This chapter reviews the different roles of covariate adjustment in the regression discontinuity (RD) literature, and to offer methodological guidance for its correct use in applications. One of the most important roles of baseline covariates in the canonical RD design is for falsification or validation purposes. Many methods are available for estimation, inference, and validation of RD designs within the continuity framework. The most common approach is to use local polynomial methods to approximate the two regression functions near the cut-off. Covariate adjustment in experimental analysis can be implemented both before and after randomization has occurred. In the context of RD designs, covariate adjustment has also been proposed to address missing data and measurement error, and to incorporate prior information via Bayesian methods. The use of covariates to explore heterogeneity has a long tradition in the analysis of both experimental and non-experimental data, as researchers are frequently interested in assessing the effects of the treatment for different subpopulations.
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