sdid, unit-level treatment effects

[guneet robin]

I have used sdid package developed by Daniel PV Damian Clarke to run a synthetic difference-in-differences analysis (as in Arkhangelsky et al., 2021). The average treatment effect results are non-significant. Given the theory, I hypothesize that significant effects for at least some units. How can I obtain unit-level treatment effects using post-estimation commands? The commands such as, matrix list e(tau) and e(omega) just provide time-level and unit-level weights.

Thanks
Guneet

[Daniel PV]

Hi guneet robin , my recommendation is to apply conditional sdid to any unit in the treatment group using the entire control group in each estimation. I think the best option is to use preserve and restore by removing the other treated drives. One thing about this is that now the inference is placebo since we have only one treated in the estimate, so I think you can consider this. For example using womparl data:

webuse set www.damianclarke.net/stata/
webuse quota_example.dta, clear
egen m = min(year) if quota==1, by(country) //indicator of year of treatment
egen mm = min(m), by(country)                //extend the indicator
keep if mm==2002 | mm==.                    //keep only those treated in 2022 or the control group

levelsof country if mm==2002, local(country)
foreach c of local country {
    di "country `c'"
    preserve
    keep if country=="`c'" | mm==.
    sdid womparl country year quota, vce(placebo)
    restore
}

[guneet robin]

Dear Daniel PV thank you for your response. Here is my set-up:

Number of cities = 103
Year range = 2003-2012
There is staggered treatment of cities from 2007-2012. In the first year 2007, e.g., 58 cities were treated followed by 69, and so on..till 90 treated cities by 2012.
Covariates = demographics at city-year level X1 X2 X3
Outcome = Y = logs = log(sales of books)

I used: sdid logs city Year treat, vce(bootstrap) seed(1213) covariates(X1 X2 X3)

ATET:

Synthetic Difference-in-Differences Estimator

-----------------------------------------------------------------------------
logs | ATT Std. Err. t P>|t| [95% Conf. Interval]
-------------+---------------------------------------------------------------
treat | 0.28149 0.19315 1.46 0.145 -0.09708 0.66006
-----------------------------------------------------------------------------
95% CIs and p-values are based on Large-Sample approximations.
Refer to Arkhangelsky et al., (2020) for theoretical derivations.


I want treat estimate at city level for all 103 cities.

Are you suggesting that I calculate the treatment effect for each unit separately, ignoring other treated units at that time?

Best,
Guneetr