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?

Thanks in advance.

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    $\begingroup$ 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. $\endgroup$ – Dimitriy V. Masterov May 9 at 17:46
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    $\begingroup$ People have also done something like what you propose where they regress the fixed effect from panel data model on time-invariant characteristics, but I can't think a any formal treatment of this approach in an article or a text book. $\endgroup$ – Dimitriy V. Masterov May 9 at 17:47
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    $\begingroup$ The problem with the SC method is that it will return a time-varying effect that you will have to aggregate. $\endgroup$ – Dimitriy V. Masterov May 9 at 17:51
  • $\begingroup$ @DimitriyV.Masterov Firstly I've just taken a quick look at Cavallo's paper, I'll read it in more detail. Secondly I was not aware that this "method" of regressing the fixed effect of time invariant characteristics has been already implemented, I'll dig deeper on it. Finally, I agree with your last comment, my idea was to analyse the effect by comparing the control and the treated unit 10 years (for instance) after the disaster. $\endgroup$ – RScrlli May 11 at 7:52
  • $\begingroup$ @DimitriyV.Masterov Something like an static comparison, does it make any sense or is it better to aggregate variables in the period? The problem with aggregation is that , as some authors have shown, the effects of the disaster are very heterogeneous, in particular short-run effects are almost negligible while long-run are not, so aggregating might not be a good idea. $\endgroup$ – RScrlli May 11 at 7:55

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