On Interpreting the Regression Discontinuity Design as a Local Experiment

Sekhon, Jasjeet S.; Titiunik, Rocío

doi:10.1108/s0731-905320170000038001

Cited by 37 publications

(33 citation statements)

References 26 publications

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“…Part 3 states that, inside the window, the distribution of the treatment vector is known to the researcher. In the Supporting Information Appendix, we offer a discussion linking this notion of local randomization using fixed potential outcomes to other notions of local randomization using random potential outcomes (building on Cattaneo et al., ; Sekhon & Titiunik, 2017) and to related ideas based on continuity‐based identification, including Lee’s () model of imprecise manipulation…”

Section: Rd Based On Randomization Near the Cutoffmentioning

confidence: 99%

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Cattaneo¹,

Titiunik²,

Vázquez-Baré³

2017

J. Pol. Anal. Manage.

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133

145

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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.

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Section: Rd Based On Randomization Near the Cutoffmentioning

confidence: 99%

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Cattaneo¹,

Titiunik²,

Vázquez-Baré³

2017

J. Pol. Anal. Manage.

Self Cite

133

145

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“…From the specific perspective of covariate adjustment, our paper is related to two strands of the literature. First, a portion of the RD literature re-interprets the data as being "as good as randomized" within a small window around the cutoff, though this requires stronger conditions than just continuity/smoothness of conditional expectations as we maintain here (Lee, 2008;Cattaneo, Frandsen and Titiunik, 2015;Cattaneo, Titiunik and Vazquez-Bare, 2017;Sekhon and Titiunik, 2017). Adopting a local randomization perspective, our work is related in obvious ways to the large literature on covariate adjustment in randomized experiments (e.g., Imbens and Rubin, 2015, and references therein), and shows two interesting connections.…”

Section: Introductionmentioning

confidence: 99%

Regression Discontinuity Designs Using Covariates

Calónico

Cattaneo

Farrell

et al. 2019

The Review of Economics and Statistics

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510

445

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We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. An empirical illustration and an extensive simulation study is presented. All methods are implemented in R and Stata software packages.

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“…As such, the appropriate neighborhood under local randomization can not be generated by MSE-or CE-optimal bandwidth choices, and other methods are more appropriate: see Section 3 in Cattaneo, Frandsen and Titiunik (2015) for one example. For further discussion of these different assumptions and methodologies, as well as comparisons between neighborhood selectors, see , Cattaneo, Titiunik and Vazquez-Bare (2017), and Sekhon and Titiunik (2017).…”

Section: Introductionmentioning

confidence: 99%

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

Calónico

Cattaneo

Farrell

2019

The Econometrics Journal

264

176

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Modern empirical work in Regression Discontinuity (RD) designs 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 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 must be shrank 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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On Interpreting the Regression Discontinuity Design as a Local Experiment

Cited by 37 publications

References 26 publications

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

Regression Discontinuity Designs Using Covariates

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

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