IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v238y2024i2s0304407623003470.html
   My bibliography  Save this article

The likelihood ratio test for structural changes in factor models

Author

Listed:
  • Bai, Jushan
  • Duan, Jiangtao
  • Han, Xu

Abstract

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data.

Suggested Citation

  • Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    • Handle: RePEc:eee:econom:v:238:y:2024:i:2:s0304407623003470
    DOI: 10.1016/j.jeconom.2023.105631
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407623003470
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.105631?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. Ma, Shujie & Su, Liangjun, 2018. "Estimation of large dimensional factor models with an unknown number of breaks," Journal of Econometrics, Elsevier, vol. 207(1), pages 1-29.
    4. Guanhao Feng & Stefano Giglio & Dacheng Xiu, 2020. "Taming the Factor Zoo: A Test of New Factors," Journal of Finance, American Finance Association, vol. 75(3), pages 1327-1370, June.
    5. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    6. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    7. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    8. Chen, Liang, 2015. "Estimating the common break date in large factor models," Economics Letters, Elsevier, vol. 131(C), pages 70-74.
    9. 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.
    10. Han, Xu, 2018. "Estimation and inference of dynamic structural factor models with over-identifying restrictions," Journal of Econometrics, Elsevier, vol. 202(2), pages 125-147.
    11. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    12. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    13. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    14. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    15. 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.
    16. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1511-1543.
    17. 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.
    18. 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.
    19. 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.
    20. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    21. Bai, Jushan, 2010. "Common breaks in means and variances for panel data," Journal of Econometrics, Elsevier, vol. 157(1), pages 78-92, July.
    22. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2017. "Identification and estimation of a large factor model with structural instability," Journal of Econometrics, Elsevier, vol. 197(1), pages 87-100.
    23. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    24. 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.
    25. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2019. "Testing jointly for structural changes in the error variance and coe¢ cients of a linear regression model," Boston University - Department of Economics - Working Papers Series WP2020-010, Boston University - Department of Economics, revised Feb 2020.
    26. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    27. Su, Liangjun & Wang, Xia, 2020. "Testing For Structural Changes In Factor Models Via A Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1127-1158, December.
    28. Mehmet Caner & Xu Han, 2014. "Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case With Group Bridge Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 359-374, July.
    29. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 395-432.
    30. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    31. 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.
    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. Duan, Jiangtao & Bai, Jushan & Han, Xu, 2023. "Quasi-maximum likelihood estimation of break point in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 233(1), pages 209-236.
    2. Ma, Chenchen & Tu, Yundong, 2023. "Group fused Lasso for large factor models with multiple structural breaks," Journal of Econometrics, Elsevier, vol. 233(1), pages 132-154.
    3. Wang, Lu & Wu, Jianhong, 2022. "Estimation of high-dimensional factor models with multiple structural changes," Economic Modelling, Elsevier, vol. 108(C).
    4. 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.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    6. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," PSE Working Papers halshs-02262202, HAL.
    7. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2017. "Identification and estimation of a large factor model with structural instability," Journal of Econometrics, Elsevier, vol. 197(1), pages 87-100.
    8. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    9. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers halshs-02262202, HAL.
    10. 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.
    11. 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.
    12. 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.
    13. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    14. Ma, Shujie & Su, Liangjun, 2018. "Estimation of large dimensional factor models with an unknown number of breaks," Journal of Econometrics, Elsevier, vol. 207(1), pages 1-29.
    15. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    16. Thomas Despois & Catherine Doz, 2021. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," PSE Working Papers halshs-02235543, HAL.
    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. 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.
    19. Chen, Sanpan & Cui, Guowei & Zhang, Jianhua, 2017. "On testing for structural break of coefficients in factor-augmented regression models," Economics Letters, Elsevier, vol. 161(C), pages 141-145.
    20. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.

    More about this item

    Keywords

    High-dimensional factor models; Structural breaks; LR test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

    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:eee:econom:v:238:y:2024:i:2:s0304407623003470. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.