IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Bayesian and classical approaches to instrumental variable regression

  • Kleibergen, Frank
  • Zivot, Eric

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.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6VC0-476KDK5-1/2/d9cbc5d94494134f91a8d3b2e3ae7d6b
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

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

as
in new window

Handle: RePEc:eee:econom:v:114:y:2003:i:1:p:29-72
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Econometrics 9905001, EconWPA.
  3. Diebold & Lamb, . "Why Are Estimates of Agricultural Supply Response So Variable?," Home Pages _055, University of Pennsylvania.
  4. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
  5. Zellner, Arnold & Bauwens, Luc & Van Dijk, Herman K., 1988. "Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 39-72.
  6. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  7. Anderson, T W, 1977. "Asymptotic Expansions of the Distributions of Estimates in Simultaneous Equations for Alternative Parameter Sequences," Econometrica, Econometric Society, vol. 45(2), pages 509-18, March.
  8. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  9. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-75, September.
  10. Zivot, E & Startz, R & Nelson, C-R, 1997. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Working Papers 97-17, University of Washington, Department of Economics.
  11. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  12. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
  13. 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.
  14. Kajal Lahiri & Chuanming Gao, 2001. "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Discussion Papers 01-15, University at Albany, SUNY, Department of Economics.
  15. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
  16. DREZE, Jacques H., . "Bayesian regression analysis using poly-t densities," CORE Discussion Papers RP -316, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-51, March.
  18. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
  19. John Shea, 1996. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," NBER Technical Working Papers 0193, National Bureau of Economic Research, Inc.
  20. Zellner, Arnold, 1978. "Estimation of functions of population means and regression coefficients including structural coefficients : A minimum expected loss (MELO) approach," Journal of Econometrics, Elsevier, vol. 8(2), pages 127-158, October.
  21. John C. Chao & Peter C.B. Phillips, 1998. "Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables," Cowles Foundation Discussion Papers 1198, Cowles Foundation for Research in Economics, Yale University.
  22. Zellner, Arnold, 1998. "The finite sample properties of simultaneous equations' estimates and estimators Bayesian and non-Bayesian approaches," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 185-212.
  23. 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.
  24. Zellner, Arnold & Tobias, Justin, 2001. "Further Results on Bayesian Method of Moments Analysis of the Multiple Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 121-40, February.
  25. Anderson, T W & Sawa, Takamitsu, 1979. "Evaluation of the Distribution Function of the Two-Stage Least Squares Estimate," Econometrica, Econometric Society, vol. 47(1), pages 163-82, January.
  26. Anderson, T. W. & Kunitomo, Naoto & Morimune, Kimio, 1986. "Comparing Single-Equation Estimators in a Simultaneous Equation System," Econometric Theory, Cambridge University Press, vol. 2(01), pages 1-32, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:114:y:2003:i:1:p:29-72. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.