Testing parallel trends assumption in Poisson DiD model

[Christoph Mueller]

Dear experts, this is my first post in this forum, from which I already learned so much (but obviously not enough so far).

To the case: I am trying to determine the effect of a binary treatment (funding program for organizations) on a count variable (number of received grants from another program per organization). I have panel data (from 2007 to 2021) for a treatment and a control group, the treatment starts at 2019.

I used the following code for estimating a Poisson Difference-in-Difference model and getting the treatment effect in form of an incidence rate ratio:

xtpois grant_number i.treat##i.post i.year, fe robust irr

(where
treat = binary treatment variable
post = period from 2019)

Hoping I was correct with estimating the model, there is one thing I couldn't find out so far, namely to test the parallel trends assumption for this model. As I have read other-where, testing this assumption works differently with count data models compared with a linear approach (for which I could have used the built-in post-estimation command(s) in xtdidregress). Unfortunately, I couldn't find out how to do it by my selves in Stata.

I would be very happy about a hint.

[Maxence Morlet]

1. I would recommend the community-contributed command ppmlhdfe.

2. You cannot test the // trends assumption, merely make it more plausible. For instance, you can produce a graph of trends and eyeball it to see if they are parallel. You can also do a conditional means comparison in the pre-treatment period, and if the mean of the control diverges significantly from that of the treatment, this makes the // trends assumption less plausible.

However, the most important thing is to argue in favour of the exogeneity of your intervention (using words). Even if you produce a graph with parallel trends, however the reader does not believe (intuitively) that the intervention is exogenous with respect to the outcome, you'll have a hard time convincing people that your results are causal.

Wooldridge (2021) discusses this at length.

Hope this helps

[Christoph Mueller]

Thanks a lot, that really helps!