Fuzzy Regression Discontinuity for Policy Evaluation
Fuzzy Regression Discontinuity Design for Policy Evaluation · Also known as: Fuzzy RDD, Fuzzy RD, Fuzzy Regression Discontinuity, Imperfect Compliance RDD
Fuzzy Regression Discontinuity Design (Fuzzy RDD) estimates the causal effect of a policy when eligibility is determined by crossing a threshold on a continuous score, but actual take-up or compliance is imperfect. Developed formally by Hahn, Todd, and Van der Klaauw (2001), it uses the threshold as an instrumental variable to recover a Local Average Treatment Effect (LATE) among compliers near the cutoff.
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When to use it
Use Fuzzy RDD when a policy assigns eligibility by a score threshold and compliance is imperfect — some eligible units do not participate and some ineligible units do. The method is appropriate when the running variable is continuous and not precisely manipulated, and when you can plausibly argue that units near the threshold are as-good-as-randomly assigned to eligibility. Sufficient observations near the cutoff are needed for reliable local estimation. Do not use it when compliance is essentially perfect (use sharp RDD instead), when the running variable is discrete with few values near the cutoff, when there is clear evidence of sorting around the threshold, or when the sample is too thin within a reasonable bandwidth to achieve adequate power.
Strengths & limitations
- Exploits a naturally occurring discontinuity to identify a causal effect without randomisation.
- Recovers the LATE for compliers — exactly the subpopulation most relevant for policy decisions about marginal participants.
- Handles the common real-world situation where policy eligibility and actual participation diverge.
- Transparent and easily visualised: a scatter plot and local polynomial fit at the cutoff communicate the key finding intuitively.
- Requires no untreated comparison group from a separate population; the control group is defined locally by the running variable.
- Estimates only a Local Average Treatment Effect at the cutoff; results do not generalise to units far from the threshold.
- Requires a sufficient density of observations near the cutoff; sparse data around the threshold produce wide confidence intervals.
- The exclusion restriction — that the cutoff affects outcomes only through treatment take-up — can be violated if crossing the threshold triggers other policy responses.
- Bandwidth choice involves a bias-variance trade-off; results can be sensitive to bandwidth selection in small samples.
- A weak first stage (small jump in take-up probability) leads to imprecise and potentially biased LATE estimates.
Frequently asked
What is the difference between sharp and fuzzy RDD?
In a sharp RDD, crossing the cutoff deterministically assigns treatment — all above receive treatment and all below do not. In a fuzzy RDD, crossing the cutoff changes the probability of treatment but compliance is imperfect: some eligible units do not participate and some ineligible units do. The fuzzy design uses the cutoff as an instrument to estimate a LATE among compliers.
What does the LATE estimated by Fuzzy RDD represent?
The LATE (Local Average Treatment Effect) is the causal effect of treatment for the subgroup of compliers near the cutoff — units whose treatment status is determined by whether they cross the eligibility threshold. It does not represent the effect for always-takers (who participate regardless) or never-takers (who never participate).
How do I test whether manipulation of the running variable is a problem?
Run the McCrary (2008) density test or the Cattaneo et al. manipulation test. These check whether the density of the running variable shows a discontinuous jump at the cutoff, which would indicate that units are sorting around the threshold and the identifying assumption may be violated.
What bandwidth should I use?
Data-driven selectors such as the Imbens-Kalyanaraman (IK) or Calonico-Cattaneo-Titiunik (CCT) optimal bandwidth are recommended as the primary choice. Always report results for at least two alternative bandwidths (narrower and wider) to demonstrate robustness.
Can I use Fuzzy RDD with panel data?
Yes. With repeated observations you can include unit fixed effects and multiple pre- and post-period observations to improve precision and conduct richer pre-trend validation. The core identification logic — the jump in treatment probability at the cutoff — remains unchanged.
Sources
- Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and estimation of treatment effects with a regression-discontinuity design. Review of Economic Studies, 68(1), 201-209. DOI: 10.1111/1468-0262.00183 ↗
- Imbens, G. W., & Lemieux, T. (2008). Regression discontinuity designs: A guide to practice. Journal of Econometrics, 142(2), 615-635. DOI: 10.1016/j.jeconom.2007.05.001 ↗
How to cite this page
ScholarGate. (2026, June 3). Fuzzy Regression Discontinuity Design for Policy Evaluation. ScholarGate. https://scholargate.app/en/causal-inference/policy-evaluation-fuzzy-regression-discontinuity
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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