Inference in regression discontinuity designs with high-dimensional covariates

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.

Automated summary

We study regression discontinuity designs and propose a two-step estimator to increase the precision of treatment effect estimates by including many predetermined covariates. The estimator first selects important covariates through a localised lasso-type procedure and then estimates the treatment effect using a local linear estimator. The algorithm's theoretical properties are analyzed, showing that the resulting estimator is asymptotically normal under certain conditions.