Difference-in-difference robustness (all control variables interact with #post)

[Rudolf Velt]

Dear sir/madam,

I found a paper where the authors use a difference-in-difference approach and as a robustness check they interact all their control variables with their #post dummy. Could anyone explain if this is a common robustness check for difference-in-difference and what the rationale behind it is (instead of just adding the controls without interaction)?

I am referring to the following paper: Title: "When investors call for climate responsibility, how do mutual funds respond?", Authors: Ceccarelli , Ramelli & Wagner (2019), page 50.

Thank you very much in advance.

Kind regards,
Rudolf

[Carlo Lazzaro]

Rudolf:
as far as I know, there's no a hard and fast rule that can help in spotting an universal approach for robustness check after regression.
That said:
1) whenever we talk about robusteness, we should define robustness against what? (model misspecification; heteroskedasticity; else);
2) the aim of each regression is to give a fair and true view of the data generating process the reseracher is interested in. Hence, the issue is whether, according to theory, -Post- predictor shoud have been included in the right-hand side of the regression equation at the beginning or not;
3) Authors' original aim seems more in line with performing a set of sensitivity analyses than with a robustness check;
4) from Table A2, it is not clear whether Authors (who used the Stata community-contributed module -reghdfe-) reported the within or the overall R_sq.

[Maxence Morlet]

Dear Rudolf,

You may want to have a look here: https://www.statalist.org/forums/for...end-assumption

Tom Scott provided a great answer to test the plausibility of the parallel trends assumption in the abovementioned post, the most important assumption of diff-in-diff. In the pre-treatment period, you may want to interact regress your dependent variable on time dummies, treated dummy, and an interaction of the two. If the interaction term is significant, this suggests the parallel trends hypothesis may be violated as trends between treated and control were already deviating prior to the policy's implementation.

The other assumptions can only be argued and not tested to the best of my knowledge: no anticipation effects prior to policy implementation, no displacement effects from treated to control, plausible exogeneity of policy.