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Bias Transmission and Variance Reduction in Two-Stage Quantile Regression


  • Tae-Hwan Kim

    () (School of Economics, Yonsei University - Yonsei University)

  • Christophe Muller

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - CNRS - Centre National de la Recherche Scientifique - ECM - Ecole Centrale de Marseille)


In this paper, we propose a variance reduction method for quantile regressions with endogeneity problems. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions on both error terms and exogenous variables. Second, we exhibit a bias transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a trade-off between an asymptotic bias confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the excellent performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad range of distributions.

Suggested Citation

  • Tae-Hwan Kim & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," Working Papers halshs-00793372, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00793372 Note: View the original document on HAL open archive server:

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    References listed on IDEAS

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    5. Thanaset Chevapatrakul & Tae-Hwan Kim & Paul Mizen, 2009. "The Taylor Principle and Monetary Policy Approaching a Zero Bound on Nominal Rates: Quantile Regression Results for the United States and Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(8), pages 1705-1723, December.
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    Cited by:

    1. Thanaset Chevapatrakul & Tae-Hwan Kim & Paul Mizen, 2009. "The Taylor Principle and Monetary Policy Approaching a Zero Bound on Nominal Rates: Quantile Regression Results for the United States and Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(8), pages 1705-1723, December.
    2. Thanaset Chevapatrakul & Kai-Hong Tee, 2014. "The Effects of News Events on Market Contagion: Evidence from the 2007-2009 Financial Crisis," Discussion Papers 2014/08, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    3. Tae-Hwan Kim & Christophe Muller, 2017. "A Robust Test of Exogeneity Based on Quantile Regressions," AMSE Working Papers 1716, Aix-Marseille School of Economics, Marseille, France.
    4. Christophe Muller, 2017. "Heterogeneity and Non-Constant Effect in Two-Stage Quantile Regression," Working Papers halshs-01157552, HAL.
    5. Tae-Hwan Kim & Christophe Muller, 2013. "A Test for Endogeneity in Conditional Quantiles," Working Papers halshs-00854527, HAL.
    6. Chevapatrakul, Thanaset & Tee, Kai-Hong, 2014. "The effects of news events on market contagion: Evidence from the 2007–2009 financial crisis," Research in International Business and Finance, Elsevier, vol. 32(C), pages 83-105.
    7. Tae-Hwan Kim & Christophe Muller, 2015. "A Particular Form of Non-Constant Effect in Two-Stage Quantile Regression," Working papers 2015rwp-82, Yonsei University, Yonsei Economics Research Institute.
    8. William Miles & Sam Schreyer, 2012. "Is monetary policy non-linear in Indonesia, Korea, Malaysia, and Thailand? A quantile regression analysis," Asian-Pacific Economic Literature, Asia Pacific School of Economics and Government, The Australian National University, vol. 26(2), pages 155-166, November.
    9. Thanaset Chevapatrakul & Juan Paez-Farrell, 2014. "Monetary Policy Reaction Functions in Small Open Economies: a Quantile Regression Approach," Manchester School, University of Manchester, vol. 82(2), pages 237-256, March.

    More about this item


    Two-Stage Estimation; Variance Reduction; Quantile Regression; Asymptotic Bias;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General


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