Simple least squares estimator for treatment effects using propensity score residuals

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17 Citations (Scopus)


Propensity score matching is widely used to control covariates when analysing the effects of a nonrandomized binary treatment. However, it requires several arbitrary decisions, such as how many matched subjects to use and how to choose them. In this paper a simple least squares estimator is proposed, where the treatment, and possibly the response variable, is replaced by the propensity score residual. The proposed estimator controls covariates semiparametrically if the propensity score function is correctly specified. Furthermore, it is numerically stable and relatively easy to use, compared with alternatives such as matching, regression imputation, weighting, and doubly robust estimators. The proposed estimator also has a simple valid asymptotic variance estimator that works well in small samples. The least squares estimator is extended to multiple treatments and noncontinuously distributed responses. A simulation study demonstrates that it has lower mean squared error than its competitors.

Original languageEnglish
Pages (from-to)149-164
Number of pages16
Issue number1
Publication statusPublished - 2018 Mar 1

Bibliographical note

Publisher Copyright:
© 2017 Biometrika Trust.


  • Binary treatment
  • Generalized propensity score
  • Multiple treatments
  • Propensity score

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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