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Borusyak, 2021 has a sentence

We show that this estimator takes a particularly transparent form under unrestricted treatment effect heterogeneity, while our construction also yields efficiency when some restrictions on treatment effects are imposed.

I am wondering what does under unrestricted treatment effect heterogeneity mean? I translate it to that "when the treatment effect heterogeneity is not restricted", and it also means that this situation works in both cases "treatment effect heterogeneity" and "treatment effect homogeneity". Is it a correct thought?

I did ask this in the English Learner but they said this content is beyond the English language question.

The answer from English learner's expert is

However, I am more inclined to interpret it as "the transparency of our estimator when there are no restrictions is greater than the transparency of other people's estimator when there are no restrictions" and "the efficiency of our construction when there are restrictions is greater than the efficiency of other people's construction when there are restrictions."

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"unrestricted treatment effect heterogeneity" means the effect of treatment can differ for each individual, and there are no assumptions or limitations on how the effect differs.

Diff-in-diff models using twoway fixed effects with heterogeneous treatment effects and heterogeneous treatment times are known to be biased. Sun and Abraham 2020 is a major reference.

This idea has very recently become a hot topic in econometrics. While I haven't read the paper you cite, it appears to be pushing this idea forward even more.

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  • $\begingroup$ @Micheal , exactly this idea, it is mainly about the heterogeneous treatment onset. Just the language confuses me a little bit. Thanks a heap $\endgroup$
    – Phil Nguyen
    Sep 16, 2021 at 9:49
  • $\begingroup$ I think "Diff-in-diff models using twoway fixed effects with heterogeneous treatment effects and heterogeneous treatment times are known to be biased" should be " "Diff-in-diff models using twoway fixed effects with homogeneous treatment effects and heterogeneous treatment times are known to be biased". Is it correct? $\endgroup$
    – Phil Nguyen
    Sep 16, 2021 at 9:52
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    $\begingroup$ I don't think so. I think if treatment effects are homogeneous, then things are fine. The Sun and Abraham results (theorem 3) would imply this. There is of course a chance I am unaware of something. $\endgroup$
    – Michael Gmeiner
    Sep 16, 2021 at 10:00
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    $\begingroup$ Ah yeah, it is what I mean, if the treatment effect is homogeneous (very rare case), things are fine. I may mistranslate your words. $\endgroup$
    – Phil Nguyen
    Sep 16, 2021 at 10:01

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