A semi-parametric Bayesian approach to the instrumental variable problem |
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Authors: | Timothy G Conley Christian B HansenRobert E McCulloch Peter E Rossi |
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Institution: | Graduate School of Business, University of Chicago, USA |
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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. |
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Keywords: | C11 C14 C3 |
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