Koop, Gary M; Tobias, Justin

Journal of Econometrics (2006)

We describe procedures for Bayesian estimation and testing in cross
sectional, panel data and nonlinear smooth coefficient models. The
smooth coefficient model is a generalization of the partially linear or
additive model wherein coefficients on linear explanatory variables
are treated as unknown functions of an observable covariate. In the approach
we describe, points on the regression lines are regarded as unknown
parameters and priors are placed on differences between adjacent points to
introduce the potential for smoothing the curves. The algorithms we describe
are quite simple to implement - for example, estimation, testing and
smoothing parameter selection can be carried out analytically in
the cross-sectional smooth coefficient model.

We apply our methods using data from the National Longitudinal Survey of
Youth (NLSY). Using the NLSY data we first explore the relationship between
ability and log wages and flexibly model how returns to schooling vary with
measured cognitive ability. We also examine model of female labor supply and
use this example to illustrate how the described techniques can been applied
in nonlinear settings.