2011 | OriginalPaper | Chapter
Partial Compliance, Effect of Treatment on the Treated and Instrumental Variables
Author : Antonio Forcina
Published in: Classification and Multivariate Analysis for Complex Data Structures
Publisher: Springer Berlin Heidelberg
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Under the assumption that treatment assignment has no direct effect on the response, a non parametric probabilistic model of the distribution involving the latent confounder under partial compliance leads to a generalized definition of the effect of treatment on the treated and reveals that the instrumental variable estimand equals a suitable average of such causal effects only when certain restrictions hold. An application to a popular data set concerning reduction of cholesterol level is used as an illustration.