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Missing Treatments

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  • Molinari, Francesca

    (Cornell U)

Abstract

The existing literature on treatment e¤ects assumes perfect observability of the treatments received by the population of interest. Even in cases of imperfect compliance, it is usually as- sumed that both the assigned and administered treatment are observed (or missing completely at random). This paper abandons such assumptions. Imperfect observability of the received treatment can arise as a result of survey nonresponse in observational studies, or noncompliance with randomly assigned treatments that are not directly monitored. I study the problem in the context of observational studies. I derive sharp worst case bounds without assuming anything about treatment selection, and I show that the bounds are a function of the available prior information on the distribution of the missing treatments. Under the maintained assumption of monotone treatment response, I show that no prior information on the distribution of missing treatments is necessary to get sharp informative bounds. I apply the methodologies recently proposed by Imbens and Manski (2004) and Chernozhukov, Hong, and Tamer (2004) to derive two types of confidence intervals for the partially identi.ed parameters. The results are illustrated with an empirical analysis of drug use and employment using data from the National Longitudinal Survey of Youth.

Suggested Citation

  • Molinari, Francesca, 2005. "Missing Treatments," Working Papers 05-11, Cornell University, Center for Analytic Economics.
  • Handle: RePEc:ecl:corcae:05-11
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    File URL: https://cae.economics.cornell.edu/05-11.pdf
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    References listed on IDEAS

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    1. Robert Kaestner, 1994. "The Effect of Illicit Drug Use on the Labor Supply of Young Adults," Journal of Human Resources, University of Wisconsin Press, vol. 29(1), pages 126-155.
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    3. Juan Carlos Chavez-Martin del Campo, 2004. "Partial Identification of Poverty Measures with Contaminated Data," Econometric Society 2004 Latin American Meetings 221, Econometric Society.
    4. Kaestner, Robert & Grossman, Michael, 1995. "Wages, Workers' Compensation Benefits, and Drug Use: Indirect Evidence of the Effect of Drugs on Workplace Accidents," American Economic Review, American Economic Association, vol. 85(2), pages 55-60, May.
    5. E. Tamer & V. Chernozhukov & H. Hong, 2004. "Parameter Set Inference in a Class of Econometric Models," Econometric Society 2004 North American Winter Meetings 382, Econometric Society.
    6. Horowitz, Joel L. & Manski, Charles F., 1998. "Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations," Journal of Econometrics, Elsevier, vol. 84(1), pages 37-58, May.
    7. Kaestner, Robert, 1991. "The Effect of Illicit Drug Use on the Wages of Young Adults," Journal of Labor Economics, University of Chicago Press, vol. 9(4), pages 381-412, October.
    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. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    10. Pizer, William & Imbens, Guido, 2000. "The Analysis of Randomized Experiments with Missing Data," Discussion Papers dp-00-19, Resources For the Future.
    11. V. Joseph Hotz & Charles H. Mullin & Seth G. Sanders, 1997. "Bounding Causal Effects Using Data from a Contaminated Natural Experiment: Analysing the Effects of Teenage Childbearing," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 575-603.
    12. Andrew M. Gill & Robert J. Michaels, 1992. "Does Drug Use Lower Wages?," ILR Review, Cornell University, ILR School, vol. 45(3), pages 419-434, April.
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    Cited by:

    1. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    2. Brent Kreider & John V. Pepper & Craig Gundersen & Dean Jolliffe, 2012. "Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 958-975, September.
    3. Brent Kreider & Steven C. Hill, 2009. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    4. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.
    5. Gundersen, Craig & Kreider, Brent, 2009. "Bounding the effects of food insecurity on children's health outcomes," Journal of Health Economics, Elsevier, vol. 28(5), pages 971-983, September.
    6. Gundersen, Craig & Kreider, Brent & Pepper, John, 2012. "The impact of the National School Lunch Program on child health: A nonparametric bounds analysis," Journal of Econometrics, Elsevier, vol. 166(1), pages 79-91.
    7. Campo, Juan Carlos Chavez-Martin del, 2006. "Does Conditionality Generate Heterogeneity and Regressivity in Program Impacts? The Progresa Experience," Working Papers 127042, Cornell University, Department of Applied Economics and Management.
    8. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, pages 305-335.
    9. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, pages 667-709.
    10. Christopher R. Bollinger & Barry T. Hirsch, 2006. "Match Bias from Earnings Imputation in the Current Population Survey: The Case of Imperfect Matching," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 483-520, July.
    11. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
    12. Robert P. Sherman & Jeff Dominitz, 2006. "Identification and estimation of bounds on school performance measures: a nonparametric analysis of a mixture model with verification," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1295-1326.
    13. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.

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