Xiaojun Song, Haojiao Zhao
arXiv 23 Sep 2026 · Econometrics
arXiv:2609.27691 · PDF · Extracted main text
We propose a nonparametric test for unobserved treatment effect heterogeneity in regression discontinuity designs. Under the null of no unobserved heterogeneity, a transformed outcome that imputes treated potential outcomes for untreated units must have a continuous conditional distribution at the cutoff. We convert this implication into an integrated conditional-moment restriction using characteristic functions, thereby allowing the conditional local average treatment effect to be an unrestricted function of covariates. We derive the asymptotic distribution of the test statistics via a $U$-process and establish the validity of a multiplier bootstrap procedure for calculating critical values. Monte Carlo experiments show well-controlled size and increasing power. Two empirical applications illustrate how the test distinguishes between heterogeneity explained by observables and that explained by unobserved factors.
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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 | Calonico, S., M. D. Cattaneo, and R. Titiunik (2014) Robust nonparametric confidence intervals for regression-discontinuity designs | 0.894 | 7 | 4 | 71% |
| 2 | Hsu, Y.-C. and S. Shen (2019) Testing treatment effect heterogeneity in regression discontinuity designs | 0.894 | 7 | 3 | 71% |
| 3 | Calonico, S., M. D. Cattaneo, M. H. Farrell, and R. Titiunik (2019) Regression discontinuity designs using covariates | 0.874 | 6 | 4 | 67% |
| 4 | Hsu, Y.-C. and S. Shen (2021) Testing monotonicity of conditional treatment effects under regression discontinuity designs | 0.843 | 4 | 3 | 75% |
| 5 | Imbens, G. and K. Kalyanaraman (2012) Optimal bandwidth choice for the regression discontinuity estimator | 0.737 | 3 | 3 | 67% |
| 6 | Meyersson, E (2014) Islamic rule and the empowerment of the poor and pious | 0.644 | 4 | 1 | 100% |
| 7 | Bierens, H. J (1982) Consistent model specification tests | 0.644 | 2 | 2 | 100% |
| 8 | Chesher, A (2003) Identification in nonseparable models | 0.644 | 2 | 2 | 100% |
| 9 | Pop-Eleches, C. and M. Urquiola (2013) Going to a better school: Effects and behavioral responses | 0.585 | 3 | 1 | 100% |
| 10 | van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 54 scored citations.