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Heterogeneous Treatment Effects: Instrumental Variables Without Monotonicity?

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  • Klein, T.J.

    (Tilburg University, Center for Economic Research)

Abstract

A fundamental identification problem in program evaluation arises when idiosyncratic gains from participation and the treatment decision depend on each other. Imbens and Angrist (1994) were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables. More recently, Heckman and Vytlacil (1999) suggested estimation of a variety of treatment effect parameters using a local version of their approach. However, identification hinges on the same monotonicity assumption that is fundamentally untestable. We investigate the sensitivity of respective estimates to reasonable departures from monotonicity that are likely to be encountered in practice. Approximations to respective bias terms are derived. In an empirical application the bias is calculated and bias corrected estimates are obtained. The accuracy of the approximation is investigated in a Monte Carlo study.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-45.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:200845

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Web page: http://center.uvt.nl

Related research

Keywords: Program evaluation; heterogeneity; identification; dummy endogenous variable; selection on unobservables; instrumental variables; monotonicity; nonseparable index selection model;

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References

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  1. Chesher, Andrew & Schluter, Christian, 2002. "Welfare Measurement and Measurement Error," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 357-78, April.
  2. Klein, T.J., 2009. "College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables," Discussion Paper 2009-88, Tilburg University, Center for Economic Research.
  3. Eric Gautier & Yuichi Kitamura, 2008. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Working Papers 2008-15, Centre de Recherche en Economie et Statistique.
  4. Ichimura, H. & Thompson, S., 1993. "Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distributions," Papers 268, Minnesota - Center for Economic Research.
  5. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
  6. Chesher, Andrew & Santos Silva, J M C, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Wiley Blackwell, vol. 69(1), pages 147-68, January.
  7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  8. 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.
  9. Battistin, Erich & Rettore, Enrico, 2008. "Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs," Journal of Econometrics, Elsevier, vol. 142(2), pages 715-730, February.
  10. Andrew Chesher & Erich Battistin, 2004. "The Impact of Measurement Error on Evaluation Methods Based on Strong Ignorability," Econometric Society 2004 North American Summer Meetings 339, Econometric Society.
  11. 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.
  12. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  13. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, October.
  14. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  15. 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.
  16. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-09, January.
  17. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
  18. 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.
  19. Pedro Carneiro & Sokbae 'Simon' Lee, 2005. "Ability, sorting and wage inequality," CeMMAP working papers CWP16/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  20. Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, 08.
  21. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, vol. 52(4), pages 873-85, July.
  22. Heckman, James J. & Vytlacil, Edward J., 2000. "The relationship between treatment parameters within a latent variable framework," Economics Letters, Elsevier, vol. 66(1), pages 33-39, January.
  23. 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.
  24. Angrist, Joshua D & Graddy, Kathryn & Imbens, Guido W, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 499-527, July.
  25. Harmon, Colm & Walker, Ian, 1999. "The marginal and average returns to schooling in the UK," European Economic Review, Elsevier, vol. 43(4-6), pages 879-887, April.
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Citations

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Cited by:
  1. Klein, Tobias J., 2007. "College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables," IZA Discussion Papers 2761, Institute for the Study of Labor (IZA).
  2. Ben Edwards & Mario Fiorini & Katrien Stevens & Matthew Taylor, 2013. "Is Monotonicity in an IV and RD Design Testable? No, But You Can Still Check on it," Working Paper Series 7, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
  3. Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.
  4. Bernal, Noelia & Carpio, Miguel A. & Klein, Tobias J., 2014. "The Effects of Access to Health Insurance for Informally Employed Individuals in Peru," IZA Discussion Papers 8213, Institute for the Study of Labor (IZA).
  5. Eric Gautier & Stefan Hoderlein, 2012. "A Triangular Treatment Effect Model With Random Coefficients In The Selection Equation," Boston College Working Papers in Economics 838, Boston College Department of Economics.
  6. repec:hal:wpaper:halshs-00699646 is not listed on IDEAS
  7. de Chaisemartin, Clement, 2013. "Defying the LATE? Identification of local treatment effects when the instrument violates monotonicity," The Warwick Economics Research Paper Series (TWERPS) 1020, University of Warwick, Department of Economics.
  8. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
  9. Clément de Chaisemartin, 2012. "Late again, whithout Monotonicity," Working Papers 2012-12, Centre de Recherche en Economie et Statistique.
  10. Lechner, Michael, 2013. "Treatment effects and panel data," Economics Working Paper Series 1314, University of St. Gallen, School of Economics and Political Science.
  11. Edwards, Ben & Fiorini, Mario & Stevens, Katrien & Taylor, Matthew, 2013. "Is Monotonicity in an IV and RD design testable? No, but you can still check it," Working Papers 2013-06, University of Sydney, School of Economics.

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