scholarly journals Inference in Regression Discontinuity Designs with a Discrete Running Variable

2018 ◽  
Vol 108 (8) ◽  
pp. 2277-2304 ◽  
Author(s):  
Michal Kolesár ◽  
Christoph Rothe
Keyword(s):  
Confidence Intervals ◽  
Conditional Expectation ◽  
Regression Discontinuity ◽  
Model Misspecification ◽  
Standard Errors ◽  
Moderate Number ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Present Simulation ◽  
Theoretical Results

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable as a means to make inference robust to model misspecification (Lee and Card 2008). We derive theoretical results and present simulation and empirical evidence showing that these CIs do not guard against model misspecification, and that they have poor coverage properties. We therefore recommend against using these CIs in practice. We instead propose two alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function. (JEL C13, C51, J13, J31, J64, J65)

scholarly journals Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Otávio Bartalotti
Keyword(s):  
Bias Correction ◽  
Asymptotic Theory ◽  
Regression Discontinuity ◽  
Traditional Approach ◽  
Standard Errors ◽  
Test Coverage ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Theoretical Results ◽  
Robust Standard Errors

AbstractIn regression discontinuity designs (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the “fixed-bandwidth” alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators aslocallyparametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

Model Uncertainty and Model Averaging in Regression Discontinuity Designs

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Patrick Button
Keyword(s):  
Model Uncertainty ◽  
Regression Discontinuity ◽  
Model Averaging ◽  
Parametric Model ◽  
Parametric Models ◽  
Standard Errors ◽  
Randomized Experiments ◽  
Monte Carlo Experiments ◽  
Regression Discontinuity Designs ◽  
Frequentist Model Averaging

AbstractParametric (polynomial) models are popular in research employing regression discontinuity designs and are required when data are discrete. However, researchers often choose a parametric model based on data inspection or pretesting. These approaches lead to standard errors and confidence intervals that are too small because they do not incorporate model uncertainty. I propose using Frequentist model averaging to incorporate model uncertainty into parametric models. My Monte Carlo experiments show that Frequentist model averaging leads to mean square error and coverage probability improvements over pretesting. An application to [Lee, D. S. 2008. “Randomized Experiments From Non-Random Selection in US House Elections.”

scholarly journals Regression Discontinuity Designs Using Covariates

2019 ◽  
Vol 101 (3) ◽  
pp. 442-451 ◽  
Author(s):  
Sebastian Calonico ◽  
Matias D. Cattaneo ◽  
Max H. Farrell ◽  
Rocío Titiunik
Keyword(s):  
Mean Squared Error ◽  
Regression Discontinuity ◽  
Standard Errors ◽  
Local Polynomial ◽  
Squared Error ◽  
Software Packages ◽  
Continuous Covariates ◽  
Regression Functions ◽  
Regression Discontinuity Designs ◽  
Robust Standard Errors

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. We provide an empirical illustration and an extensive simulation study. All methods are implemented in R and Stata software packages.

scholarly journals Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs

Econometrica ◽  
2014 ◽  
Vol 82 (6) ◽  
pp. 2295-2326 ◽  
Author(s):  
Sebastian Calonico ◽  
Matias D. Cattaneo ◽  
Rocio Titiunik
Keyword(s):  
Confidence Intervals ◽  
Regression Discontinuity ◽  
Regression Discontinuity Designs ◽  
Nonparametric Confidence Intervals

scholarly journals Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals

2020 ◽  
Vol 23 (2) ◽  
pp. 211-231
Author(s):  
Yang He ◽  
Otávio Bartalotti
Keyword(s):  
Confidence Intervals ◽  
Class Size ◽  
Student Outcomes ◽  
Regression Discontinuity ◽  
Fuzzy Regression ◽  
New Method ◽  
Wild Bootstrap ◽  
Bootstrap Procedure ◽  
Related Literature ◽  
Regression Discontinuity Designs

Summary This paper develops a novel wild bootstrap procedure to construct robust bias-corrected valid confidence intervals for fuzzy regression discontinuity designs, providing an intuitive complement to existing robust bias-corrected methods. The confidence intervals generated by this procedure are valid under conditions similar to the procedures proposed by Calonico et al. (2014) and related literature. Simulations provide evidence that this new method is at least as accurate as the plug-in analytical corrections when applied to a variety of data-generating processes featuring endogeneity and clustering. Finally, we demonstrate its empirical relevance by revisiting Angrist and Lavy (1999) analysis of class size on student outcomes.

scholarly journals Equivalence Testing for Regression Discontinuity Designs

2020 ◽  
pp. 1-17
Author(s):  
Erin Hartman
Keyword(s):  
Political Science ◽  
Current Practice ◽  
Regression Discontinuity ◽  
Regression Function ◽  
Superior Performance ◽  
Equivalence Testing ◽  
Simulation Studies ◽  
Equivalence Tests ◽  
Regression Discontinuity Designs ◽  
Testing Approach

Abstract Regression discontinuity (RD) designs are increasingly common in political science. They have many advantages, including a known and observable treatment assignment mechanism. The literature has emphasized the need for “falsification tests” and ways to assess the validity of the design. When implementing RD designs, researchers typically rely on two falsification tests, based on empirically testable implications of the identifying assumptions, to argue the design is credible. These tests, one for continuity in the regression function for a pretreatment covariate, and one for continuity in the density of the forcing variable, use a null of no difference in the parameter of interest at the discontinuity. Common practice can, incorrectly, conflate a failure to reject evidence of a flawed design with evidence that the design is credible. The well-known equivalence testing approach addresses these problems, but how to implement equivalence tests in the RD framework is not straightforward. This paper develops two equivalence tests tailored for RD designs that allow researchers to provide statistical evidence that the design is credible. Simulation studies show the superior performance of equivalence-based tests over tests-of-difference, as used in current practice. The tests are applied to the close elections RD data presented in Eggers et al. (2015b).

scholarly journals The Choice of Neighborhood in Regression Discontinuity Designs

2017 ◽  
Vol 3 (2) ◽  
pp. 134-146
Author(s):  
Matias D. Cattaneo ◽  
Gonzalo Vazquez-Bare
Keyword(s):  
Regression Discontinuity ◽  
Regression Discontinuity Designs
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