Survey calibration for causal inference: a simple method to balance covariate distributions

This paper proposes a simple method for balancing distributions of covariates for causal inference based on observational studies. The method makes it possible to balance an arbitrary number of quantiles (e.g., medians, quartiles, or deciles) together with means if necessary. The proposed approach is based on the theory of calibration estimators (Deville and S\"arndal 1992), in particular, calibration estimators for quantiles, proposed by Harms and Duchesne (2006). By modifying the entropy balancing method and the covariate balancing propensity score method, it is possible to balance the distributions of the treatment and control groups. The method does not require numerical integration, kernel density estimation or assumptions about the distributions; valid estimates can be obtained by drawing on existing asymptotic theory. Results of a simulation study indicate that the method efficiently estimates average treatment effects on the treated (ATT), the average treatment effect (ATE), the quantile treatment effect on the treated (QTT) and the quantile treatment effect (QTE), especially in the presence of non-linearity and mis-specification of the models. The proposed methods are implemented in an open source R package jointCalib.