Regression Kink Design (RKD)
Generalized Regression Kink Design (RKD) · Also known as: RKD, regression kink design, kink regression discontinuity, Regresyon Kırılma Tasarımı (RKD — Regression Kink Design)
The Regression Kink Design is a quasi-experimental method that estimates a causal effect when a policy rule creates a change in slope (a kink) — rather than a jump — at a known threshold of a running variable. It was formalised as a generalized design by Card, Lee, Pei and Weber (2015) and is the slope-based counterpart of the regression discontinuity design.
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When to use it
Use RKD when a policy assigns treatment through a continuous formula whose slope changes at a known threshold — for example a tax rate, a subsidy amount, or a social-benefit formula with a cap or bend. It requires a continuous outcome, a known kink point, and a reasonably large sample (at least about 200 observations) concentrated around the threshold. The key assumptions are that the policy creates a genuine slope change rather than a level jump at the cutoff, and that the density of the running variable is smooth there (no manipulation or bunching).
Strengths & limitations
- Identifies causal effects from kinked policy rules where a level discontinuity (and hence a standard RDD) is absent.
- Exploits an institutional feature already present in the data, so no experimental assignment is required.
- Has a rigorous inference framework (Card, Lee, Pei & Weber, 2015) and reuses familiar RDD tooling such as local polynomials and CCT bandwidth selection.
- Slope changes are weaker signals than level jumps, so estimates have wide confidence intervals unless the sample is large (at least about 200 observations near the threshold).
- Highly sensitive to bandwidth and polynomial-order choices, because it relies on estimating derivatives rather than levels.
- Fails if the running variable is manipulated around the threshold, which can produce a spurious discontinuity instead of a clean kink.
Frequently asked
How is RKD different from a regression discontinuity design?
RDD looks for a jump in the level of the outcome at a cutoff, while RKD looks for a change in the slope of the outcome. Use RDD when the policy itself jumps at the threshold and RKD when the policy's rate of change bends there.
How large a sample do I need?
Slope changes are subtler than level jumps, so RKD needs substantial data concentrated near the threshold — roughly 200 observations or more. With fewer, the derivative estimates become unstable and the confidence intervals too wide to trust; a regression discontinuity design may be a better fit.
Why does the density of the running variable matter?
If people can manipulate where they fall relative to the threshold, the running variable bunches there and the smoothness assumption fails. That can mimic a kink or even a discontinuity, so a manipulation (density) test is an essential robustness check.
How is the effect actually estimated?
RKD fits local polynomial regressions on each side of the threshold to recover the one-sided slopes of the outcome, then divides the change in the outcome's slope by the change in the policy's slope. The bandwidth is usually chosen with a CCT-style optimal rule, as in modern RDD practice.
Sources
- Card, D., Lee, D. S., Pei, Z. & Weber, A. (2015). Inference on Causal Effects in a Generalized Regression Kink Design. Econometrica, 83(6), 2453-2483. DOI: 10.3982/ECTA11224 ↗
How to cite this page
ScholarGate. (2026, June 1). Generalized Regression Kink Design (RKD). ScholarGate. https://scholargate.app/en/causal-inference/regression-kink-design
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