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Estimating Treatment Effects in the Presence of Noncompliance and Nonresponse: The Generalized Endogenous Treatment Model

Published online by Cambridge University Press:  04 January 2017

Kevin M. Esterling*
Affiliation:
Department of Political Science, UC—Riverside, 900 University Ave., Riverside, CA 92506
Michael A. Neblo
Affiliation:
Department of Political Science, Ohio State University, 2114 Derby Hall, 154 N Oval Mall, Columbus, OH 43210 e-mail: [email protected]
David M. J. Lazer
Affiliation:
Departments of Political Science and Computer Science, Northeastern University, 301 Meserve Hall, Boston, MA 02115 e-mail: [email protected]
*
e-mail: [email protected] (corresponding author)

Abstract

If ignored, noncompliance with a treatment or nonresponse on outcome measures can bias estimates of treatment effects in a randomized experiment. To identify and estimate causal treatment effects in the case where compliance and response depend on unobservables, we propose the parametric generalized endogenous treatment (GET) model. GET incorporates behavioral responses within an experiment to measure each subject's latent compliance type and identifies causal effects via principal stratification. Using simulation methods and an application to field experimental data, we show GET has a dramatically lower mean squared error for treatment effect estimates than existing approaches to principal stratification that impute, rather than measure, compliance type. In addition, we show that GET allows one to relax and test the instrumental variable exclusion restriction assumption, to test for the presence of treatment effect heterogeneity across a range of compliance types, and to test for treatment ignorability when treatment and control samples are balanced on observable covariates.

