In this paper, we address the problems of identifying linear structural equation models and discovering the constraints they imply. We first extend the half-trek criterion to cover a broader class of models and apply our extension to finding testable constraints implied by the model. We then show that any semi-Markovian linear model can be recursively decomposed into simpler sub-models, resulting in improved identification and constraint discovery power. Finally, we show that, unlike the

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... g methods developed for linear models, the resulting method subsumes the identification and constraint discovery algorithms for non-parametric models. 1 We will also use the term "identified" with respect to individual variables and the model as a whole.