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Borusyak, 2021 has a sentence

First, we note that failing to rule out anticipation effects in “fully-dynamic” specifications (with all leads and lags of treatment included) leads to an underidentification problem, where the dynamic path of anticipation and treatment effects over time is not point-identified

I am wondering what do "underidentification" and "point-identified" mean in this case? I ask these words here because these words are not in the vocabulary (I checked with Cambridge dictionary) and I believe it belongs to econometrics words.

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A parameter is "identified" if it can be known from an infinite amount of data. "Underidentified" thus means, "even if we had infinite data, we could never learn the true parameter".

"Point identified" contrasts with "set identified" with "point" meaning, "we know the exact value" and "set" meaning "we have a set and know the true value is in the set".

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    $\begingroup$ Thank @Michael, I am wondering if "Identified" also means if we have enough data, we will have the more precise result, or something similar to that? $\endgroup$
    – Phil Nguyen
    Commented Sep 15, 2021 at 22:37
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    $\begingroup$ And, a very clear and great answer, thank Micheal! $\endgroup$
    – Phil Nguyen
    Commented Sep 15, 2021 at 22:43
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    $\begingroup$ "Identified" makes no comment on the variance (precision) of an estimator. "Efficiency" or a presentation of the asymptotic distribution are the key things to look for regarding precision. $\endgroup$
    – Michael Gmeiner
    Commented Sep 16, 2021 at 7:36

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