Identification and estimation of causal effects of multiple treatments under the conditional independence assumption
IZA, 1999 - 18 pages
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.
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assignment mechanism conditional average treatment effects balancing score property Bauer K. F. Zimmermann binary case considered Bonn C. M. Schmidt causal effects causal model comparison observations conditional choice probabilities conditional independence assumption considered by Rosenbaum CORNELL UNIVERSITY covariance defined denotes discuss identification E(Ym econometric evaluation literature Estimation of Causal estimation problem Evidence from Count G. G. Wagner Germany Hence I. N. Gang K. F. Identification and Estimation identifies 6mJ Immigrant implies E(Y IZA Discussion Papers K. F. Zimmermann K. F. labor economics Lechner Lindbeck D. J. Snower matching estimator matching protocol Migration multinomial Multiple Treatments mutually exclusive treatments non-parametric outcome variables participants in treatment participation probabilities Pm(x Poland population potential outcomes proof propensity score R. A. Hart R. T. Riphahn random variable respective balancing scores Rosenbaum and Rubin Rotte K. F. Zimmermann Rubin model step subsample sufficient to identify Var(Ym\S Vogler Vxez Wage Winkelmann