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Does somebody know if there exist results and estimators to deal with controls in IV estimation under heterogeneous treatment effects, analogous to Abadie's Kappa (2003) for the binary case?

Abadie, Alberto, “Semiparametric Instrumental Variable Estimation of Treatment Response Mod- els,” Journal of Econometrics, 2003, 113 (2), 231–263.

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No. There is not. I tried working on deriving one for a while. I struggled for a month, failed, and then emailed some contacts at the University of Chicago to ask if they had any ideas. My buddy asked Alex Torgovitsky who said something like "the concept of a complier is quite tied to the existence of a binary treatment, so it's really not obvious how the result could generalize".

Good luck. I'd be delighted if someone has a better answer.

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  • $\begingroup$ Thanks! Somewhat surprised about Torgovitsky's comment, since I thought for continuous instruments / treatments without controls there is a way to interpret the estimates as average causal responses. Angrist covers it in his IV slides p. 32 ff, there is also a section in MWE about it. ocw.mit.edu/courses/… Compliers are those moved from intensity s to intensity s'. $\endgroup$
    – Papayapap
    Sep 27, 2023 at 13:18
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    $\begingroup$ Oh, you can get an interpretation as an Average causal response when estimating via 2SLS and a nonbinary treatment. Abadie's Kappa is about getting the characteristics of compliers though. $\endgroup$ Sep 27, 2023 at 15:36
  • $\begingroup$ Yea, that also. In my case, I am more interested to avoid the criticism that when including X linearly I will not get a positively weighted average of LATEs dropbox.com/s/7ub35oqau2if7qb/tsls-weights%20%281%29.pdf?dl=0. That can be also done with Abadie's Kappa and using IPW (in binary case). $\endgroup$
    – Papayapap
    Sep 27, 2023 at 16:52

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