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My understanding of LATE was that it was the effect of a treatment on individuals who were induced to be treated by the experiment. That is, the effect on compliers. My understanding of Treatment-on-the-treated (TOT) is that it is the effect of individuals who are in the treatment group (which can include both individuals who were induced to be treated, and always-takers who would have accepted the treatment regardless)

However, my notes say the opposite -- that TOT is a subset of LATE, and that LATE allows for the existence of treated individuals who would have been treated even in the absence of experiment. But I don't really understand why one of them is capturing always-takers and the other isn't

What is the right way to think about this?

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  • $\begingroup$ I don't know anything about this subject, but I believe that should be "compliers", not "compilers". $\endgroup$ – Mark L. Stone May 10 '16 at 21:30
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    $\begingroup$ obviously. I never wrote "compilers." $\endgroup$ – Parseltongue May 10 '16 at 22:06
  • $\begingroup$ @Parseltongue Is TOT the same thing as ATET? $\endgroup$ – Dimitriy V. Masterov May 11 '16 at 0:44
  • $\begingroup$ if ATET is average treatment effect on the treated-- yes, it sounds the same. $\endgroup$ – Parseltongue May 11 '16 at 1:07
  • $\begingroup$ I would agree with your first interpretation! ToT/ATET is a larger set! Which notes do you have? $\endgroup$ – Matifou May 12 '16 at 0:03
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LATE is a subset of TOT....I quote from Mastering 'Metrics by Angrist and Pischke:

"Researchers and policy makers are sometimes interested in average causal effects for the entire treated population, as well as in LATE. This average causal effect is called the treatment effect on the treated (TOT for short)" (Chapter 3 Section 1)

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