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Bayesian and Classical Approaches to Instrumental Variables Regression

Author

Listed:
  • 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.

Suggested Citation

  • Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variables Regression," Econometrics 9812002, University Library of Munich, Germany.
    • 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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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Bayesian; diffuse prior; instrumental variables; Jeffreys prior; limited information maximum likelihood; reduced rank; two stage least squares;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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