Dealing with parallel trends violations

[Collin James]

Hello,

I am trying to implement the following solution from a paper on a diff-n-diff that has a parallel trends violation. My question is the following:

I have the following regression: y=treat+post+treat*post + covariates + dummies_all_post_intervention
--This paragrahp by Bilinski and Hatfield (2019) notes that the treatment effect is the average of all the dummies. How should I think about obtaining this? Can you assist? TIA- CJ

[Maxence Morlet]

Suppose a classical two way fixed effects model with difference-in-difference specification:

xtreg outcome i.time#i.treated, fe cluster(unit_var)

If before the treatment time one interaction term above is significant, this means the parallel trends assumptions is relatively implausible, as there is suggestive evidence of differential pre-trends.

This would however give you CV1 standard errors, which may over-reject in finite samples. You may want to look into the community contributed command summclust.

[Collin James]

So, I definitely have a parallel trends violation. I am trying to figure out how to deal with it by controlling for differential trends within my equation following Bilinski (2019)

[Maxence Morlet]

If pre-trends are not parallel, there's really nothing substantial you can do about it. If your field is economics, it will be quite causal to convince your readership that your results are causal.

Your best bet is to use the community contributed command sdid, but that will not just magically remove endogeneity.

[Jared Greathouse]

How many treated units? As Max says, the real way you deal with this is by not fooling with DD, and instead use SDID, SCUL (by me), or plain old fashioned synthetic controls (allsynth, for example).