[Clyde Schechter]

For parallel trends analysis the outcome variable should always be the same variable used as the outcome in the DID analysis. The whole idea is to show that prior to the intervention, the treatment and control entities' outcomes overall were evolving similarly.

[Annika Katharina]

Thank you! I know how to test this assumption graphically (by comparing means for both groups over the years), however, is there a way to test for parallel trends employing a statistical test rather than graphically comparing trend lines?

[Clyde Schechter]

If you want to do it with a statistical test, which I do not recommend, you can simply regress your outcome variable against treatment group, time, and treatment group#time interactions using only pre-intervention observations. A test of the interaction term(s) is then a test of the parallel trends assumption.

[Annika Katharina]

Great, thank you! With regards to your statement below from a few posts back, would I look for statistically not significant levels of my in_treatment variable with coefficients being close to zero? If that is not the case, how could the outcomes be explained?

And yes, you should do robustness checks where you move every treatment start date forward one or more years, and another where you move every treatment start date backward one or more years.

[Clyde Schechter]

With regards to your statement below from a few posts back, would I look for statistically not significant levels of my in_treatment variable with coefficients being close to zero?

Basically, yes. For my part, I would ignore statistical significance and focus on the coefficients being close to zero. But if you are working in the framework of null hypothesis significance testing, then you would look at statistical significance as well.

[Annika Katharina]

One more question regarding something you mentioned a while back. Say I want to check development of treatment effects over the years applying what you outlined here.

So it sometimes makes sense to have a polytomous in_treatment variable. You code it 0 before treatment, 1 in the first year of treatment, 2 in the second, etc. This allows for the treatment effect to vary independently from year to year following inception. Each year's effect is estimated in the coefficient of the corresponding level of in_treatment. That is, the treatment effect in year 4 is given by the coefficient of 4.in_treatment. What is typically observed is that the treatment effect increases for a while, reaches a peak some number of years out, and then declines again. Whether it rises sharply or gradually, and decays sharply or gradually depends on the particular treatment and the environment in which it is operating. But, you are now introducing a lot more variables, and if you are to get usefully precise estimates of their coefficients, you need an ample number of observations in each level of in_treatment (including the 0 level). There is no hard and fast rule about how many observations constitute an ample number, a good rule of thumb is that you need 50 observations for each level, and would prefer to have 100 or more.

Then, for post-treatment observation, it would be 0 for all observations of my control group, whereas it would be 0 for the year prior to treatment and then 1, 2, 3, ... for the years following the first introduction of treatment for the treated firms.

If I were to also use this approach to look at pre-treatment values, I obviously cannot use negative data. Thus, I would transform my -1, -2, -3, ... years of the treatment group into positive values by adding +x. Which values would my control observations take then? I assume it should be x rather than remaining 0?

In addition, I found the following command to mitigate concerns of staggered DiD and compare outcomes:

eventstudyinteract

Based on the information below, if you have insights regarding this topic, could you by any chance advise me on how to populate this command

https://lost-stats.github.io/Model_Estimation/Research_Design/event_study.html

[Clyde Schechter]

If I were to also use this approach to look at pre-treatment values, I obviously cannot use negative data. Thus, I would transform my -1, -2, -3, ... years of the treatment group into positive values by adding +x. Which values would my control observations take then? I assume it should be x rather than remaining 0?

No. In this context, you would code all pre-treatment values as 0, and you would code all control observations as 0 as well. There should never be any -1, -2, -3... to transform in the first place.

eventstudyinteract

I am not familiar with this command and have no advice to offer regarding its use.