On the Testable Implications of Causal Models with Hidden Variables

The validity of a causal model can be tested only if the model imposes constraints on the probability distribution that governs the gen­ erated data. In the presence of unmeasured variables, causal models may impose two types of constraints: conditional independen­ cies, as read through the d-separation crite­ rion, and functional constraints, for which no general criterion is available. This paper of­ fers a systematic way of identifying functional constraints and, thus, facilitates the task of testing causal models as well as inferring such models from data.