Multi-period Fuzzy Regression Discontinuity Design
Also known as: multi-period fuzzy RDD, fuzzy RD with repeated assignment, multi-wave fuzzy RD, staggered fuzzy RDD
Multi-period fuzzy regression discontinuity design estimates a local average treatment effect when a cutoff rule only partially determines treatment — that is, crossing the threshold raises the probability of treatment but does not guarantee it — and when this assignment process is observed across two or more time periods or cohorts, enabling pooled or period-specific causal estimates under repeated near-threshold comparisons.
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When to use it
Use this design when treatment is determined by a cutoff on a measurable score, compliance is imperfect (fuzzy), and data are available across at least two periods or cohorts. It is appropriate when you want more power than a single-period fuzzy RD provides, or when you wish to trace effect heterogeneity over time. It is not appropriate when the running variable is not continuous or is partially under the agent's control (manipulation), when the cutoff threshold changes so frequently that no wave has sufficient bandwidth, when fewer than roughly 50 observations fall within the optimal bandwidth in any given period, or when treatment effects at the cutoff are implausible to remain locally stable across periods.
Strengths & limitations
- Pools multiple local experiments near the cutoff, substantially increasing statistical power compared to a single-period fuzzy RD.
- Estimates a credible LATE for compliers near the cutoff with minimal parametric assumptions, even in observational data.
- Period-specific estimates allow researchers to detect whether treatment effects grow, decay, or reverse over time.
- Threshold-based assignment is transparent and easy to communicate to policymakers and reviewers.
- Fixed-effects specifications can be incorporated to remove time-invariant unit heterogeneity when the data are panel.
- The LATE applies only to compliers close to the cutoff; it does not generalise to units far from the threshold or to never-takers and always-takers.
- If the running variable is manipulable (agents sort around the cutoff), the local randomisation is violated and the estimates are biased.
- Combining periods implicitly assumes that the treatment effect is either constant across periods or that period-specific estimates are correctly specified; unmodelled heterogeneity can produce misleading pooled estimates.
- Bandwidth selection is more complex in multi-period settings, particularly when sample sizes differ substantially across periods.
- Requires a strong first stage in every period; weak instruments in some periods inflate the pooled standard error or bias the LATE toward the OLS estimate.
Frequently asked
What makes this design 'fuzzy' as opposed to 'sharp'?
In a sharp RD, crossing the cutoff perfectly determines treatment: everyone above the threshold is treated and everyone below is not. In a fuzzy RD, crossing the threshold only changes the probability of treatment — some who qualify refuse, and some who do not qualify still receive treatment. The threshold is therefore used as an instrument, and the LATE applies to the compliers whose treatment status is actually switched by the cutoff.
How do I choose the bandwidth in a multi-period fuzzy RD?
Apply a data-driven bandwidth selector (such as the MSE-optimal or CER-optimal selectors from Calonico, Cattaneo, and Titiunik) within each period separately. If period-specific sample sizes are small, a common bandwidth across periods may be imposed, but this trades off bias in the larger periods for stability in the smaller ones.
Can I include unit fixed effects?
Yes, if the same units appear in multiple periods (panel data). Fixed effects remove time-invariant unobserved heterogeneity and can improve precision. However, the identifying variation still comes from threshold-crossing within each period, so bandwidth and manipulation checks must be applied within each period.
What if the cutoff value changes across periods?
Period-specific estimates remain valid as long as the cutoff is known and the local randomisation assumption holds near each period's cutoff. Pooling is more complex because the complier populations may differ; presenting separate estimates is safer, and the researcher should argue that the treatment mechanism is comparable across the different thresholds.
How is this different from a panel-data fuzzy RD?
The two labels overlap substantially. 'Panel-data fuzzy RD' emphasises that the same units are tracked over time, enabling fixed effects. 'Multi-period fuzzy RD' emphasises that threshold assignment occurs in multiple waves and that period-specific or pooled estimates are the primary output. In practice, the two designs often coincide; the distinction is more about framing and estimator choice than a fundamental methodological difference.
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 ↗
- Cattaneo, M. D., Idrobo, N., & Titiunik, R. (2021). A Practical Introduction to Regression Discontinuity Designs: Extensions. Cambridge Elements in Quantitative and Computational Methods for the Social Sciences. Cambridge University Press. link ↗
How to cite this page
ScholarGate. (2026, June 3). Multi-period Fuzzy Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/multi-period-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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