Universal Formulas for Treatment Effects from Noncompliance Data

  • Alexander A. Balke
  • Judea Pearl


This paper establishes formulas that can be used to bound the actual treatment effect in any experimental study in which treatment assignment is random but subject compliance is imperfect. These formulas provide the tightest bounds on the average treatment effect that can be inferred given the distribution of assignments, treatments, and responses. Our results reveal that even with high rates of noncompliance, experimental data can yield significant and sometimes accurate information on the effect of a treatment on the population.


Causal Effect Treatment Assignment Average Treatment Effect Tight Bound Universal Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Angrist, J.D., Imbens, G.W., and Rubin, D.B. (1993), “Identification of causal effects using instrumental variables,” Technical Report No. 136, Department of Economics, Harvard University, Cambridge, MA.Google Scholar
  2. Balke, A., and Pearl, J. (1993), “Nonparametric bounds on causal effects from partial com¬pliance data,” Technical Report R-199, Cognitive Systems Laboratory, Computer Science Department, UCLA. Submitted.Google Scholar
  3. Balke, A., and Pearl, J. (1994), “Counterfactual probabilities: Computational methods, bounds and applications,” Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, Seattle, WA, pages 46–54, San Fransisco, CA, Morgan Kauffman.Google Scholar
  4. Efron, B., and Feldman, D. (1991), “Compliance as an explanatory variable in clinical trials,” Journal of the American Statistical Association, 86 (413), 9–26.CrossRefGoogle Scholar
  5. Holland, P.W. (1988), “Causal inference, path analysis, and recursive structural equations models,” in C. Clogg, editor, Sociological Methodology, 449–484, American Sociological Association, Washington, DC.Google Scholar
  6. Manski, C.F (1990), “Nonparametric bounds on treatment effects,” American Economic Review, Papers and Proceedings, 80, 319–323.Google Scholar
  7. Pearl, J. (1994), “Causal diagrams for empirical research,” Technical Report R-218-L, Re vision I, UCLA Cognitive Systems Laboratory. To appear in Biometrika.Google Scholar
  8. Robins, J.M. (1989), “The analysis of randomized and non-randomized AIDS treatment trials using a new approach to causal inference in longitudinal studies,” in L. Sechrest, H. Freeman, and A. Mulley, editors, Health Service Research Methodology: A Focus on AIDS, 113–159, NCHSR, U.S. Public Health Service.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Alexander A. Balke
    • 1
  • Judea Pearl
    • 1
  1. 1.Cognitive Systems LaboratoryUniversity of CaliforniaLos AngelesUSA

Personalised recommendations