Notes on Regression Discontinuity Methods - [athena.sas.upenn ...

Comparison of RD Approach with a Matching Approach
• Matching assumes
Y (0),Y (1) ⊥⊥ W |X (8)
• In that case, treatment effect can be obtained by comparing
people with same x values who did and did not receive
treatment
E(Y (1) − Y (0)|X = x)=E(Y |W = 1,X = c) − E(Y |W = 0,X = c)
• This approach would not exploit the jump in the probability of
assignment at the discontinuity point
• It could not be implemented with a sharp design, where there
is no overlap.
• Treated units with xi = c include both compliers and
alwaystakers.
• Unconfoundedness is based on units being comparable if
covariates are similar.