Semiparametric Bayesian inference in multiple equation models
Version of Record online: 9 JUN 2005
Copyright © 2005 John Wiley & Sons, Ltd.
Journal of Applied Econometrics
Volume 20, Issue 6, pages 723–747, September/October 2005
How to Cite
Koop, G., Poirier, D. J. and Tobias, J. (2005), Semiparametric Bayesian inference in multiple equation models. J. Appl. Econ., 20: 723–747. doi: 10.1002/jae.810
- Issue online: 26 SEP 2005
- Version of Record online: 9 JUN 2005
- Manuscript Revised: 27 APR 2004
- Manuscript Received: 24 JUN 2003
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.