The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Rubin Causal Model

  • Guido W. Imbens
  • Donald B. Rubin
Reference work entry


The Rubin Causal Model (RCM), a framework for causal inference, has three distinctive features. First, it uses ‘potential outcomes’ to define causal effects at the unit level, first introduced by Neyman in the context of randomized experiments and randomization-based inference, but not used formally in non-randomized studies or with other modes of inference until Rubin (1974, 1975). Second is its formal use of a probabilistic assignment mechanism, which mathematically describes how treatments are given to units, with possible dependence on background variables and the potential outcomes themselves. Third is an optional probability distribution on all variables, including the potential outcomes, which thereby unifies frequentist and model-based forms of statistical inference for causal effects within one framework.


Assignment mechanism Assignment-based inference Bayesian inference Causal inference Fisher, R. A. Haavelmo, T. Hurwicz, L. Instrumental variables Interval estimates Markov chain Monte Carlo methods Matching Multiple imputation Neyman, J. Posterior predictive distribution Potential outcomes Principal stratification Probability Program evaluation Propensity scores Randomization-based inference Randomized experiment Regression coefficients Roy model Rubin causal model Simultaneous equations models Tinbergen, J. treatments Units 

JEL classifications

This is a preview of subscription content, log in to check access.


  1. Abadie, A., and G.W. Imbens. 2006. Large sample properties of matching estimators for average treatment effects. Econometrica 74: 235–267.CrossRefGoogle Scholar
  2. 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, 444–72 (an applications invited discussion article with discussion and rejoinder).Google Scholar
  3. Barnard, J., J. Hill, C. Frangakis, and D. Rubin. 2003. A principal stratification approach to broken randomized experiments: a case study of vouchers in New York City. Journal of the American Statistical Association 98: 299–323 (with discussion and rejoinder).CrossRefGoogle Scholar
  4. Belson, W.A. 1956. A technique for studying the effect of a television broadcast. Applied Statistics 5: 195–202.CrossRefGoogle Scholar
  5. Bertrand, M., and S. Mullainathan. 2004. Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review 94: 991–1013.CrossRefGoogle Scholar
  6. Cochran, W.G., and D.B. Rubin. 1973. Controlling bias in observational studies: A review. Sankhya 35: 417–446.Google Scholar
  7. Cox, D.R. 1958. The planning of experiments. New York: Wiley.Google Scholar
  8. Crump, R., Hotz, J., Imbens, G. and Mitnik, O. 2005. Moving the goalposts: addressing limited overlap in estimation of average treatment effects by changing the estimand. Unpublished manuscript, Department of Economics, University of California, Berkeley.Google Scholar
  9. Dawid, A.P. 2000. Causal inference without counterfactuals. Journal of the American Statistical Association 95: 407–424 (with discussion).CrossRefGoogle Scholar
  10. Dehijia, R., and S. Wahba. 1999. Causal effects in non-experimental studies: reevaluating the evaluations of training programs. Journal of the American Statistical Association 94: 1053–1062.CrossRefGoogle Scholar
  11. Fisher, R.A. 1918. The causes of human variability. Eugenics Review 10: 213–220.Google Scholar
  12. Fisher, R.A. 1925. Statistical methods for research workers. 1st ed. Edinburgh: Oliver and Boyd.Google Scholar
  13. Frangakis, C., and D.B. Rubin. 1999. Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika 86: 366–379.CrossRefGoogle Scholar
  14. Frangakis, C.E., and D.B. Rubin. 2001. Addressing an idiosyncrasy in estimating survival curves using double sampling in the presence of self-selected right censoring. Biometrics 57: 333–342 (with discussion and rejoinder, 343–53).CrossRefGoogle Scholar
  15. Frangakis, C.E., and D.B. Rubin. 2002. Principal stratification in causal inference. Biometrics 58: 21–29.CrossRefGoogle Scholar
  16. Haavelmo, T. 1944. The probability approach in econometrics. Econometrica 15: 413–419.Google Scholar
  17. Heckman, J., and R. Robb. 1984. Alternative methods for evaluating the impact of interventions. In Longitudinal analysis of labor market data, ed. J. Heckman and B. Singer. Cambridge: Cambridge University Press.Google Scholar
