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Testing the Correlated Random Coefficient Model

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Listed author(s):
  • James J. Heckman
  • Daniel A. Schmierer
  • Sergio S. Urzua

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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15463.

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Date of creation: Oct 2009
Publication status: published as Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2010. "Testing the correlated random coefficient model," Journal of Econometrics, Elsevier, vol. 158(2), pages 177-203, October.
Handle: RePEc:nbr:nberwo:15463
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Find related papers by JEL classification:
  • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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  1. Hansen, Karsten T. & Heckman, James J. & Mullen, K.J.Kathleen J., 2004. "The effect of schooling and ability on achievement test scores," Journal of Econometrics, Elsevier, vol. 121(1-2), pages 39-98.
  2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
  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. 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,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 71 Elsevier.
  6. 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.
  7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  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. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74 Elsevier.
  10. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
  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. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
  14. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
  15. 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.
  16. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  17. 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.
  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. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  20. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
  21. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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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 2754-2781, October.
  2. Otto Toivanen & Lotta Väänänen, 2016. "Education and Invention," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 382-396, May.
  3. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
  4. 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.
  5. 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.
  6. Gao, Yichen & Li, Cong & Liang, Zhongwen, 2015. "Binary response correlated random coefficient panel data models," Journal of Econometrics, Elsevier, vol. 188(2), pages 421-434.
  7. Dionissi Aliprantis, 2012. "When should children start school?," Working Paper 1126, Federal Reserve Bank of Cleveland.
  8. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
  9. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
  10. 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, Statistics Norway, Research Department.

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