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Nuclear norm regularized estimation of panel regression models

Author

Listed:
  • Hyungsik Roger Moon

    (Institute for Fiscal Studies and USC)

  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

Abstract
In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The fi rst method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are de fined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identifi cation problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a nite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.

Suggested Citation

  • Hyungsik Roger Moon & Martin Weidner, 2019. "Nuclear norm regularized estimation of panel regression models," CeMMAP working papers CWP14/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:14/19
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    References listed on IDEAS

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    Cited by:

    1. Jörg Breitung & Philipp Hansen, 2021. "Alternative estimation approaches for the factor augmented panel data model with small T," Empirical Economics, Springer, vol. 60(1), pages 327-351, January.
    2. Norkutė, Milda & Sarafidis, Vasilis & Yamagata, Takashi & Cui, Guowei, 2021. "Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure," Journal of Econometrics, Elsevier, vol. 220(2), pages 416-446.
    3. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    4. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Cambridge Working Papers in Economics 2242, Faculty of Economics, University of Cambridge.
    5. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.
    6. Alexandre Belloni & Mingli Chen & Oscar Hernan Madrid Padilla & Zixuan & Wang, 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," Papers 1912.02151, arXiv.org, revised Aug 2022.
    7. Luca Margaritella & Joakim Westerlund, 2023. "Using information criteria to select averages in CCE," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 405-421.
    8. Martin Mugnier, 2022. "A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models," Papers 2203.08879, arXiv.org, revised Sep 2024.
    9. Denis Chetverikov & Elena Manresa, 2022. "Spectral and post-spectral estimators for grouped panel data models," Papers 2212.13324, arXiv.org, revised Dec 2022.
    10. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2218, Faculty of Economics, University of Cambridge.
    11. Junlong Feng, 2019. "Regularized Quantile Regression with Interactive Fixed Effects," Papers 1911.00166, arXiv.org, revised Mar 2021.
    12. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.
    13. Martin Mugnier, 2022. "Make the Difference! computationally Trivial Estimators for Grouped Fixed Effects Models," Working Papers 2022-07, Center for Research in Economics and Statistics.
    14. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

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