Causal Transportability of Experiments on Controllable Subsets of
  Variables: z-Transportability
  We introduce z-transportability, the problem of estimating the causal effect
of a set of variables X on another set of variables Y in a target domain from
experiments on any subset of controllable variables Z where Z is an arbitrary
subset of observable variables V in a source domain. z-Transportability
generalizes z-identifiability, the problem of estimating in a given domain the
causal effect of X on Y from surrogate experiments on a set of variables Z such
that Z is disjoint from X;. z-Transportability also generalizes
transportability which requires that the causal effect of X on Y in the target
domain be estimable from experiments on any subset of all observable variables
in the source domain. We first generalize z-identifiability to allow cases
where Z is not necessarily disjoint from X. Then, we establish a necessary and
sufficient condition for z-transportability in terms of generalized
z-identifiability and transportability. We provide a correct and complete
algorithm that determines whether a causal effect is z-transportable; and if it
is, produces a transport formula, that is, a recipe for estimating the causal
effect of X on Y in the target domain using information elicited from the
results of experimental manipulations of Z in the source domain and
observational data from the target domain. Our results also show that
do-calculus is complete for z-transportability.
