Regression Discontinuity Design

Regression discontinuity (RD) designs are commonly used for program evaluation with continuous treatment assignment variables. But in practice, treatment assignment is frequently based on ordinal variables. In this study, we propose an RD design with an ordinal running variable to assess the effects of extended time accommodations (ETA) for English-language learners (ELLs). ETA eligibility is determined by ordinal ELL English-proficiency categories of National Assessment of Educational Progress data. We discuss the identification and estimation of the average treatment effect (ATE), intent-to-treat effect, and the local ATE at the cutoff. We also propose a series of sensitivity analyses to probe the effect estimates’ robustness to the choices of scaling functions and cutoff scores and remaining confounding.

While regression discontinuity designs (RDDs) offer credible identification of treatment effects near cutoff points, their external validity remains inherently limited. To address this, a conditional independence assumption may be required. However, in multiple-score RDDs, this requires joint independence between all running variables and both potential outcomes and treatment assignments—a restriction often too strong to hold in practice. We relax this by assuming only mean independence between potential outcomes and the interaction of running variables, conditional on covariates. This weaker assumption allows us to link treatment effects at boundary and non-boundary points. We propose a non-parametric testing procedure and illustrate our method using simulation experiments and an empirical application in Colombian education policy, respectively.

We examine the heterogeneous and dynamic impact of China's New Rural Pension Scheme on intergenerational wealth dependence using a nationally representative longitudinal household survey covering the period 2011-13.We adopt an instrumental quantile regressiondiscontinuity design to address the endogeneity of partial compliance of the pension scheme and the observed individual heterogeneity.Overall, we find that the pension scheme smooths wealth dependence between generations in the short term, but strengthens the persistence of assets among the wealthiest households in the medium term.The mechanisms underlying these distributional effects are intergenerational transfers, time reallocation, and filial adjustments of the wealth portfolio.Complementary policy interventions, particularly for the poor across generations, would be needed to neutralize the distributional impact of the pension in terms of intergenerational wealth persistence.

This article provides a detailed discussion of the theory and practice of modern regression discontinuity (RD) analysis for estimating the effects of interventions or treatments. Part 1 briefly chronicles the history of RD analysis and summarizes its past applications. Part 2 explains how in theory an RD analysis can identify an average effect of treatment for a population and how different types of RD analyses—“sharp” versus “fuzzy”—can identify average treatment effects for different conceptual subpopulations. Part 3 of the article introduces graphical methods, parametric statistical methods, and nonparametric statistical methods for estimating treatment effects in practice from regression discontinuity data plus validation tests and robustness tests for assessing these estimates. Section 4 considers generalizing RD findings and presents several different views on and approaches to the issue. Part 5 notes some important issues to pursue in future research about or applications of RD analysis.

Quantile treatment effects in the regression discontinuity design

Regression discontinuity (RD) designs are a popular approach to estimating a treatment effect of cutoff-based interventions. Two current estimation approaches dominate the literature. One fits separate regressions on either side of the cutoff, and the other performs finite sample inference based on a local randomization assumption. Recent developments of these approaches have often focused on asymptotic properties and large sample sizes. Educational applications often contain relatively small samples or sparsity near the cutoff, making estimation more difficult. As an alternative to the aforementioned approaches, we develop a partial linear estimator for RD designs. We show in simulations that our estimator outperforms certain leading estimators in several realistic, small-sample scenarios. We apply our estimator to school accountability scores in Indiana.

In a traditional regression-discontinuity design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous assignment variable. The treatment effect is measured at a single cutoff location along the assignment variable. This article introduces the multivariate regression-discontinuity design (MRDD), where multiple assignment variables and cutoffs may be used for treatment assignment. For an MRDD with two assignment variables, we show that the frontier average treatment effect can be decomposed into a weighted average of two univariate RDD effects. The article discusses four methods for estimating MRDD treatment effects and compares their relative performance in a Monte Carlo simulation study under different scenarios.

This chapter addresses two different but related approaches, both widely used within the literature on the econometrics of program evaluation: the Local average treatment effect (LATE) and the Regression-discontinuity-design (RDD). Considered as nearly quasi-experimental methods, these approaches have recently been the subject of a vigorous interest as tools for detecting treatment effects within special statistical settings. The first part of the chapter covers the theory behind LATE, thus illustrating how such approach can be embedded within the setting of a randomized experiment with imperfect compliance. The discussion then goes on to present the Wald estimator of LATE, and to extend LATE to the case of multiple instruments and multiple treatments. The second part of the chapter illustrates the RDD econometric theoretical background; in particular, it discusses separately sharp RDD and fuzzy RDD, and suggests a protocol for the empirical implementation of such approaches. The chapter ends with some illustrative empirical implementation of both LATE and RDD performed using Stata on both real and simulative examples.

IntroductionWith the results of the 2015 and 2018 randomized clinical trials, hospital-based protocols and society-based guidelines have emerged to define candidacy for endovascular stroke therapy (EST) for large vessel occlusion...

Education is related to a wide variety of beneficial health, behavioral, and societal outcomes. However, whether education causes long-term structural changes in the brain remains unclear. A pressing challenge is that individuals self-select into continued education, thereby introducing a wide variety of environmental and genetic confounders. Fortunately, natural experiments allow us to isolate the causal impact of increased education from individual (and societal) characteristics. Here, we exploit a policy change in the UK (the 1972 ROSLA act) that increased the amount of mandatory schooling from 15 to 16 years of age to study the impact of education on long-term structural brain outcomes in the UK Biobank. Using regression discontinuity (RD) – a causal inference method – we find no evidence of an effect from an additional year of education on any structural neuroimaging outcomes. This null result is robust across modalities, regions, and analysis strategies. An additional year of education is a substantial cognitive intervention, yet we find no evidence for sustained experience-dependent plasticity. Our results provide a challenge for prominent accounts of cognitive or ‘brain reserve’ theories which identify education as a major protective factor to lessen adverse aging effects. Our preregistered findings are one of the first implementations of RD on neural data – opening the door for causal inference in population-based neuroimaging.

