arXiv 13 Jun 2025 · Econometrics
arXiv:2506.11663 · PDF · DOI · OpenAlex · Extracted main text
The partial effect refers to the impact of a change in a target variable D on the distribution of an outcome variable Y . This study examines the identification and inference of a wide range of partial effects at the threshold in the sharp regression kink (RK) design under general policy interventions. We establish a unifying framework for conducting inference on the effect of an infinitesimal change in D on smooth functionals of the distribution of Y, particularly when D is endogenous and instrumental variables are unavailable. This framework yields a general formula that clarifies the causal interpretation of numerous existing sharp RK estimands in the literature. We develop the relevant asymptotic theory, introduce a multiplier bootstrap procedure for inference, and provide practical implementation guidelines. Applying our method to the effect of unemployment insurance (UI) benefits on unemployment duration, we find that while higher benefits lead to longer durations, they also tend to reduce their dispersion. Furthermore, our results show that the magnitude of the partial effect can change substantially depending on the specific form of the policy intervention.
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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 | Card, D., Lee, D. S., Pei, Z., and Weber, A (2015) Inference on causal effects in a generalized regression kink design | 1.000 | 18 | 5 | 100% |
| 2 | Chiang, H. D., Hsu, Y.-C., and Sasaki, Y (2019) Robust uniform inference for quantile treatment effects in regression discontinuity designs | 1.000 | 7 | 3 | 100% |
| 3 | Chiang, H. D. and Sasaki, Y (2019) Causal inference by quantile regression kink designs | 0.974 | 40 | 8 | 92% |
| 4 | Calonico, S., Cattaneo, M. D., and Titiunik, R (2014) Robust nonparametric confidence intervals for regression-discontinuity designs | 0.843 | 4 | 4 | 75% |
| 5 | Hoderlein, S. and Mammen, E (2007) Identification of marginal effects in nonseparable models without monotonicity | 0.843 | 4 | 4 | 75% |
| 6 | Hoderlein, S. and Mammen, E (2009) Identification and estimation of local average derivatives in non-separable models without monotonicity | 0.843 | 3 | 3 | 100% |
| 7 | Hoderlein, S., Holzmann, H., Kasy, M., and Meister, A (2017) Corrigendum: Instrumental variables with unrestricted heterogeneity and continuous treatment | 0.737 | 3 | 2 | 100% |
| 8 | Landais, C (2015) Assessing the welfare effects of unemployment benefits using the regression kink design | 0.737 | 3 | 2 | 100% |
| 9 | Qu, Z. and Yoon, J (2019) Uniform inference on quantile effects under sharp regression discontinuity designs | 0.737 | 3 | 2 | 100% |
| 10 | Florens, J.-P., Heckman, J. J., Meghir, C., and Vytlacil, E (2008) Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous ef… | 0.644 | 4 | 1 | 100% |
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