SDID (Synthetic Difference-In-Difference) | methods Criteria

[Luis Pecht]

I am performing a diff-in-diff analysis using Clarke and Palanir's sdid command.
My question is whether there is a, objective way to choose among available methods ( sdid, did,sc) as I was not able to capture the answer from https://www.damianclarke.net/research/papers/SDID.pdf

Note: In "did" method ATT matches xtdidregress, as expected, rejecting Null Hyphotesis however, in "sdid" method, ATT becomes significant.

thanks

. xtset S T, weekly 

Panel variable: S (strongly balanced)
 Time variable: T, 2023w15 to 2023w37
         Delta: 1 week


. sdid Y S T D,vce(bootstrap) method(sc)
Bootstrap replications (50). This may take some time.
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................     50


Synthetic Control

-----------------------------------------------------------------------------
           Y |     ATT     Std. Err.     t      P>|t|    [95% Conf. Interval]
-------------+---------------------------------------------------------------
           D |  44.76957   35.05688     1.28    0.202   -23.94065   113.47979
-----------------------------------------------------------------------------
95% CIs and p-values are based on Large-Sample approximations.

. sdid Y S T D,vce(bootstrap) method(sdid)
Bootstrap replications (50). This may take some time.
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................     50


Synthetic Difference-in-Differences Estimator

-----------------------------------------------------------------------------
           Y |     ATT     Std. Err.     t      P>|t|    [95% Conf. Interval]
-------------+---------------------------------------------------------------
           D |  54.69791   28.26938     1.93    0.053    -0.70906   110.10488
-----------------------------------------------------------------------------
95% CIs and p-values are based on Large-Sample approximations.
Refer to Arkhangelsky et al., (2020) for theoretical derivations.

. sdid Y S T D,vce(bootstrap) method(did) 
Bootstrap replications (50). This may take some time.
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................     50


Difference-in-Differences Estimator

-----------------------------------------------------------------------------
           Y |     ATT     Std. Err.     t      P>|t|    [95% Conf. Interval]
-------------+---------------------------------------------------------------
           D |  30.46574   26.07602     1.17    0.243   -20.64232    81.57380
-----------------------------------------------------------------------------
95% CIs and p-values are based on Large-Sample approximations.


. xtdidregress (Y) (D), group(S) time(T)

Treatment and time information

Time variable: T
Control:       D = 0
Treatment:     D = 1
-----------------------------------
             |   Control  Treatment
-------------+---------------------
Group        |
           S |        90          6
-------------+---------------------
Time         |
     Minimum |      3290       3305
     Maximum |      3290       3305
-----------------------------------

Difference-in-differences regression                     Number of obs = 2,208
Data type: Longitudinal

                                     (Std. err. adjusted for 96 clusters in S)
------------------------------------------------------------------------------
             |               Robust
           Y | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
ATET         |
           D |
   (1 vs 0)  |   30.46574   21.26164     1.43   0.155    -11.74395    72.67543
------------------------------------------------------------------------------
Note: ATET estimate adjusted for panel effects and time effects.

[Jared Greathouse]

It all hinges on how well parallel trends holds and/or if it's reasonable for a convex combination of donors to match outcome pretrends and the underlying factor structure.

[Luis Pecht]

thanks Jared, for the theoretical guidance.