Regression discontinuity designs with unknown discontinuity points: Testing and estimation

The regression discontinuity design has become a common framework among applied economists for measuring treatment effects. A key restriction of the existing literature is the assumption that the discontinuity point is known, which does not always hold in practice. This paper extends the applicability of the regression discontinuity design by allowing for an unknown discontinuity point. First, we construct a unified test statistic to check whether there are selection or treatment effects. Our tests are shown to be consistent, and local powers are derived. Also, a bootstrap method is proposed to obtain critical values. Second, we estimate the treatment effect by first estimating the nuisance discontinuity point. It is shown that estimating the discontinuity point does not affect the efficiency of the treatment effect estimator. Simulation studies illustrate the usefulness of our procedures in finite samples.