The regression discontinuity (RD) design is a popular quasi‐experimental design for causal inference and policy evaluation. The most common inference approaches in RD designs employ “flexible” parametric and nonparametric local polynomial methods, which rely on extrapolation and large‐sample approximations of conditional expectations using observations somewhat near the cutoff that determines treatment assignment. An alternative inference approach employs the idea of local randomization, where the very few units closest to the cutoff are regarded as randomly assigned to treatment and finite‐sample exact inference methods are used. In this paper, we contrast these approaches empirically by re‐analyzing the influential findings of Ludwig and Miller (), who studied the effect of Head Start assistance on child mortality employing parametric RD methods. We first review methods based on approximations of conditional expectations, which are relatively well developed in the literature, and then present new methods based on randomization inference. In particular, we extend the local randomization framework to allow for parametric adjustments of the potential outcomes; our extended framework substantially relaxes strong assumptions in prior literature and better resembles other RD inference methods. We compare all these methods formally, focusing on both estimands and inference properties. In addition, we develop new approaches for randomization‐based sensitivity analysis specifically tailored to RD designs. Applying all these methods to the Head Start data, we find that the original RD treatment effect reported in the literature is quite stable and robust, an empirical finding that enhances the credibility of the original result. All the empirical methods we discuss are readily available in general purpose software in R and Stata; we also provide the dataset and software code needed to replicate all our results.

We introduce the Stata (and R) package rdmulti, which includes three commands (rdmc, rdmcplot, rdms) for analyzing Regression Discontinuity (RD) designs with multiple cutoffs or multiple scores. The command rdmc applies to non-cummulative and cummulative multi-cutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects, and provides robust bias-corrected inference procedures. Post estimation and inference is allowed. The command rdmcplot offers RD plots for multi-cutoff settings. Finally, the command rdms concerns multi-score settings, covering in particular cumulative cutoffs and two running variables contexts. It also calculates pooled and cutoff-specific RD treatment effects, provides robust bias-corrected inference procedures, and allows for post-estimation estimation and inference. These commands employ the Stata (and R) package rdrobust for plotting, estimation, and inference. Companion R functions with the same syntax and capabilities are provided.• Non-Cumulative Multiple Cutoffs: units in different groups (e.g., schools) receive an univariate score (e.g., test score) but the RD cutoff varies by group;• Cumulative Multiple Cutoffs: units receive the an univariate score (e.g., age) but different treatments are assigned at distinct score levels (e.g., at age 60 and at age 65);• Multiple Scores: units receive two scores (e.g., latitude and longitude) and treatment is assigned based on a boundary depending on both scores (e.g., geographic boundary).

We introduce the package, which contains four commands to conduct finite-sample inference in regression discontinuity (RD) designs under a local randomization assumption, following the framework and methods proposed in Cattaneo, Frandsen, and Titiunik (2015, Journal of Causal Inference 3: 1–24) and Cattaneo, Titiunik, and Vazquez-Bare (2016, Working Paper, University of Michigan, http://www-personal.umich.edu/∼titiunik/papers/ CattaneoTitiunikVazquezBare2015_wp.pdf). Assuming a known assignment mechanism for units close to the RD cutoff, these functions implement a variety of procedures based on randomization inference techniques. First, the command uses randomization methods to conduct point estimation, hypothesis testing, and confidence interval estimation under different assumptions. Second, the command uses finite-sample methods to select a window near the cutoff where the assumption of randomized treatment assignment is most plausible. Third, the command uses randomization techniques to conduct a sequence of hypothesis tests for different windows around the RD cutoff, which can be used to assess the sensitivity of the methods and to construct confidence intervals by inversion. Finally, the command implements Rosenbaum (2002, Observational Studies [Springer]) sensitivity bounds for the context of RD designs under local randomization. Companion R functions with the same syntax and capabilities are also provided.

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In this article, we introduce two commands, rdpow and rdsampsi, that conduct power calculations and survey sample selection when using local polynomial estimation and inference methods in regression-discontinuity designs. rdpow conducts power calculations using modern robust bias-corrected local polynomial inference procedures and allows for new hypothetical sample sizes and bandwidth selections, among other features. rdsampsi uses power calculations to compute the minimum sample size required to achieve a desired level of power, given estimated or user-supplied bandwidths, biases, and variances. Together, these commands are useful when devising new experiments or surveys in regression-discontinuity designs, which will later be analyzed using modern local polynomial techniques for estimation, inference, and falsification. Because our commands use the communitycontributed (and R) package rdrobust for the underlying bandwidths, biases, and variances estimation, all the options currently available in rdrobust can also be used for power calculations and sample-size selection, including preintervention covariate adjustment, clustered sampling, and many bandwidth selectors. Finally, we also provide companion R functions with the same syntax and capabilities.