A semi-parametric Bayesian approach to the instrumental variable problem

Timothy G. Conley, Christian B. Hansen, Robert E. McCulloch, Peter E. Rossi

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)276-305
Number of pages30
JournalJournal of Econometrics
Volume144
Issue number1
DOIs
StatePublished - May 1 2008
Externally publishedYes

Keywords

  • Dirichlet process priors
  • Instrumental variables
  • Semi-parametric Bayesian inference

ASJC Scopus subject areas

  • Economics and Econometrics

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