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1. Constructing multiple, independent analyses in the regression discontinuity design with multiple cutoffs

   https://doi.org/10.1353/obs.2024.a946585  

   Lee, Youjin; Tan, Chichun; Karmakar, Bikram (January 2024, Observational Studies)

   Abstract: The regression discontinuity (RD) design is a commonly used non-experimental approach for evaluating policy or program effects. However, this approach heavily relies on the untestable assumption that distribution of confounders or average potential outcomes near or at the cutoff are comparable. When there are multiple cutoffs that create several discontinuities in the treatment assignments, factors that can lead this assumption to the failure at one cutoff may overlap with those at other cutoffs, invalidating the causal effects from each cutoff. In this study, we propose a novel approach for testing the causal hypothesis of no RD treatment effect that can remain valid even when the assumption commonly considered in the RD design does not hold. We propose leveraging variations in multiple available cutoffs and constructing a set of instrumental variables (IVs). We then combine the evidence from multiple IVs with a direct comparison under the local randomization framework. This reinforced design that combines multiple factors from a single data can produce several, nearly independent inferential results that depend on very different assumptions with each other. Our proposed approach can be extended to a fuzzy RD design. We apply our method to evaluate the effect of having access to higher achievement schools on students' academic performances in Romania. 

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2. A guide to regression discontinuity designs in medical applications

   https://doi.org/10.1002/sim.9861  

   Cattaneo, Matias D.; Keele, Luke; Titiunik, Rocío (October 2023, Statistics in Medicine)

   We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity‐based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias‐corrected inference methods for uncertainty quantification. We also overview empirical falsification tests that can be used to support key assumptions. Our discussion focuses on two particular features that are relevant in biomedical research: (i) fuzzy RD designs, which often arise when therapeutic treatments are based on clinical guidelines, but patients with scores near the cutoff are treated contrary to the assignment rule; and (ii) RD designs with discrete scores, which are ubiquitous in biomedical applications. We illustrate our discussion with three empirical applications: the effect CD4 guidelines for anti‐retroviral therapy on retention of HIV patients in South Africa, the effect of genetic guidelines for chemotherapy on breast cancer recurrence in the United States, and the effects of age‐based patient cost‐sharing on healthcare utilization in Taiwan. Complete replication materials employing publicly available data and statistical software inPython,RandStataare provided, offering researchers all necessary tools to conduct an RD analysis. 

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

   https://doi.org/10.1093/ectj/utz022  

   Calonico, Sebastian; Cattaneo, Matias D; Farrell, Max H (November 2019, The Econometrics Journal)

   Summary 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. 

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4. Binscatter regressions

   https://doi.org/10.1177/1536867X251322960  

   Cattaneo, Matias D; Crump, Richard K; Farrell, Max H; Feng, Yingjie (March 2025, The Stata Journal: Promoting communications on statistics and Stata)

   In this article, we introduce the packagebinsreg, which implements the binscatter methods developed by Cattaneo et al. (2024a, arXiv:2407.15276 [stat.EM]; 2024b,American Economic Review114: 1488–1514). The package comprises seven commands:binsreg, binslogit, binsprobit, binsqreg, binstest binspwc, andbinsregselect. The first four commands implement binscatter plotting, point estimation, and uncertainty quantification (confidence intervals and confidence bands) for least-squares linear binscatter regression (binsreg) and for nonlinear binscatter regression (binslogitfor logit regression,binsprobitfor. probit regression, andbinsqregfor quantile regression). The next two commands focus on pointwise and uniform inference:binstestimplements hypothesis testing procedures for parametric specifications and for nonparametric shape restrictions of the unknown regression function, whilebinspwcimplements multigroup pairwise statistical comparisons. The last command,binsregselect, implements. data-driven number-of-bins selectors. The commands offer binned scatterplots and allow for covariate adjustment, weighting, clustering, and multisample analysis, which is useful when studying treatment-effect heterogeneity in randomizec and observational studies, among many other features. 

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5. Regression Discontinuity Designs

   https://doi.org/10.1146/annurev-economics-051520-021409  

   Cattaneo, Matias D.; Titiunik, Rocío (August 2022, Annual Review of Economics)

   The regression discontinuity (RD) design is one of the most widely used nonexperimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and matured, and there is now a large number of methodological results for RD identification, estimation, inference, and validation. We offer a curated review of this methodological literature organized around the two most popular frameworks for the analysis and interpretation of RD designs: the continuity framework and the local randomization framework. For each framework, we discuss three main topics: ( a) designs and parameters, focusing on different types of RD settings and treatment effects of interest; ( b) estimation and inference, presenting the most popular methods based on local polynomial regression and methods for the analysis of experiments, as well as refinements, extensions, and alternatives; and ( c) validation and falsification, summarizing an array of mostly empirical approaches to support the validity of RD designs in practice. 

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