Identi cation and Identi cation Failure for Treatment E ¤ ects using Structural Systems

We provide necessary and su¢ cient conditions for e¤ect identi…cation, thereby characterizing the limits to identi…cation. Our results link the non-structural potential outcome framework for identifying and estimating treatment e¤ects to structural approaches in economics. This permits economic theory to be built into treatment e¤ect methods. We elucidate the sources and consequences of identi…cation failure by examining the biases arising when the necessary conditions fail, and we clarify the relations between unconfoundedness, conditional exogeneity, and the necessary and su¢ cient identi…cation conditions. A new quantity, the exogeneity score, plays a central role in this analysis, permitting an omitted variable representation for e¤ect biases. This analysis also provides practical guidance for selecting covariates and insight into the price paid for making various identifying assumptions and the bene…ts gained. JEL Classi…cation Numbers: C10, C20, C30, C50.

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