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Heterogeneous treatment effects: Instrumental variables without monotonicity?

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  • Klein, Tobias J.

Abstract

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 the estimation of a variety of treatment effect parameters using a local version of their approach. We investigate the sensitivity of the respective estimates to random departures from monotonicity. Approximations to the 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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 155 (2010)
Issue (Month): 2 (April)
Pages: 99-116

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Handle: RePEc:eee:econom:v:155:y:2010:i:2:p:99-116

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Web page: http://www.elsevier.com/locate/jeconom

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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. 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.
  2. Tobias J. Klein, 2006. "College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables," JEPS Working Papers 06-001, JEPS.
  3. 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.
  4. Andrew Chesher & J. M. C. Santos Silva, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 147-168.
  5. 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.
  6. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
  8. 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.
  9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
  10. 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.
  11. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, vol. 79(2), pages 185-191, May.
  12. Chesher, Andrew & Schluter, Christian, 2002. "Welfare Measurement and Measurement Error," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 357-78, April.
  13. 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.
  14. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  15. 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.
  16. Eric Gautier & Yuichi Kitamura, 2009. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Cowles Foundation Discussion Papers 1721, Cowles Foundation for Research in Economics, Yale University.
  17. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, vol. 52(4), pages 873-85, July.
  18. 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.
  19. 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).
  20. 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.
  21. 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.
  22. 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.
  23. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  24. 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.
  25. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115.
  26. 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.
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Citations

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Cited by:
  1. Clément de Chaisemartin, 2012. "Late again, whithout Monotonicity," Working Papers 2012-12, Centre de Recherche en Economie et Statistique.
  2. Eric Gautier & Stefan Hoderlein, 2012. "A triangular treatment effect model with random coefficients in the selection equation," CeMMAP working papers CWP39/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. 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, vol. 44(1), pages 135-161, February.
  4. 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.
  5. 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.
  6. 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.
  7. Lechner, Michael, 2013. "Treatment effects and panel data," Economics Working Paper Series 1314, University of St. Gallen, School of Economics and Political Science.
  8. repec:hal:wpaper:halshs-00699646 is not listed on IDEAS
  9. 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.
  10. 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).
  11. Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.

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