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Testing the Correlated Random Coefficient Model

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Author Info

  • James J. Heckman

    (University of Chicago; University College Dublin; Cowles Foundation, Yale University; American Bar Foundation)

  • Daniel Schmierer

    (University of Chicago)

Abstract

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coefficient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coefficient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and find evidence of sorting into schooling based on unobserved components of gains.

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File URL: http://www.ucd.ie/geary/static/publications/workingpapers/gearywp200937.pdf
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Bibliographic Info

Paper provided by Geary Institute, University College Dublin in its series Working Papers with number 200937.

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Length: 69 pages
Date of creation: 13 Nov 2009
Date of revision:
Handle: RePEc:ucd:wpaper:200937

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Keywords: Correlated random coefficient; testing; instrumental variables; power of tests based on IV;

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References

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  1. Hansen, Karsten T. & Heckman, James J. & Mullen, Kathleen J., 2003. "The Effect of Schooling and Ability on Achievement Test Scores," IZA Discussion Papers 826, Institute for the Study of Labor (IZA).
  2. James J. Heckman & Sergio Urzua & Edward J. Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," NBER Working Papers 12574, National Bureau of Economic Research, Inc.
  3. 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.
  4. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
  5. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72 Elsevier.
  6. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Technical Working Papers 0306, National Bureau of Economic Research, Inc.
  7. Hidehiko Ichimura & Petra E. Todd, 2006. "Implementing Nonparametric and Semiparametric Estimators," CIRJE F-Series CIRJE-F-452, CIRJE, Faculty of Economics, University of Tokyo.
  8. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  9. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  10. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  11. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
  12. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
  13. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  14. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70 Elsevier.
  15. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  16. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
  17. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  18. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  19. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-86, October.
  20. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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Citations

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Cited by:
  1. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-81, October.
  2. Heckman, James J. & Urzua, Sergio, 2009. "Comparing IV with Structural Models: What Simple IV Can and Cannot Identify," IZA Discussion Papers 3980, Institute for the Study of Labor (IZA).
  3. Heckman, James J. & Schmierer, Daniel, 2010. "Tests of hypotheses arising in the correlated random coefficient model," Economic Modelling, Elsevier, vol. 27(6), pages 1355-1367, November.
  4. Steven N. Durlauf & Chao Fu & Salvador Navarro, 2011. "Capital Punishment and Deterrence: Understanding Disparate Results," Working Papers 2012-005, Human Capital and Economic Opportunity Working Group.
  5. Dionissi Aliprantis, 2012. "When should children start school?," Working Paper 1126, Federal Reserve Bank of Cleveland.
  6. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2012. "Beyond LATE with a discrete instrument. Heterogeneity in the quantity-quality interaction of children," Discussion Papers 703, Research Department of Statistics Norway.

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