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Bayesian and classical approaches to instrumental variable regression

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Author Info
Kleibergen, F.R.
Zivot, E. (Erasmus Econometric Institute)

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Abstract

We establish the relationships between certain Bayesian and classical approaches to instrumental variable regression. We determine the form of priors that lead to posteriors for structural parameters 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 determine the exact finite sample density of the LIML estimator and the prior 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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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 9835 Revision_Date: 2009-08-05.

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Date of creation: 26 Nov 1998
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Handle: RePEc:dgr:eureir:1765001540

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Related research
Keywords: instrumental variable regression; bayesian approaches; classical approaches; LIML;

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  1. Frank Kleibergen & Richard Kleijn & Richard Paap, 2000. "The Bayesian Score Statistic," Tinbergen Institute Discussion Papers 00-035/4, Tinbergen Institute. [Downloadable!]
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  2. DUFOUR, Jean-Marie Dufour & KHALAF, Lynda & KICHIAN, Maral, 2005. "Inflation dynamics and the New Keynesian Phillips Curve: an identification robust econometric analysis," Cahiers de recherche 2005-17, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  3. Holden, Tom, 2008. "Rational macroeconomic learning in linear expectational models," MPRA Paper 10872, University Library of Munich, Germany. [Downloadable!]
  4. Khalaf, Lynda & Kichian, Maral, 2003. "Are New Keynesian Phillips Curved Identified?," Cahiers de recherche 0312, GREEN. [Downloadable!]
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  5. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation, Yale University. [Downloadable!]
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  6. Chuanming Gao & Kajal Lahiri, 2000. "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Econometric Society World Congress 2000 Contributed Papers 0230, Econometric Society. [Downloadable!]
  7. Gary Koop & Dale Poirier & Justin Tobias, 2003. "Bayesian Semiparametric Inference in Multiple Equation Models," Discussion Papers in Economics 04/17, Department of Economics, University of Leicester. [Downloadable!]
  8. Antipin, Jan-Erik & Mavrotas, George, 2006. "On the Empirics of Aid and Growth: A Fresh Look," Working Papers RP2006/05, World Institute for Development Economic Research (UNU-WIDER). [Downloadable!]
  9. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics. [Downloadable!]
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  10. Stanislav Radchenko, 2004. "Limited Information Bayesian Analysis of a Simultaneous Equation with an Autocorrelated Error Term and its Application to the U.S. Gasoline Market," Econometrics 0408001, EconWPA. [Downloadable!]
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  11. Erkki Siivonen & Arto Luoma & Jani Luoto, 2003. "Growth, Institutions and Productivity: An empirical analysis using the Bayesian approach," Research Reports 104, Government Institute for Economic Research Finland (VATT). [Downloadable!]
  12. Lynda Khalaf & Maral Kichian, 2004. "Estimating New Keynesian Phillips Curves Using Exact Methods," Working Papers 04-11, Bank of Canada. [Downloadable!]
  13. Dale J. Poirier & Gary Koop & Justin Tobias, 2005. "Semiparametric Bayesian inference in multiple equation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 723-747. [Downloadable!]
    Other versions:
  14. H.K. Van Dijk, 2002. "On Bayesian structural inference in a simultaneous equation model," Econometric Institute Report 263, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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