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Quantile Regression Random Effects


  • Antonio F. Galvao
  • Alexandre Poirier


This paper develops a random effects model for quantile regression (QR). We establish identification of the QR coefficients, and develop practical estimation and inference procedures. We employ a simple pooled QR estimator to estimate the coefficients of interest, and derive its statistical properties. The random effects induce cluster dependence hence we use a cluster-robust variance-covariance matrix estimator for inference, and establish its uniform consistency over the set of quantiles. We also develop a new test procedure for uniform testing of linear hypotheses in QR models. This procedure is a modified Wald test applied on a growing number of quantiles such that, asymptotically, the test is uniform over the quantiles. We show this procedure can be applied to test the random effects hypothesis in QR panel data models. Two significant differences between our model and fixed-effects QR models are that effects of time-invariant regressors can be estimated, and that the time-series dimension can be small and finite. We provide Monte Carlo simulations to evaluate the finite sample performance of the estimation and inference procedures. Finally, we apply the proposed methods to study the roles of education and ability in wage determination. We document strong heterogeneity in returns to education along the conditional distribution of earnings.

Suggested Citation

  • Antonio F. Galvao & Alexandre Poirier, 2019. "Quantile Regression Random Effects," Annals of Economics and Statistics, GENES, issue 134, pages 109-148.
  • Handle: RePEc:adr:anecst:y:2019:i:134:p:109-148
    DOI: 10.15609/annaeconstat2009.134.0109

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    Cited by:

    1. Paulo M.M. Rodrigues & Matei Demetrescu & Mehdi Hosseinkouchack, 2022. "Cross-Sectional Error Dependence in Panel Quantile Regressions," Working Papers w202213, Banco de Portugal, Economics and Research Department.
    2. Demetrescu, Matei & Hosseinkouchack, Mehdi & Rodrigues, Paulo M. M., 2023. "Tests of no cross-sectional error dependence in panel quantile regressions," Ruhr Economic Papers 1041, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    3. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    4. Martina Pons & Blaise Melly, 2022. "Stata commands to estimate quantile regression with panel and grouped data," Swiss Stata Conference 2022 05, Stata Users Group.
    5. Schorr, A. & Lips, M., 2018. "Influence of milk yield on profitability a quantile regression analysis," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277000, International Association of Agricultural Economists.
    6. Jennifer Betz & Maximilian Nagl & Daniel Rösch, 2022. "Credit line exposure at default modelling using Bayesian mixed effect quantile regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2035-2072, October.

    More about this item


    Quantile Regression; Panel Data; Random Effects; Hypothesis Testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models


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