  This paper proposes a~simple, yet powerful, 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). 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. An~illustrative example of the proposed approach is
presented for the entropy balancing method and the covariate balancing
propensity score method. 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 approach can be
further generalized to other designs (e.g. multi-category, continuous) or
methods (e.g. synthetic control method). An open source software implementing
proposed methods is available.
