Regression Discontinuity in Sentencing
Also known as: Sentencing Threshold RDD, Cutoff-Based Justice Evaluation, Risk-Score Discontinuity Design, Age-of-Majority Discontinuity
Regression discontinuity (RD) in sentencing exploits the sharp thresholds built into justice policy — sentencing-guideline cutoffs, the age of majority, risk-score thresholds that trigger detention or diversion — to estimate causal effects without a randomized trial. Units just above the cutoff receive a different treatment from units just below it, yet they are otherwise nearly identical, so comparing their outcomes isolates the effect of crossing the line. Berk and Rauma's 1983 evaluation of a crime-control program showed how criminologists can 'capitalize on nonrandom assignment' created by such rules.
Key highlights
- Delivers a transparent, credible causal effect from observational administrative data when randomization is impossible.
- Relies on a weak, partly testable continuity assumption rather than the strong no-unmeasured-confounding assumption of weighting.
- Exploits rules that justice systems already use, so the data and the threshold occur naturally without intervention.
- Supports visual, intuitive presentation: the discontinuity in a plot is itself the estimated effect.
- Offers built-in falsification tests — placebo cutoffs, covariate continuity, and density (McCrary) checks — that strengthen credibility.
Intuition
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How it works
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When to use it
Use an RD design when a justice treatment is assigned by a known cutoff on a continuous (or finely graded) running variable and you want a credible causal effect without randomization. It fits sentencing-guideline thresholds, age-of-majority and juvenile-versus-adult boundaries, risk-score cutoffs that trigger detention, diversion, or supervision, and eligibility lines for programs. It is unsuitable when assignment does not actually follow the rule sharply (a fuzzy or manipulated cutoff requires the fuzzy RD or careful adjustment), when units can precisely manipulate their running variable to land on the favorable side, when there are too few cases near the threshold for precise estimation, or when you need an effect for the whole population rather than units at the cutoff. Interrupted time series or propensity weighting may be better when no threshold exists.
Strengths & limitations
- Delivers a transparent, credible causal effect from observational administrative data when randomization is impossible.
- Relies on a weak, partly testable continuity assumption rather than the strong no-unmeasured-confounding assumption of weighting.
- Exploits rules that justice systems already use, so the data and the threshold occur naturally without intervention.
- Supports visual, intuitive presentation: the discontinuity in a plot is itself the estimated effect.
- Offers built-in falsification tests — placebo cutoffs, covariate continuity, and density (McCrary) checks — that strengthen credibility.
- Identifies only a local effect at the cutoff, which may not generalize to offenders far from the threshold.
- Requires enough observations near the cutoff; sparse data around the threshold yield imprecise, bandwidth-sensitive estimates.
- Breaks down if units can precisely manipulate the running variable to sort to the favorable side of the line.
- Sensitive to bandwidth choice and polynomial order, so poorly chosen specifications can manufacture or hide a jump.
- Many sentencing thresholds are 'fuzzy' (crossed imperfectly), requiring instrumental-variable adjustment and weaker conclusions.
Common pitfalls
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Applications
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Frequently asked
What is the difference between sharp and fuzzy RD in sentencing?
In a sharp design, crossing the cutoff deterministically changes treatment — every offender at or above a points threshold gets the harsher sanction. In a fuzzy design, crossing the cutoff only changes the probability of treatment (judges retain discretion, so some above-cutoff cases still get the lighter sanction). Fuzzy RD rescales the jump in outcomes by the jump in treatment probability, essentially an instrumental-variable estimator, and identifies the effect for compliers near the cutoff.
How do you test whether the running variable was manipulated?
If offenders or court actors can precisely control the running variable to land on the favorable side, units will pile up just past the cutoff, violating the as-good-as-random logic. The standard check is a McCrary-style density test for a discontinuity in the distribution of the running variable at the cutoff, supplemented by confirming that pre-treatment covariates are continuous across the threshold. Bunching or covariate jumps are red flags.
Why does RD estimate only a local effect?
RD compares units immediately above and below the cutoff, where they are nearly identical, so the estimate is the treatment effect specifically for units at the threshold (a local average treatment effect). Offenders far from the cutoff may respond very differently to the same sanction, so the design says little about them without strong extrapolation. This local validity is the price RD pays for its high internal credibility.
Sources
- 1.Berk, R. A., & Rauma, D. (1983). Capitalizing on nonrandom assignment to treatments: A regression-discontinuity evaluation of a crime-control program. Journal of the American Statistical Association, 78(381), 21–27.
- 2.Lee, D. S., & Lemieux, T. (2010). Regression discontinuity designs in economics. Journal of Economic Literature, 48(2), 281–355.
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Cite this page
ScholarGate. (2026, June 22). Regression Discontinuity in Sentencing. ScholarGate. https://scholargate.app/criminology/regression-discontinuity-sentencing