  We developed a novel approach to identification and model testing in linear
structural equation models (SEMs) based on auxiliary variables (AVs), which
generalizes a widely-used family of methods known as instrumental variables.
The identification problem is concerned with the conditions under which causal
parameters can be uniquely estimated from an observational, non-causal
covariance matrix. In this paper, we provide an algorithm for the
identification of causal parameters in linear structural models that subsumes
previous state-of-the-art methods. In other words, our algorithm identifies
strictly more coefficients and models than methods previously known in the
literature. Our algorithm builds on a graph-theoretic characterization of
conditional independence relations between auxiliary and model variables, which
is developed in this paper. Further, we leverage this new characterization for
allowing identification when limited experimental data or new substantive
knowledge about the domain is available. Lastly, we develop a new procedure for
model testing using AVs.
