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

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

Abstract

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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Bibliographic Info

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

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

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References

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  1. John F. Geweke, 1995. "Bayesian reduced rank regression in econometrics," Working Papers 540, Federal Reserve Bank of Minneapolis.
  2. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
  3. Steel, M.F.J., 1989. "A Bayesian Analysis Of Simultaneous Equation Models By Combining Recursive Analytical And Numerical Approaches," Papers 8908, Tilburg - Center for Economic Research.
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  5. 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.
  6. 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.
  7. 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.
  8. Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-51, March.
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Citations

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Cited by:
  1. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Possibly Ill-behaved Posteriors in Econometric Models," Tinbergen Institute Discussion Papers 08-036/4, Tinbergen Institute, revised 18 Apr 2008.
  2. Lennart Hoogerheide & Joern H. Block & Roy Thurik, 2010. "Family Background Variables as Instruments for Education in Income Regressions: A Bayesian Analysis," Tinbergen Institute Discussion Papers 10-075/3, Tinbergen Institute.
  3. Sylvia Frühwirth-Schnatter & Martin Halla & Alexandra Posekany & Gerald J. Pruckner & Thomas Schober, 2014. "The Quantity and Quality of Children: A Semi-Parametric Bayesian IV Approach," Economics working papers 2014-03, Department of Economics, Johannes Kepler University Linz, Austria.
  4. Joern H. Block & Lennart Hoogerheide & Roy Thurik, 2009. "Education and Entrepreneurial Choice: An Instrumental Variables Analysis," Tinbergen Institute Discussion Papers 09-088/4, Tinbergen Institute, revised 23 Nov 2010.
  5. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 711-724, July.
  6. Giuseppe Migali & Ian Walker, 2011. "Estimates of the Causal Effects of Education on Earnings over the Lifecycle with Cohort Eects and Endogenous Education," Working Papers 2248796, Lancaster University Management School, Economics Department.
  7. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Possibly Ill-behaved Posteriors in Econometric Models," Tinbergen Institute Discussion Papers 08-036/4, Tinbergen Institute, revised 18 Apr 2008.
  8. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
  9. Joern H. Block & Lennart Hoogerheide & Roy Thurik, 2010. "Are Education and Entrepreneurial Income Endogenous and do Family Background Variables make Sense as Instruments? A Bayesian Analysis," Tinbergen Institute Discussion Papers 10-024/4, Tinbergen Institute.
  10. Cogley, Timothy & Startz, Richard, 2012. "Bayesian IV: the normal case with multiple endogenous variables," University of California at Santa Barbara, Economics Working Paper Series qt40v0x246, Department of Economics, UC Santa Barbara.
  11. Li, Mingliang & Tobias, Justin L., 2011. "Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling," Journal of Econometrics, Elsevier, vol. 162(2), pages 345-361, June.
  12. Kraay, Aart, 2008. "Instrumental variables regressions with honestly uncertain exclusion restrictions," Policy Research Working Paper Series 4632, The World Bank.
  13. Nalan Basturk & Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2012. "The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation," Tinbergen Institute Discussion Papers 12-096/III, Tinbergen Institute.
  14. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
  15. Lennart Hoogerheide & Joern H. Block & Roy Thurik, 2010. "Family Background Variables as Instruments for Education in Income Regressions: A Bayesian Analysis," Tinbergen Institute Discussion Papers 10-075/3, Tinbergen Institute.

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