Covariate balancing propensity score

Kosuke Imai, Marc Ratkovic

Research output: Contribution to journalArticlepeer-review

690 Scopus citations


The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in the analysis of observational data. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. We introduce covariate balancing propensity score (CBPS) methodology, which models treatment assignment while optimizing the covariate balance. The CBPS exploits the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment. The estimation of the CBPS is done within the generalized method-of-moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to other important settings, including the estimation of the generalized propensity score for non-binary treatments and the generalization of experimental estimates to a target population. Open source software is available for implementing the methods proposed.

Original languageEnglish (US)
Pages (from-to)243-263
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - Jan 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Causal inference
  • Instrumental variables
  • Inverse propensity score weighting
  • Marginal structural models
  • Observational studies
  • Propensity score matching
  • Randomized experiments


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