  We consider inference in regression discontinuity designs when the running
variable only takes a moderate number of distinct values. In particular, we
study the common practice of using confidence intervals (CIs) based on standard
errors that are clustered by the running variable as a means to make inference
robust to model misspecification (Lee and Card, 2008). We derive theoretical
results and present simulation and empirical evidence showing that these CIs do
not guard against model misspecification, and that they have poor coverage
properties. We therefore recommend against using these CIs in practice. We
instead propose two alternative CIs with guaranteed coverage properties under
easily interpretable restrictions on the conditional expectation function.
