ATT of did_imputation by Borusyak et al. 2021

[Tariq Abdullah]

I know in case of csdid if I run the following regression then I'll get the ATT.

csdid ln_wage, ivar(county) time(year) gvar(policy_year) agg(event)
estat simple

estat simple
Average Treatment Effect on Treated
------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         ATT |  -.0033592     .00675    -0.50   0.619    -.0165889    .0098706
------------------------------------------------------------------------------

However, I have tried several methods to find the ATT like the one I get in CSDID when I apply the did_imputation but I've not been successful to do so. Would you kindly guide me how I can end up getting the ATT in case of did_imputation ?

ssc install did_imputation, replace

did_imputation ln_wage county year policy_year, autosample horizons(0/5) pretrend(5) minn(0)

Would really appreciate your valuable input!

[Jared Greathouse]

I don't understand the problem.

[Tariq Abdullah]

If I run the following command

did_imputation ln_wage county year policy_year, autosample horizons(0/5) pretrend(5) minn(0)

I get a table like this , but not the ATT.

                                                        Number of obs = 66,581
------------------------------------------------------------------------------
      ln_emp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        tau0 |   .0078529   .0141983     0.55   0.580    -.0199752     .035681
        tau1 |    .006906    .016485     0.42   0.675     -.025404     .039216
        tau2 |   .0077604   .0177336     0.44   0.662    -.0269969    .0425177
        tau3 |   .0109745   .0188022     0.58   0.559    -.0258772    .0478262
        tau4 |   .0189137   .0193346     0.98   0.328    -.0189815    .0568089
        tau5 |   .0392954   .0212797     1.85   0.065    -.0024121    .0810029
        pre1 |  -.0002982    .018568    -0.02   0.987    -.0366908    .0360944
        pre2 |   .0187492   .0167825     1.12   0.264    -.0141438    .0516423
        pre3 |   .0071949   .0164604     0.44   0.662     -.025067    .0394567
        pre4 |   .0061025    .014488     0.42   0.674    -.0222935    .0344984

My question is with did_imputation command of Borusyak et al. (2021) how can I get the ATT like the one CSDID of Calaaway and Sant'Anna provides like the following

csdid ln_wage, ivar(county) time(year) gvar(policy_year) agg(event)
estat simple

Average Treatment Effect on Treated
------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         ATT |   -.008374   .0208924    -0.40   0.689    -.0493223    .0325743

[Jared Greathouse]

Note that I've not used this estimator, and I do think it's pretty silly the authors didn't make this a scalar, but this is what I've tried

clear *
timer clear
set seed 10
global T = 15
global I = 300

set obs `=$I*$T'
gen i = int((_n-1)/$T )+1                     // unit id
gen t = mod((_n-1),$T )+1                    // calendar period
tsset i t

// Randomly generate treatment rollout years uniformly across Ei=10..16 (note that periods t>=16 would not be useful since all units are treated by then)
gen Ei = ceil(runiform()*7)+$T -6 if t==1    // year when unit is first treated
bys i (t): replace Ei = Ei[1]
gen K = t-Ei                                 // "relative time", i.e. the number periods since treated (could be missing if never-treated)
gen D = K>=0 & Ei!=.                         // treatment indicator

// Generate the outcome with parallel trends and heterogeneous treatment effects
gen tau = cond(D==1, (t-12.5), 0)             // heterogeneous treatment effects (in this case vary over calendar periods)
gen eps = rnormal()                            // error term
gen Y = i + 3*t + tau*D + eps                 // the outcome (FEs play no role since all methods control for them)
//save five_estimators_data, replace
cls
// Estimation with did_imputation of Borusyak et al. (2021)
did_imputation Y i t Ei, allhorizons pretrend(5)

su tau if tau ~= 0