From **Professor Nozer Singpurwalla, from The George Washington University:**

My basic point is that since causality has not been defined, the causal calculus is a technology which could use a foundation. However, the calculus does give useful insights and is thus valuable. Finally, according to my understanding of the causal calculus, I am inclined to state that the calculus of probability is the calculus of causality, notwithstanding Dennis' [Lindley] concerns about Suppes probabilistic causality.

From **Bill Shipley, Universite de Sherbrooke, (Quebec) CANADA: **

In most experiments, the external manipulation consists of adding (or subtracting) some amount from *X* without removing pre-existing causes of *X*. For example, adding 5 *kg*/*h* of fertilizer to a field, adding 5 *mg/l* of insulin to subjects etc. Here, the pre-existing causes of the manipulated variable still exert effects but a new variable (*M*) is added.

… The problem that I see with the *do*(*x*) operator as a general operator of external manipulation is that it requires two things: (1) removing any pre-existing causes of *x* and (2) setting *x* to some value. This corresponds to some types of external manipulations, but not all (or even most) external manipulations. I would introduce an *add*(*x=n*) operator, meaning "*add*, external to the pre-existing causal process, an amount '*n*' of *x*''. Graphically, this consists of augmenting the pre-existing causal graph with a new edge, namely *M-n*–>*X*. Algebraically, this would consist of adding a new term –*n*– as a cause of *X*.

**From L. H., University of Alberta and S.M., Georgia Tech **

In response to my comments (e.g., *Causality,* Section 5.4) that the causal interpretation of structural coefficients is practically unknown among SEM researchers, and my more recent comment that a correct causal interpretation is conspicuously absent from *all* SEM books and papers, including *all* 1970-1999 texts in economics, two readers wrote that the "unit-change" interpretation is common and well accepted in the SEM literature.

L.H. from the University of Alberta wrote:

"Page 245 of L. Hayduk, Structural Equation Modeling with LISREL: Essentials and Advances, 1986, has a chapter headed "Interpreting it All", whose first section is titled "The basics of interpretation," whose first paragraph, has a second sentence which says in italics (with notation changed to correspond to the above) that a slope can be interpreted as: the magnitude of the change in *y* that would be predicted to accompany a unit change in *x* with the other variables in the equation left untouched at their original values." … "Seems to me that O.D. Duncan, Introduction to Structural Equation Models 1975 pages 1 and 2 are pretty clear on *b* as causal. "More precisely, it [*byx*] says that a change of one unit in *x* … produces a change of *b* units in *y*" (page 2). I suspect that H. M. Blalock's book "Causal models in the social Sciences", and D. Heise's book "Causal analysis." probably speak of *b* as causal."

S.M., from Georgia Tech concurs:

"I concur with L.H. that Heise, author of Causal Analysis (1975) regarded the *b* of causal equations to be how much a unit change in a cause produced an effect in an effect variable. This is a well-accepted idea."