1 Introduction

The regression discontinuity (RD) design has become one of the most credible strategies for causal inference in economics, medicine, and political science. Its appeal lies in a transparent identification assumption: the continuity of potential outcomes at the cutoff. If individuals just below the threshold are comparable to individuals just above it differing only in their treatment status, not in their underlying characteristics then the jump in observed outcomes at the cutoff identifies the causal treatment effect.

But the continuity assumption is not a data-generating fact; it is a maintained hypothesis. A growing literature has documented systematic threats to RD validity that are difficult to detect and easy to overlook. Three concerns stand out: (1) manipulation of the running variable, (2) heaping and rounding near the cutoff, and (3) compound treatments triggered by crossing the threshold. This article presents both sides of the debate: the case that RD designs remain among the most trustworthy quasi-experimental designs when properly validated, and the sceptical view that their apparent credibility can be illusory.

2 The Case for RD Credibility

Proponents argue that RD designs have two decisive advantages over other quasi-experimental strategies:

Local randomisation. Near the cutoff, the assignment of individuals to treatment versus control is effectively random not because of explicit randomisation, but because small fluctuations in the running variable are unpredictable. A student whose exam score is 70.1 versus 69.9 has effectively been randomly assigned to just above versus just below a pass/fail threshold. This local-randomisation view, formalised by Lee [2008] and Cattaneo et al. [2015], suggests that RD designs provide the closest non-experimental analogue to a randomised experiment.

Falsifiability. Unlike most observational study assumptions, the continuity assumption has testable implications. McCrary [2008] provides a density test: if the continuity assumption holds, the density of the running variable should be continuous at the cutoff. A jump in the density signals that individuals are sorting into one side of the threshold, violating local randomisation. Similarly, pre-determined covariates should not jump at the cutoff ("covariate balance tests"), and outcomes should not jump at placebo cutoffs where no policy change occurred.

Growing methodological toolkit. Calonico et al. [2014] provide bias-corrected robust inference. Cattaneo et al. [2015] develop finite-sample inference under local randomisation. Sensitivity analyses quantifying how large a violation of continuity would need to be to overturn a result have been developed by Armstrong and Kolesar [2018]. These tools make it possible to quantify uncertainty about the continuity assumption in ways that parallel what Rambachan and Roth [2023] have done for parallel trends in DiD.

3 The Sceptical View: When RD Goes Wrong

Critics argue that standard RD validity tests are too weak to catch many real-world violations, and that several systematic threats undermine the design in common applications.

3.1 Manipulation of the Running Variable

The McCrary density test detects jumps in the density of the running variable at the cutoff, which would indicate that individuals are selectively sorting above or below the threshold. However, the test has well-documented limitations:

Low power. The density test uses a local linear estimator on either side of the cutoff, which discards information about the shape of the density away from the boundary. With realistic sample sizes, the test has low power against smooth forms of manipulation that do not create an obvious discontinuity in the density [Gerard et al., 2020].

Heaping, not manipulation. A common pattern that mimics manipulation is heaping: when running variables are measured in coarse units (age in years, income in thousands of dollars, test scores in integer units), there are mechanically many individuals at round numbers. A cutoff at a round number will inherit the heaping pattern, creating apparent discontinuities in density that reflect measurement granularity, not gaming. Barreca et al. [2011] documented this problem in the context of low-birth-weight studies, where birth weight is reported in round grams and ounces, creating heaps at the 1500g threshold that confound RD estimates of the effect of intensive neonatal care.

Sorting near but not at the cutoff. Individuals may be aware of the threshold and adjust their running variable upward or downward in ways that are locally smooth but still correlated with outcome potential. For example, teachers who know that a student's score of 69.5 rounds to 70 (the passing threshold) may engage in selective grade rounding, placing students with the best unobserved potential outcomes just above the threshold.

3.2 Compound Treatments

A subtler threat is the compound treatment problem: crossing the cutoff often triggers not just one policy change, but many simultaneously. The Lee (2008) incumbency RD estimates the effect of winning an election, but winning also confers fundraising advantages, increased name recognition, improved staffing, and access to committee assignments. The RD identifies the aggregate effect of all these bundled changes, not the effect of incumbency per se. Disentangling the components requires additional design assumptions beyond continuity [Cattaneo et al., 2015].

