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Sharp IV bounds on average treatment effects under endogeneity and noncompliance

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  • Martin Huber
  • Giovanni Mellace

Abstract

In the presence of an endogenous treatment and a valid instrument, causal effects are (nonparametrically) point identified only for the subpopulation of compliers, given that the treatment is monotone in the instrument. Further populations of likely policy interest have been widely ignored in econometrics. Therefore, we use treatment monotonicity and/or stochastic dominance assumptions to derive sharp bounds on the average treatment effects of the treated population, the entire population, the compliers, the always takers, and the never takers. We also provide an application to labor market data and briefly discuss testable implications of the instrumental exclusion restriction and stochastic dominance.

Suggested Citation

  • Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
    • Handle: RePEc:usg:dp2010:2010-31
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    References listed on IDEAS

    as
    1. Angus Deaton, 2010. "Instruments, Randomization, and Learning about Development," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 424-455, June.
    2. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    3. Michael Lechner & Blaise Melly, 2007. "Earnings Effects of Training Programs," University of St. Gallen Department of Economics working paper series 2007 2007-28, Department of Economics, University of St. Gallen.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    5. Markus Frölich & Blaise Melly, 2013. "Unconditional Quantile Treatment Effects Under Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 346-357, July.
    6. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    7. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    8. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    9. 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.
    10. repec:pri:rpdevs:deaton_instruments_randomization_learning_all_04april_2010 is not listed on IDEAS
    11. 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.
    12. Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, February.
    13. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    14. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    15. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    16. Guido W. Imbens, 2010. "Better LATE Than Nothing: Some Comments on Deaton (2009) and Heckman and Urzua (2009)," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 399-423, June.
    17. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    18. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    19. Imai, Kosuke, 2008. "Sharp bounds on the causal effects in randomized experiments with "truncation-by-death"," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 144-149, February.
    20. Bhattacharya, Jay & Shaikh, Azeem M. & Vytlacil, Edward, 2012. "Treatment effect bounds: An application to Swan–Ganz catheterization," Journal of Econometrics, Elsevier, vol. 168(2), pages 223-243.
    21. Michael Lechner & Markus Froelich, 2010. "Combining Matching and Nonparametric IV Estimation: Theory and an Application to the Evaluation of Active Labour Market Policies," University of St. Gallen Department of Economics working paper series 2010 2010-21, Department of Economics, University of St. Gallen.
    22. Jing Cheng & Dylan S. Small, 2006. "Bounds on causal effects in three‐arm trials with non‐compliance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 815-836, November.
    23. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Amanda Kowalski, 2016. "Doing more when you're running LATE: Applying marginal treatment effect methods to examine treatment effect heterogeneity in experiments," Artefactual Field Experiments 00560, The Field Experiments Website.
    2. Laffers, Lukas & Mellace, Giovanni, 2015. "A Note on Testing the LATE Assumptions," Discussion Papers on Economics 4/2015, University of Southern Denmark, Department of Economics.
    3. 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.
    4. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute of Labor Economics (IZA).
    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. Huber, Martin, 2012. "Statistical verification of a natural "natural experiment": Tests and sensitivity checks for the sibling sex ratio instrument," Economics Working Paper Series 1219, University of St. Gallen, School of Economics and Political Science.
    7. Amanda E. Kowalski, 2016. "Doing More When You're Running LATE: Applying Marginal Treatment Effect Methods to Examine Treatment Effect Heterogeneity in Experiments for the Young and Privately Insured"," Cowles Foundation Discussion Papers 2045, Cowles Foundation for Research in Economics, Yale University.
    8. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    9. Murard, Elie, 2019. "The Impact of Migration on Family Left Behind: Estimation in Presence of Intra-Household Selection of Migrants," IZA Discussion Papers 12094, Institute of Labor Economics (IZA).
    10. Steinmayr, Andreas, 2014. "When a random sample is not random: Bounds on the effect of migration on household members left behind," Kiel Working Papers 1975, Kiel Institute for the World Economy (IfW Kiel).

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    More about this item

    Keywords

    Instrument; noncompliance; principal stratification; nonparametric bounds;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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