Semiparametric Bayes instrumental variable estimation with many weak instruments

We develop a new semiparametric Bayes instrumental variables estimation method. We employ the form of the regression function of the first-stage equation, and the disturbances are modeled nonparametrically to achieve better predictive power of the endogenous variables, whereas we use parametric formulation in the second-stage equation, which is of interest in inference. Our simulation studies show that under small sample sizes, the proposed method obtains more efficient estimates and very precise credible intervals compared with existing IV methods with smaller mean squared error. We applied our proposed method to a Mendelian randomization dataset where a large number of instruments are available and semiparametric specification is appropriate. We obtained statistically significant results that cannot be obtained by the existing methods, including standard Bayesian IV.