arXiv 5 Nov 2025 · Econometrics
arXiv:2511.03424 · PDF · DOI · OpenAlex · Extracted main text
The standard fuzzy regression discontinuity (FRD) estimator is a ratio of differences of local polynomial estimators. I show that this estimator does not have finite moments of any order in finite samples, regardless of the choice of kernel function, bandwidth, or order of polynomial. This leads to an imprecise estimator with a heavy-tailed sampling distribution, and inaccurate inference with small sample sizes or when the discontinuity in the probability of treatment assignment at the cutoff is small. I present a generalised class of computationally simple FRD estimators, which contains a continuum of estimators with finite moments of all orders in finite samples, and nests both the standard FRD and sharp (SRD) estimators. The class is indexed by a single tuning parameter, and I provide simple values that lead to substantial improvements in median bias, median absolute deviation and root mean squared error. These new estimators remain very stable in small samples, or when the discontinuity in the probability of treatment assignment at the cutoff is small. Simple confidence intervals that have strong coverage and length properties in small samples are also developed. The improvements are seen across a wide range of models and using common bandwidth selection algorithms in extensive Monte Carlo simulations. The improved stability and performance of the estimators and confidence intervals is also demonstrated using data on class size effects on educational attainment.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Noack, Claudia and Rothe, Christoph (2024) Bias-Aware Inference in Fuzzy Regression Discontinuity Designs | 1.000 | 8 | 5 | 100% |
| 2 | Hahn, Jinyong and Todd, Petra and Van der Klaauw, Wilbert (2001) Identification and estimation of treatment effects with a regression-discontinuity design | 1.000 | 7 | 4 | 100% |
| 3 | Calonico, Sebastian and Cattaneo, Matias D and Titiunik, Rocio (2014) Robust nonparametric confidence intervals for regression-discontinuity designs | 1.000 | 6 | 4 | 100% |
| 4 | Imbens, Guido and Kalyanaraman, Karthik (2012) Optimal bandwidth choice for the regression discontinuity estimator | 1.000 | 5 | 5 | 100% |
| 5 | Calonico, Sebastian and Cattaneo, Matias D and Farrell, Max H (2020) Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs | 0.843 | 3 | 3 | 100% |
| 6 | Angrist, Joshua D and Lavy, Victor (1999) Using Maimonides' rule to estimate the effect of class size on scholastic achievement | 0.811 | 4 | 2 | 100% |
| 7 | Imbens, Guido W and Lemieux, Thomas (2008) Regression discontinuity designs: A guide to practice | 0.811 | 4 | 2 | 100% |
| 8 | Fan, Jianqing and Gijbels, Irene (1996) Local polynomial modelling and its applications: monographs on statistics and applied probability 66 | 0.737 | 4 | 3 | 50% |
| 9 | Gelman, Andrew and Imbens, Guido (2019) Why high-order polynomials should not be used in regression discontinuity designs | 0.737 | 3 | 2 | 100% |
| 10 | Chao, John and Hausman, Jerry and Newey, Whitney and Swanson, Norman… (2013) An expository note on the existence of moments of Fuller and HFUL estimators | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 29 scored citations.