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Bayesian quantile regression methods

  • 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)

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.

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File URL: http://hdl.handle.net/10.1002/jae.1069
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File URL: http://qed.econ.queensu.ca:80/jae/2010-v25.2/
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 25 (2010)
Issue (Month): 2 ()
Pages: 287-307

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Handle: RePEc:jae:japmet:v:25:y:2010:i:2:p:287-307
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  1. 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.
  2. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
  3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  4. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
  5. 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.
  6. 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.
  7. Graddy, K., 1993. "Testing for Imperfect Competition at the Fulton Fish Market," Papers 137, Princeton, Department of Economics - Financial Research Center.
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