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Sharp bounds on causal effects under sample selection

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  • Huber, Martin

    ()

  • Mellace, Giovanni

    ()

Abstract

In many empirical problems, the evaluation of treatment effects is complicated by sample selection such that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the "always selected" (whose outcomes are observed irrespective of the treatment). This paper complements those studies by considering further populations, namely the "compliers" (whose selection states react to the treatment) and the selected population. We derive sharp bounds under various assumptions (monotonicity and stochastic dominance) and provide an empirical application to a school voucher experiment.

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File URL: http://www1.vwa.unisg.ch/RePEc/usg/econwp/EWP-1134.pdf
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Bibliographic Info

Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1134.

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Length: 44 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:usg:econwp:2011:34

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Keywords: Causal inference; principal stratification; nonparametric bounds; sample selection;

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References

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  1. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 82(6), pages 1119-43, Nov.-Dec..
  2. Giovanni Mellace & Roberto Rocci, 2011. "Principal Stratification in sample selection problems with non normal error terms," CEIS Research Paper, Tor Vergata University, CEIS 194, Tor Vergata University, CEIS, revised 02 May 2011.
  3. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Gerfin, Michael & Schellhorn, Martin, 2005. "Nonparametric Bounds on the Effect of Deductibles in Health Care Insurance on Doctor Visits – Swiss Evidence," IZA Discussion Papers 1616, Institute for the Study of Labor (IZA).
  5. Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1311-1334, November.
  7. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1109, University of St. Gallen, School of Economics and Political Science.
  8. Kreider, Brent & Hill, Steven C., 2005. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Staff General Research Papers, Iowa State University, Department of Economics 12296, Iowa State University, Department of Economics.
  9. Mealli, Fabrizia & Pacini, Barbara, 2008. "Comparing principal stratification and selection models in parametric causal inference with nonignorable missingness," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(2), pages 507-516, December.
  10. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0294, National Bureau of Economic Research, Inc.
  11. Blundell, Richard & Gosling, Amanda & Ichimura, Hidehiko & Meghir, Costas, 2004. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," IZA Discussion Papers 1350, Institute for the Study of Labor (IZA).
  12. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(s1), pages S217-S229, 01.
  13. Lechner, Michael & Melly, Blaise, 2007. "Earnings Effects of Training Programs," CEPR Discussion Papers, C.E.P.R. Discussion Papers 6400, C.E.P.R. Discussion Papers.
  14. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, Econometric Society, vol. 47(1), pages 153-61, January.
  15. 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.
  16. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, Econometric Society, vol. 63(2), pages 281-302, March.
  17. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, American Economic Association, vol. 96(3), pages 847-862, June.
  18. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 70(1), pages 33-58, January.
  19. Blanco, German & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2011. "Bounds on Quantile Treatment Effects of Job Corps on Participants' Wages," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania, Agricultural and Applied Economics Association 103761, Agricultural and Applied Economics Association.
  20. Martin Huber, 2010. "Identification of average treatment effects in social experiments under different forms of attrition," University of St. Gallen Department of Economics working paper series 2010, Department of Economics, University of St. Gallen 2010-22, Department of Economics, University of St. Gallen.
  21. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
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Citations

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Cited by:
  1. Martin Huber & Blaise Melly, 2012. "A test of the conditional independence assumption in sample selection models," Working Papers 2012-11, Brown University, Department of Economics.
  2. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1109, University of St. Gallen, School of Economics and Political Science.
  3. 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, Department of Economics, University of St. Gallen 2010-31, Department of Economics, University of St. Gallen.

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