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Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities

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  • Xu Cheng
  • Zhipeng Liao
  • Frank Schorfheide

Abstract

In large-scale panel data models with latent factors the number of factors and their loadings may change over time. Treating the break date as unknown, this article proposes an adaptive group-LASSO estimator that consistently determines the numbers of pre- and post-break factors and the stability of factor loadings if the number of factors is constant. We develop a cross-validation procedure to fine-tune the data-dependent LASSO penalties and show that after the number of factors has been determined, a conventional least-squares approach can be used to estimate the break date consistently. The method performs well in Monte Carlo simulations. In an empirical application, we study the change in factor loadings and the emergence of new factors in a panel of U.S. macroeconomic and financial time series during the Great Recession.

Suggested Citation

  • Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1511-1543.
  • Handle: RePEc:oup:restud:v:83:y:2016:i:4:p:1511-1543.
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    File URL: http://hdl.handle.net/10.1093/restud/rdw005
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    Cited by:

    1. repec:eee:econom:v:207:y:2018:i:1:p:1-29 is not listed on IDEAS
    2. Badi Baltagi & Qu Feng & Chihwa Kao, 2019. "Structural Changes in Heterogeneous Panels with Endogenous Regressors," Center for Policy Research Working Papers 214, Center for Policy Research, Maxwell School, Syracuse University.
    3. repec:eme:aecozz:s0731-905320150000035011 is not listed on IDEAS
    4. Yohei Yamamoto, 2016. "Forecasting With Nonspurious Factors in U.S. Macroeconomic Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 81-106, January.
    5. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1117-1152, October.
    6. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    7. Laurent Callot & Johannes Tang Kristensen, 2016. "Regularized Estimation of Structural Instability in Factor Models: The US Macroeconomy and the Great Moderation," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 437-479 Emerald Publishing Ltd.
    8. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    9. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    10. Likai Chen & Weining Wang & Wei Biao Wu, 2017. "Dynamic Semiparametric Factor Model with a Common Break," SFB 649 Discussion Papers SFB649DP2017-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Badi H. Baltagi & Chihwa Kao & Fa Wang, 2016. "The Identification and Estimation of a Large Factor Model with Structural Instability," Center for Policy Research Working Papers 194, Center for Policy Research, Maxwell School, Syracuse University.
    12. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786, arXiv.org, revised Mar 2018.
    13. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    14. Maxime Leroux & Rachidi Kotchoni & Dalibor Stevanovic, 2017. "Forecasting economic activity in data-rich environment," CIRANO Working Papers 2017s-05, CIRANO.
    15. Chen, Liang, 2015. "Estimating the common break date in large factor models," Economics Letters, Elsevier, vol. 131(C), pages 70-74.
    16. 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.
    17. 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.
    18. Knut Are Aastveit & Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2017. "Have Standard VARS Remained Stable Since the Crisis?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(5), pages 931-951, August.
    19. Pierre Guerin & Danilo Leiva-Leon & Massimiliano Marcellino, 2016. "Markov-Switching Three-Pass Regression Filter," Working Papers 591, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    20. Markus Pelger & Ruoxuan Xiong, 2018. "State-Varying Factor Models of Large Dimensions," Papers 1807.02248, arXiv.org, revised Apr 2019.
    21. repec:eee:jbfina:v:82:y:2017:i:c:p:244-264 is not listed on IDEAS
    22. Jushan Bai & Kunpeng Li & Lina Lu, 2016. "Estimation and Inference of FAVAR Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 620-641, October.
    23. Ryo Okui & Wendun Wang, 2018. "Heterogeneous structural breaks in panel data models," Papers 1801.04672, arXiv.org, revised Nov 2018.
    24. repec:eee:ecolet:v:161:y:2017:i:c:p:141-145 is not listed on IDEAS

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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