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We present a new procedure for nonparametric Bayesian estimation of regression functions. Specifically, our method makes use of an idea described in Frühwirth-Schnatter and Wagner (2010) to impose linearity exactly (conditional upon an unobserved binary indicator), yet also permits departures from linearity while imposing smoothness of the regression curves. An advantage of this approach is that the posterior probability of linearity is essentially produced as a by-product of the procedure. We apply our methods in both generated data experiments as well as in an illustrative application involving the impact of body mass index (BMI) on labor market earnings.

© 2014 John Wiley & Sons, Ltd. In this paper we, like several studies in the recent literature, employ a Bayesian approach to estimation and inference in models with endogeneity concerns by imposing weaker prior assumptions than complete excludability. When allowing for instrument imperfection of this type, the model is only partially identified, and as a consequence standard estimates obtained from the Gibbs simulations can be unacceptably imprecise. We thus describe a substantially improved 'semi-analytic' method for calculating parameter marginal posteriors of interest that only require use of the well-mixing simulations associated with the identifiable model parameters and the form of the conditional prior. Our methods are also applied in an illustrative application involving the impact of body mass index on earnings.