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Semiparametric Bayesian inference in multiple equation models

Author

Listed:
  • 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
Abstract
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.

Suggested Citation

  • Dale J. Poirier & Gary Koop & Justin Tobias, 2005. "Semiparametric Bayesian inference in multiple equation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 723-747.
    • Handle: RePEc:jae:japmet:v:20:y:2005:i:6:p:723-747
    DOI: 10.1002/jae.810
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