Difference in discontinuities setup

[Pasquale Giacobbe]

Dear All,
I am recently involved in some analysis where I am trying to combine the difference-in-difference approach with the Regression Discontinuity Design in the spirit of Grembi et Al. (2016) on the AEJ. Basically, like them, in analysing Italian municipalities, I would like to combine the before/after variation coming from the relaxing of some binding fiscal rules at the population threshold of 5,000 inhabitants. I exploit a user written routine which comes in very handy, but I would like to run the same model through a linear regression validate the results.
Does anyone have any experience in such an identification setting?

Greetings,
Pasquale

[Jared Greathouse]

I don't, but I do have an idea of where you might start.

There's a user written command called adoedit. It opens the ado file like a normal do file. If you're comfortable with getting into the guts of Stata's ado language, you'll be able to see (or at least, try) how you might replicate it with linear regression.

From a modeling standpoint however, if I recall correctly, you're just using two sets of interaction terms, before and after the policy and above and below a given cutoff within a certain bandwidth.

Don't mind me, I've never really used this design before, so others may be able to give a much better treatment of this than I ever could. What user written command are you using, anyways?

For further commentary, you'd need to post your example data, as well as the hyperlink/full citation to the AEJ paper; I know what paper you mean, but others would have a better idea I'd you included the link.

[Pasquale Giacobbe]

Dear Jared,
Thanks for your answer. I am exploiting a routine called mdrd which works very well and allows to run multi and unidimensional regression discontinuity and difference in discontinuity. The results I get sound good, but I would like to run some robustness exercises. You summarised perfectly the problem: basically diff-in-disc combines the before/after variation (diff-in-diff) with the below/above variation proper of the rdd design. So, theoretically the problem is straightforward. I checked the replication package the authors provide but I didn't figure out yet how they create all the variables they use in the linear regression approach and which one targets the estimated diff-in-disc parameter. There are no labels in the variables and also the results I get do not perfectly fit with those of the paper. So, it is not so easy to orient myself through their codes and paper's results.
If someone has any experience with this kind of regression design would be much appreciated.

Greetings,
Pasquale