The assumption that the assignment to treatments is ignorable conditional on attributes plays an important role in the applied statistic and econometric evaluation literature. Another term for it is conditional independence assumption. This paper discusses identification when there are more than two types of mutually exclusive treatments. It turns out that low dimensional balancing scores, similar to the ones valid in the case of only two treatments, exist and be used for identification of various causal effects. Therefore, a comparable reduction of the dimension of the estimation problem is achieved and the approach retains its basic simplicity. The paper also outlines a matching estimator potentially suitable in that framework.
Treatment effects balancing score propensity score causal model program evaluation matching