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Semiparametric Bayesian inference in multiple equation models

  • Dale J. Poirier

    (Department of Economics, University of California at Irvine, Irvine, CA, USA)

  • Gary Koop

    (Department of Economics, University of Leicester, Leicester, UK)

  • Justin Tobias

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labour and returns to schooling literatures. Copyright © 2005 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.810
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File URL: http://qed.econ.queensu.ca:80/jae/2005-v20.6/
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 20 (2005)
Issue (Month): 6 ()
Pages: 723-747

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Handle: RePEc:jae:japmet:v:20:y:2005:i:6:p:723-747
DOI: 10.1002/jae.810
Contact details of provider: Web page: http://www.interscience.wiley.com/jpages/0883-7252/

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  10. McKinley L. Blackburn & David Neumark, 1993. "Are OLS Estimates of the Return to Schooling Biased Downward? Another Look," NBER Working Papers 4259, National Bureau of Economic Research, Inc.
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  12. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier.
  13. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
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