honestly re-reading my comment, that is a very fair question. That part was very poorly phrased.
I think what I had in mind is that the issue with continuous DID goes away if you assume constant effect sizes that are linear in treatment effect. When this doesn’t hold, you start to estimate some weird parameter, which Goodman-Bacon, Sant’Anna, and Callaway describe in detail in the link you provided.
I like this paper because it tells us what happens under misspecification, which is exciting because in practice everything is misspecified all the time! But a concern I have with interpreting it is that I think the problem is inherent to linear regression, not the DID case specifically, which means we should really have this kind of problem in mind any time anybody linearly controls for anything.
(So maybe a better way of phrasing this would have been “we should be this nervous all the time, except in cases where misspecification doesn’t matter” rather than “it isn’t a huge issue here.”)
honestly re-reading my comment, that is a very fair question. That part was very poorly phrased.
I think what I had in mind is that the issue with continuous DID goes away if you assume constant effect sizes that are linear in treatment effect. When this doesn’t hold, you start to estimate some weird parameter, which Goodman-Bacon, Sant’Anna, and Callaway describe in detail in the link you provided.
I like this paper because it tells us what happens under misspecification, which is exciting because in practice everything is misspecified all the time! But a concern I have with interpreting it is that I think the problem is inherent to linear regression, not the DID case specifically, which means we should really have this kind of problem in mind any time anybody linearly controls for anything.
(So maybe a better way of phrasing this would have been “we should be this nervous all the time, except in cases where misspecification doesn’t matter” rather than “it isn’t a huge issue here.”)
This paper makes that point about linear regressions in general.