Fuzzy Regression Discontinuity Design
Also known as: Fuzzy RD, Fuzzy RDD, Fuzzy RD Design, Imperfect RDD
Fuzzy Regression Discontinuity Design (Fuzzy RDD) estimates causal effects when eligibility for a treatment is determined by a threshold on a running variable but actual take-up of that treatment is imperfect — some eligible units do not receive treatment and some ineligible units do. The cutoff acts as an instrument, and the estimand is a Local Average Treatment Effect (LATE) for compliers near the threshold.
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When to use it
Use Fuzzy RDD when treatment eligibility is determined by a threshold on a measurable running variable but compliance is imperfect — meaning that not every eligible unit takes up treatment and/or some ineligible units gain access. The method requires a sufficient density of observations near the cutoff, a running variable that units cannot precisely manipulate, and no other discontinuous policies at the same cutoff. The estimand is local: it applies only to units near c who comply with the eligibility rule. Do not use Fuzzy RDD if the first-stage jump in treatment probability is very small (weak instrument problem), if the running variable can be precisely sorted around the cutoff, or if the outcome of interest is only relevant far from the threshold.
Strengths & limitations
- Provides credible causal identification from observational data when compliance with an eligibility rule is imperfect, using the threshold as a natural instrument.
- Requires minimal assumptions compared to selection-on-observables methods: only local continuity of potential outcomes at the cutoff, not full ignorability.
- Transparent design: the cutoff, the running variable, and the compliance jump are all observable and directly testable.
- Extends naturally to multi-cutoff settings and can be combined with covariate adjustment to improve precision without changing the identification strategy.
- Graphical evidence (outcome and first-stage plots around the cutoff) provides intuitive, non-parametric support for the estimate.
- Estimates a LATE for compliers near the cutoff, which may not extrapolate to units far from the threshold or to always-takers and never-takers.
- Requires a sufficient density of observations near the cutoff; sparse data close to c yields wide confidence intervals and sensitivity to bandwidth choice.
- A weak first stage — a small jump in treatment probability — leads to a near-zero denominator and inflated variance (weak instrument bias).
- Sensitive to bandwidth and polynomial order choices; results can change meaningfully across reasonable specifications.
- Cannot identify effects for non-compliers (always-takers and never-takers), which limits the policy-relevant scope of the estimate.
Frequently asked
What makes an RDD 'fuzzy' rather than 'sharp'?
In a sharp RDD, crossing the cutoff perfectly determines treatment: everyone above receives it and no one below does. A fuzzy RDD arises when the threshold only changes the probability of treatment — some eligible units do not take up treatment and some ineligible units receive it. The cutoff is then used as an instrument rather than as treatment itself.
What does the Fuzzy RDD estimator actually measure?
It estimates the Local Average Treatment Effect (LATE) for compliers — the units who receive treatment because they crossed the cutoff and would not have received it otherwise. Always-takers (treated regardless) and never-takers (untreated regardless) are not identified, so the estimate is local to compliers near the threshold.
How do I know whether my first stage is strong enough?
Estimate the first-stage regression and check that the jump in treatment probability at the cutoff is both statistically significant and economically meaningful (e.g., at least 10-20 percentage points). A first-stage F-statistic well above 10 is the conventional threshold for ruling out weak-instrument concerns.
How should I choose the bandwidth?
Use a data-driven optimal bandwidth selector such as the Calonico, Cattaneo, and Titiunik (CCT) procedure, which balances bias and variance. Always report results for at least two alternative bandwidths (e.g., half and double the optimal) to show that findings are not driven by the specific choice.
What happens if units can manipulate the running variable?
If units can precisely sort themselves just above or below the cutoff, the continuity assumption breaks down and the RDD estimate is biased. Test for this by inspecting the density of the running variable around c using the McCrary (2008) density test. A significant jump in density at the cutoff is a warning sign.
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. ScholarGate. https://scholargate.app/en/causal-inference/fuzzy-regression-discontinuity
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