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We developed a novel approach to identification and model testing in linearstructural equation models (SEMs) based on auxiliary variables (AVs), whichgeneralizes a widely-used family of methods known as instrumental variables.The identification problem is concerned with the conditions under which causalparameters can be uniquely estimated from an observational, non-causalcovariance matrix. In this paper, we provide an algorithm for theidentification of causal parameters in linear structural models that subsumesprevious state-of-the-art methods. In other words, our algorithm identifiesstrictly more coefficients and models than methods previously known in theliterature. Our algorithm builds on a graph-theoretic characterization ofconditional independence relations between auxiliary and model variables, whichis developed in this paper. Further, we leverage this new characterization forallowing identification when limited experimental data or new substantiveknowledge about the domain is available. Lastly, we develop a new procedure formodel testing using AVs.

Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables