Specification of triple difference-in-differences with 2 treatment groups and 1 control group

[Leo Nard]

Hello everyone,

I have an outcome which I measure between two dates for three different cohorts. The treatment whose effect I want to measure is COVID-19.
My control group is observed in 2016 (t=0) and 2019 (t=1), my first treatment group is observed in 2017 (t=0) and 2020 (t=1), and my second control group in 2018 (t=0) and 2021 (t=1).

Group	t=0	t=1
Control	2016	2019
Treated 1	2017	2020
Treated 2	2018	2021

I tried to apply a triple difference regression using the following code, but I seem to be specifying something wrong...

clear
set obs 9999
egen id = seq(), from(1) to(9999) block(1)
gen outcome = 1 + rnormal()
generate year=2016 if id<=3333
replace year=2017 if id>3333 & id <=6666
replace year=2018 if id>6666 & id <=9999
generate t=0
save samplet0, replace
replace year=2019 if id<=3333
replace year=2020 if id>3333 & id <=6666
replace year=2021 if id>6666 & id <=9999
replace t=1
append using samplet0
generate treated1=0
replace treated1=1 if year==2020
generate treated2=0
replace treated2=1 if year==2021

reg outcome t##treated1##treated2

Does anyone have an idea? Thank you in advance!

[Leo Nard]

I also tried this specification to be more in line with a triple difference but without success.

clear
set obs 9999
egen id = seq(), from(1) to(9999) block(1)
gen outcome = 1 + rnormal()
generate year=2016 if id<=3333
replace year=2017 if id>3333 & id <=6666
replace year=2018 if id>6666 & id <=9999
generate t=0
save samplet0, replace
replace year=2019 if id<=3333
replace year=2020 if id>3333 & id <=6666
replace year=2021 if id>6666 & id <=9999
replace t=1
append using samplet0

generate treated=0
replace treated=1 if year==2021 | year==2018  | year==2020 | year==2017

generate group = 0
replace group = 1 if year == 2016 | year == 2019
replace group = 2 if year == 2017 | year == 2020
replace group = 3 if year == 2018 | year == 2021

generate treated_t=treated*t
generate treated_group_t=treated*group*t
generate treated_group=treated*group 
generate group_t=group*t

regress outcome t treated group treated_t treated_group group_t treated_group_t

Here is the error message that stata returns to me

Any idea how to specify the model in DDD with my setting?