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Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models

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  • Kock, Anders Bredahl

Abstract

In this paper we study high-dimensional correlated random effects panel data models. Our setting is useful as it allows including time invariant covariates as under random effects yet allows for correlation between covariates and unobserved heterogeneity as under fixed effects. We use the Mundlak–Chamberlain device to model this correlation. Allowing for a flexible correlation structure naturally leads to a high-dimensional model in which least squares estimation easily becomes infeasible with even a moderate number of explanatory variables.

Suggested Citation

  • Kock, Anders Bredahl, 2016. "Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models," Journal of Econometrics, Elsevier, vol. 195(1), pages 71-85.
    • Handle: RePEc:eee:econom:v:195:y:2016:i:1:p:71-85
    DOI: 10.1016/j.jeconom.2016.06.001
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    Citations

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    2. 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.
    3. Harold D. Chiang, 2018. "Many Average Partial Effects: with An Application to Text Regression," Papers 1812.09397, arXiv.org, revised Jan 2022.
    4. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    5. Babii, Andrii & Ball, Ryan T. & Ghysels, Eric & Striaukas, Jonas, 2023. "Machine learning panel data regressions with heavy-tailed dependent data: Theory and application," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Oliver Linton & Maximilian Ruecker & Michael Vogt & Christopher Walsh, 2022. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org, revised Nov 2024.
    7. Lamarche, Carlos & Parker, Thomas, 2023. "Wild bootstrap inference for penalized quantile regression for longitudinal data," Journal of Econometrics, Elsevier, vol. 235(2), pages 1799-1826.
    8. Harold D. Chiang & Kengo Kato & Yukun Ma & Yuya Sasaki, 2022. "Multiway Cluster Robust Double/Debiased Machine Learning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1046-1056, June.
    9. Mehmet Caner & Kfir Eliaz, 2021. "Shoiuld Humans Lie to Machines: The Incentive Compatibility of Lasso and General Weighted Lasso," Papers 2101.01144, arXiv.org, revised Sep 2021.
    10. Jiatong Li & Hongqiang Yan, 2024. "Uniform Inference in High-Dimensional Threshold Regression Models," Papers 2404.08105, arXiv.org, revised Aug 2024.
    11. Linton, O. B. & Rücker, M. & Vogt, M. & Walsh, C., 2024. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2429, Faculty of Economics, University of Cambridge.
    12. Xi Chen & Ye Luo & Martin Spindler, 2019. "Adaptive Discrete Smoothing for High-Dimensional and Nonlinear Panel Data," Papers 1912.12867, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    Panel data; Lasso; Oracle inequality; Sup-norm bounds; High-dimensional models; Weak sparsity; Correlated random effects; Mundlak–Chamberlain; Variable selection; Uniform inference;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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