SMU SOE Seminar Series (April 10, 2025): Stochastic Compliance and Identification of Treatment Effects

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ABSTRACT

The exclusion restriction plays a key role in the identification of LATE (Imbens & Angrist (1994), Angrist, Imbens & Rubin (1996)). We discuss a particularly ubiquitous way in which the exclusion restriction would seem to be generically violated. We argue that this form of violation is not addressed in the many applications that rely on this influential framework. We characterize the bias that this particular violation gives rise to and, more constructively, discuss how to use the particular structure of the violation along with milder assumptions and additional data to restore identification. We provide sharper bounds by exploiting the specific structure of the exclusion restriction violation we uncover. Further, with an additional assumption which is plausible in many empirical settings, we restore point identification of LATE. We illustrate with examples and discuss why this violation is likely present in most existing empirical applications. We discuss how our arguments naturally extend to other IV settings where the LATE parameter is commonly invoked, such as randomized controlled trials with imperfect compliance and fuzzy regression discontinuity designs. Moving beyond LATE, we also consider how the same problems and solution ideas apply to identification of the MTE profile and more structural "Roy" models of treatment effects.

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