Correct interpretation of `estat aggregation, dynamic graph`

[Giuseppe Polito]

In the causal hdidregress manual, at "Example 4: Dynamic treatment effects", the command `estat aggregation, dynamic graph` generates the following plot:

1. What is the correct interpreation of the plot? Does it show the ATET for individuals exposed for a certain time, or does it show the yearly ATET?
   For instance, if an observation is exposed to treatment for 2 years. Its ATET is -2 (the y point corresponding to x=2), or is it -2.3 (the y point corresponding to x=0) - 2.3 (the y point corresponding to x=1) - 2 (the y point corresponding to x=2) = -6.6?
   Does the ATET shown accumulate over time? So to compute the total ATET I have to sum all the yearly ATET?
2. What is the exact model that is being estimated? What is its mathematical formula?
3. What do we make of the fact that the ATET in t=-5 is negative? The guide doesn't mention this fact. Don't we have treatment effect before treatment?

[Di Liu (StataCorp)]

For the formula of dynamic effects, see the description in https://www.stata.com/manuals/causal...postestimation. Please look at the the Methods and formula sections (Aggregations for the RA, IPW, and AIPW estimators).

[Giuseppe Polito]

Sorry, I still have trouble with this.

For instance, take the following code:

use https://www.stata-press.com/data/r18/hhabits
hdidregress aipw (bmi medu i.girl i.sports) (hhabit parksd), group(schools) time(year)
estat aggregation, overall

"estat aggregation, overall" gives me an estimated coefficient of -1.9025.

The dataset contains student-level observations (not school-district level, as Example 1 of the causalhdidregress guide says), observed from 2032 until 2040 (9 years).

The coefficient of -1.9, is to be interpreted as the average reduction in BMI caused by the program across all 9 years, or as the average reduction _per year_?