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Testing the Correlated Random Coefficient Model

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Author Info

  • Heckman, James J.

    ()
    (University of Chicago)

  • Schmierer, Daniel

    ()
    (University of Chicago)

  • Urzua, Sergio

    ()
    (University of Maryland)

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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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4525.

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Length: 70 pages
Date of creation: Oct 2009
Date of revision:
Publication status: published in: Journal of Econometrics, 2010, 158 (2), 177-203
Handle: RePEc:iza:izadps:dp4525

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

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References

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  1. 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, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72 Elsevier.
  2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  3. Joseph Romano & Michael Wolf, 2003. "Exact and approximate stepdown methods for multiple hypothesis testing," Economics Working Papers 727, Department of Economics and Business, Universitat Pompeu Fabra.
  4. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 109(4), pages 673-748, August.
  5. Hansen, Karsten T. & Heckman, James J. & Mullen, Kathleen, 2003. "The Effect of Schooling and Ability on Achievement Test Scores," IZA Discussion Papers 826, Institute for the Study of Labor (IZA).
  6. 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.
  7. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1443-58, November.
  8. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, Econometric Society, vol. 45(1), pages 1-22, January.
  9. 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, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70 Elsevier.
  10. Heckman, James J. & Urzua, Sergio & Vytlacil, Edward, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," IZA Discussion Papers 2320, Institute for the Study of Labor (IZA).
  11. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1129-1152, September.
  12. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 71 Elsevier.
  13. Hidehiko Ichimura & Petra E. Todd, 2006. "Implementing Nonparametric and Semiparametric Estimators," CIRJE F-Series CIRJE-F-452, CIRJE, Faculty of Economics, University of Tokyo.
  14. 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, Econometric Society, vol. 69(3), pages 599-631, May.
  15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 1047-70, September.
  16. 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.
  17. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 331-341, January.
  18. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  19. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(4), pages 478-86, October.
  20. 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.
  21. 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. James J Heckman & Daniel Schmierer, 2010. "Tests of Hypotheses Arising In the Correlated Random Coefficient Model," Working Papers, Geary Institute, University College Dublin 201045, Geary Institute, University College Dublin.
  2. Dionissi Aliprantis, 2012. "When should children start school?," Working Paper 1126, Federal Reserve Bank of Cleveland.
  3. 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.
  4. Salvador Navarro & Chao Fu & Steven Durlauf, 2012. "Capital Punishment and Deterrence: Understanding Disparate Results," 2012 Meeting Papers, Society for Economic Dynamics 53, Society for Economic Dynamics.
  5. Pedro Carneiro & James Heckman & Edward Vytlacil, 2010. "Estimating marginal returns to education," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP29/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Toivanen, Otto & Väänänen, Lotta, 2011. "Education and Invention," CEPR Discussion Papers 8537, C.E.P.R. Discussion Papers.
  7. James Heckman & Sergio Urzua, 2010. "Comparing IV with structural models: what simple IV can and cannot identify," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP08/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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