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Bayesian quantile regression methods

Author

Listed:
  • Tony Lancaster

    (Department of Economics, Brown University, Providence, RI, USA)

  • Sung Jae Jun

    (The Center for the Study of Auctions, Procurements and Competition Policy, Department of Economics, The Pennsylvania State University, University Park, PA, USA)

Abstract

This paper is a study of the application of Bayesian exponentially tilted empirical likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys' method. For regression quantiles we derive the asymptotic form of the posterior density. We also examine Markov chain Monte Carlo simulations with a proposal density formed from an overdispersed version of the limiting normal density. We show that the algorithm works well even in models with an endogenous regressor when the instruments are not too weak. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Tony Lancaster & Sung Jae Jun, 2010. "Bayesian quantile regression methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 287-307.
  • Handle: RePEc:jae:japmet:v:25:y:2010:i:2:p:287-307
    DOI: 10.1002/jae.1069
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    File URL: http://qed.econ.queensu.ca:80/jae/2010-v25.2/
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    References listed on IDEAS

    as
    1. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    2. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    3. Kathryn Graddy, 1995. "Testing for Imperfect Competition at the Fulton Fish Market," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 75-92, Spring.
    4. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    5. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    6. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    7. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Lane F. Burgette & Jerome P. Reiter, 2012. "Modeling Adverse Birth Outcomes via Confirmatory Factor Quantile Regression," Biometrics, The International Biometric Society, vol. 68(1), pages 92-100, March.
    2. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-72, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Theodore Panagiotidis & Gianluigi Pelloni, 2014. "Asymmetry and Lilien’s Sectoral Shifts Hypothesis: A Quantile Regression Approach," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 6(1), pages 68-86, June.
    4. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
    5. Ando, Tomohiro & Bai, Jushan, 2018. "Quantile co-movement in financial markets: A panel quantile model with unobserved heterogeneity," MPRA Paper 88765, University Library of Munich, Germany.
    6. repec:eee:econom:v:200:y:2017:i:2:p:282-294 is not listed on IDEAS
    7. repec:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0595-4 is not listed on IDEAS
    8. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    9. Wu Wang & Zhongyi Zhu, 2017. "Conditional empirical likelihood for quantile regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 1-16, January.
    10. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," MPRA Paper 64341, University Library of Munich, Germany.
    11. Korobilis, Dimitris, 2017. "Quantile regression forecasts of inflation under model uncertainty," International Journal of Forecasting, Elsevier, vol. 33(1), pages 11-20.
    12. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
    13. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.

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