paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces. It is shown that variance of the GPCE of the common component is smaller than that of the principal component estimator studied in Bai (2003, Econometrica 71, 135–172). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component estimator. The feasible GPCE (FGPCE) of the factor space is shown to be asymptotically equivalent to the GPCE. The GPCE and FGPCE are shown to be more efficient than the principal component estimator in finite samples.

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  • Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(02), pages 274-308, April.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:274-308_00
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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
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    13. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
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    Cited by:

    1. Hansen, Christian & Liao, Yuan, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," MPRA Paper 75313, University Library of Munich, Germany.
    2. repec:eme:aecozz:s0731-905320150000035010 is not listed on IDEAS
    3. Bai, Jushan & Liao, Yuan, 2012. "Efficient Estimation of Approximate Factor Models," MPRA Paper 41558, University Library of Munich, Germany.
    4. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    5. In Choi & Dukpa Kim & Yun Jung Kim & Noh-Sun Kwark, 2016. "A Multilevel Factor Model: Identification, Asymptotic Theory and Applications," Working Papers 1609, Research Institute for Market Economy, Sogang University.
    6. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Papers 1611.09420, arXiv.org, revised Dec 2016.
    7. Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    8. Simon Freyaldenhoven, 2017. "A Generalized Factor Model with Local Factors," 2017 Papers pfr361, Job Market Papers.
    9. In Choi & Seong Jin Hwang, 2012. "Forecasting Korean inflation," Working Papers 1202, Research Institute for Market Economy, Sogang University.
    10. In Choi, 2013. "Model Selection for Factor Analysis: Some New Criteria and Performance Comparisons," Working Papers 1209, Research Institute for Market Economy, Sogang University.
    11. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    12. Trapani, Lorenzo, 2013. "On bootstrapping panel factor series," Journal of Econometrics, Elsevier, vol. 172(1), pages 127-141.
    13. Jörg Breitung & In Choi, 2013. "Factor models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265 Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Research Institute for Market Economy, Sogang University, revised Dec 2011.
    14. Bai, Jushan & Wang, Peng, 2012. "Identification and estimation of dynamic factor models," MPRA Paper 38434, University Library of Munich, Germany.
    15. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 401-434 Emerald Publishing Ltd.
    16. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    17. repec:eee:macchp:v2-415 is not listed on IDEAS
    18. repec:eee:econom:v:200:y:2017:i:1:p:59-78 is not listed on IDEAS
    19. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Departmental Working Papers 201610, Rutgers University, Department of Economics.
    20. Rachida Ouysse, 2017. "Constrained principal components estimation of large approximate factor models," Discussion Papers 2017-12, School of Economics, The University of New South Wales.

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