Koop, Gary M; Poirier, Dale J; Tobias, Justin

Journal of Applied Econometrics Vol. 20 (2005): 723-747.

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 labor and returns to schooling literatures.