68 Pages Posted: 19 Jul 2006
Date Written: June 2007
We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.
Keywords: instrumental variables, non-parametric Bayesian inference, Dirichlet process priors
JEL Classification: C11, C14, C3
Suggested Citation: Suggested Citation
Conley, Timothy G. and Hansen, Christian and McCulloch, Robert E. and Rossi , Peter E., A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem (June 2007). Available at SSRN: https://ssrn.com/abstract=917432 or http://dx.doi.org/10.2139/ssrn.917432