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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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  • Hoogerheide, Lennart & Kleibergen, Frank & van Dijk, Herman K., 2007. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Journal of Econometrics, Elsevier, vol. 138(1), pages 63-103, May.
  • Handle: RePEc:eee:econom:v:138:y:2007:i:1:p:63-103
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    1. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
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    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. 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.
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    Cited by:

    1. Giuseppe Migali & Ian Walker, 2011. "Estimates of the causal effects of education on earnings over the lifecycle with cohort effects and endogenous education," Working Papers 2248796, Lancaster University Management School, Economics Department.
    2. Kraay, Aart, 2008. "Instrumental variables regressions with honestly uncertain exclusion restrictions," Policy Research Working Paper Series 4632, The World Bank.
    3. Gary Koop & M. Hashem Pesaran & Ron P. Smith, 2013. "On Identification of Bayesian DSGE Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 300-314, July.
    4. 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.
    5. Lawrence Kessler & Murat Munkin, 2015. "Bayesian estimation of panel data fractional response models with endogeneity: an application to standardized test rates," Empirical Economics, Springer, vol. 49(1), pages 81-114, August.
    6. 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.
    7. 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.
    8. Nalan Baştürk & Stefano Grassi & Lennart Hoogerheide & Herman K. van Dijk, 2016. "Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-20, March.
    9. Huzeyfe Torun & Semih Tumen, 2017. "The empirical content of season-of-birth effects: An investigation with Turkish data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 37(57), pages 1825-1860, December.
    10. 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.
    11. Halla, Martin & Zweimüller, Martina, 2014. "Parental Response to Early Human Capital Shocks: Evidence from the Chernobyl Accident," IZA Discussion Papers 7968, Institute for the Study of Labor (IZA).
    12. 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.
    13. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    14. 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.
    15. 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.
    16. Hoogerheide, Lennart & Block, Joern H. & Thurik, Roy, 2012. "Family background variables as instruments for education in income regressions: A Bayesian analysis," Economics of Education Review, Elsevier, vol. 31(5), pages 515-523.
    17. 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.
    18. 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.
    19. Block Joern H. & Hoogerheide Lennart & Thurik Roy, 2012. "Are Education and Entrepreneurial Income Endogenous? A Bayesian Analysis," Entrepreneurship Research Journal, De Gruyter, vol. 2(3), pages 1-29, July.
    20. repec:gam:jecnmx:v:4:y:2016:i:1:p:11:d:65219 is not listed on IDEAS

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