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these posts by my pal @Andrew___Baker are way too pessimistic about the current state of design-based potential outcomes applied micro (thread)
the death of IV has been greatly exaggerated. input costs, shift-share with exogenous industry level shocks, examiner IV, and many other Classic IV Designs are appropriate in many contexts https://arxiv.org/abs/1806.01221
Alwyn Young showed that a selection of IV regressions were highly leveraged. so IV clearly has to raise the bar for inference. bootstraps and pre-analysis will help. but this is more typical gradual scientific progress than a funeral, imo
Andrew Gelman cherry-picks RD papers that don't use good inference and do polynomial curve over-fitting bc he is a scold and loves trolling Jim Heckman; but those are not representative of the state of the art RD. one randomly chosen example of the latter: https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20171019
note that the above paper uses Cattaneo et al robust nonparametric confidence intervals, which basically every RD paper now has to use. you could do an Alwyn Young-style review of early RD papers and find leverage. but now things have changed for the better
to my knowledge the authors of the new DiD papers have shown that regression methods *can* be biased with staggered timing, but haven't *yet* majorly over-turned or reversed sign of results of any big papers. the example from @agoodmanbacon 's opus:
note that many event studies don't rely on staggered implementation. and you do see some truly beautiful pre-trends these days, esp with matching in admin data. look at this beauty from @michaelstepner jmp 
by the way, Michael's event-study would be vulnerable to the staggered implementation critique if thrown into one big regression, but he pools event-studies by averaging to get around it. so papers are already adapting for the better
Andrew asks if we "know the model[s] really well." for inference arguably not, but in terms of IDENTIFICATION, we do. everyone and their dog can critique the PO designs. that's NOT true of DAGs: there are ZERO papers that derive identification from a DAG https://twitter.com/fuiud/status/1193456645419847680
the PO designs (IV, RD, DD) are not a panacea and social science is insanely hard and still basically impossible, but i am much more optimistic than Andrew. many economists hate them for quasi-philosophical reasons. imo it's OK for the rest of us to love them, responsibly 
