Kernel Choice Matters for Boundary Inference Using Local Polynomial Density: With Application to Manipulation Testing

Abstract: The local polynomial density (LPD) estimator has been a useful tool for inference concerning boundary points of density functions. While it is commonly believed that kernel selection is not crucial for the performance of kernel-based estimators, this paper argues that this does not hold true for LPD estimators at boundary points. We find that the commonly used kernels with compact support lead to larger asymptotic and finite-sample variances. Furthermore, we present theoretical and numerical evidence showing that such unfavorable variance properties negatively affect the performance of manipulation testing in regression discontinuity designs, which typically suffer from low power. Notably, we demonstrate that these issues of increased variance and reduced power can be significantly improved just by using a kernel function with unbounded support. We recommend the use of the spline-type kernel (the Laplace density) and illustrate its superior performance.