Subtopic Deep Dive
Regression Discontinuity Designs
Research Guide
What is Regression Discontinuity Designs?
Regression Discontinuity Designs (RDD) estimate causal effects by exploiting discontinuities in treatment assignment at a known cutoff in a running variable.
RDD includes sharp designs where treatment jumps fully at the cutoff and fuzzy designs with imperfect compliance. Researchers select optimal bandwidths and use local randomization tests to validate assumptions. Imbens and Lemieux (2007) provide a practical guide with 889 citations; Calonico et al. (2014) develop robust confidence intervals, cited 2858 times.
Why It Matters
RDD identifies causal effects in policy evaluations like age-based eligibility rules or test score cutoffs for scholarships. Imbens and Wooldridge (2009, 4723 citations) survey RDD applications in program evaluation across economics. Lee (2007, 1735 citations) applies RDD to U.S. House elections, showing quasi-random treatment near vote share cutoffs. These designs require fewer assumptions than RCTs, enabling credible estimates from observational data in education and labor markets.
Key Research Challenges
Optimal Bandwidth Selection
Choosing bandwidth balances bias and variance in local polynomial regressions. Narrow bandwidths increase variance; wide ones introduce bias from smoothness violations. Calonico et al. (2014) propose robust methods for bias-corrected intervals.
Fuzzy RDD Compliance
Treatment probability jumps at cutoff but compliance is imperfect, requiring instrumental variable approaches. Imbens and Lemieux (2007) detail estimation strategies for fuzzy cases. Validation tests check monotonicity assumptions empirically.
Manipulation Testing
Running variable must not bunch at cutoff due to agent manipulation. Density tests like McCrary (2008) detect discontinuities, though not in provided list. Local randomization tests validate as in Lee (2007).
Essential Papers
Recent Developments in the Econometrics of Program Evaluation
Guido W. Imbens, Jeffrey M. Wooldridge · 2009 · Journal of Economic Literature · 4.7K citations
Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statist...
Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs
Sebastián Calónico, Matias D. Cattaneo, Rocío Titiunik · 2014 · Econometrica · 2.9K citations
Peer Reviewed
Randomized experiments from non-random selection in U.S. House elections
David S. Lee · 2007 · Journal of Econometrics · 1.7K citations
A More Credible Approach to Parallel Trends
Ashesh Rambachan, Jonathan Roth · 2023 · The Review of Economic Studies · 913 citations
Abstract This paper proposes tools for robust inference in difference-in-differences and event-study designs where the parallel trends assumption may be violated. Instead of requiring that parallel...
Regression Discontinuity Designs: A Guide to Practice
Guido W. Imbens, Thomas Lemieux · 2007 · 889 citations
In Regression Discontinuity (RD) designs for evaluating causal effects of interventions, assignment to a treatment is determined at least partly by the value of an observed covariate lying on eithe...
Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data
Joseph D. Y. Kang, Joseph L. Schafer · 2007 · Statistical Science · 775 citations
When outcomes are missing for reasons beyond an investigator’s control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to mis...
Difference-in-Differences with Variation in Treatment Timing
Andrew Goodman-Bacon · 2018 · 770 citations
The canonical difference-in-differences (DD) model contains two time periods, "pre" and "post", and two groups, "treatment" and "control".Most DD applications, however, exploit variation across gro...
Reading Guide
Foundational Papers
Start with Imbens and Lemieux (2007) for RDD practice guide, then Imbens and Wooldridge (2009) for program evaluation context, Lee (2007) for empirical example.
Recent Advances
Calonico et al. (2014) for robust CIs; Rambachan and Roth (2023) for parallel trends extensions adaptable to RDD.
Core Methods
Local linear/polynomial regression; bandwidth selectors (IK, CCT); fuzzy IV; density/McCrary tests; randomization inference.
How PapersFlow Helps You Research Regression Discontinuity Designs
Discover & Search
Research Agent uses citationGraph on Imbens and Lemieux (2007) to map RDD foundational works, then findSimilarPapers for bandwidth methods citing Calonico et al. (2014). exaSearch queries 'sharp fuzzy RDD policy evaluation' to retrieve 250M+ OpenAlex papers beyond the list.
Analyze & Verify
Analysis Agent runs readPaperContent on Calonico et al. (2014) to extract confidence interval formulas, then runPythonAnalysis with pandas to simulate bandwidth selection on user data. verifyResponse (CoVe) with GRADE grading checks RDD assumption violations; statistical verification tests density discontinuities.
Synthesize & Write
Synthesis Agent detects gaps in fuzzy RDD applications via contradiction flagging across Imbens and Wooldridge (2009) reviews. Writing Agent uses latexEditText for RDD equations, latexSyncCitations for 4723-cite Imbens paper, and latexCompile for policy report; exportMermaid diagrams cutoff jumps.
Use Cases
"Simulate RDD bandwidth selection on my election data CSV."
Research Agent → searchPapers 'Calonico bandwidth' → Analysis Agent → runPythonAnalysis (pandas local polynomial regression, MSE-optimal bandwidth) → matplotlib plot of bias-variance tradeoff.
"Write LaTeX appendix for fuzzy RDD estimation in policy paper."
Synthesis Agent → gap detection (Imbens Lemieux 2007) → Writing Agent → latexEditText (IV formulas), latexSyncCitations (Lee 2007), latexCompile → PDF with cutoff figure.
"Find GitHub code for RDD density tests."
Research Agent → paperExtractUrls (Lee 2007) → Code Discovery → paperFindGithubRepo → githubRepoInspect (McCrary test Python impl) → runPythonAnalysis on repo code.
Automated Workflows
Deep Research workflow scans 50+ RDD papers via searchPapers on 'regression discontinuity designs', structures report with Imbens and Wooldridge (2009) as anchor, outputs GRADE-graded summary. DeepScan's 7-step chain verifies assumptions: readPaperContent → runPythonAnalysis (density tests) → CoVe checkpoints. Theorizer generates extensions like RDD with heterogeneous effects from Calonico et al. (2014).
Frequently Asked Questions
What defines sharp vs fuzzy RDD?
Sharp RDD has deterministic treatment at cutoff; fuzzy has probability jump, estimated via IV (Imbens and Lemieux 2007).
What are key RDD methods?
Local polynomial regression estimates conditional means near cutoff; robust bias-corrected CI from Calonico et al. (2014); local randomization tests (Lee 2007).
What are foundational RDD papers?
Imbens and Lemieux (2007, 889 cites) guide; Imbens and Wooldridge (2009, 4723 cites) survey; Lee (2007, 1735 cites) election application.
What open problems exist in RDD?
Heterogeneous effects beyond cutoff; extrapolation outside bandwidth; manipulation-robust density tests under clustering.
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