Adaptive Estimation of the Regression Discontinuity Model
In order to reduce the finite sample bias and improve the rate of convergence, local polynomial estimators have been introduced into the econometric literature to estimate the regression discontinuity model. In this paper, we show that, when the degree of smoothness is known, the local polynomial estimator achieves the optimal rate of convergence within the Hölder smoothness class. However, when the degree of smoothness is not known, the local polynomial estimator may actually inflate the finite sample bias and reduce the rate of convergence. We propose an adaptive version of the local polynomial estimator which selects both the bandwidth and the polynomial order adaptively and show that the adaptive estimator achieves the optimal rate of convergence up to a logarithm factor without knowing the degree of smoothness. Simulation results show that the finite sample performance of the locally cross-validated adaptive estimator is robust to the parameter combinations and data generating processes, reflecting the adaptive nature of the estimator. The root mean squared error of the adaptive estimator compares favorably to local polynomial estimators in the Monte Carlo experiments.
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