arXiv 18 Apr 2022 · Econometrics
arXiv:2204.08168 · PDF · DOI · OpenAlex · Extracted main text
Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.
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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 | Hahn, J., P. Todd, and W. Van der Klaauw (2001) Identification and estimation of treatment effects with a regression-discontinuity design | 1.000 | 6 | 4 | 100% |
| 2 | Dong, Y., Y.-Y. Lee, and M. Gou (2021) Regression discontinuity designs with a continuous treatment | 0.941 | 6 | 3 | 83% |
| 3 | Matzkin, R. L (2003) Nonparametric estimation of nonadditive random functions | 0.928 | 4 | 3 | 100% |
| 4 | Giuntella, O. and F. Mazzonna (2019) Sunset time and the economic effects of social jetlag: evidence from us time zone borders | 0.874 | 5 | 2 | 100% |
| 5 | Torgovitsky, A (2017) Minimum distance from independence estimation of nonseparable instrumental variables models | 0.843 | 5 | 4 | 60% |
| 6 | Torgovitsky, A (2015) Identification of nonseparable models using instruments with small support | 0.811 | 4 | 2 | 100% |
| 7 | Qu, Z. and J. Yoon (2015) Nonparametric estimation and inference on conditional quantile processes | 0.644 | 4 | 2 | 50% |
| 8 | Dong, Y (2018) Alternative assumptions to identify late in fuzzy regression discontinuity designs | 0.644 | 2 | 2 | 100% |
| 9 | Hoderlein, S. and E. Mammen (2007) Identification of marginal effects in nonseparable models without monotonicity | 0.644 | 2 | 2 | 100% |
| 10 | Imbens, G. W. and W. K. Newey (2009) Identification and estimation of triangular simultaneous equations models without additivity | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 54 scored citations.