Multi-period Regression Discontinuity Design
Also known as: multi-wave RD, repeated RDD, dynamic RD, multi-cutoff RDD
Multi-period Regression Discontinuity Design extends the classic RDD to settings where a cutoff-based treatment is applied in multiple waves, across repeated time periods, or with varying thresholds. By pooling or comparing period-specific discontinuity estimates, researchers gain statistical precision and can examine how causal effects evolve or persist over time.
Key highlights
- Increases statistical precision by pooling multiple locally-randomized samples near the cutoff across time.
- Enables investigation of effect dynamics — whether impacts grow, diminish, or shift over successive periods.
- Supports richer placebo and pre-trend testing than a single-period RDD, strengthening the credibility of the continuity assumption.
- Allows detection of time-varying heterogeneity in treatment effects that a single-wave design cannot reveal.
- Can accommodate time-varying thresholds or multi-cutoff settings within a unified estimation framework.
Intuition
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How it works
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When to use it
Use multi-period RDD when treatment is assigned by a threshold rule that recurs across several time periods, academic cohorts, or policy waves, and you want to pool evidence or compare effects over time. It is especially valuable when a single period's sample near the cutoff is small, because pooling across periods increases effective sample size. Do not use it when the running variable or the cutoff changes its meaning across periods in a way that makes estimates incomparable, when there is systematic sorting or anticipation that affects multiple waves simultaneously, or when units carry over from one period to the next in ways that confound the local comparison.
Strengths & limitations
- Increases statistical precision by pooling multiple locally-randomized samples near the cutoff across time.
- Enables investigation of effect dynamics — whether impacts grow, diminish, or shift over successive periods.
- Supports richer placebo and pre-trend testing than a single-period RDD, strengthening the credibility of the continuity assumption.
- Allows detection of time-varying heterogeneity in treatment effects that a single-wave design cannot reveal.
- Can accommodate time-varying thresholds or multi-cutoff settings within a unified estimation framework.
- Requires the fundamental RDD continuity assumption to hold in every period; if sorting or manipulation occurs in any wave, that wave's estimate is invalid.
- Pooling estimates across periods is only interpretable if the treatment, running variable, and outcome measure are comparable across waves.
- Multiple testing across periods increases the risk of spurious findings without appropriate correction.
- Bandwidth selection becomes more complex when cutoffs or data distributions differ by period.
- Does not handle units that are treated in one period and serve as controls in another without careful accounting.
Common pitfalls
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Applications
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Frequently asked
How does multi-period RDD differ from a standard RDD?
A standard RDD uses a single period or cross-section with one cutoff. Multi-period RDD applies the same threshold-based identification strategy across multiple time periods or cohorts, producing a set of period-specific estimates that can be pooled for precision or compared to detect effect dynamics.
Can I use different cutoffs in different periods?
Yes, but comparability must be ensured. If the threshold changes in a way that fundamentally alters who is marginally treated, the estimates are not directly comparable and pooling requires caution. Document cutoff values for each period and assess whether the local complier populations are similar.
How do I test the identifying assumption across multiple periods?
Run density (McCrary) tests at each period's cutoff to check for manipulation. Use pre-treatment periods as placebo tests: RD estimates should be near zero before treatment begins. Examine covariate smoothness at the cutoff in each wave.
What software can I use?
The rdrobust package in R and Stata (Calonico, Cattaneo, Titiunik) provides MSE-optimal bandwidth selection and robust confidence intervals and can be applied period by period. Results can then be pooled manually or with meta-analytic weights.
Is multi-period RDD the same as difference-in-discontinuities?
No. Difference-in-discontinuities combines RDD with a before-after contrast to remove confounds that are continuous at the threshold. Multi-period RDD instead pools or compares separate RD estimates from repeated periods with the same assignment rule, without requiring a comparison group that never crosses the threshold.
Sources
- 1.Cattaneo, M. D., Idrobo, N., & Titiunik, R. (2020). A Practical Introduction to Regression Discontinuity Designs: Foundations. Cambridge University Press.
- 2.Calonico, S., Cattaneo, M. D., & Titiunik, R. (2019). Regression Discontinuity Designs Using Covariates. Review of Economics and Statistics, 101(3), 442-451.
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Cite this page
ScholarGate. (2026, June 3). Multi-period Regression Discontinuity Design. ScholarGate. https://scholargate.app/causal-inference/multi-period-regression-discontinuity-design