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In regression discontinuity (RD) with a running variable  S  crossing a known cutoff  c , an unexpectedly small break magnitude is due to  S  being a mis-measured version of the genuine running variable  G . Has all been lost, and is RD useless when  G≠S ? This paper proves three things. First, when  P ( G=S )=0, nonparametric RD identification fails. Second, when  P ( G=S )&gt;0, although the usual RD effect on the margin  E (·| G=c ) is not nonparametrically identified, the “effect on the  truthful  margin”  E (·| G=S=c ) is. Third, under a no-selection-problem assumption, the effect on the truthful margin becomes the effect on the margin; the no-selection-problem assumption is unnecessary, as long as the effect on the truthful margin is taken as a parameter of interest.

Regression Discontinuity with Errors in the Running Variable: Effect on Truthful Margin