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Conditioning on the Probability of Selection to Control Selection Bias

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  • Joshua D. Angrist

Abstract

Problems of sample selection arise in the analysis of both experimental and non-experimental data. In clinical trials to evaluate the impact of an intervention on health and mortality, treatment assignment is typically nonrandom in a sample of survivors even if the original assignment is random. Similarly, randomized training interventions like National Supported Work (NSW) are not necessarily randomly assigned in the sample of working men. A non- experimental version of this problem involves the use of instrumental variables (IV) to estimate behavioral relationships. A sample selection rule that is related to the instruments can induce correlation between the instruments and unobserved outcomes, possibly invalidating the use of conventional IV techniques in the selected sample. This paper shows that conditioning on the probability of selection given the instruments can provide a solution to the selection problem as long as the relationship between instruments and selection status satisfies a simple monotonicity condition. A latent index structure is not required for this result, which is motivated as an extension of earlier work on the propensity score. The conditioning approach to selection problems is illustrated using instrumental variables techniques to estimate the returns to schooling in a sample with positive earnings.

Suggested Citation

  • Joshua D. Angrist, 1995. "Conditioning on the Probability of Selection to Control Selection Bias," NBER Technical Working Papers 0181, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0181
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    References listed on IDEAS

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    12. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
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    Citations

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    Cited by:

    1. Abhijit Banerjee & Shawn Cole & Esther Duflo & Leigh Linden, 2005. "Remedying Education: Evidence from Two Randomized Experiments in India," NBER Working Papers 11904, National Bureau of Economic Research, Inc.
    2. C. Kirabo Jackson, 2010. "Do Students Benefit from Attending Better Schools? Evidence from Rule-based Student Assignments in Trinidad and Tobago," Economic Journal, Royal Economic Society, vol. 120(549), pages 1399-1429, December.
    3. Angrist, Joshua D., 1997. "Conditional independence in sample selection models," Economics Letters, Elsevier, vol. 54(2), pages 103-112, February.
    4. J. B. Engberg & T. Kim, "undated". "Person or Place? Parametric and semiparametric estimates of intrametropolitan earnings variation," Institute for Research on Poverty Discussion Papers 1089-96, University of Wisconsin Institute for Research on Poverty.
    5. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," Econometrica, Econometric Society, vol. 70(6), pages 2367-2420, November.
    6. C. Kirabo Jackson, 2009. "Ability-grouping and Academic Inequality: Evidence From Rule-based Student Assignments," NBER Working Papers 14911, National Bureau of Economic Research, Inc.
    7. Grant, William C. & Anstrom, Kevin J., 2008. "Minimizing selection bias in randomized trials: A Nash equilibrium approach to optimal randomization," Journal of Economic Behavior & Organization, Elsevier, vol. 66(3-4), pages 606-624, June.
    8. Esther Duflo, 2001. "Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment," American Economic Review, American Economic Association, vol. 91(4), pages 795-813, September.
    9. Andrabi, Tahir & Das, Jishnu & Khwaja, Asim Ijaz, 2013. "Students today, teachers tomorrow: Identifying constraints on the provision of education," Journal of Public Economics, Elsevier, vol. 100(C), pages 1-14.
    10. Denis Conniffe & Vanessa Gash & Philip J., 2000. "Evaluating Programmes: Experiments, Non-Experiments and Propensity Scores," Papers WP126, Economic and Social Research Institute (ESRI).
    11. C. Kirabo Jackson, 2010. "The Effects of an Incentive-Based High-School Intervention on College Outcomes," NBER Working Papers 15722, National Bureau of Economic Research, Inc.
    12. Porto, Guido, 2011. "Methods for Program Evaluation," Papers 197, World Trade Institute.
    13. Spohr, Chris A., 2003. "Formal schooling and workforce participation in a rapidly developing economy: evidence from "compulsory" junior high school in Taiwan," Journal of Development Economics, Elsevier, vol. 70(2), pages 291-327, April.
    14. Jackson, C. Kirabo, 2013. "Can higher-achieving peers explain the benefits to attending selective schools? Evidence from Trinidad and Tobago," Journal of Public Economics, Elsevier, vol. 108(C), pages 63-77.
    15. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    16. Gravelle, Hugh & Dusheiko, Mark & Sutton, Matthew, 2002. "The demand for elective surgery in a public system: time and money prices in the UK National Health Service," Journal of Health Economics, Elsevier, vol. 21(3), pages 423-449, May.
    17. Denis Conniffe & Vanessa Gash & Philip J. O'Connell, 2000. "Evaluating State Programmes - “Natural Experiments” and Propensity Scores," The Economic and Social Review, Economic and Social Studies, vol. 31(4), pages 283-308.
    18. Mark Dusheiko & Hugh Gravelle & Stephen Campbell, "undated". "Estimating and explaining differences in income related inequality in health across general practices," Discussion Papers 02/07, Department of Economics, University of York.

    More about this item

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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