Inconsistency transmission and variance reduction in two-stage quantile regression

Tae Hwan Kim, Christophe Muller

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, we propose a new variance reduction method for quantile regressions with endogeneity problems, for alpha-mixing or m-dependent covariates and error terms. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions. Second, we exhibit an inconsistency 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 tradeoff between an inconsistency confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the fine 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 set of distributions. Finally, we apply our method to food demand equations in Egypt.

Original languageEnglish
Pages (from-to)1044-1077
Number of pages34
JournalCommunications in Statistics: Simulation and Computation
Issue number4
Publication statusPublished - 2020 Apr 2

Bibliographical note

Funding Information:
We are grateful to R. Davidson, W. Newey, J. Powell, H. White, O. Linton, C.B. Phillips, S. Portnoy, R. Blundell and P. Lavergne for useful discussions and to participants in presentations in the University of Nottingham, CREST-INSEE in Paris, London School of Economics, University of California at San Diego, Durham University, University of Alicante, University of Aix-Marseille, University of Cergy-Pontoise, Toulouse School of Economics, Yonsei University and several conferences for their comments. Remaining errors are ours. We acknowledge the Award No. 30,649 from the British Academy. Tae-Hwan Kim is grateful for the financial support from the National Research Foundation of Korea - a grant funded by the Korean Government (NRF-2009-327-B00088). Christophe Muller is grateful for support from the A*MIDEX project (No. ANR-11-IDEX-0001-02) funded by the” Investissements d'Avenir” French Government program, managed by the French National Research Agency (ANR).

Publisher Copyright:
© 2019, © 2019 Taylor & Francis Group, LLC.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation


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