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Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

  • Li, Mingliang
  • Tobias, Justin L.
Registered author(s):

    We consider the problem of causal effect heterogeneity from a Bayesian point of view. This is accomplished by introducing a three-equation system, similar in spirit to the work of Heckman and Vytlacil (1998), describing the joint determination of a scalar outcome, an endogenous "treatment" variable, and an individual-specific causal return to that treatment. We describe a Bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population, the object which has been the focus of most previous work. Parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed. Combining data sets from High School and Beyond (HSB) and the 1980 Census, we illustrate our methods in practice and investigate heterogeneity in returns to education. Our analysis decomposes the impact of key HSB covariates on log wages into three parts: a "direct" effect and two separate indirect effects through educational attainment and returns to education. Our results strongly suggest that the quantity of schooling attained is determined, at least in part, by the individual's own return to education. Specifically, a one percentage point increase in the return to schooling parameter is associated with the receipt of (approximately)Â 0.14 more years of schooling. Furthermore, when we control for variation in returns to education across individuals, we find no difference in predicted schooling levels for men and women. However, women are predicted to attain approximately 1/4 of a year more schooling than men on average as a result of higher rates of return to investments in education.

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    File URL: http://www.sciencedirect.com/science/article/B6VC0-5282JWP-2/2/9d2478e05dbe9b204118366de2ecde1e
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 162 (2011)
    Issue (Month): 2 (June)
    Pages: 345-361

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    Handle: RePEc:eee:econom:v:162:y:2011:i:2:p:345-361
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
    2. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November.
    3. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, vol. 79(2), pages 185-191, May.
    4. Koop, Gary M & Poirier, Dale J & Tobias, Justin, 2007. "Bayesian Econometric Methods," Staff General Research Papers 12722, Iowa State University, Department of Economics.
    5. Grogger, Jeff, 1996. "Does School Quality Explain the Recent Black/White Wage Trend?," Journal of Labor Economics, University of Chicago Press, vol. 14(2), pages 231-53, April.
    6. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
    7. Poirier, Dale J & Tobias, Justin, 2003. "On the Predictive Distributions of Outcome Gains in the Presence of an Unidentified Parameter," Staff General Research Papers 12014, Iowa State University, Department of Economics.
    8. 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.
    9. repec:cup:cbooks:9780521671736 is not listed on IDEAS
    10. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
    11. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
    12. Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variables Regression," Econometrics 9812002, EconWPA.
    13. Koop, Gary & Poirier, Dale J., 1997. "Learning about the across-regime correlation in switching regression models," Journal of Econometrics, Elsevier, vol. 78(2), pages 217-227, June.
    14. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
    15. Eric A. Hanushek & Lori L. Taylor, 1990. "Alternative Assessments of the Performance of Schools: Measurement of State Variations in Achievement," Journal of Human Resources, University of Wisconsin Press, vol. 25(2), pages 179-201.
    16. 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.
    17. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
    18. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
    19. Munkin, Murat K. & Trivedi, Pravin K., 2003. "Bayesian analysis of a self-selection model with multiple outcomes using simulation-based estimation: an application to the demand for healthcare," Journal of Econometrics, Elsevier, vol. 114(2), pages 197-220, June.
    20. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
    21. Kai, Li, 1998. "Bayesian inference in a simultaneous equation model with limited dependent variables," Journal of Econometrics, Elsevier, vol. 85(2), pages 387-400, August.
    22. repec:cup:cbooks:9780521855716 is not listed on IDEAS
    23. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    24. Mingliang Li & Dale J. Poirier & Justin L. Tobias, 2004. "Do dropouts suffer from dropping out? Estimation and prediction of outcome gains in generalized selection models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 203-225.
    25. Mingliang Li, 2006. "High school completion and future youth unemployment: new evidence from High School and Beyond," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 23-53.
    26. Henderson, Daniel J. & Polachek, Solomon W. & Wang, Le, 2011. "Heterogeneity in schooling rates of return," Economics of Education Review, Elsevier, vol. 30(6), pages 1202-1214.
    27. Mingliang Li, 2007. "Bayesian Proportional Hazard Analysis of the Timing of High School Dropout Decisions," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 529-556.
    28. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    29. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
    30. Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
    31. Grogger, Jeff, 1996. "School Expenditures and Post-schooling Earnings: Evidence from High School and Beyond," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 628-37, November.
    32. Chib, Siddhartha & Hamilton, Barton H., 2000. "Bayesian analysis of cross-section and clustered data treatment models," Journal of Econometrics, Elsevier, vol. 97(1), pages 25-50, July.
    33. Koop, Gary M & Tobias, Justin, 2004. "Learning About Heterogeneity in Returns to Schooling," Staff General Research Papers 12008, Iowa State University, Department of Economics.
    34. Murat K. Munkin & Partha Deb & Pravin K. Trivedi, 2006. "Bayesian analysis of the two-part model with endogeneity: application to health care expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1081-1099.
    35. Ganderton, Philip T., 1992. "The effect of subsidies in kind on the choice of a college," Journal of Public Economics, Elsevier, vol. 48(3), pages 269-292, August.
    36. Chib, Siddhartha, 2007. "Analysis of treatment response data without the joint distribution of potential outcomes," Journal of Econometrics, Elsevier, vol. 140(2), pages 401-412, October.
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