Regression Discontinuity - Institute for Policy Research

Typical estimation strategy for
RDs with Multiple Cutoffs
Where Y ij is the outcome for participant i in cutoff group j; D is whether
unit i is in treatment or comparison in cutoff group j; AV i is assignment
score for unit i (standardized and centered by cutoff group); X i and Z j
are vectors of unit and cutoff-group level covariates (respectively); u j
and ε ij are the unit and cutoff group level random error terms, assumed
to be iid, and τ is the treatment effect for unit i in cutoff group j.
• Alternatively, cutoff group-based fixed effects might be included in the
model.
• This model assumes that 1) each cutoff group has the same functional
form; 2) constant treatment effects across cutoffs (though we could
include treatment by cutoff interaction terms); and 3) standardizing and
centering assignment scores by cutoff group weighs units appropriately
for estimating desired treatment effects.