Interpreting Regression Discontinuity Designs with Multiple Cutoffs

@article{Cattaneo2016InterpretingRD,
  title={Interpreting Regression Discontinuity Designs with Multiple Cutoffs},
  author={M. D. Cattaneo and Rocı́o Titiunik and Gonzalo V{\'a}zquez-Bar{\'e} and Luke J. Keele},
  journal={The Journal of Politics},
  year={2016},
  volume={78},
  pages={1229 - 1248}
}
We consider a regression discontinuity (RD) design where the treatment is received if a score is above a cutoff, but the cutoff may vary for each unit in the sample instead of being equal for all units. This multi-cutoff regression discontinuity design is very common in empirical work, and researchers often normalize the score variable and use the zero cutoff on the normalized score for all observations to estimate a pooled RD treatment effect. We formally derive the form that this pooled… 
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