How to discern the coefficients and their p-values of covariates using sdid

[Venessa Yu]

Hello everyone who is interested in sdid (synthesis control DID), my name is Meng, and I am working on my sdid models while having some troubles when adding on covariates: how I can find out the coefficients and p-value for my covariates that I added on one by one? It looks like all the models give similar results in terms of ATTs and overall p-values...please find the attached screen captures (sorry this is my first post and I am still learning how to put code and data here..)
(Maybe Prof. Daniel would help to answer? Daniel PV) Thank you so much in advance!!!

Meng

[Daniel PV]

To get the coefficient of covariates you can access a scalar

e(beta)

after run sdid. In your case, you can replicate this coefficient and standard error by running a preregression https://github.com/skranz/xsynthdid/...covariates.pdf. You must create an indicator for all control units (W = 0) and estimate

reghdfe Y covariates if W==0, abs(state time) cluster(state)

. For future versions we will automatically add these estimators, thanks for commenting.

[Venessa Yu]

Hi Daniel PV,
Thank you so much for replying my questions! Appreciate so much! Here are my findings based on your advices:

I first used `matrix list e(beta)` to obtain the coefficients for all covariates (please see below);

Then, for the p-values of them, I created an indicator "W = 0" for those units/observations which NEVER been treated (I think this is what you meant), and run the "reghdfe" regression to replicate, unfortunately, I got errors of "insufficient observations"...while I next replaced with "treated = 0" (instead of W=0) to run the "reghdfe" command again, I could get something (please see below) but none of them is same as my sdid regression coefficient, which in fact did not replicate. May you please advice what I should do with "insufficient observations"? Thanks a lot!!

Meng

[Daniel PV]

you need to run the regression only on the control units (untreated in the whole period). Maybe if you generate the

egen W = mean(hsr_dummy), by(id)

and then condition if W==0. Let me know if it works.

[Venessa Yu]

Daniel PV Hi Daniel, thank you so much for your reply!
Yes, your code works very well! And now I can obtain the coefficients and p-values of the covariates via "reghdfe" regression exactly the same as what I received from the "sdid" regression using "e(beta)" command.
May I follow up with two more questions?
(1) what are the exact functions of covariates in a sdid model (how we interpret them in the report)? Since I realize that the p-value of each covariate is not significant at all, while the p-value of ATT is significant.
(2) given that the ATT coefficients and p-values merely vary as I add on one more covariate into the "sdid" model every time, how to identify which "sdid" regression fits better?

Thank you!
Best,
Meng