Heterogeneous Treatment Effect Fuzzy Regression Discontinuity
Heterogeneous Treatment Effect Estimation in Fuzzy Regression Discontinuity Design · Also known as: HTE-Fuzzy RDD, heterogeneous LATE at threshold, subgroup fuzzy RD, fuzzy RD with effect heterogeneity
Heterogeneous Treatment Effect Fuzzy RDD extends the standard fuzzy regression discontinuity design — where treatment probability, not treatment status itself, jumps at a threshold — by examining whether the Local Average Treatment Effect (LATE) estimated at the threshold differs systematically across subgroups defined by covariates such as gender, socioeconomic status, or prior ability. It combines the instrumental-variable logic of fuzzy RDD with structured heterogeneity analysis.
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When to use it
Use this method when you have a fuzzy RDD setting — a threshold that shifts treatment probability but not perfectly — and a substantive research question about whether the causal effect varies by a pre-treatment characteristic. It is best suited when sample sizes near the bandwidth are large enough to support subgroup analyses (each subgroup should have at least 100-200 complier observations near the threshold), the running variable is continuous and not manipulable, and the subgroups are defined a priori rather than data-dredged. Avoid it when the first stage is weak (F < 10), when bandwidth-splitting yields very thin cells, when the running variable is discrete (requiring different methods), or when the subgroup variable is itself affected by the intervention.
Strengths & limitations
- Inherits the causal identification of fuzzy RDD: the threshold provides exogenous variation, so complier-LATE estimates are credibly causal even from observational data.
- Reveals policy-relevant treatment effect heterogeneity among the marginal compliers near the threshold, which is precisely the population most affected by the policy.
- Combining IV and subgroup analysis mitigates omitted-variable bias; group differences in LATE cannot be explained by fixed confounders that are constant within subgroups.
- Extensions to quantile fuzzy RDD allow studying distributional heterogeneity, not just mean differences across groups.
- The approach scales naturally to multiple covariates via interaction terms in the local-linear regression.
- Subgroup analysis within a bandwidth sharply reduces effective sample size, requiring large original samples to maintain adequate power.
- A weak first stage (low compliance jump) inflates IV standard errors in each subgroup, making heterogeneity tests underpowered.
- External validity is inherently limited: all estimates refer to compliers at the threshold and may not generalise to inframarginal units or different populations.
- Multiple subgroup comparisons inflate Type I error; pre-registration and adjustment for multiple testing are essential.
- Optimal bandwidth for the pooled analysis may not be optimal for individual subgroups, complicating bandwidth choice.
Frequently asked
How is fuzzy RDD different from sharp RDD?
In sharp RDD, crossing the threshold perfectly determines treatment (everyone above is treated, everyone below is not). In fuzzy RDD, crossing the threshold only changes the probability of treatment. The threshold then serves as an instrumental variable, and the LATE is identified as the ratio of the outcome discontinuity to the treatment-probability discontinuity.
What sample size is needed for subgroup heterogeneity tests?
There is no single rule, but each subgroup should have enough complier observations within the bandwidth to produce a reliable first stage (F > 10) and a reasonably precise reduced-form estimate. In practice this often requires several hundred observations near the threshold per subgroup; with small samples the test will be underpowered.
Can the subgroup variable be endogenous?
No. The covariate used to define subgroups must be determined before the running variable is observed — typically a baseline pre-treatment characteristic — and must not itself be affected by crossing the threshold. If the covariate is post-treatment, the subgroup comparison is no longer causally interpretable.
How should I handle multiple subgroup comparisons?
Pre-register the subgroups and the direction of expected heterogeneity before analysing data. If conducting exploratory subgroup analyses, apply a Bonferroni or Benjamini-Hochberg correction for multiple comparisons and report all subgroups tested, not only those with significant effects.
What if the first stage is weak in a subgroup?
A first-stage F-statistic below 10 in a subgroup signals a weak-instrument problem: the IV estimate will be biased toward OLS and the standard errors unreliable. You should report this, consider Anderson-Rubin confidence intervals that are robust to weak instruments, and exercise caution in interpreting the subgroup LATE.
Sources
- Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design. Econometrica, 69(1), 201-209. DOI: 10.1111/1468-0262.00183 ↗
- Calonico, S., Cattaneo, M. D., & Titiunik, R. (2014). Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs. Econometrica, 82(6), 2295-2326. DOI: 10.3982/ECTA11757 ↗
How to cite this page
ScholarGate. (2026, June 3). Heterogeneous Treatment Effect Estimation in Fuzzy Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/heterogeneous-treatment-effect-fuzzy-regression-discontinuity
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Fuzzy Regression DiscontinuityCausal inference↔ compare
- Heterogeneous Treatment Effect Regression Discontinuity DesignCausal inference↔ compare
- Instrumental Variables in Health ResearchHealth Economics↔ compare
- Local Average Treatment EffectCausal inference↔ compare
- Quantile RegressionEconometrics↔ compare