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Bayesian and Classical Approaches to Instrumental Variables Regression

Frank Kleibergen () and Eric Zivot ()

Econometrics from University Library of Munich, Germany

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.

Keywords: Bayesian; diffuse prior; instrumental variables; Jeffreys prior; limited information maximum likelihood; reduced rank; two stage least squares (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 1998-12-31
Note: Type of Document - Adobe Acrobat (.pdf); prepared on IBM PC ; to print on PostScript; pages: 38; figures: included
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Related works:
Journal Article: Bayesian and classical approaches to instrumental variable regression (2003) Downloads
Working Paper: Bayesian and Classical Approaches to Instrumental Variable Regression (2003)
Working Paper: Bayesian and classical approaches to instrumental variable regression (1998)
Working Paper: Bayesian and Classical Approaches to Instrumental Variable Regression (1998) Downloads
Working Paper: Bayesian and Classical Approaches to Instrumental Variable Regression (1998)
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