Covariate selection for non-parametric estimation of treatment effects

In observational studies, the non-parametric estimation of a binary treatment effect is often performed by matching each treated individual with a control unit which is similar in observed characteristics (covariates). In practical applications, the reservoir of covariates available may be extensive and the question arises which covariates should be matched for. The current practice consists in matching for covariates which are not balanced for the treated and the control groups, i.e. covariates affecting the treatment assignment. This paper develops a theory based on graphical models, whose results emphasize the need for methods looking both at how the covariates affect the treatment assignment and the outcome. Furthermore, we propose identification algorithms to select at minimal set of covariates to match for. An application to the estimation of the effect of a social program is used to illustrate the implementation of such algorithms.