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One of the most common mistakes made when performing data analysis isattributing causal meaning to regression coefficients. Formally, a causaleffect can only be computed if it is identifiable from a combination ofobservational data and structural knowledge about the domain underinvestigation (Pearl, 2000, Ch. 5). Building on the literature of instrumentalvariables (IVs), a plethora of methods has been developed to identify causaleffects in linear systems. Almost invariably, however, the most powerful suchmethods rely on exponential-time procedures. In this paper, we investigategraphical conditions to allow efficient identification in arbitrary linearstructural causal models (SCMs). In particular, we develop a method toefficiently find unconditioned instrumental subsets, which are generalizationsof IVs that can be used to tame the complexity of many canonical algorithmsfound in the literature. Further, we prove that determining whether an effectcan be identified with TSID (Weihs et al., 2017), a method more powerful thanunconditioned instrumental sets and other efficient identification algorithms,is NP-Complete. Finally, building on the idea of flow constraints, we introducea new and efficient criterion called Instrumental Cutsets (IC), which is ableto solve for parameters missed by all other existing polynomial-timealgorithms.

Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets