  Causal models communicate our assumptions about causes and effects in
real-world phe- nomena. Often the interest lies in the identification of the
effect of an action which means deriving an expression from the observed
probability distribution for the interventional distribution resulting from the
action. In many cases an identifiability algorithm may return a complicated
expression that contains variables that are in fact unnecessary. In practice
this can lead to additional computational burden and increased bias or
inefficiency of estimates when dealing with measurement error or missing data.
We present graphical criteria to detect variables which are redundant in
identifying causal effects. We also provide an improved version of a well-known
identifiability algorithm that implements these criteria.