Type
Regular Articles
Copyright
Copyright © The Author 2011. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Aakvik, A., Heckman, J. J., and Vytlacil, E. J. 2005. Estimating treatment effects for discrete outcomes when responses to treatment vary: An application to Norwegian vocational rehabilitation programs. Journal of Econometrics 125: 1551.CrossRefGoogle Scholar
Abadie, A., Drukker, D., Herr, J. L., and Imbens, G. W. 2001. Implementing matching estimators for average treatment effects in stata. The Stata Journal 1: 118.Google Scholar
Achen, C. H. 1975. Mass political attitudes and the survey response. American Political Science Review 69: 1218–31.CrossRefGoogle Scholar
Acock, A. C., Clarke, H. D., and Stewart, M. C. 1985. A new model for old measures: A covariance structure analysis of political efficacy. Journal of Politics 47: 1062–84.CrossRefGoogle Scholar
Angrist, J. D., Imbens, G. W., and Rubin, D. B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444–55.Google Scholar
Barnard, J., Frangakis, C. E., Hill, J. L., and Rubin, D. B. 2003. Principal stratification approach to broken randomized experiments: A case study of school choice vouchers in New York city. Journal of the American Statistical Association 98: 299323.Google Scholar
Bizer, G. Y., Krosnick, J. A., Holbrook, A. L., Wheeler, S. C., Rucker, D. D., and Petty, R. E. 2004. The impact of personality on cognitive, behavioral, and affective political processes: The effects of need to evaluate. Journal of Personality 72: 9951027.Google Scholar
Björkland, A., and Moffitt, R. 1987. The estimation of wage gains and welfare gains in self-selection models. The Review of Economics and Statistics 69: 42–9.Google Scholar
Bollen, K. A. 1989. Structural equations with latent variables. New York, NY: John Wiley & Sons, Ltd.Google Scholar
Cacioppo, J. T., Petty, R. E., and Kao, C. F. 1984. The efficient assessment of need for cognition. Journal of Personality Assessment 48: 306–7.Google Scholar
Delli Carpini, M. X. and Keeter, S. 1993. Measuring political knowledge: Putting first things first. American Journal of Political Science 37: 1179–206.Google Scholar
Diamond, A., and Sekhon, J. S. 2007. Genetic matching for estimating causal effects: A general multivariate matching method for achieving balance in observational studies Department of Political Science typescript, University of California, Berkeley.Google Scholar
Esterling, K. M., Neblo, M. A., and Lazer, D. M. J. 2011. Replication data for: “Estimating Treatment Effects in the Presence of Noncompliance and Nonresponse: The Generalized Endogenous Treatment Model”. http://hdl.handle.net/1902.1/15619UNF:5:6fj98k0/hbVkkWd2ouG35w==Murray Research Archive [Distributor] V1 [Version].Google Scholar
Frangakis, C. E., and Rubin, D. B. 1999. Addressing complications of intention-totreat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika 86: 365–79.Google Scholar
Frangakis, C. E., and Rubin, D. B. 2002. Principal stratification in causal inference. Biometrics 58: 21–9.Google Scholar
Hirano, K., Imbens, G. W., and Zhou, D. B. R. X. -H. 2000. Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics 1: 6988.CrossRefGoogle Scholar
Ho, D. E., Imai, K., King, G., and Stuart, E. A. 2004. Matchit: Matching as nonparametric preprocessing for causal inference. Technical report. Cambridge, MA: Harvard University. http://gking.harvard.edu/matchit/ (accessed March 28, 2011).Google Scholar
Ho, D. E., Imai, K., King, G., and Stuart, E. A. 2007. Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political Analysis 15: 199236.Google Scholar
Holland, P. W. 1986. Statistics and causal analysis. Journal of the American Statistical Association 81: 945–60.Google Scholar
Horiuchi, Y., Imai, K., and Taniguchi, N. 2007. Designing and analyzing randomized experiments: Application to a Japanese election survey experiment. American Journal of Political Science 51: 669–87.Google Scholar
Imai, K. 2009. Experiment, version 1.1-0, noncompli function, Bayesian analysis of randomized experiments with noncompliance and missing outcomes under the assumption of latent ignorability. Documentation available at http://imai.princeton.edu (accessed March 28, 2011).Google Scholar
Imai, K., King, G., and Stuart, E. A. 2008. Misunderstandings among experimentalists and observationalists about causal inference. Journal of the Royal Statistical Society, Series A: Statistics in Society 171: 481502.Google Scholar
Imai, K., and Yamamoto, T. 2010. Causal inference with differential measurement error: Nonparametric identification and sensitivity analysis. American Journal of Political Science 54: 543–60.Google Scholar
Imbens, G. W. 2004. Nonparametric estimation of average treatment effects under exogeneity: A review. The Review of Economics and Statistics 86: 429.Google Scholar
Imbens, G. W., and Rubin, D. B. 1997. Bayesian inference for causal effects in randomized experiments with noncompliance. The Annals of Statistics 25: 305–27.Google Scholar
Jackman, S. 2000. Estimation and inference via Bayesian simulation: An introduction to Markov chain Monte Carlo. American Journal of Political Science 44: 369–98.Google Scholar
Mealli, F., Imbens, G. W., Ferro, S., and Biggeri, A. 2004. Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes. Biostatistics 5: 207–22.Google Scholar
Mealli, F., and Rubin, D. B. 2003. Commentary: Assumptions allowing the estimation of direct causal effects. Journal of Econometrics 112: 7987.Google Scholar
Miranda, A., and Rabe-Hesketh, S. 2006. Maximum likelihood estimation of endogenous switching and sample selection model for binary, count, and ordinal variables. The Stata Journal 6: 285308.Google Scholar
Morgan, S. L., and Winship, C. 2007. Counterfactuals and causal inference: Methods and principles for social research. New York, NY: Cambridge University Press.Google Scholar
Morrell, M. 2005. Deliberation, democratic decision-making and internal political efficacy. Political Behavior 27: 4969.Google Scholar
Patz, R. J., and Junker, B. W. 1999. Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses. Journal of Educational and Behavioral Statistics 24: 342–66.Google Scholar
Rosenbaum, P. R., and Rubin, D. B. 1985. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician 39: 33–8.Google Scholar
Rubin, D. B. 1974. Estimating casual effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66: 688701.Google Scholar
Skrondal, A., and Rabe-Hesketh, S. 2004. Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman and Hall.Google Scholar
Tanner, M. A., and Wong, W. H. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82: 528–40.Google Scholar
Terza, J. V. 1998. Estimating count data with endogenous switching: Sample selection and endogenous treatment effects. Journal of Econometrics 84: 129–54.Google Scholar
Trier, S., and Jackman, S. 2008. Democracy as a latent variable. American Journal of Political Science 52: 201–17.Google Scholar
Young, I. M. 1990. Justice and the politics of difference. Princeton, NJ: Princeton University Press.Google Scholar