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

Author

Listed:
  • 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. Andrei Zeleneev & Weisheng Zhang, 2025. "Tractable Estimation of Nonlinear Panels with Interactive Fixed Effects," Papers 2511.15427, arXiv.org, revised Mar 2026.
    3. 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.
    4. Gobillon, Laurent & Magnac, Thierry & Roux, Sébastien, 2022. "Lifecycle Wages and Human Capital Investments: Selection and Missing Data," TSE Working Papers 22-1299, Toulouse School of Economics (TSE).
    5. 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.
    6. Jad Beyhum, 2024. "Counterfactuals in factor models," Papers 2401.03293, arXiv.org.
    7. Maximilian Rücker & Michael Vogt & Oliver Linton & Christopher Walsh, 2025. "Estimation and inference in high‐dimensional panel data models with interactive fixed effects," Quantitative Economics, Econometric Society, vol. 16(4), pages 1457-1509, November.
    8. Jad Beyhum & Eric Gautier, 2020. "Factor and factor loading augmented estimators for panel regression," Working Papers hal-02957008, HAL.
    9. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    10. repec:cam:camjip:2218 is not listed on IDEAS
    11. Juan M. Rodriguez-Poo & Alexandra Soberon & Stefan Sperlich, 2025. "Inference on panel data models with a generalized factor structure," Papers 2506.10690, arXiv.org.
    12. repec:cam:camjip:2429 is not listed on IDEAS
    13. Timothy B. Armstrong & Martin Weidner & Andrei Zeleneev, 2024. "Robust estimation and inference in panels with interactive fixed effects," CeMMAP working papers 28/24, Institute for Fiscal Studies.
    14. Mugnier, Martin, 2025. "A simple and computationally trivial estimator for grouped fixed effects models," Journal of Econometrics, Elsevier, vol. 250(C).

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