  In this paper, we extend graph-based identification methods by allowing
background knowledge in the form of non-zero parameter values. Such information
could be obtained, for example, from a previously conducted randomized
experiment, from substantive understanding of the domain, or even an
identification technique. To incorporate such information systematically, we
propose the addition of auxiliary variables to the model, which are constructed
so that certain paths will be conveniently cancelled. This cancellation allows
the auxiliary variables to help conventional methods of identification (e.g.,
single-door criterion, instrumental variables, half-trek criterion), as well as
model testing (e.g., d-separation, over-identification). Moreover, by
iteratively alternating steps of identification and adding auxiliary variables,
we can improve the power of existing identification methods via a bootstrapping
approach that does not require external knowledge. We operationalize this
method for simple instrumental sets (a generalization of instrumental
variables) and show that the resulting method is able to identify at least as
many models as the most general identification method for linear systems known
to date. We further discuss the application of auxiliary variables to the tasks
of model testing and z-identification.
