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A semi-parametric Bayesian approach to the instrumental variable problem

Timothy Conley (), Christian Hansen (), Robert E. McCulloch and Peter Rossi ()

Journal of Econometrics, 2008, vol. 144, issue 1, 276-305

Abstract: 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.

Date: 2008
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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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