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Is there a statistical test that would allow me to test whether I should use a sharp or fuzzy regression discontinuity design?

Intuitively, I can think of two decision rules:

(i) Test whether the estimated treatment coefficient is the same across fuzzy and fuzzy. If different, use fuzzy.

(ii) Test if the first stage of the fuzzy rd (where actual treatment status is instrumented using whether obs lies above the cut-off) is unity. If it is not, use fuzzy.

Can anyone comment on these? I couldn't find an established rule in the literature.

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  • $\begingroup$ sorry, i obviously meant for (i) "same across fuzzy and sharp. If different, use fuzzy." $\endgroup$
    – misologie
    Commented Jan 16, 2016 at 22:13
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    $\begingroup$ Please just edit your post, then. You can learn more about how this site works on our help center. Welcome, and enjoy! $\endgroup$
    – whuber
    Commented Jan 16, 2016 at 22:26
  • $\begingroup$ Well strictly speaking, you can see immediately if it is fuzzy or sharp, by just looking at whether the rule is enforced. I guess your question is rather whether it is worth to use fuzzy if you have just a few departures from sharp? But indeed, as you point in rule 1), in this case you should have only a small difference in the estimates. But then why not use always fuzzy, as soon as even just a single observation makes it fuzzy? $\endgroup$
    – Matifou
    Commented Jan 20, 2016 at 4:45

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It depends on what you're interested in - if you're interested in the ITT, you shouldn't use the approach you described in i) and ii). In this case, you'd always use a sharp RD.

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  • $\begingroup$ This seems rather short and you refer to a) and b) which do not appear in the question. Perhaps you can expand it into a more explicit answer with details of why your advice is sound? $\endgroup$
    – mdewey
    Commented Jun 6, 2017 at 15:52
  • $\begingroup$ Thanks for pointing this out - I just changed a) and b) to i) and ii) $\endgroup$
    – user162760
    Commented Jun 6, 2017 at 16:19

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