Bayesian quantile regression methods

Authors

  • Tony Lancaster,

    1. Department of Economics, Brown University, Providence, RI, USA
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  • Sung Jae Jun

    Corresponding author
    1. The Center for the Study of Auctions, Procurements and Competition Policy, Department of Economics, The Pennsylvania State University, University Park, PA, USA
    • Department of Economics, 619 Kern Bldg, The Pennsylvania State University, University Park, PA 16802, USA.
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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.

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