Regression Discontinuity Methods in Causal Analysis

Regression discontinuity (RD) methods constitute a quasi-experimental approach to causal inference that exploits a predetermined rule linking treatment assignment to a continuous forcing variable. At its core, an RD design compares outcomes just above and just below a specified cutoff, mimicking a randomised experiment in the immediate vicinity of the threshold. Sharp designs assume perfect adherence to the rule, whereas fuzzy designs allow for imperfect compliance and identify a local average treatment effect for compliers. Estimation typically relies on local polynomial or spline regression, with careful bandwidth selection to balance bias and variance. Credible identification rests on the continuity of potential outcomes and the forcing variable’s density at the cutoff, which can be assessed via falsification tests and placebo thresholds. Recent advances have refined bandwidth selectors, introduced robust bias correction, and extended inference to quantile and Bayesian frameworks. Applications span economics, public policy, education, environmental science and clinical medicine, where policy eligibility, exam scores, pollution indices or risk scores generate natural thresholds. By delivering transparent and replicable estimates of local causal effects, RD methods have become central to evidence-based policy evaluation and to understanding treatment heterogeneity across disciplines.

Research from Nature Portfolio

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Research from all publishers

Recent work has applied RD methods to firm-level investment grants, exploiting discontinuities in application scores to demonstrate that a second grant produces substantially larger gains in labour productivity for micro- and small-sized firms than a single grant, while showing no effect on total factor productivity. In agricultural and environmental economics, researchers have showcased best practices for panel-data RD designs, outlined tests of identifying assumptions, and combined remote sensing with environmental modelling to estimate causal effects of policy thresholds on land use and ecosystem outcomes. Methodological extensions include local composite quantile regression, which improves boundary performance and inference by fitting multiple quantile curves around the cutoff, coupled with bias-corrected t-tests and optimised bandwidth selectors, yielding confidence intervals with excellent coverage in both simulated and empirical contexts.

Regression Discontinuity Methods in Causal Analysis publication trend

The graph below shows the total number of articles in regression discontinuity methods in causal analysis across all publications each year (not limited to Nature Index journals).

Technical terms

Forcing variable: A continuous measure that determines treatment eligibility according to a threshold.

Cutoff (threshold): The point on the forcing variable scale that separates treated from untreated units.

Sharp RD design: A setting where all units above the cutoff receive treatment and all below do not.

Fuzzy RD design: A setting where treatment probability jumps at the cutoff but compliance is imperfect, identifying a local average treatment effect.

Bandwidth: The window around the cutoff within which data are used for local estimation, trading off bias and variance.

References

1. Investment grants and firms’ productivity: how effective is a grant booster shot?. Small Business Economics (2024).
2. Regression discontinuity designs in agricultural and environmental economics. European Review of Agricultural Economics (2022).
3. Local Composite Quantile Regression for Regression Discontinuity. Journal of Business and Economic Statistics (2021).
4. Bayesian regression discontinuity designs: incorporating clinical knowledge in the causal analysis of primary care data. Statistics in Medicine (2015).
5. Approaches to the Estimation of the Local Average Treatment Effect in a Regression Discontinuity Design. Scandinavian Journal of Statistics (2016).
6. Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator. Quantitative Economics (2018).