Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference

Abstract

In observational studies, the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. To make the assumption of an unconfounded treatment plausible researchers might include many, possibly correlated, covariates in the propensity score model. In this paper, we study how the asymptotic efficiency of matching and inverse probability weighting estimators for average causal effects change when the covariates are correlated. We investigate the case with multivariate normal covariates, a logistic model for the propensity score and linear models for the potential outcomes and show results under different model assumptions. We show that the correlation can both increase and decrease the large sample variances of the estimators, and that the correlation affects the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Moreover, the strength of the confounding towards the outcome and the treatment plays an important role.

Keywords:

• correlation
• efficiency bound
• observational study
• propensity score

AMS Subject Classification:

• 62F12
• 62H12

View correction statement:

ERRATUM

Acknowledgements

We thank conference participants at the 26th International Biometric Conference in Kobe and seminar participants at the joint IFAU and Department of Statistics seminar. We would also like to thank Marcus Frölich and Per Johansson for valuable comments. Financial support from the Institute for Evaluation of Labour Market and Education Policy, Sweden, is acknowledged.