Dynamic Fuzzy Regression Discontinuity Design
Also known as: Dynamic Fuzzy RDD, DFRD, Time-varying Fuzzy RD, Dynamic Fuzzy RD Design
Dynamic Fuzzy Regression Discontinuity Design extends the standard fuzzy RDD to a panel or multi-period setting, allowing researchers to estimate how the causal effect of a probabilistic threshold-based treatment evolves over time. By combining an IV-based fuzzy first stage with time-indexed outcomes, it traces treatment effects across multiple post-treatment periods, not just at a single cross-sectional snapshot.
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When to use it
Use this design when you have a continuous forcing variable with a policy cutoff, imperfect compliance with treatment assignment (making the design fuzzy), and panel or repeated cross-sectional data that allow outcomes to be observed across multiple periods after treatment. It is well-suited to questions about whether programme effects persist or fade, such as the multi-year returns to school funding, health interventions with time-varying effects, or benefit eligibility. Do not use it when compliance is near-perfect (a sharp RDD is simpler), when the running variable is manipulable near the cutoff, or when the panel is very short (fewer than two post-treatment periods) — in those cases a standard fuzzy RDD or a DiD-based design is more appropriate.
Strengths & limitations
- Recovers a credible causal effect even when treatment assignment is probabilistic, by using the threshold as an instrument.
- Traces the dynamic time profile of treatment effects, revealing whether impacts grow, plateau, or decay.
- Controls for unit-specific and period-specific confounders through fixed effects in the panel dimension.
- Relies only on local variation near the cutoff, reducing concerns about extrapolation to units far from the threshold.
- Complements power analysis: the bandwidth and number of periods together determine effective sample size near the cutoff.
- Identification is local — the LATE applies only to compliers near the cutoff, limiting generalisability to the broader population.
- Requires a sufficiently dense running variable near the cutoff in every time period; sparse data at the margin weakens precision.
- Assumes the instrument (cutoff crossing) is excludable from the outcome equation other than through treatment — contamination of the exclusion restriction invalidates the IV.
- Bandwidth selection must balance bias and variance; a common bandwidth across all time periods may not be optimal for each separately.
- Long-run dynamic effects can be confounded by attrition or compositional changes in units near the cutoff over time.
Frequently asked
What distinguishes the fuzzy from the sharp version?
In a sharp RDD every unit above the cutoff is treated and every unit below is not. In the fuzzy version, crossing the cutoff raises the probability of treatment without guaranteeing it, so the threshold serves as an instrument and the estimate is a Local Average Treatment Effect for compliers near the cutoff only.
How many time periods do I need for the dynamic extension?
At minimum two post-treatment periods are needed to trace any dynamics. Cellini et al. (2010) used up to ten post-treatment periods. More periods increase precision for detecting growth or decay patterns, but each period must have enough units near the cutoff to yield reliable local estimates.
How do I choose the bandwidth in the dynamic setting?
The bandwidth controls how far from the cutoff you include observations. You can use either a common bandwidth across all periods (simpler, comparable) or period-specific optimal bandwidths (more efficient). Data-driven selectors such as Imbens and Kalyanaraman (2012) are standard; sensitivity checks across bandwidths are always advisable.
What if my running variable is partially manipulable?
Manipulation near the cutoff — units sorting just above or below — invalidates the quasi-random assignment and breaks the IV. Run a McCrary (2008) density test in each period. If manipulation is detected, a different identification strategy such as DiD or matching should be considered.
Can I pool all time periods into one regression?
Yes, a stacked or pooled regression with period-by-threshold interactions is common and increases statistical power. It imposes a functional form on the time path of effects. Report both pooled and period-specific estimates to show the full dynamic profile.
Sources
- 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 ↗
- Cellini, S. R., Ferreira, F., & Rothstein, J. (2010). The Value of School Facility Investments: Evidence from a Dynamic Regression Discontinuity Design. Quarterly Journal of Economics, 125(1), 215-261. DOI: 10.1162/qjec.2010.125.1.215 ↗
How to cite this page
ScholarGate. (2026, June 3). Dynamic Fuzzy Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/dynamic-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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