Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs

By Sebastian Calonico, M. D. Cattaneo, Max H. Farrell. Econometrics Journal, 2018

386 citations recorded by the source corpus.

Modern empirical work in regression discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias-corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show that they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smaller coverage error rate. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in R and Stata packages.

View Paper: https://www.semanticscholar.org/paper/1e062f0eeb2e0e6d8a217e09dac3f56195584e86

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Citations in the corpus

Coverage error optimal confidence intervals for local polynomial regression (2018, methodology): “Last but not least, some of the ideas in this paper have been applied to causal inference and treatment effect estimation in the context of regression discontinuity designs in [7].”
Regression Discontinuity Designs (2021, unknown): “The band-width that determines which observations are included in the fit can be chosen in different ways, depending on the optimality criterion used (Calonico, Cattaneo and Farrell, 2020).”
Regression discontinuity design with many thresholds (2017, unknown): “The same idea applies to the coverage-error optimal bandwidths by Calonico et al. (2018), which converge to zero at rate n−0.25, and need to be adjusted.”