  We address the problem of estimating the effect of intervening on a set of
variables X from experiments on a different set, Z, that is more accessible to
manipulation. This problem, which we call z-identifiability, reduces to
ordinary identifiability when Z = empty and, like the latter, can be given
syntactic characterization using the do-calculus [Pearl, 1995; 2000]. We
provide a graphical necessary and sufficient condition for z-identifiability
for arbitrary sets X,Z, and Y (the outcomes). We further develop a complete
algorithm for computing the causal effect of X on Y using information provided
by experiments on Z. Finally, we use our results to prove completeness of
do-calculus relative to z-identifiability, a result that does not follow from
completeness relative to ordinary identifiability.
