Panel Data Fuzzy Regression Discontinuity Design
Also known as: Panel Fuzzy RDD, Panel FRD, Fuzzy RD with Panel Data, Panel Fuzzy RD
Panel Data Fuzzy Regression Discontinuity Design (Panel FRD) extends the fuzzy RDD framework to settings where multiple observations per unit are available over time. It exploits a probabilistic — rather than deterministic — threshold-crossing rule to identify a local average treatment effect (LATE) while controlling for unit-level and time-level fixed effects, sharpening identification in repeated-measures contexts.
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When to use it
Use Panel FRD when (a) treatment assignment is governed by a score or index with a known cutoff but compliance is imperfect, (b) you have panel data — the same units observed across multiple periods — allowing unit and time fixed effects, and (c) the running variable is continuous with no evidence of systematic manipulation at the cutoff. It is particularly valuable when a pure sharp RDD is implausible because institutional or behavioral factors lead to incomplete takeup. Do not use it when compliance is effectively complete (sharp RDD suffices), when the running variable is discrete without density near the cutoff, when the sample within the bandwidth is too small to sustain IV estimation, or when the panel is very short (fewer than three periods) and fixed-effect purging gains little.
Strengths & limitations
- Combines the local identification of fuzzy RDD with the unit and time fixed-effect controls of panel analysis, reducing omitted-variable bias from stable unit characteristics.
- The threshold-crossing rule provides a credible instrumental variable that is plausibly exogenous conditional on smooth running-variable controls.
- Multiple periods increase the number of observations near the cutoff, improving precision of the first-stage and LATE estimates.
- LATE is well-defined and policy-relevant: it applies specifically to compliers — units whose behavior is actually altered by the threshold.
- Validity is assessable through established diagnostic tools: density tests, covariate-balance checks at the cutoff, and placebo outcomes.
- Estimates are local: the LATE applies only to compliers near the cutoff and may not generalize to the broader population.
- Requires a sufficiently large and dense sample near the cutoff within each period; sparse data at the margin renders the IV weak.
- Assumes no manipulation of the running variable by agents anticipating the cutoff — violations (e.g., strategic scoring) invalidate the design.
- Panel fixed effects require that the cutoff and its compliance structure remain stable across periods; structural breaks in the assignment rule undermine identification.
- Two-stage estimation propagates first-stage uncertainty; a weak first stage (F < 10) inflates IV bias and requires special weak-instrument inference.
Frequently asked
How does Panel FRD differ from a standard fuzzy RDD?
A standard fuzzy RDD is typically estimated cross-sectionally or by pooling cross-sections without unit fixed effects. Panel FRD adds unit-level and time-level fixed effects to absorb permanent differences across units and aggregate period shocks, reducing omitted-variable bias and improving precision when the same units are observed repeatedly.
What makes compliance 'fuzzy' rather than 'sharp'?
Compliance is fuzzy when crossing the cutoff raises the probability of treatment but does not guarantee it — some above-cutoff units are untreated (non-compliers) and some below-cutoff units are treated (defiers or always-takers). The Wald/2SLS ratio corrects for this imperfect compliance to recover the effect on compliers.
How do I choose the bandwidth in a panel setting?
Apply standard data-driven bandwidth selectors such as the Calonico-Cattaneo-Titiunik (CCT) optimal bandwidth, computed within the panel-data context. Present results across a range of bandwidths as a robustness check; the estimate should be stable across reasonable bandwidth choices.
Can I use time-varying running variables?
Yes — if the running variable changes across periods for the same unit, you have more variation near the cutoff, which is helpful. However, if units strategically adjust their running-variable value over time to cross the threshold, manipulation concerns become more acute and must be carefully tested.
What if my first stage is weak?
A first-stage F-statistic below 10 signals a weak instrument. Report the Anderson-Rubin confidence interval or other weak-instrument-robust statistics. Consider whether the bandwidth is too narrow (too few compliers) or whether compliance in the population is genuinely very low, in which case the design may not be viable.
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 ↗
- Lee, D. S., & Lemieux, T. (2010). Regression Discontinuity Designs in Economics. Journal of Economic Literature, 48(2), 281-355. DOI: 10.1257/jel.48.2.281 ↗
How to cite this page
ScholarGate. (2026, June 3). Panel Data Fuzzy Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/panel-data-fuzzy-regression-discontinuity
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