A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem

68 Pages Posted: 19 Jul 2006  

Timothy G. Conley

University of Chicago - Booth School of Business

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics

Robert E. McCulloch

University of Chicago - Booth School of Business

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management

Date Written: June 2007

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.

Keywords: instrumental variables, non-parametric Bayesian inference, Dirichlet process priors

JEL Classification: C11, C14, C3

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

Timothy G. Conley

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7281 (Phone)

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States
773-834-1702 (Phone)

Robert E. McCulloch (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States
773-294-8616 (Phone)

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