Bounds on average causal effects in studies with a latent response variable

Consider a case where cause-effect relationships between variables can be described as a directed acylic graph and the corresponding recursive factorization of a joint distribution. In order to provide the bounds on average causal effects in studies with a latent response variable, this paper proposes a graphical criterion for selecting covariates and variables caused by the response variable. The result enables us not only to judge from the graph structure whether the bounds on an average causal effect can be expressed through the observed quantities, but also to provide their closed-form expressions in case where its answer is affirmative. The graphical criterion of this paper is helpful to evaluate the bounds on average causal effects when it is difficult to observe a response variable. Copyright Springer-Verlag 2005