Heteroscedasticity in synthetic control methods

Question

A reviewer asked me: to what extent the empirical method (Syntethic Control Method) controls for potential heteroskedasticity problems according to the problem under analysis?

The problem under analysis is how oil income affects tax income in a set of countries. However, that is not the important thing here.

Question 1: I wanted to ask if someone can explain to me how heteroskedasticity can be an issue in SCM?

I understand heteroscedasticity in basic regression models where it is defined as "the circumstance in which the variability of a variable is unequal across the range of values of a second variable that predicts it". Also in regression models, this variability usually relates to the error terms and now, I am uncertain how this shows in an SCM because I don't see traditional error terms in the SCM.

Please, correct me if I am wrong (I also appreciate it if you could confirm if I am right). Question 2: Could it be that heteroscedasticity in an SCM basically means that the analysed size of the event/shock/dependent variable varies over time? or is it anything else, which I am not seeing?

and Question 3: how can I deal with it? (Preferable in Stata)

And finally, I would be happy if someone could give me a pointer to related literature.

Best

Answer 1

SCM generally (as far as I'm aware) does well with heteroskedasticity. I'm not sure if you've seen it, but you should look at Abadie's recent paper (I think in journal of economic literature) called "Using Synthetic Controls".

If I were you, unless you've a bigger reason to suspect there's an issue, (i.e., noisy data), just use sandwich SE's in your regression modeling or, if it makes sense, log your intervention variable.

Answer 2

if someone needs an answer see this discussion that helped me now to understand it https://www.statalist.org/forums/forum/general-stata-discussion/general/1636246-heteroscedasticity-and-synthetic-control-method-scm