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Borusyak, 2021 has a sentence

Third, in dynamic specifications, implicit assumptions about treatment effect homogeneity lead to the spurious identification of long-run treatment effects for which no DiD contrasts valid under heterogeneous treatment effects are available

In staggered DiD, I understand that the dynamic specification is to use the leads and lags in a model to capture the dynamic of treatment effects.

I also understand treatment effect homogeneity is a disadvantage of standard DiD in staggered laws implementation cases (rolling-pout event dates) because it does not account for the heterogeneous effects during the treatment onset.

I understand that "spurious relationship" is

The spurious relationship is said to have occurred if the statistical summaries are indicating that two variables are related to each other when in fact there is no theoretical relationship between two variables

But I do not understand why homogeneous treatment assumption leads to "spurious identification of long-run treatment" in staggered DiD as quoted in the above sentence. In large, I did not catch the theme of the sentence in this paper

Third, in dynamic specifications, implicit assumptions about treatment effect homogeneity lead to the spurious identification of long-run treatment effects for which no DiD contrasts valid under heterogeneous treatment effects are available.

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    $\begingroup$ Is the author commenting on the role of heterogeneous treatment effects? Is the author perhaps saying "If the effect is heterogenous, but we assume homogeneous, then there are problems"? $\endgroup$
    – Michael Gmeiner
    Commented Sep 16, 2021 at 9:05
  • $\begingroup$ Hi @MichaelGmeiner, they implied excatly what you mean ""If the effect is heterogenous, but we assume homogeneous, then there are problems"?. And the author also says that heterogeneous is almost the case in this econometric setting. Thanks a heap. $\endgroup$
    – Phil Nguyen
    Commented Sep 16, 2021 at 9:37

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As I understand it, the issue is the following:

  • Under the assumption of homogeneous treatment effects, you can estimate long run treatment effects.
  • On the other hand, if treatment effects are heterogeneous, these long run treatment effects are not identified (as eventually everyone gets treated, there are no control group anymore).
  • This means that identification of the long run treatment effect relies on the homogeneous treatment assumption.
  • The homogeneous treatment assumption is an assumption that the authors believe to be not credible or which is often used too implicit (i.e. taken for granted) in existing papers.

The term "spurious identification" is (to my knowledge) not standard (but I might be wrong as this is a fast evolving literature). You can talk about spurious correlation as correlation which is not causal. So I guess spurious identification related to identifying something that should not be identifiable (as it relies on non-credible assumptions).

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