Graphical Condition for Identification in recursive SEM

The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a directed acyclic graph (DAG). The DAG represents a set of linear equations called Structural Equations Model (SEM), whose coefficients are parameters representing direct causal effects. Reliable quantitative conclusions can only be obtained from the model if the causal effects are uniquely determined by the data. That is, if there exists a unique parametrization for the model that makes it compatible with the data. If this is the case, the model is called identified. The main result of the paper is a general sufficient condition for identification of recursive SEM models.