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Bayesian quantile regression methods

Author

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  • 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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    References listed on IDEAS

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    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.
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    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. Bernstein, David H. & Parmeter, Christopher F. & Tsionas, Mike G., 2023. "On the performance of the United States nuclear power sector: A Bayesian approach," Energy Economics, Elsevier, vol. 125(C).
    4. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    5. Theodore Panagiotidis & Gianluigi Pelloni, 2014. "Asymmetry and Lilien’s Sectoral Shifts Hypothesis: A Quantile Regression Approach," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 6(1), pages 68-86, June.
    6. 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.
    7. Tomohiro Ando & Jushan Bai, 2020. "Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 266-279, January.
    8. Ramsey, A., 2018. "Conditional Distributions of Crop Yields: A Bayesian Approach for Characterizing Technological Change," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277253, International Association of Agricultural Economists.
    9. Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "Bayesian moment-based inference in a regression model with misclassification error," Journal of Econometrics, Elsevier, vol. 200(2), pages 282-294.
    10. Siddharta Chib & Minchul Shin & Anna Simoni, 2016. "Bayesian Empirical Likelihood Estimation and Comparison of Moment Condition Models," Working Papers 2016-21, Center for Research in Economics and Statistics.
    11. A Ford Ramsey, 2020. "Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach," American Journal of Agricultural Economics, John Wiley & Sons, vol. 102(1), pages 220-239, January.
    12. Michael Kohler & Adam Krzyżak & Reinhard Tent & Harro Walk, 2018. "Nonparametric quantile estimation using importance sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 439-465, April.
    13. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    14. 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.
    15. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," MPRA Paper 64341, University Library of Munich, Germany.
    16. Korobilis, Dimitris, 2017. "Quantile regression forecasts of inflation under model uncertainty," International Journal of Forecasting, Elsevier, vol. 33(1), pages 11-20.
    17. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
    18. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    19. Yuanying Zhao & Dengke Xu, 2023. "A Bayesian Variable Selection Method for Spatial Autoregressive Quantile Models," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    20. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    21. Chang-Sheng Liu & Han-Ying Liang, 2023. "Bayesian empirical likelihood of quantile regression with missing observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 285-313, April.
    22. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.

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