  Estimation of a treatment effect by a regression discontinuity design faces a
severe challenge when the running variable contains measurement errors since
the errors smoothen the discontinuity on which the identification depends. The
existing studies show that the variance of the measurement errors plays a vital
role in both bias correction and identification under such situations. However,
the methodologies to estimate the variance from data are relatively
undeveloped. This paper proposes two estimators for the variance of measurement
errors of running variables of sharp regression continuity designs. The
proposed estimators can be constructed merely from data of observed running
variable and treatment assignment, and do not require any other external source
of information.
