Computing ATT and ACRT event study estimates and confidence intervals for discrete doses

[julienberman]

Hi,

I understand that the package does not yet support discrete doses. I have attempted to compute these by hand, though I am having trouble computing confidence intervals. Here is my process for computing point estimates:

1. Compute $ATT(g,t,d|g,d)$ using att_gt from the did package to get the average treatment effect of dose d for timing group g in time period t (among all units in g that experienced dose d), using never treated as controls.
2. Compute $\tilde{ATT}_{dose}(d|e)$ using aggte from the did package, separately for each dose d.
3. By hand (without a package), compute $\tilde{ACRT}_{dose}(l_1,l_2|e) = \frac{E[TE(l_2|e)|D=l_2] - E[TE(l_1|e)|D=l_1]}{l_2 - l_1}$ for all pairs of doses $l_1$ and $l_2$.
4. By hand (without a package), compute ATT(e) as the average over all doses D of the dose-specific ATTs from (2), and compute ACRT(e) as the average over all doses L1 and L2 (with L1 < L2) of the dose-specific ACRTs from (3).

I have two questions:
a) In (4), what is the proper way to average over all doses? How should I weight the different doses?
b) How can I compute standard errors for ATT(e) and ACRT(e)?

Thanks so much for creating this wonderful package!