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Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data

  • Hoogerheide, Lennart
  • Kleibergen, Frank
  • van Dijk, Herman K.

We propose a natural conjugate prior for the instrumental variables regression model. The prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior. The Jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator. We construct informative priors for the Angrist-Krueger (1991) data and show that the marginal posterior of the return on education in the US coincides with the marginal posterior from the Southern region when we use the Jeffreys prior. This result occurs since the instruments are the strongest in the Southern region and the posterior using the Jeffreys prior, identical to maximum likelihood, focusses on the strongest available instruments. We construct informative priors for the other regions that make their posteriors of the return on education similar to that of the US and the Southern region. These priors show the amount of prior information needed to obtain comparable results for all regions.

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File URL: http://www.sciencedirect.com/science/article/B6VC0-4KGX8FG-2/2/18d7ebd4bcca2a33733f570c16548879
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 138 (2007)
Issue (Month): 1 (May)
Pages: 63-103

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Handle: RePEc:eee:econom:v:138:y:2007:i:1:p:63-103
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. 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.
  2. Frank Kleibergen & Eric Zivot, 2003. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers UWEC-2002-21-P, University of Washington, Department of Economics.
  3. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  4. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," NBER Working Papers 4483, National Bureau of Economic Research, Inc.
  5. Steel, Mark F. J., 1991. "A Bayesian analysis of simultaneous equation models by combining recursive analytical and numerical approaches," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 83-117.
  6. Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-51, March.
  7. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
  8. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
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