We will respond to our commentators individually, but the order of our
responses follows naturally from the issues they bring up. Judea Pear
l describes SEM's unfortunate retreat from the clear causal semantics
articulated by Sewall Wright (1921) and later by Haavelmo (1943) to th
e algebraic interpretation preferred more recently by econometricians.
We agree with Pearl about the history and also the problem, namely th
at the algebraic interpretation is suitable for estimation but express
ively too weak to even distinguish among competing causal claims. Here
we try to elaborate on the distinction between the semantics of a cau
sal SEM acid 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 assumption
s at length, especially the Causal Independence assumption, and we spe
nd the second part of our response defending it. Phil Wood seems to ac
cept the fundamental assumptions upon which TETRAD rests, and even the
utility of tools like it, but he brings out a wide array of subtle di
fficulties 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.