Causal Inference, Matching, and Regression Discontinuity

Regression Discontinuity Design

The purpose of this study was to compare the results of a regression discontinuity design (RDD) with those of an experimental design of a tiered vocabulary intervention for children at risk for reading disability to determine RDD’s feasibility as a research methodology for this type of study. Researchers reanalyzed an archival dataset of a previous study that determined the effectiveness of the intervention through a randomized experiment. Results were comparable for the receptive outcome scores in direction, magnitude, and significance, although the magnitude of the treatment effect for the RDD was slightly higher. Results were also comparable for contextual outcome scores with respect to direction and magnitude. We present possible reasons for the different results between studies, limitations, and future research.

Estimation and Inference of Regression Discontinuity Design with Ordered or Discrete Duration Outcomes

I. Preface (Maureen A. Pirog). II. The State of Social Experimentation and Program (Maureen A. Pirog). III. Social Experiments Versus Quasi-Experiments. The Role of Random Assignment in Social Policy Research (Richard P. Nathan). The Role of Random Assignment in Social Policy Research (Robinson Hollister). Nathan Response to Robinson Hollister's Opening Statement (Richard P. Nathan). Hollister Response to Richard Nathan's Opening Statement (Robinson Hollister). Do Experimental and Nonexperimental Evaluations Give Different Answers About the Effectiveness of Government-Funded Training Programs? (David H. Greenberg, Charles Michalopoulos, and Philip K. Robins). How Close is Close Enough? Evaluating Propensity Score Matching Using Data from a Class Size Reduction Experiment (Elizabeth Ty Wilde and Robinson Hollister). Three Conditions under which Experiments and Observational Studies Produce Comparable Causal Estimates: New findings from within-study comparisons 27(4) (Thomas D. Cook, William R. Shadish, and Vivian C. Wong). IV. Randomized Experiments. Impacts of Abstinence-Only Education on Teen Sexual Activity, Risk of Pregnancy, and Risk of Sexually Transmitted Diseases (Barbara Devaney, Chris Trenholm, Ken Forston, Melissa Clark, Lisa Quay, and Justin Wheeler). Five-Year Effects of an Anti-Poverty Program on Marriage among Never-Married Mothers (Anna Gassman-Pines and Hirokazu Yoshikawa). Alternative Routes to Teaching: The Impacts of Teach for America on Student Achievement and Other Outcomes (Steven Glazerman, Daniel Mayer, and Paul Decker). V. Quasi-Experiments A. Natural Experiments. Anti-Depressants, Suicide, and Drug Regulation (Jens Ludwig and Dave E. Marcotte). Lowering Blood Alcohol Content Levels to Save Lives: The European Experience (Daniel Albalate). The Impact of the Family and Medical Leave Act (Jane Waldfogel). The Effects of State and Local Antidiscrimination Policies on Earnings for Gays and Lesbians (Marieka M. Klawitter and Victor Flatt). B. Pretests and Posttests with Comparison Groups and Selection Controls. A Cure for Crime: Can Mental Health Treatment Diversion Reduce Crime among Youth? (Allison Evans Cuellar, Larkin S. McReynolds, and Gail A. Wasserman). Cashing Out Food Stamps: Impacts on Food Expenditures and Diet Quality (Barbara Devaney and Thomas Fraker). C. Interrupted Time Series with Comparison Groups. The Effect of Drinking Age Laws and Alcohol-Related Crashes: Time-Series Evidence from Wisconsin (David N. Figlio). Evaluating the Effects of Automobile Safety Regulation (John D. Graham and Steven Garber). D. Posttests Only with Comparison Groups. Does WIC Work? The Effects of WIC on Pregnancy and Birth Outcomes (Marianne P. Bitler and Janet Currie). The Changing Association between Prenatal Participation in WIC and Birth Outcomes in New York City (Ted Joyce, Diane Gibson, and Silvie Colman). The Changing Association between Prenatal Participation in WIC and Birth Outcomes in New York City: What Does It Mean? (Marianne P. Bitler and Janet Currie). Interpreting the WIC DEBATE (Jens Ludwig and Mathew Miller). E. Regression Discontinuity Design. An Effectiveness-Based of Five State Pre-Kindergarten Programs (Vivian C. Wong, Thomas D. Cook, W. Steven Barnett, and Kwanghee Jung). VII. Meta-Analyses. Assessing Evidence of Environmental Inequities: A Meta-Analysis (Evan J. Ringquist). VIII. Implementation, Performance Management, and Program Impacts. Linking Program Implementation and Effectiveness: Lessons from a Pooled Sample of Welfare-to-Work Experiments (Howard S. Bloom, Carolyn J. Hill, and James A. Riccio). Exploring the Relationship between Performance Management and Program Impact: A Case Study of the JPTA (Burt S. Barnow). IX. Ethics and Human Subjects. a More Public Discussion of the Ethics of Federal Social Program (Jan Blustein). The Ethics of Federal Social Program Evaluation: A Response to (Blustein Burt S. Barnow). To Learn or Not to Learn (Howard Rolston). Comments on Dr. Blustein's Paper, Toward a More Public Discussion of the Ethics of Federal Social Program Evaluation (Peter Z. Schochet). Jan Blustein's Response (Jan Blustein). X. The Use of Program Evaluations by Policy Makers. The Dissemination and Utilization of Welfare-to-Work Experiments in State Policymaking (David Greenberg, Marvin Mandell, and Matthew Onstott).