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Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models

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  • Anders Bredahl Kock

    () (CREATES, Aarhus University)

Abstract

This paper generalizes the results for the Bridge estimator of Huang et al. (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular, we show that the Bridge estimator is oracle efficient. It can correctly distinguish between relevant and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in the model, i.e. as if an oracle had revealed the true model prior to estimation. In the case of more explanatory variables than observations we prove that the Marginal Bridge estimator can asymptotically correctly distinguish between relevant and irrelevant explanatory variables. We do this without assuming sub-Gaussianity of the error terms. However, a partial orthogonality condition of the same type as in Huang et al. (2008) is needed.

Suggested Citation

  • Anders Bredahl Kock, 2010. "Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models," CREATES Research Papers 2010-56, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-56
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    References listed on IDEAS

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    1. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
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    Cited by:

    1. Mehmet Caner & Anders Bredahl Kock, 2016. "Oracle Inequalities for Convex Loss Functions with Nonlinear Targets," Econometric Reviews, Taylor & Francis Journals, pages 1377-1411.
    2. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, pages 148-175.
    3. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, pages 325-344.
    4. Mehmet Caner & Anders Bredahl Kock, 2014. "Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso," CREATES Research Papers 2014-36, Department of Economics and Business Economics, Aarhus University.
    5. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    6. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    7. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    8. 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.
    9. Jia Chen & Jiti Gao, 2014. "Semiparametric Model Selection in Panel Data Models with Deterministic Trends and Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/14, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Panel data; high dimensional modeling; variable selection; Bridge estimators; oracle property;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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