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I recently read a paper which used a regression discontinuity design (RDD) to study the effects of a law. The key variable was = 1 for all counties following the introduction of the ban. The model also included two-way fixed effects and the dependent variable was logged.

Is this not technically a Differences in Differences (DiD) and RDD?

I understand that DiD needs an untreated group while RDD does not, but if year fixed effects are included, the model suffers from perfect multicollinearity in the absence of an untreated group.

The paper I'm referencing is an example of the aforementioned specification error—outlined in this re-analysis. I'm just trying to understand what the authors were trying to estimate and what would the model had been called had the data allowed for its use.

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    $\begingroup$ Please spell out acronyms. Not all user of CrossVolidated are native English speakers and acroyms can be particularly tricky. $\endgroup$
    – Peter Flom
    Apr 2 at 23:13
  • $\begingroup$ Can you provide a citation to the paper you are talking about? $\endgroup$
    – wzbillings
    Apr 2 at 23:35
  • $\begingroup$ Difference in difference involves repeated measurements on the same units, such data on the same counties before and after the law changed, with some experiencing no change. If the model is comparing just before vs after the law changed and the law changed everywhere its probably an interrupted time series. en.m.wikipedia.org/wiki/Interrupted_time_series $\endgroup$
    – N Brouwer
    Apr 3 at 4:45
  • $\begingroup$ @N Brouwer What about if there are untreated units (then year fixed effects can be included). Would then, an RDD with two-way fixed effects, be a DiD + RDD hybrid? $\endgroup$
    – Liam
    Apr 3 at 17:34
  • $\begingroup$ @wzbillings I cited the paper. $\endgroup$
    – Liam
    Apr 3 at 21:40

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