Local Polynomial Order in Regression Discontinuity Designs

The local linear estimator has become the standard in the regression discontinuity design literature, but we argue that it should not always dominate other local polynomial estimators in empirical studies. We show that the local linear estimator in the data generating processes (DGP’s) based on two well- known empirical examples does not always have the lowest (asymptotic) mean squared error (MSE). Therefore, we advocate for a more flexible view towards the choice of the polynomial order, p, and suggest two complementary approaches for picking p: comparing the MSE of alternative estimators from Monte Carlo simulations based on an approximating DGP, and comparing the estimated asymptotic MSE using actual data.Length: 47 pages