Inference in regression discontinuity designs with high-dimensional covariates
研究了当协变量数量远多于观测值时，如何通过两阶段估计法（先局部lasso选重要变量，再线性纳入局部线性估计）提高断点回归中处理效应的估计精度，并证明了渐近正态性。
Summary We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator which first selects a small number of ‘important’ covariates through a localised lasso-type procedure, and then, in a second step, estimates the treatment effect by including the selected covariates linearly into the usual local linear estimator. We provide an in-depth analysis of the algorithm’s theoretical properties, showing that, under an approximate sparsity condition, the resulting estimator is asymptotically normal, with asymptotic bias and variance that are conceptually similar to those obtained in low-dimensional settings. Bandwidth selection and inference can be carried out using standard methods. We also provide simulations and an empirical application.