[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/37514.html
   My bibliography  Save this paper

Identifying observed factors in approximate factor models: estimation and hypothesis testing

Author

Listed:
  • Chen, Liang
Abstract
Despite their popularities in recent years, factor models have long been criticized for the lack of identification. Even when a large number of variables are available, the factors can only be consistently estimated up to a rotation. In this paper, we try to identify the underlying factors by associating them to a set of observed variables, and thus give interpretations to the orthogonal factors estimated by the method of Principal Components. We first propose a estimation procedure to select a set of observed variables, and then test the hypothesis that true factors are exact linear combinations of the selected variables. Our estimation method is shown to able to correctly identity the true observed factor even in the presence of mild measurement errors, and our test statistics are shown to be more general than those of Bai and Ng (2006). The applicability of our methods in finite samples and the advantages of our tests are confirmed by simulations. Our methods are also applied to the returns of portfolios to identify the underlying risk factors.

Suggested Citation

  • Chen, Liang, 2012. "Identifying observed factors in approximate factor models: estimation and hypothesis testing," MPRA Paper 37514, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37514
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/37514/1/MPRA_paper_37514.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Jörg Breitung & Sandra Eickmeier, 2006. "Dynamic Factor Models," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 3, pages 25-40, Springer.
    3. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    4. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
    5. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    6. Mr. Maxym Kryshko, 2011. "Data-Rich DSGE and Dynamic Factor Models," IMF Working Papers 2011/216, International Monetary Fund.
    7. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    8. Altug, Sumru, 1989. "Time-to-Build and Aggregate Fluctuations: Some New Evidence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 889-920, November.
    9. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    10. Shanken, Jay & Weinstein, Mark I., 2006. "Economic forces and the stock market revisited," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 129-144, March.
    11. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    12. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    13. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
    14. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    15. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    16. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
    17. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    18. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    19. Sargent, Thomas J, 1989. "Two Models of Measurements and the Investment Accelerator," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 251-287, April.
    20. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    21. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    22. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    23. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    24. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    25. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
    2. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    3. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    4. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), 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, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    5. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    6. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    7. Matteo Luciani, 2015. "Monetary Policy and the Housing Market: A Structural Factor Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 199-218, March.
    8. Jianqing Fan & Yuling Yan & Yuheng Zheng, 2024. "When can weak latent factors be statistically inferred?," Papers 2407.03616, arXiv.org, revised Sep 2024.
    9. Bai, Jushan & Han, Xu & Shi, Yutang, 2020. "Estimation and inference of change points in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 219(1), pages 66-100.
    10. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    11. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    12. Mao Takongmo, Charles Olivier & Stevanovic, Dalibor, 2015. "Selection Of The Number Of Factors In Presence Of Structural Instability: A Monte Carlo Study," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 177-233, Mars-Juin.
    13. Mario Forni & Luca Gambetti & Luca Sala, 2014. "No News in Business Cycles," Economic Journal, Royal Economic Society, vol. 124(581), pages 1168-1191, December.
    14. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2014. "Dynamic factor models: A review of the literature," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2013(2), pages 73-107.
    15. Fu, Zhonghao & Hong, Yongmiao & Wang, Xia, 2023. "Testing for structural changes in large dimensional factor models via discrete Fourier transform," Journal of Econometrics, Elsevier, vol. 233(1), pages 302-331.
    16. Chou, Ray Yeutien & Yen, Tso-Jung & Yen, Yu-Min, 2020. "Macroeconomic forecasting using approximate factor models with outliers," International Journal of Forecasting, Elsevier, vol. 36(2), pages 267-291.
    17. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    18. Forni, Mario & Gambetti, Luca, 2010. "Fiscal Foresight and the Effects of Goverment Spending," CEPR Discussion Papers 7840, C.E.P.R. Discussion Papers.
    19. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2021. "Estimating and testing high dimensional factor models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 220(2), pages 349-365.
    20. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.

    More about this item

    Keywords

    factor models; observed factors; estimation; hypothesis testing; Fama-French three factors;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:37514. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.