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Borusyak (2021) writes:

The first lead,..., is often excluded as a normalization.

In a dynamic two-way fixed effect model, when we included some leads and lags, we normally exclude the first lead. Can I ask what is the reason behind that?

Thomas Bilach
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Phil Nguyen
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1 Answers1

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The principal reason is to provide a reference period. If you saturate your model with a full set of lead and lag indicators, then you must omit a period as a reference. Evaluators typically select the period before policy adoption, though you could choose a more distant pre-period. Assuming we don't have any anticipatory concerns to address before treatment actually starts, then it's quite common to drop the first lead.

Thomas Bilach
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  • thanks a heap, but why in this post, you did not exclude the first lead then? https://stats.stackexchange.com/a/531748/319998 – Phil Nguyen Sep 16 '21 at 23:15
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    That equation generalizes to whatever lead/lag structure you feel is appropriate. Note that you don't have to omit the first lead. If you want, you can omit the third lead. Maybe you want to get a sense of how important anticipation is in the period right before treatment starts. In some papers, I've seen authors estimate just the first and second lead, ignoring the more distant periods. In my interpretation, all the periods before the second lead serve as a reference. In short, I've seen so many lead/lag variations that I cannot say there is one perfect structure. – Thomas Bilach Sep 16 '21 at 23:22