Wavelet Estimators for LATE under Discontinuous (Kink) Incentive Assignment Mechanism

In an eort to improve the asymptotic properties of the jump size estimators, a number of alternatives have been suggested. These include partial spline estimator, Speckman estimator, kernel estimator, partial linear estimator and the recent wavelet OLS estimators constructed by Chen and Fan (2011). We show that all these estimators share a common structure, being members of a class of local least squares wavelet estimators. We use this structure to compare their asymptotic bias and mean square error. We …nd that the local least squares wavelet estimator attains the optimal convergence rate for semiparametric estimation of the local average treatment eect (LATE) under a broader set of conditions. We also …nd that the local least squares wavelet estimator has the better …nite sample performance and could jointly estimate other order derivative discontinuous jump sizes. These features are illustrated by a comprehensive Monte Carlo simulations. The scale selection, discontinuous order speci…cation and estimation for the unknown discontinuous location are also discussed.