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Bayesian and classical approaches to instrumental variable regression

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  • Kleibergen, Frank
  • Zivot, Eric

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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 114 (2003)
Issue (Month): 1 (May)
Pages: 29-72

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Handle: RePEc:eee:econom:v:114:y:2003:i:1:p:29-72

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Nelson, C.R. & Startz, R. & Zivot, E., 1996. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Working Papers 96-15, University of Washington, Department of Economics.
  2. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
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  15. Park, Soo-Bin, 1982. "Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients," Journal of Econometrics, Elsevier, vol. 18(3), pages 295-311, April.
  16. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Econometrics 9905001, EconWPA.
  17. Tobias, Justin & Zellner, Arnold, 2001. "Further Results on Bayesian Method of Moments Analysis of the Multiple Regression Model," Staff General Research Papers 12021, Iowa State University, Department of Economics.
  18. Sawa, Takamitsu, 1973. "The mean square error of a combined estimator and numerical comparison with the TSLS estimator," Journal of Econometrics, Elsevier, vol. 1(2), pages 115-132, June.
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