Reply to Comments

We will respond to our commentators individually, but the order of our responses follows naturally from the issues they bring up. Judea Pearl describes SEM's unfortunate retreat from the clear causal semantics articulated by Sewall Wright (1921) and later by Haavelmo (1943) to the algebraic interpretation preferred more recently by econometricians. We agree with Pearl about the history and also the problem, namely that the algebraic interpretation is suitable for estimation but expressively too weak to even distinguish among competing causal claims. Here we try to elaborate on the distinction between the semantics of a causal SEM and the epistemological connections between statistical data, background knowledge, and causal structure. We argue that many modern critics of SEM make their hay by conflating this distinction. Having tried to make it clear, we then turn to the assumptions that give the epistemological issues their structure, namely the Causal Independence and Faithfulness assumptions. Jim Woodward questions these assumptions at length, especially the Causal Independence assumption, and we spend the second part of our response defending it. Phil Wood seems to accept the fundamental assumptions upon which TETRAD rests, and even the utility of tools like it, but he brings out a wide array of subtle difficulties that we have not had time to discuss, some of which we now cover. Kwok-fai Ting questions the utility of any specification search done by computer, and we attempt to address his concerns last.