Difference in differences when the effect starts in the year of the treatment

[Mateus Maciel]

I want to ask for help with the following issue that I am facing with this data set. I want to analyze the impact of a drought on the tariff level of water-regulated and unregulated firms. The drought happened in 2014, meaning the treatment would start this year. Moreover, the treated group is the firms that are regulated, and the control group is the unregulated firms. Therefore, I am running the following command:

xtdidregress (tarifa $controles) (did), group(id) time(ano)

Then, I got the following out:

I want to test for the parallel trend assumption. Thus, I ran the following command:

estat trend plots

Then, I obtained the following graphs:

My main issue is that the command fixed the horizontal line one year (ano) before the treatment, which is why it was in 2013. The treatment (drought) occurred in 2014, but the tariff was already increased in 2014 in response to the exogenous shock. Therefore, the difference in the tariff level between the treated and not treated groups starts in the year of the treatment and not one year before (2015). My doubt is: in this setup, would the diff-in-diff approach be valid? If I had monthly data, I would have a different pattern in the graph as I could use the exact month of the drought as the treatment timing. Nevertheless, I do not have it.

[Clyde Schechter]

I don't think the simple DID design you are using applies to your data. You have two different "treatments" in play here: the drought, and regulatory status, and your research question, as best I can understand it, is whether the drought effect is modified by regulatory status. In a simple DID design there can be only one treatment.

For what you are trying to do, you need a different analysis. You need firms in each of four conditions in each of two time periods: regulated+drought, regulated + no drought, unregulated + drought, unregulated + no drought, both before and after the drought year. Now, from your description in #1, it appears, if I understand it correctly, that you have only firms that did experience the drought. Without a no-drought control group, you cannot do a full identification of causal effects: your analysis would reduce to the level of a simple pre-post comparison on the drought treatment, though it would be DID-like for the regulatory effect.

I'm accustomed to doing these analyses "from scratch" rather than using the convenience DID commands that recent versions of Stata have added, so I haven't learned the details of things like where xtdid applies the cutoff. Suffice it to say, if you do your analysis "from scratch" you can easily control this:

gen pre_post = year >= 2014 if !missing(year)
xtreg tarifa i.regulated##i.pre_post covariates, fe

If you had the full 8-fold data that I describe in the second paragraph, then it would be

gen pre_post = year >= 2014 if !missing(year)
xtreg tarifa i.regulated##i.drought#i.pre_post covariates, fe

[Mateus Maciel]

Dear Clyde Schechter, what you said makes a lot of sense. Thanks again for the helpful comments.