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Compulsory introduction
I repeatedly take into consideration the aim of pre-trends in diff-in-diff. And it’s most likely as a result of the brand new estimators permit one, through completely different syntax decisions in econometricians’ personal papers and authored R and Stata code, to select alternative ways to calculate the pre-trends. So I assumed I’d simply publish a brief substack immediately, not a lot arguing there’s a proper or mistaken strategy to do these pre-trends (although I’ve a robust opinion), however to supply up my very own beliefs about why we do pre-trend exams within the first place.
Falsifiable Hypotheses
I believe, personally, that the rationale we put up pre-trend exams in diff-in-diff is identical motive we take a look at issues like covariate stability and re-estimating our fashions on the pre-treatment interval (even outdoors of a diff-in-diff). And that’s as a result of we are attempting to supply proof for the figuring out assumptions. I’m placing this beneath a heading of falsifiability as a result of I need to hyperlink the considerably a-theoretical method to causal inference within the Rubin potential outcomes custom with one thing extra akin to falsifiability within the Popper-Friedman custom of scientific theories.
Beneath the Popper-Friedman custom of falsifiability being a key a part of any scientific principle, what you’re sometimes doing is wanting “out of pattern” on the logical penalties of the mannequin, however empirically — not theoretically. So if the comparative statics of the mannequin does one thing like “and never solely must you see results right here, they need to be exactly one thing else over right here”. You’ll be able to see that in Einstein’s principle of relativity even — his “mannequin of actuality” made an especially exact prediction in regards to the bending of sunshine round giant objects. And astronomers and physicists solely managed to work this out a number of years after its publication with an ingenious pure experiment method utilizing an eclipse. I wrote about this within the first version of the Mixtape (within the triple diff subsection the place I focus on the third chapter of my dissertation — essentially the most illogical place to place this admittedly). Take a look at this cool image my buddy Seth Hahne drew for me within the e book too.
