Regression Discontinuity Design Services
When treatment is assigned by a cutoff on some continuous measure—a score, a threshold, an eligibility line—units just above and just below that line are nearly identical except for the treatment. Regression discontinuity design (RDD) exploits that to estimate a credible causal effect, often described as one of the most transparent quasi-experimental designs.
Regression discontinuity design (RDD) estimates a causal effect when treatment is assigned by whether a continuous “running variable” crosses a cutoff. Because units just above and just below the cutoff are otherwise similar, comparing outcomes on either side—the jump at the threshold—estimates the treatment effect for units near the cutoff, under weak and largely checkable assumptions.
What regression discontinuity does
Sometimes who gets a treatment is decided by a rule: a threshold on a test or credit score, an eligibility income line, a vote share above 50%, a firm-size cutoff for a regulation, a performance rank that triggers an award. Whenever assignment is governed by whether a continuous running variable crosses a known cutoff, regression discontinuity turns that rule into a research design.
The logic is simple and powerful. A unit that falls just below the cutoff and one that falls just above are, in almost every respect, alike—the tiny difference in the running variable is close to random. Yet one is treated and the other is not. So comparing the outcomes of units just on either side of the cutoff isolates the effect of the treatment, free of the confounding that plagues ordinary observational comparisons. The estimate is the size of the jump (discontinuity) in the outcome exactly at the threshold. The RDD design is prized because that jump is visible—you can often see the effect in a single plot—and its central assumption is unusually checkable.
When to use it
RDD applies wherever a cutoff rule determines treatment and the running variable is measured. In a sharp design, crossing the cutoff determines treatment exactly (everyone above gets it, no one below). In a fuzzy design, crossing the cutoff changes the probability of treatment rather than guaranteeing it—handled by using the cutoff as an instrument. Related to RDD is the regression kink design, which is used when a policy changes the slope of a relationship at a threshold (for example, how a benefit amount changes with income) rather than producing a level jump.
The key requirement, and RDD’s great strength, is that units should not be able to precisely manipulate their position around the cutoff. If they can—sorting themselves just onto the favourable side—the units either side are no longer comparable and the design breaks. This is checkable, and testing for it is a standard, non-negotiable step. One trade-off to be clear about: because RDD identifies the effect at the cutoff, its estimate is local—it applies to units near the threshold and does not automatically generalise to those far from it.
Sharp, fuzzy, and kink designs
| Design | What changes at the cutoff | Typical setting |
|---|---|---|
| Sharp RDD | Treatment status (0 → 1 exactly) | Strict eligibility rule at a threshold |
| Fuzzy RDD | Probability of treatment jumps | Cutoff strongly affects, but doesn’t force, take-up |
| Regression kink | The slope of the relationship | A formula changes rate at a threshold |
Doing RDD credibly
A credible RDD rests on a few decisions made carefully. The bandwidth—how far either side of the cutoff to include—trades bias against precision: too wide and units far from the cutoff (which differ in more than treatment) contaminate the estimate; too narrow and there are too few observations. Current practice uses data-driven, optimal bandwidth selection and reports sensitivity to that choice. The functional form matters too: fitting an overly flexible high-order polynomial can create spurious jumps, so local linear or local quadratic fits within the bandwidth are generally preferred to global high-order polynomials.
Two validity checks are essential rather than optional. A manipulation (density) test checks whether units bunch just on one side of the cutoff, which would signal sorting and undermine the design. Covariate-continuity checks verify that pre-determined characteristics do not jump at the cutoff—if they did, something other than the treatment changes there. We also report placebo cutoffs and bandwidth-sensitivity analyses. Together these are what let a reader trust that the jump reflects the treatment and not an artefact.
The estimate is local to the cutoff, and manipulation breaks it. RDD identifies the effect for units near the threshold—not everywhere—and only if units cannot precisely sort across the cutoff. We test the density at the cutoff and the continuity of covariates before interpreting the jump.
Software
We deliver RDD in established, reproducible tools—the rdrobust and rddensity family in R and Stata—with optimal bandwidth selection, robust bias-corrected inference, the manipulation and covariate tests, and clear discontinuity plots, all with versioned code.
How we deliver an RDD study
RDD sits within our wider causal-inference practice—so the design is validated, the estimate is local and honestly framed, and the assumption checks are reported in full.
We start by confirming that a genuine cutoff rule governs treatment and identifying the running variable and threshold, then determine whether the design is sharp, fuzzy, or a kink. We select an optimal bandwidth, fit local polynomial regressions on each side, and run the manipulation, covariate-continuity, placebo, and bandwidth-sensitivity checks before interpreting anything.
Reporting sets out the design and its assumptions, the discontinuity plot, the estimate with robust bias-corrected inference, and the full battery of validity checks—so the causal claim can be judged transparently.
You receive the treatment-effect estimate at the cutoff with robust inference, the discontinuity and density plots, the covariate-continuity and placebo results, the bandwidth-sensitivity analysis, and reproducible analytical code and analysis-ready files (where appropriate and permitted)—with the local nature of the estimate stated plainly.
Regression discontinuity across Management & Allied Studies
Cutoff rules are everywhere in institutions, policy, and organizations—so RDD applies across the disciplines we serve.
Economics & Public Policy
Eligibility thresholds for programmes, benefits, or grants; close-election cutoffs; income or means-test lines—classic RDD settings.
Finance & Accounting
Regulatory thresholds based on firm size, index-inclusion cutoffs, or rating boundaries that switch treatment at a line.
Management & Organizational Research
Performance-rank cutoffs triggering awards, promotions, or interventions, and size thresholds for firm-level rules.
Marketing & Consumer Research
Loyalty-tier or spending thresholds that switch benefits or status, and score-based eligibility for offers.
Education & Learning Sciences
Test-score cutoffs for admission, scholarships, remediation, or programme entry—a heavily used RDD context.
Operations & Information Systems
Threshold-based triggers for interventions, service tiers, or system rules assigned by a measured cutoff.
Regression discontinuity: common questions
Is treatment assigned by a cutoff?
If a score, threshold, or eligibility line decides who is treated, regression discontinuity can turn that rule into a credible causal estimate—with manipulation and continuity checks, optimal bandwidths, and the local scope stated plainly.