Regression Discontinuity with Unknown Discontinuity Points: Testing and Estimation

Abstract

The regression discontinuity design has become a common framework among applied economists for measuring treatment e§ects, while a key restriction in these works is to assume the discontinuity point to be known, which is not always possible in practice. This paper extends the applicability of the regression discontinuity design by allowing an unknown discontinuity point. First, we construct tests to test whether there is selection or treatment e§ect. Second, we estimate the treatment e§ect by estimating the nuisance discontinuity point Örst. In testing, we show that our tests are consistent. Also, a bootstrap method is proposed to Önd the critical values. In estimation, we show that the estimating of the discontinuity point will not a§ect the e¢ ciency of the treatment e§ect estimator. Simulation studies conÖrm the usefulness of our procedures in Önite samples.