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In this article, we introduce the Stata (and R) package rdmulti, which consists of three commands (rdmc, rdmcplot, rdms) for analyzing regression-discontinuity (RD) designs with multiple cutoffs or multiple scores. The command rdmcapplies to noncumulative and cumulative multicutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects and provides robust biascorrected inference procedures. Postestimation and inference is allowed. The command rdmcplotoffers RD plots for multicutoff settings. Finally, the command rdmsconcerns multiscore settings, covering in particular cumulative cutoffs and two running variable contexts. It also calculates pooled and cutoff-specific RD treatment effects, provides robust bias-corrected inference procedures, and allows for postestimation and inference. These commands use the Stata (and R) package rdrobustfor plotting, estimation, and inference. Companion R functions with the same syntax and capabilities are provided.

In this article, we introduce two commands, rdpowand rdsampsi, that conduct power calculations and survey sample selection when using local polynomial estimation and inference methods in regression-discontinuity designs. rdpowconducts power calculations using modern robust bias-corrected local polynomial inference procedures and allows for new hypothetical sample sizes and bandwidth selections, among other features. rdsampsiuses 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 rdrobustfor the underlying bandwidths, biases, and variances estimation, all the options currently available in rdrobustcan 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.

In this article, we introduce two community-contributed commands, rddensityand rdbwdensity, that implement automatic manipulation tests based on density discontinuity and are constructed using the results for local-polynomial density estimators in Cattaneo, Jansson, and Ma (2017b, Simple local polynomial density estimators, Working paper, University of Michigan). These new tests exhibit better size properties (and more power under additional assumptions) than other conventional approaches currently available in the literature. The first command, rddensity, implements manipulation tests based on a novel local-polynomial density estimation technique that avoids prebinning of the data (improving size properties) and allows for restrictions on other features of the model (improving power properties). The second command, rdbwdensity, implements several bandwidth selectors specifically tailored for the manipulation tests discussed herein. We also provide a companion R package with the same syntax and capabilities as rddensityand rdbwdensity.

We describe a major upgrade to the Stata (and R) rdrobustpackage, which provides a wide array of estimation, inference, and falsification methods for the analysis and interpretation of regression-discontinuity designs. The main new features of this upgraded version are as follows: i) covariate-adjusted bandwidth selection, point estimation, and robust bias-corrected inference, ii) cluster–robust bandwidth selection, point estimation, and robust bias-corrected inference, iii) weighted global polynomial fits and pointwise confidence bands in regression-discontinuity plots, and iv) several new bandwidth selection methods, including different bandwidths for control and treatment groups, coverage error-rate optimal bandwidths, and optimal bandwidths for fuzzy designs. In addition, the upgraded package has superior performance because of several numerical and implementation improvements. We also discuss issues of backward compatibility and provide a companion R package with the same syntax and capabilities.

We introduce the rdlocrandpackage, 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 Inference3: 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 rdrandinfcommand uses randomization methods to conduct point estimation, hypothesis testing, and confidence interval estimation under different assumptions. Second, the rdwinselectcommand uses finite-sample methods to select a window near the cutoff where the assumption of randomized treatment assignment is most plausible. Third, the rdsensitivitycommand 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 rdrboundscommand 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.

In the Regression Discontinuity (RD) design, units are assigned a treatment based on whether their value of an observed covariate is above or below a fixed cutoff. Under the assumption that the distribution of potential confounders changes continuously around the cutoff, the discontinuous jump in the probability of treatment assignment can be used to identify the treatment effect. Although a recent strand of the RD literature advocates interpreting this design as a local randomized experiment, the standard approach to estimation and inference is based solely on continuity assumptions that do not justify this interpretation. In this article, we provide precise conditions in a randomization inference context under which this interpretation is directly justified and develop exact finite-sample inference procedures based on them. Our randomization inference framework is motivated by the observation that only a few observations might be available close enough to the threshold where local randomization is plausible, and hence standard large-sample procedures may be suspect. Our proposed methodology is intended as a complement and a robustness check to standard RD inference approaches. We illustrate our framework with a study of two measures of party-level advantage in U.S. Senate elections, where the number of close races is small and our framework is well suited for the empirical analysis.

In this article, we introduce three commands to conduct robust data-driven statistical inference in regression-discontinuity (RD) designs. First, we present rdrobust, a command that implements the robust bias-corrected confidence intervals proposed in Calonico, Cattaneo, and Titiunik (2014d, Econometrica82: 2295–2326) for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. This command also implements other conventional nonparametric RD treatment-effect point estimators and confidence intervals. Second, we describe the companion command rdbwselect, which implements several bandwidth selectors proposed in the RD literature. Following the results in Calonico, Cattaneo, and Titiunik (2014a, Working paper, University of Michigan), we also introduce rdplot, a command that implements several data-driven choices of the number of bins in evenly spaced and quantile-spaced partitions that are used to construct the RD plots usually encountered in empirical applications. A companion R package is described in Calonico, Cattaneo, and Titiunik (2014b, Working paper, University of Michigan).

This article discusses the poparmscommand, which implements two semiparametric estimators for multivalued treatment effects discussed in Cattaneo (2010, Journal of Econometrics155: 138–154). The first is a properly reweighted inverse-probability weighted estimator, and the second is an efficient-influence-function estimator, which can be interpreted as having the double-robust property. Our implementation jointly estimates means and quantiles of the potential-outcome distributions, allowing for multiple, discrete treatment levels. These estimators are then used to estimate a variety of multivalued treatment effects. We discuss pre- and postestimation approaches that can be used in conjunction with our main implementation. We illustrate the program and provide a simulation study assessing the finite-sample performance of the inference procedures.