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Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved Heterogeneity

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  • Beyhum, Jad
  • Gautier, Eric

Abstract

This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size. The estimator is solution of a well-structured convex optimization problem and can be solved in polynomial-time. We derive rates of convergence, study the low-rank properties of the estimator, estimation of the rank and of annihilator matrices when the number of time periods grows with the sample size. Two-stage estimators can be asymptotically normal. None of the procedures require knowledge of the variance of the errors.

Suggested Citation

  • Beyhum, Jad & Gautier, Eric, 2019. "Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved Heterogeneity," TSE Working Papers 19-1008, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:122931
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hugo Freeman & Martin Weidner, 2021. "Low-rank approximations of nonseparable panel models," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 40-77.
    2. 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.
    3. Iv'an Fern'andez-Val & Hugo Freeman & Martin Weidner, 2020. "Low-Rank Approximations of Nonseparable Panel Models," Papers 2010.12439, arXiv.org, revised Mar 2021.
    4. Jad Beyhum & Eric Gautier, 2020. "Factor and factor loading augmented estimators for panel regression," Working Papers hal-02957008, HAL.
    5. 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.
    6. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.

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