  18. Heckman, J., H. Ichimura, and P. Todd. 1998. Matching as an econometric evaluation estimator. Review of Economic Studies 65: 261–294.CrossRefGoogle Scholar
  19. Hirano, K., G. Imbens, D.B. Rubin, and X. Zhou. 2000. Estimating the effect of an influenza vaccine in an encouragement design. Biostatistics 1: 69–88.CrossRefGoogle Scholar
  20. Hirano, K., G. Imbens, and G. Ridder. 2003. Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71: 1161–1189.CrossRefGoogle Scholar
  21. Holland, P.W. 1986. Statistics and causal inference. Journal of the American Statistical Association 81: 945–970.CrossRefGoogle Scholar
  22. Hurwicz, L. 1962. On the structural form of interdependent systems. In Logic, methodology, and philosophy of science, proceedings of the 1960 international congress, ed. E. Nagel, P. Suppes, and A. Tarski. Stanford, CA: Stanford University Press.Google Scholar
  23. Imbens, G.W., and J. Angrist. 1994. Identification and estimation of local average treatment effects. Econometrica 62: 467–476.CrossRefGoogle Scholar
  24. Imbens, G.W., and D.B. Rubin. 1997. Bayesian inference for causal effects in randomized experiments with noncompliance. Annals of Statistics 25: 305–327.CrossRefGoogle Scholar
  25. Imbens, G.W., and D.B. Rubin. 2006. Causal inference in statistics and the medical and social sciences. Cambridge: Cambridge University Press.Google Scholar
  26. Jin, H., and D.B. Rubin. 2007. Principal stratification for causal inference with extended partial compliance: application to Efron–Feldman data. Journal of the American Statistical Association 103(481): 101–111.CrossRefGoogle Scholar
  27. Lalonde, R. 1986. Evaluating the econometric evaluations of training programs. American Economic Review 76: 604–620.Google Scholar
  28. Manski, C.F. 2003. Partial identification of probability distributions. New York: Springer-Verlag.Google Scholar
  29. Mealli, F., and D.B. Rubin. 2002. Assumptions when analyzing randomized experiments with noncompliance and missing outcomes. Health Services Outcome Research Methodology 3: 225–232.CrossRefGoogle Scholar
  30. Mealli, F., and D.B. Rubin. 2003. Assumptions allowing the estimation of direct causal effects: discussion of ‘Healthy, wealthy, and wise? Tests for direct causal paths between health and socioeconomic status’ by Adams et al. Journal of Econometrics 112: 79–87.CrossRefGoogle Scholar
  31. Mill, J.S. 1843. A system of logic. In Collected works of John Stuart Mill, ed. J.M. Robson, Vol. 7. Toronto: University of Toronto Press 1973.Google Scholar
  32. Neyman, J. 1923. On the application of probability theory to agricultural experiments: Essay on principles, section 9. Statistical Science 5(1990): 465–480 .TranslatedGoogle Scholar
  33. Neyman, J. 1935. Statistical problems in agricultural experimentation. Journal of the Royal Statistical Society B2: 107–108 (Supplement) (with discussion). (With cooperation of K. Kwaskiewicz and St. Kolodziejczyk.).Google Scholar
  34. Peters, C.C. 1941. A method of matching groups for experiments with no loss of population. Journal of Educational Research 34: 606–612.CrossRefGoogle Scholar
  35. Rosenbaum, P.R., and D.B. Rubin. 1983a. The central role of the propensity score in observational studies for causal effects. Biometrika 70: 41–55.CrossRefGoogle Scholar
  36. Rosenbaum, P.R., and D.B. Rubin. 1983b. Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society, B 45: 212–218.Google Scholar
  37. Rosenbaum, P.R., and D.B. Rubin. 1984. Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association 79: 516–524.CrossRefGoogle Scholar
  38. Rosenbaum, P.R., and D.B. Rubin. 1985. Constructing a control group using multivariate matched sampling incorporating the propensity score. American Statistician 39: 33–38.Google Scholar
  39. Roy, A.D. 1951. Some thoughts on the distribution of earnings. Oxford Economic Papers 3: 135–146.CrossRefGoogle Scholar
  40. Rubin, D.B. 1973a. Matching to remove bias in observational studies. Biometrics 29: 159–183 .Correction note: 1974. Biometrics 30, 728CrossRefGoogle Scholar
  41. Rubin, D.B. 1973b. The use of matched sampling and regression adjustment to remove bias in observational studies. Biometrics 29: 185–203.CrossRefGoogle Scholar
  42. Rubin, D.B. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66: 688–701.CrossRefGoogle Scholar
  43. Rubin, D.B. 1975. Bayesian inference for causality: The importance of randomization. Proceedings of the social statistics section of the American Statistical Association, 233–239.Google Scholar
