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Bayesian and Classical Approaches to Instrumental Variables Regression

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Author Info

  • Frank Kleibergen

    (Erasmus University Rotterdam)

  • Eric Zivot

    (University of Washington)

Abstract

We estabilsh the relationships between certain Bayesian and classical approaches to instrumental variables regression. We determine the form of priors that lead to posteriors for structural paameters that have similar properties as classical 2SLS and LIML and in doing so provide some new insight to the small sample behavior of Bayesian and classical procedures in the limited information simultaneous equations model. Our approach is motivated by the relationship between Bayesian and classical procedures in linear regression models: i.e., Bayesian analysis with a diffuse prior leads to posteriors that are identical in form to the finite sample density of classical least squares estimators. We use the fact that the instrumental variables regression model can be obtained from a reduced rank restriction on a multivariate linear model to determine the priors that give rise to posteriors that have properties similar to classical 2SLS and LIML. As a by-product of this approach we provide a novel way to dtermine the exact finite sample density of the LIML estimator and theprior that corresponds with classical LIML. We show that the traditional Dreze (1976) and a new Bayesian Two Stage approach are similar to 2SLS whereas the approach based on the Jeffreys' prior corresponds to LIML.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9812002.

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Length: 38 pages
Date of creation: 31 Dec 1998
Date of revision:
Handle: RePEc:wpa:wuwpem:9812002

Note: Type of Document - Adobe Acrobat (.pdf); prepared on IBM PC ; to print on PostScript; pages: 38; figures: included
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Web page: http://128.118.178.162

Related research

Keywords: Bayesian; diffuse prior; instrumental variables; Jeffreys prior; limited information maximum likelihood; reduced rank; two stage least squares;

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References

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  21. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
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  23. Dreze, Jacques H., 1977. "Bayesian regression analysis using poly-t densities," Journal of Econometrics, Elsevier, vol. 6(3), pages 329-354, November.
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