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Apart from paralell trend assumption, another assumption in parallel trend is strict exogeneity. I have read this answer from Thomas and this paper of Miller. The strict exogeneity in Miller is described in his third equation:

enter image description here

It seems to me that it is the additional effect of treatment group after the event date, I am wondering it is a correct thought and whether it is a must in DiD setting? Normally, I just think the parallel assumption is the main one to be satisfied before conducting a DiD test.

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    $\begingroup$ In equation (3) the positive values for $\gamma_s$ represent the treatment leads. In your question, though, you state that this is the additional effect of treatment "after" the event date. Could you provide clarification here? I think these refer to the periods before treatment actually starts. $\endgroup$
    – Thomas Bilach
    Commented Sep 16, 2021 at 23:14
  • $\begingroup$ @Thomas, yes, they said "leading" but leading in their case is later (equalling to lag in normal understanding) "be tested by including leading (i.e., later) measures". I am quite confused here. $\endgroup$
    – Phil Nguyen
    Commented Sep 16, 2021 at 23:40

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