  44. Rubin, D.B. 1976. Inference and missing data. Biometrika 63: 581–592.CrossRefGoogle Scholar
  45. Rubin, D.B. 1977. Assignment of treatment group on the basis of a covariate. Journal of Educational Statistics 2: 1–26.CrossRefGoogle Scholar
  46. Rubin, D.B. 1978. Bayesian inference for causal effects: the role of randomization. Annals of Statistics 6: 34–58.CrossRefGoogle Scholar
  47. Rubin, D.B. 1979. Discussion of ‘Conditional independence in statistical theory’ by A.P. Dawid. Journal of the Royal Statistical Society Series B 41: 27–28.Google Scholar
  48. Rubin, D.B. 1980. Discussion of ‘Randomization analysis of experimental data in the Fisher randomization test’ by Basu. Journal of the American Statistical Association 75: 591–593.Google Scholar
  49. Rubin, D.B. 1987. Multiple imputation for nonresponse in surveys. New York: Wiley.CrossRefGoogle Scholar
  50. Rubin, D.B. 1990a. Formal modes of statistical inference for causal effects. Journal of Statistical Planning and Inference 25: 279–292.CrossRefGoogle Scholar
  51. Rubin, D.B. 1990b. Neyman (1923) and causal inference in experiments and observational studies. Statistical Science 5: 472–480.CrossRefGoogle Scholar
  52. Rubin, D.B. 1991. Practical implications of modes of statistical inference for causal effects. Biometrics 47: 1213–1234.CrossRefGoogle Scholar
  53. Rubin, D.B. 2000. The utility of counterfactuals for causal inference. Comment on A.P. Dawid, ‘Causal inference without counterfactuals’. Journal of the American Statistical Association 95: 435–438.Google Scholar
  54. Rubin, D.B. 2002. Using propensity scores to help design observational studies: Application to the tobacco litigation. Health Services and Outcomes Research Methodology 2: 169–188.CrossRefGoogle Scholar
  55. Rubin, D.B. 2004a. Multiple imputation for nonresponse in surveys. New York: Wiley Reprinted with new appendices as a Wiley Classic.Google Scholar
  56. Rubin, D.B. 2004b. Direct and indirect causal effects via potential outcomes. Scandinavian Journal of Statistics 31: 161–170 (with discussion and reply, 196–8).CrossRefGoogle Scholar
  57. Rubin, D.B. 2005. Causal inference using potential outcomes: Design, modeling, decisions, 2004 Fisher Lecture. Journal of the American Statistical Association 100: 322–331.CrossRefGoogle Scholar
  58. Rubin, D.B. 2006a. Matched sampling for causal effects. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  59. Rubin, D.B. 2006b. Causal inference through potential outcomes and principal stratification: applications to studies with ‘censoring’ due to death. Statistical Science 21: 299–321.CrossRefGoogle Scholar
  60. Rubin, D.B. 2007. Statistical inference for causal effects, with emphasis on applications in epidemiology and medical statistics. In Handbook of statistics: Epidemiology and medical statistics, ed. C.R. Rao, J.P. Miller, and D.C. Rao. Amsterdam: North-Holland.Google Scholar
  61. Rubin, D.B., and N. Thomas. 1992a. Affinely invariant matching methods with ellipsoidal distributions. Annals of Statistics 20: 1079–1093.CrossRefGoogle Scholar
  62. Rubin, D.B., and N. Thomas. 1992b. Characterizing the effect of matching using linear propensity score methods with normal covariates. Biometrika 79: 797–809.CrossRefGoogle Scholar
  63. Rubin, D.B., and N. Thomas. 1996. Matching using estimated propensity scores: relating theory to practice. Biometrics 52: 249–264.CrossRefGoogle Scholar
  64. Rubin, D.B., and N. Thomas. 2000. Combining propensity score matching with additional adjustments for prognostic covariates. Journal of the American Statistical Association 95: 573–585.CrossRefGoogle Scholar
  65. Tinbergen, J. 1930. Determination and interpretation of supply curves: an example. Zeitschrift fur Nationalokonomie. Reprinted in The Foundations of Econometric Analysis, ed. D.F. Hendry and M.S. Morgan. Cambridge: Cambridge University Press, 1997.Google Scholar
  66. Zhang, J., and D.B. Rubin. 2003. Estimation of causal effects via principal stratification when some outcomes are truncated by ‘death’. Journal of Educational and Behavioral Statistics 28: 353–368.CrossRefGoogle Scholar
  67. Zhang, J., D. Rubin, and F. Mealli. 2007. Evaluating the effects of job training programs on wages through principal stratification. Advances in Econometrics 21.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Guido W. Imbens
    • 1
  • Donald B. Rubin
    • 1
  1. 1.