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Heterogeneous Treatment Effects: Instrumental Variables without Monotonicity?

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  • Klein, Tobias J.

    ()
    (Tilburg University)

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 an 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 and relate it to properties of a structural parameter. One of our results is that the bias vanishes under a testable linearity condition. Our findings are illustrated in a Monte Carlo analysis.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 2738.

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Length: 36 pages
Date of creation: Apr 2007
Date of revision:
Publication status: published in: Journal of Econometrics, 2010, 155 (2), 99-116; more recent version available here
Handle: RePEc:iza:izadps:dp2738

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Keywords: monotonicity; heterogeneity; identification; program evaluation; dummy endogenous variable; selection on unobservables; instrumental variables;

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References

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  1. 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, Elsevier, vol. 149(2), pages 191-208, April.
  2. 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, University of Wisconsin Press, vol. 33(4), pages 974-987.
  3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521766555.
  4. James J. Heckman & Sergio Urzua & Edward J. Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," NBER Working Papers, National Bureau of Economic Research, Inc 12574, National Bureau of Economic Research, Inc.
  5. Pedro Carneiro & Sokbae 'Simon' Lee, 2005. "Ability, sorting and wage inequality," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP16/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Tobias Klein, 2013. "College education and wages in the U.K.: estimating conditional average structural functions in nonadditive models with binary endogenous variables," Empirical Economics, Springer, Springer, vol. 44(1), pages 135-161, February.
  7. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers, National Bureau of Economic Research, Inc 3572, National Bureau of Economic Research, Inc.
  8. Chesher, Andrew & Santos Silva, J M C, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(1), pages 147-68, January.
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  10. 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, Wiley Blackwell, vol. 67(3), pages 499-527, July.
  11. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521355643.
  12. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 62(2), pages 467-75, March.
  13. Andrew Chesher & Erich Battistin, 2004. "The Impact of Measurement Error on Evaluation Methods Based on Strong Ignorability," Econometric Society 2004 North American Summer Meetings, Econometric Society 339, Econometric Society.
  14. Heckman, James J. & Vytlacil, Edward J., 2000. "The relationship between treatment parameters within a latent variable framework," Economics Letters, Elsevier, Elsevier, vol. 66(1), pages 33-39, January.
  15. Eric Gautier & Yuichi Kitamura, 2009. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1721, Cowles Foundation for Research in Economics, Yale University.
  16. Battistin, Erich & Rettore, Enrico, 2008. "Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs," Journal of Econometrics, Elsevier, Elsevier, vol. 142(2), pages 715-730, February.
  17. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics, Boston College Department of Economics 454, Boston College Department of Economics.
  18. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers, National Bureau of Economic Research, Inc 11259, National Bureau of Economic Research, Inc.
  19. Andrew Chesher & Christian Schluter, 2001. "Welfare measurement and measurement error," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP03/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  20. Ichimura, H. & Thompson, S., 1993. "Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distributions," Papers, Minnesota - Center for Economic Research 268, Minnesota - Center for Economic Research.
  21. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 873-85, July.
  22. Harmon, Colm & Walker, Ian, 1999. "The marginal and average returns to schooling in the UK," European Economic Review, Elsevier, Elsevier, vol. 43(4-6), pages 879-887, April.
  23. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, Econometric Society, vol. 69(1), pages 201-09, January.
  24. 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, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, 08.
  25. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, Elsevier, vol. 56(2), pages 129-133, October.
  26. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, Elsevier, vol. 79(2), pages 185-191, May.
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Citations

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Cited by:
  1. Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers, HAL halshs-00699646, HAL.
  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, Economics Discipline Group, UTS Business School, University of Technology, Sydney 7, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
  3. Eric Gautier & Stefan Hoderlein, 2012. "A Triangular Treatment Effect Model With Random Coefficients In The Selection Equation," Boston College Working Papers in Economics, Boston College Department of Economics 838, Boston College Department of Economics.
  4. 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, Tilburg University, Center for Economic Research 2009-88, Tilburg University, Center for Economic Research.
  5. de Chaisemartin, Clement, 2013. "Defying the LATE? Identification of local treatment effects when the instrument violates monotonicity," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 1020, University of Warwick, Department of Economics.
  6. Clément de Chaisemartin, 2012. "Late again, whithout Monotonicity," Working Papers, Centre de Recherche en Economie et Statistique 2012-12, Centre de Recherche en Economie et Statistique.
  7. 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, Institute for the Study of Labor (IZA) 8213, Institute for the Study of Labor (IZA).
  8. 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, University of Sydney, School of Economics 2013-06, University of Sydney, School of Economics.
  9. Lechner, Michael, 2013. "Treatment effects and panel data," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1314, University of St. Gallen, School of Economics and Political Science.
  10. repec:hal:wpaper:halshs-00699646 is not listed on IDEAS
  11. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1212, University of St. Gallen, School of Economics and Political Science.

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