Inference in Regression Discontinuity Designs with High-Dimensional Covariates

TL;DR

This paper introduces a method for regression discontinuity analysis with high-dimensional covariates, using a two-step procedure involving covariate selection and local linear estimation, supported by theoretical guarantees and empirical validation.

Contribution

It develops a novel high-dimensional covariate selection approach for RDDs, with proven asymptotic properties and practical inference procedures.

Findings

Estimator is asymptotically normal under sparsity.

Standard inference methods are applicable.

Method improves precision in high-dimensional settings.

Abstract

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 localized 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.