Fuzzy RDD:why is there an inconsistency between rdplot and fuzzy rdrobust?

[Lorenzo Bombino]

Hi all,

I am trying to apply the fuzzy regression discontinuity framework to a dataset reporting electoral results at the candidate level for municipal elections.

Outcome variable = improvement in the candidate rank (on the basis of votes obtained) after election with respect to the rank assigned to him/her before elections.
The score and the treatment are shared by all candidates in a given municipality, thus I have many mass points. I have around 300 municipalities and 2 years of observations.

I try to apply a fuzzy regression discontinuity design because I have non-compliance on both sides.

This is the rdplot displaying the discontinuity at the cutoff, of around 1.5.






Then, if I run the sharp rdrobust (to check for the ITT), I get a plausible magnitude of the coefficient, with correct sign and strong significance:

However, If I add the fuzzy component, I get an implausible coefficient.

Do you have an idea of the reason behind this inconsistency?

Thanks a lot in advance!

[Sebastian Schirner]

Hey Lorenzo,

it would be great if you could provide some example data using dataex from ssc. I am not sure if that is a potential solution, but I realized that your treatment effect using rdrobust, fuzzy() is approx.1.5 scaled by 100. Is there a chance that the scaling of any of the variables is the issue?

Best,
Sebastian

[George Ford]

I looked at this using the senate data and get similar discrepancies. Curious if someone has an explanation.

[Lorenzo Bombino]

Hey Sebastian Schirner , thanks a lot for your feedback!
I am afraid the scale is not the issue.
You should now find attached a sample dataset for one year only. The score variable is called margin_instr, the treatment is mayor_treatment, while the outcome is rank_improv.
Data are at the municipality level, and each municipality has many candidates.
As you can see, also for 2018 only, the same issue of discrepancy arises.
If I regress the treatment on the score, I do get a very high and significant coefficient, which would make me think that the I stage is not an issue. However, when I move to the fuzzy rdrobust command, the I stage displays weird results.

Dear George Ford , thanks for the feedback! Does the same discrepancy arise when moving from the sharp to the fuzzy design?

Many thanks!

[George Ford]

Yes. The two are nothing alike. I haven't studied it to figure out why, but will eventually get around to it.