From Correlation to Causation: Econometric versus Computer Science Approaches
We compare approaches to identification of structural models developed in econometrics and computer science literature. In the econometric literature we consider the method of instrumental variables, the rank condition for simultaneous equations models, and various conditions for identification from the theory of structural vector autoregressions. In the computer science, we consider the literature on causality within the theory of probabilistic graphical mo-dels. Most results have been translated into two languages: the language of linear algebra, which is ubiquitous in econometric literature, and the language of graphical models, which is popular in computer science. Each approach that we consider has its relative advantages and weaknesses: the approach developed in computer science is more flexible when working with intricate structural shocks independence structures, and the approach developed in econometrics is more efficient for cyclical models. We also propose a unifying procedure for identification that uses advantages of both approaches. Using this procedure, the researcher can easily translate the results from one branch of the literature into the language of the other, and fully or partially identify new models, which could not be identified using any of the considered approaches separately from the others. We also review the literature on data-oriented identification, where the identification restrictions are not only theoretically justified, but also fully or partially empirically verified. Most results are formulated within linear Gaussian models; however, the unifying procedure of identification easily generalizes to nonlinear, non-Gaussian, or even nonparametric models.