Control variables in DID regression

[Monica Joshi]

Dear all,

I have a few questions pertaining to the DID model:

1. How can the controls be added to the DID model? Do we just add them as independent variables?
2. Since I am working with a panel data, would the command, "xi: reg CO2emissions i.after*i.treatment populationinmillion FDIinflowsasofGDP RealGDPinbillion", where populationinmillion FDIinflowsasofGDP RealGDPinbillion are controls and CO2 emissions is the dependent variable, work well for a two period DD model?

Hoping for a response soon since it's a little urgent.

Thank you very much in anticipation.

Regards

[FernandoRios]

Hi Monica
Unfortunately there is no simple answer for this question. And it actually depends on the assumptions you are willing to make for your model.
1. If you think covariates affect outcome only, but not treatment, then I think you can add them as controls, the usual way (as what you have). THat is how commands like did2s and did_imputation works.
2. If you think covariates affect both oucome and treatment, then you can add ex ante controls only. However, because they will be time fixed, they can be added as controls for a propensity to be treated, or potential outcomes from ex-ante period perspective. This is what Callaway and Sant'Anna (2020) -csdid- does.

So, you need to choose your assumptions, justify them, then you can decide how to control for covariates.
HTH

[Monica Joshi]

Thank you for your response

[Kumari Gunjan]

Dear sir,
If there are some covariates which affect both the treatment and the outcome, then we can use the pre-treatment explanatory variable to balance the treatment and control. But, do we also need to include the explanatory variables in the DID with matched sample? In the DRDID command only the pre-treatment covariates is taken, that means pre-treatment covariates are only used for the balancing. But, there are some studies which first uses propensity score to match the treatment and control. then in the matched sample they use the Covariates also to estimate DID.