In healthcare RD studies, a clinical threshold (e.g., HbA1c ≥ 7% for diabetes diagnosis) may trigger a comprehensive care protocol dietary counselling, medication, monitoring, and lifestyle interventions rather than a single drug treatment. The RD identifies the effect of the entire protocol, and attributing the result to any single component requires further assumptions.

3.3 Bandwidth Sensitivity and Researcher Degrees of Freedom

The choice of bandwidth is consequential. Different bandwidth selectors (mserd, cerrd, msetwo) can produce substantially different estimates. When researchers report only the result that is most statistically significant or theoretically satisfying, the effective false discovery rate exceeds the nominal level. Imbens and Kalyanaraman [2012] and Calonico et al. [2014] provide objective bandwidth selection, but researchers retain discretion in polynomial order, kernel type, covariate inclusion, and sample restrictions enough degrees of freedom to substantially influence results without explicit p-hacking.

4 The Donut RD Response

One proposed solution to heaping is the donut RD: exclude observations in a neighbourhood of the cutoff (the "hole" of the donut) where manipulation is most severe, and estimate the discontinuity using only observations further from the cutoff. Barreca et al. [2011] applied this approach to the birth weight study, finding that the standard RD estimates were substantially contaminated by heaping, while donut RD estimates were smaller and more plausible.

However, Noack and Rothe [2023] show that donut RD estimators can have higher bias and variance than conventional RD estimators, because they discard the most informative observations (those closest to the cutoff) and rely on extrapolation from more distant observations. They recommend using donut RD as a robustness check rather than a primary estimator.

5 Local Randomisation as an Alternative Framework

Cattaneo et al. [2015] propose formalising the local randomisation interpretation of RD designs more carefully. Rather than assuming continuity of the conditional expectation function (which is asymptotic and requires choosing a bandwidth), they assume that within a finite window [c-h, c+h], treatment assignment is as-good-as-random:

This assumption is stronger than continuity (it implies continuity) but makes precise what is meant by local randomisation and allows the use of Fisher randomisation inference within the window, providing exact finite-sample p-values.

The window h is determined by the data: one can test the local randomisation assumption by checking whether pre-determined covariates are balanced within progressively smaller windows around the cutoff, choosing the largest h for which balance holds. The rdrandinf package in R implements this approach.

6 Bounds Approaches

When manipulation is suspected but cannot be precisely characterised, Gerard et al. [2020] propose partial identification bounds on the RD treatment effect. They allow for the possibility that a fraction δ of units near the cutoff have been strategically sorted, without

assuming the direction or severity of sorting. The resulting bounds on the treatment effect are valid under any manipulation pattern with at most δ fraction of sorted units:

Sensitivity analysis reports how large δ must be to make the bounds include zero the "breakdown" fraction of manipulation. This parallels the Rambachan-Roth (2023) approach to parallel trends sensitivity in DiD designs.

7 A Practical Recommendation

The weight of evidence suggests that RD designs remain among the most credible quasi-experimental strategies when implemented carefully, but that standard validity tests are necessary but not sufficient conditions for credibility. Applied researchers should:

1. Run the McCrary density test (rddensity), but interpret its failure to reject as weak evidence, not proof of validity.
2. Plot the running variable histogram on a fine grid near the cutoff to detect heaping visually.
3. Conduct covariate balance tests for all pre-determined characteristics.
4. Test outcome effects at multiple placebo cutoffs.
5. Report results across a range of bandwidths and polynomial orders.
6. If heaping is suspected, report both standard and donut RD estimates.
7. Discuss the compound treatment problem explicitly: what changes at the threshold, and which component is the treatment of interest?

8 Conclusion

The RD design is not a silver bullet. Its credibility depends on the plausibility of local randomisation, which must be actively validated rather than passively assumed. Manipulation, heaping, compound treatments, and researcher degrees of freedom are real threats that standard density and covariate balance tests may fail to detect. At the same time, the accumulating toolkit for RD validation density tests, local randomisation formalisation, bounds approaches, sensitivity analyses means that researchers who are transparent about these issues and apply the full battery of diagnostics can produce genuinely credible causal estimates. The lesson is not that RD designs are unreliable, but that their credibility requires deliberate effort to establish.

References

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