I remember seeing such a comment on Twitter long time ago but I see so many prominent papers doing it that I doubt it can really bad. Does somebody know more (e.g. papers) on this?
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$\begingroup$ just because something is done in many papers does not mean its a good idea, it wasn't that long ago when even top papers ignored the requirement for first stage to have sufficient F-statistics leading to, thankfully now bygone, era of publications with wrong instruments $\endgroup$– 1muflon1 ♦Commented Mar 24, 2023 at 14:53
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Is matching combined with Diff-in-Diff a bad idea?
No.
But, as with anything, it depends on the context. One point to consider is that you should match on pre-treatment characteristics, because treatment can affect the variables used for matching.
All usual caveats of both approaches still apply, but I'm not aware of any literature diving deep into this combination per se.
