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Analysis of treatment response data from eligibility designs

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  • Chib, Siddhartha
  • Jacobi, Liana

Abstract

In this paper, we develop and compare two alternative approaches for calculating the effect of the actual intake when treatments are randomized, but compliance with the assignment in the treatment arm is less than perfect for reasons that are correlated with the outcome. The approaches are based on different identification assumptions about these unobserved confounders. In the first approach, which stems from [Sommer, A., Zeger, S., 1991. On estimating efficacy in clinical trials. Statistics in Medicine 10, 45-52], the unobserved confounders are modeled by a discrete indicator variable that represents subject-type, defined in terms of the potential intake in the face of each possible assignment. In the second approach, confounding is modeled without reference to subject-type in the spirit of the Roy model. Because the two models are non-nested, and model comparison and assessment of the approaches in a real data setting is one of our central goals, we formulate the discussion from a Bayesian perspective, comparing the two models in terms of marginal likelihoods and Bayes factors, and in terms of inferences about the treatment effects. The latter we calculate from a predictive perspective in a way that is different from that in the literature, where typically only a point summary of that effect is calculated. Our real data analysis focuses on the JOBS II eligibility trial that was implemented to test the effectiveness of a job search seminar in decreasing the negative mental health effects commonly associated with job loss. We provide a comparative analysis of the data from the two approaches with prior distributions that are both reasonable in the context of the data and comparable across the model specifications. We show that the approaches can lead to different evaluations of the treatment.

Suggested Citation

  • Chib, Siddhartha & Jacobi, Liana, 2008. "Analysis of treatment response data from eligibility designs," Journal of Econometrics, Elsevier, vol. 144(2), pages 465-478, June.
  • Handle: RePEc:eee:econom:v:144:y:2008:i:2:p:465-478
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    References listed on IDEAS

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    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Clark, Andrew E & Oswald, Andrew J, 1994. "Unhappiness and Unemployment," Economic Journal, Royal Economic Society, vol. 104(424), pages 648-659, May.
    4. Chib, Siddhartha, 2007. "Analysis of treatment response data without the joint distribution of potential outcomes," Journal of Econometrics, Elsevier, vol. 140(2), pages 401-412, October.
    5. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, Southern Economic Association, vol. 68(2), pages 210-223, October.
    6. Yau L.H.Y. & Little R.J., 2001. "Inference for the Complier-Average Causal Effect From Longitudinal Data Subject to Noncompliance and Missing Data, With Application to a Job Training Assessment for the Unemployed," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1232-1244, December.
    7. Deb, Partha & Munkin, Murat K. & Trivedi, Pravin K., 2006. "Private Insurance, Selection, and Health Care Use: A Bayesian Analysis of a Roy-Type Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 403-415, October.
    8. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    9. Chib, Siddhartha & Jacobi, Liana, 2007. "Modeling and calculating the effect of treatment at baseline from panel outcomes," Journal of Econometrics, Elsevier, vol. 140(2), pages 781-801, October.
    10. Chib, Siddhartha & Hamilton, Barton H., 2000. "Bayesian analysis of cross-section and clustered data treatment models," Journal of Econometrics, Elsevier, vol. 97(1), pages 25-50, July.
    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. Frangakis, Constantine E. & Brookmeyer, Ronald S. & Varadhan, Ravi & Safaeian, Mahboobeh & Vlahov, David & Strathdee, Steffanie A., 2004. "Methodology for Evaluating a Partially Controlled Longitudinal Treatment Using Principal Stratification, With Application to a Needle Exchange Program," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 239-249, January.
    13. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    14. Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
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    Cited by:

    1. Liana Jacobi & Helga Wagner & Sylvia Frühwirth-Schnatter, 2014. "Bayesian Treatment Effects Models with Variable Selection for Panel Outcomes with an Application to Earnings Effects of Maternity Leave," NRN working papers 2014-12, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
    2. van Hasselt, Martijn & Ferland, Timothy & Bray, Jeremy & Aldridge, Arnie, 2017. "Bayesian Estimation of the Complier Average Casual Effect," UNCG Economics Working Papers 17-14, University of North Carolina at Greensboro, Department of Economics.
    3. Jacobi, Liana & Wagner, Helga & Frühwirth-Schnatter, Sylvia, 2016. "Bayesian treatment effects models with variable selection for panel outcomes with an application to earnings effects of maternity leave," Journal of Econometrics, Elsevier, vol. 193(1), pages 234-250.

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