Graphical Interpretations of Rank Conditions for Identification of Linear Gaussian Models

The literature on graphical models and the literature on identification pursue similar goals, but do not use entirely each other's results, because represent them in different languages. To ease the communication between these fields, I translate the most important theorems on identification of linear Gaussian Simultaneous Equations Models (SEMs) and Structural Vector Autoregressions (SVARs) into the language of graphical models. I propose graphical interpretations of the rank conditions for identification of SEMs, of the rank condition of Rubio-Ramirez et al (2010) for identification of SVARs with linear and nonlinear restrictions, and of the theory of partial identification for SVARs