triple differences in stata

[Cyrus Bee]

I need some help running triple differences estimator in stata. I am using the below regression


Y=b1+b2time+b3treat+b4ESI+b5(time*treat)+b6(time*E SI)+b7(treat*ESI)+b8(time*treat*ESI).............. ..+Error
time is a dummy for year
treat is a dummy for treatment group (1 for treat 0 for comparison)
ESI is a dummy for those with access to ESI (Employer sponsored insurance thru private coverage)

My question is are those in the ESI group will also be in the treatment group? In other words, my treatment group includes those aged 26-30 and I am comparing them to those aged 20-25
In the ESI group I am only including those aged 26-30 who have access to ESI as 1 otherwise 0. Is this correct?

[Cyrus Bee]

I forgot to mention Y indicates coverage (insurance)

[Clyde Schechter]

The best way to code estimation commands involving interaction terms, especially with more than 2 levels, is to use Stata's factor variable notation. Read -help fvvarlist- and the associated manual section. Your code would look something like this:

regression_command Y i.time##i.treat##i.ESI

My question is are those in the ESI group will also be in the treatment group? In other words, my treatment group includes those aged 26-30 and I am comparing them to those aged 20-25
In the ESI group I am only including those aged 26-30 who have access to ESI as 1 otherwise 0. Is this correct?

I don' understand any of this.

[Cyrus Bee]

Thanks for your message Clyde. So to clarify My control groups are those between ages of 20-25 and treatment are those between 26-30. Now I want to see the differences in coverage by adding a further control group of those who have access to ESI. So this includes all 26-30 with access to ESI as a further control group. Does this help?

[Clyde Schechter]

Now I think I understand. But that is not what your proposed code does. It does not add 26-30 with access to ESI as a further control group. Instead it is designed to see whether or not access to ESI changes the effect of treatment over time. If you want a third group, then you change your treatment variable. Instead of 0/1 you make it 0/1/2, where 2 = access to ESI and 26-30, 1 = no access to ESI and 26-30, 0 = 20-25. Then you just need the two-way interactions i.time##i.treat in your model.

There is one serious limitation to your overall approach. 20-25 year olds are enormously different in many ways from 26-30 year olds. It is really quite a stretch to use 20-25 year olds as a control group for 26-30 year olds. Unless your outcome variable Y is definitely known not to depend on age, you are going to be unable to distinguish effects of treatment from just a plain old age effect. You might be able to reduce that problem by including a lot of covariates that might explain some of the purely age-related differences in Y, but it is always difficult to do that adequately. It would be far better to find 26-30 year olds who did not receive treatment to serve as controls so that age does not become a confounding factor.

[Cyrus Bee]

This helps thanks. Actually, I think I will change the 20-25 year olds to 23-25 year olds. I think those seem like a better comparison group.
Thanks for your help again.