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Testing the Correlated Random Coefficient Model

Author

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  • 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.

Suggested Citation

  • Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2009. "Testing the Correlated Random Coefficient Model," IZA Discussion Papers 4525, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp4525
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Yu-Chin Hsu & Ta-Cheng Huang & Haiqing Xu, 2018. "Testing for Unobserved Heterogeneous Treatment Effects with Observational Data," Papers 1803.07514, arXiv.org, revised Aug 2021.
    2. 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.
    3. Nocito, Samuel, 2021. "The effect of a university degree in english on international labor mobility," Labour Economics, Elsevier, vol. 68(C).
    4. Otto Toivanen & Lotta Väänänen, 2016. "Education and Invention," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 382-396, May.
    5. 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.
    6. 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.
    7. Natalia Radchenko & Paul Corral & Paul Winters, 2018. "Heterogeneity of commercialization gains in the rural economy," Agricultural Economics, International Association of Agricultural Economists, vol. 49(1), pages 131-143, January.
    8. 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.
    9. Cheng Hsiao & Qi Li & Zhongwen Liang & Wei Xie, 2019. "Panel Data Estimation for Correlated Random Coefficients Models," Econometrics, MDPI, Open Access Journal, vol. 7(1), pages 1-18, February.
    10. 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.
    11. Dionissi Aliprantis, 2012. "When should children start school?," Working Papers (Old Series) 1126, Federal Reserve Bank of Cleveland.
    12. Samuele Centorrino & Aman Ullah & Jing Xue, 2019. "Semiparametric Estimation of Correlated Random Coefficient Models without Instrumental Variables," Papers 1911.06857, arXiv.org.
    13. 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.
    14. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    15. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.

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    More about this item

    Keywords

    power of tests based on IV; testing; correlated random coefficient; instrumental variables;
    All these keywords.

    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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