How to calculate the Average Treatment Effect on the Untreated (ATU) vs. ATE/ATET

[Holger Luedeke]

Quite often, I am more interested in knowing how a treatment might improve the outcomes of the untreated, rather than which effect the treatment had on the treated. However, I can only find the two procedures (estat teffects, atet) and (estat teffects, ate). My intuition would be to try (estat teffects, ate subpop(if treatmentvariable==0)), but when I tested this approach for calculating the ATET, it gave me the wrong number. The correct ATET required to write (estat teffects, atet subpop(if treatmentvariable==1)). So now I wonder whether I get the ATU by writing (estat teffects, atet subpop(if treatmentvariable==0)), or whether there is a completely different alternative way. Thank you for any advice.

[Jeff Wooldridge]

You can simply defined a new treatment variable, notreat = 1 - treat, and then do the analysis using notreat as the "treatment." Then the ATET using notreat should be ATEU.

[Holger Luedeke]

Thank you. Straightforward and obvious solution, yet overlooked by me. That should do the trick.

[Holger Luedeke]

Addendum: I have tested a number of different examples by now, so I can say with a certain confidence that the easiest way to get the Average Treatment Effect on the Untreated (ATU) is to type:

estat teffects, atet subpop(if treatmentvariable ==0)

As an alternative, using a non-treatment variable leads to the same results, but requires three additional steps:
a) generating the non-treatment variable
b) running a new regression model with the generated variable
c) switching the algebraic sign of the resulting ATET (sign of the margin, z-value and confidence interval).

For those who want to see for themselves, I have added a do-file with an example from the Stata Manual on Extended Regression Models (Example 4b, page 263)

*Example from the Stata Manual on Extended Regression Models/ ERM (Example 4b, page 263)
use https://www.stata-press.com/data/r16/heartsm, clear

*First approach to calculate ATU (ATET with subpopulation if treatmentvariable==0)
eprobit attack age bmi, select(full = age bmi i.checkup) entreat(exercise = bmi i.gym) vce(robust)
estat teffects, atet subpop(if exercise==0)

*Comparison with ATE and ATET
estat teffects
estat teffects, atet

*Second approach (1-treatment variable)
gen noexercise = 1-exercise
eprobit attack age bmi, select(full = age bmi i.checkup) entreat(noexercise = bmi i.gym) vce(robust)
estat teffects, atet

[Jeff Wooldridge]

That’s good to know!

[James Rao]

Am estimating a treatment effect model using the "eregress" command and am interested in estimating the average treatment effect on the treated (ATET). I have noticed that when I estimate the model "without" interaction option (nointeract), my estimates for ATE and ATET are the same. I also find the same value of ATET for sub-populations of the treated. However, when I estimate the model "with" interaction, estimates for ATET are different from prediction of ATE. I also find different ATET values for sub-populations of the treated. Which estimation option should I use when I want to estimate ATET?

[LOKESH POSTI]

Really helpful guys even in 2021

2 clarifications required

Ques1) using the *Second approach (1-treatment variable) -- should be change the sign of the coefficient and the CI while interpretation because i am getting a negative sign

Ques 2) should ATE be always be between ATT and ATU