Apr 1, 2014 Report No：14-03
Simultaneous Selection of Optimal Bandwidths for the Sharp Regression Discontinuity Estimator
We consider the problem of the bandwidth selection for the sharp regression discontinuity (RD) estimator. The sharp RD estimator requires to estimate two conditional mean functions on the left and the right of the cut-off point nonparametrically. We propose to choose two bandwidths, one for each side for the cut-off point, simultaneously in contrast to common single-bandwidth approaches. We show that allowing distinct bandwidths leads to a nonstandard minimization problem of the asymptotic mean square error. To address this problem, we theoretically define and construct estimators of the asymptotically first-order optimal bandwidths that exploit the second-order bias term. The proposed bandwidths contribute to reduce the mean squared error mainly due to their superior bias performance. A simulation study based on designs motivated by existing empirical literatures exhibits a significant gain of the proposed method under the situations where single-bandwidth approaches can become quite misleading.
|Keywords||Bandwidth selection, local linear regression, regression discontinuity de- sign|