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Baseline, Placebo, and Treatment: Efficient Estimation for Three-Group Experiments

  • Alan S. Gerber (a1), Donald P. Green (a1), Edward H. Kaplan (a2) and Holger L. Kern (a3)
Abstract

Randomized experiments commonly compare subjects receiving a treatment to subjects receiving a placebo. An alternative design, frequently used in field experimentation, compares subjects assigned to an untreated baseline group to subjects assigned to a treatment group, adjusting statistically for the fact that some members of the treatment group may fail to receive the treatment. This article shows the potential advantages of a three-group design (baseline, placebo, and treatment). We present a maximum likelihood estimator of the treatment effect for this three-group design and illustrate its use with a field experiment that gauges the effect of prerecorded phone calls on voter turnout. The three-group design offers efficiency advantages over two-group designs while at the same time guarding against unanticipated placebo effects (which would undermine the placebo-treatment comparison) and unexpectedly low rates of compliance with the treatment assignment (which would undermine the baseline-treatment comparison).

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Corresponding author
e-mail: alan.gerber@yale.edu (corresponding author)
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Authors' note: The authors are grateful to Mark Grebner, who conceived of the intervention described here and assisted in data collection, and to the Institution for Social and Policy Studies. We also thank the editors and anonymous reviewers, who provided very valuable comments. The experiment reported in this article was reviewed and approved by the Human Subjects Committee at Yale University. Supplementary materials for this article are available on the Political Analysis Web site.

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References
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Abadie, Alberto. 2003. Semiparametric instrumental variable estimation of treatment response models. Journal of Econometrics 113(2): 231–63.
Angrist, Joshua D., Imbens, Guido W., and Rubin, Donald B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91(434): 444–55.
Angrist, Joshua D., and Pischke, Jörg-Steffen. 2009. Mostly harmless econometrics: An empiricist's companion. Princeton, NJ: Princeton University Press.
Arceneaux, Kevin, Gerber, Alan S., and Green, Donald P. 2006. Comparing experimental and matching methods using a large-scale voter mobilization experiment. Political Analysis 14(1): 3762.
Boruch, Robert F. 1997. Randomized experiments for planning and evaluation: A practical guide. Thousand Oaks, CA: SAGE Publications.
Bound, John, Jaeger, David A., and Baker, Regina M. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90(430): 443–50.
Cheng, Jing, and Small, Dylan S. 2006. Bounds on causal effects in three-arm trials with non-compliance. Journal of the Royal Statistical Society, Series B 68(5): 815–36.
Cox, David R., and Hinkley, David V. 1974. Theoretical statistics. London: Chapman and Hall.
de Craen, Anton J.M., Kaptchuk, Ted J., Tijssen, Jan G. P., and Kleijnen, J. 1999. Placebos and placebo effects in medicine: Historical overview. Journal of the Royal Society of Medicine 92(10): 511–5.
Frangakis, Constantine E., and Rubin, Donald B. 2002. Principal stratification in causal inference. Biometrics 58(1): 21–9.
Gerber, Alan S., Green, Donald P., and Kaplan, Edward H. 2004. The illusion of learning from observational research. In Problems and methods in the study of politics, eds. Shapiro, Ian, Smith, Rogers M., and Masoud, Tarek E., 251–73. Cambridge: Cambridge University Press.
Gerber, Alan S., Green, Donald P., and Larimer, Christopher W. 2008. Social pressure and voter turnout: Evidence from a large-scale field experiment. American Political Science Review 102(1): 3348.
Gertler, Paul. 2004. Do conditional cash transfers improve child health? Evidence from PROGRESA's control randomized experiment. American Economic Review 94(2): 336–41.
Green, Donald P., and Gerber, Alan S. 2008. Get out the vote: How to increase voter turnout. 2nd ed. Washington, DC: Brookings Institution Press.
Efron, B., and Feldman, D. 1991. Compliance as an explanatory variable in clinical trials. Journal of the American Statistical Association 86(413): 917.
Holland, Paul W. 1986. Statistics and causal inference. Journal of the American Statistical Association 81(396): 945–60.
Imbens, Guido W. 2007. Nonadditive models with endogenous regressors. In Advances in economics and econometrics. Vol. III. Chapter 2, eds. Blundell, Richard, Newey, Whitney, and Persson, Torsten, 1746. Cambridge: Cambridge University Press
Imbens, Guido W., and Angrist, Joshua D. 1994. Identification and estimation of local average treatment effects. Econometrica 62(2): 467–76.
Imbens, Guido W., and Rosenbaum, Paul R. 2005. Robust, accurate confidence intervals with a weak instrument: Quarter of birth and education. Journal of the Royal Statistical Society, Series A 168(1): 109–26.
Imbens, Guido W., and Rubin, Donald B. 1997. Bayesian inference for causal effects in randomized experiments with noncompliance. Annals of Statistics 25(1): 305–27.
Morgan, Stephen L., and Winship, Christopher. 2007. Counterfactuals and causal inference. Cambridge: Cambridge University Press.
Nickerson, David W. 2005. Scalable protocols offer efficient design for field experiments. Political Analysis 13(3): 233–52.
Nickerson, David W. 2008. Is voting contagious? Evidence from two field experiments. American Political Science Review 102(1): 4957.
Rosenthal, Robert. 1985. Designing, analyzing, interpreting, and summarizing placebo studies. In Placebo: Theory, research, and mechanisms, eds. White, Leonard, Tursky, Bernard, and Schwartz, Gary E., 110–36. New York: Guilford Press.
Rubin, Donald B. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66(5): 688701.
Rubin, Donald B. 1977. Assignment to treatment group on the basis of a covariate. Journal of Educational Statistics 2(1): 126.
Rubin, Donald B. 1978. Bayesian inference for causal effects: The role of randomization. Annals of Statistics 6(1): 126.
Rubin, Donald B. 1990. Comment: Neyman (1923) and causal inference in experiments and observational studies. Statistical Science 5(4): 472–80.
Shadish, William R., Cook, Thomas D., and Campbell, Donald T. 2002. Experimental and quasi-experimental designs for generalized causal inference. Boston, MA: Houghton Mifflin.
Silverman, William A. 1980. Retrolental fibroplasia: A modern parable. New York: Grune.
Torgerson, David J., and Torgerson, Carole J. 2008. Designing randomized trials in health, education and the social sciences. New York: Palgrave Macmillan.
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Political Analysis
  • ISSN: 1047-1987
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