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Missing Treatments

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  • Molinari, Francesca

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.
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Suggested Citation

  • Molinari, Francesca, 2010. "Missing Treatments," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 82-95.
    • Handle: RePEc:bes:jnlbes:v:28:i:1:y:2010:p:82-95
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.
    7. 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).
    8. 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.
    9. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 343-364.
    10. Jeff Dominitz & Robert P. Sherman, 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, December.
    11. 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.

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