DiD with multiple periods: How many pre-treatment periods to include

[Emil Alnor]

Asking this as a generic question, so say, my data is repeated cross-sectional, some treatment happened in 2007 (e.g. a university teaching reform), I want to examine the effect on some outcome (e.g. wage of its graduates) and I have data going back all the way to 1980. If I write my DiD up as:

 
 regress outcome i.treatment i.clustervariable i.timevariable, cluster(clustervariable)

...then including all years back to 1980 would increase my n, but intuitively would not be correct. So what is the rule of thumb here / what are some considerations on how many pre-treatment periods to include? Those where the parallel trends assumption seems to hold? Back untill some exogenous shock relevant to the outcome happened to the treated/control units?

[Maxence Morlet]

The main question to ask yourself is whether the intervention is plausibly exogenous with respect to your outcome (at the very least conditional on your covariates).

That is the most important for parallel trends, not the number of pre-treatment periods included.

As an aside, the classical DiD setup for repeated cross section is:

reg outcome covariates i.time [FE vectors depending on sources of variation] i.post#i.treat, cluster(clustvar)

It depends on the number of clusters you have as well.

It will be difficult to convince readers that your results are causal because in a repeated cross-section, you cannot include unit fixed effects, so systematic differences between units will subsist.

[Maxence Morlet]

Check out the paper by Wooldridge (2021) and the community-contributed command

sdid

[Emil Alnor]

Maxence Morlet Thanks for your reply. My question is not so much how to make the parallel trends most justifiable, more how much can I increase my n without biasing the model. I have an idea that this is somewhat parallel to the bias-efficiency tradeoff discussion when choosing how to do a propensity-score-matching design, but I am seeking inputs on how this "bias-efficiency" tradeoff plays out in a DiD setup.

With regards to your code, I am quite sure this similar to how I originally thought I should write the DiD regression using reg in this post https://www.statalist.org/forums/for...-a-reg-command but Andrew Musau proposed to do it the way I write in this post instead. As I understand it, your code will include a dummy for the post period (as a result of i.post#i.treat) in addition to dummies for the individual periods, whereas my code will only include dummies for the individual periods which is more efficient. Please do comment if I misunderstand anything here.

With regards to -sdid-, as I understand it, it implements the procedure explained by Arkhangelsky et al., (2021) and is only useable on panel data. I am not aware of Woolridge (2021) which explains a -sdid- in Stata, but would much appreciate if you could send me the full reference.