Local Polynomial Wavelet Estimation of Local Average Treatment Effect∗

In this paper, we introduce a new class of estimators of jump size in a nonparametric regression model and apply it to the estimation of local average treatment effect (LATE). We refer members of this class as local polynomial wavelet estimators and show that all the existing estimators, including estimators constructed from differencing two nonparametric estimates and partial linear estimators, could be asymptotically expressed as local constant/polynomial wavelet estimators. We establish asymptotic properties of local polynomial wavelet estimators and show that they attain the optimal convergence rate under a less restrictive continuous condition. In addition to estimating jump size, our method automatically leads to estimations of kink size and other higher order derivative jump sizes. The finite sample performance of the proposed estimators is investigated via a comprehensive Monte Carlo simulation.