# Comparative study using synthetic control

I am currently working on an idea for a paper and I've had an idea for a "new" methodology, but I am not sure if it's correct to apply such a method or if I should modify it in some way.

Basically what I am studying can be seen as the effect of a "shock" in different areas with different "types" (in this case the type is basically the "institutional quality").

What I would like to do is to first estimate, using Synthetic control, the effect of this "shock" (in practice I am studying natural disasters), so for that end I construct a synthetic control and then by comparing the value of the variable for this vs the "treated" unit I can estimate the effect of the "treatment" (this is somehow similar to the dif. in dif. method), and I will call it $$\hat{\alpha_i}$$.

I am working with panel data, so I will have many "treated" units, and what I would like to do is to see whether this $$\hat{\alpha_i}$$ responds to characteristic of the unit $$i$$ (in particular the institutional quality). Hence I was thinking that I can run a regression where the dependent variable is $$\hat{\alpha_i}$$ over a set of variables (including my interest variable of course).

Does this looks like a feasible method? Should I, instead of including control variables, perform a pre-estimation matching in order to have more comparability?

• Have you seen this Cavallo, Galiani, Noy, Pantano's 2013 Restat paper on earthquakes? They also wrote a very nice Stata package called synth_runner to implement this. I think you can apply this method separately for various levels of institutional quality and compare the CIs for the effects. – Dimitriy V. Masterov May 9 at 17:46