Heterogeneous Treatment Effect Regression Discontinuity Design (HTE-RDD)
Heterogeneous Treatment Effect Regression Discontinuity Design · Also known as: HTE-RDD, heterogeneous RDD, subgroup RDD, effect heterogeneity RD
Heterogeneous Treatment Effect RDD extends the classic regression discontinuity framework to detect and estimate how the causal effect of crossing an assignment cutoff varies across subgroups or along covariates. Rather than reporting a single local average treatment effect at the threshold, HTE-RDD maps how treatment impact differs by individual characteristics, enabling richer policy conclusions about who benefits most or least from a threshold-based intervention.
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When to use it
Use HTE-RDD when you have a threshold-based assignment rule (the classic RDD setting) and theory or policy interest suggests the treatment impact differs across subgroups — for example, by gender, income quartile, or baseline risk. Sufficient observations near the cutoff for each subgroup are essential; sparse subgroups produce wide confidence intervals and unreliable estimates. Do not apply this approach if the running variable is manipulable around the cutoff, if subgroups are defined post-treatment (inducing selection bias), or if the overall sample near the threshold is small, because splitting an already narrow bandwidth further compounds variance.
Strengths & limitations
- Identifies heterogeneous causal effects without randomisation by exploiting the as-good-as-random variation around a known threshold.
- Produces policy-relevant effect estimates for distinct subpopulations, revealing who gains most from a threshold-based rule.
- Inherits RDD's robustness to time-invariant unobservables: units just above and below the cutoff are comparable on average.
- Compatible with modern robust inference tools (bias-corrected CIs, CCT bandwidth selection) that control size in small samples.
- Allows both parametric (interaction) and non-parametric (separate RDDs per subgroup) implementations.
- Estimates are local to the cutoff; heterogeneous effects away from the threshold cannot be recovered.
- Splitting the sample by subgroup sharply reduces the effective sample size near the cutoff, inflating variance.
- The continuity assumption must hold within each subgroup separately, which is harder to verify and communicate.
- Risk of data dredging: testing heterogeneity across many moderators without pre-registration inflates false-discovery rates.
Frequently asked
How is HTE-RDD different from running separate RDDs for each subgroup?
Running separate RDDs for each subgroup is the most transparent implementation of HTE-RDD. The interaction approach (including a treatment-by-covariate interaction term) is more efficient when the moderator is continuous and the effect is assumed to shift smoothly with it, but the two approaches converge asymptotically. Separate RDDs are easier to interpret and communicate to non-technical audiences.
What sample size is needed near the cutoff when splitting by subgroups?
There is no universal rule, but each subgroup should have enough observations within the chosen bandwidth for a stable local linear fit — often at least 50-100 per side per subgroup as a practical floor. Power calculations using the expected subgroup share and residual variance are recommended before data collection.
Must the cutoff be the same for all subgroups?
In a standard HTE-RDD, yes — the same cutoff c applies to all units, and heterogeneity is in how the effect size varies across subgroups at that shared threshold. If different subgroups face different cutoffs, the design becomes a multi-cutoff RDD, which requires a separate modelling strategy.
How should I report and pre-register heterogeneity tests?
Specify all moderators of interest, the direction of expected heterogeneity, and the multiplicity correction method before analysing the data. Report both point estimates and bias-corrected confidence intervals for each subgroup, alongside the test for overall effect heterogeneity. Distinguish confirmatory from exploratory heterogeneity analyses.
What if the subgroups are very unequal in size near the cutoff?
Small subgroups produce wide confidence intervals and low power. Consider collapsing finely-grained moderator categories, using a continuous moderator rather than discrete subgroups, or collecting more data near the cutoff. Reporting a very wide CI honestly is preferable to suppressing the analysis.
Sources
- Dong, Y., & Lewbel, A. (2015). Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models. Review of Economics and Statistics, 97(5), 1081-1092. DOI: 10.1162/REST_a_00510 ↗
- Chiang, H. D., Hsu, Y.-C., & Sasaki, Y. (2019). Causal Inference by Quantile Regression Kink Designs. Journal of Econometrics, 210(2), 405-433. DOI: 10.1016/j.jeconom.2019.02.005 ↗
How to cite this page
ScholarGate. (2026, June 3). Heterogeneous Treatment Effect Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/heterogeneous-treatment-effect-regression-discontinuity-design
Which method?
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