arXiv 20 Aug 2024 · Econometrics · 1 citations (OpenAlex)
arXiv:2408.10509 · PDF · DOI · OpenAlex · Extracted main text
This paper extends difference-in-differences to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends assumption. Estimating the ATT in this framework requires first estimating infinite-dimensional nuisance parameters, particularly the conditional density of the continuous treatment, which can introduce substantial bias. To address this challenge, we propose estimators for the causal parameters under the double/debiased machine learning framework and establish their asymptotic normality. Additionally, we provide consistent variance estimators and construct uniform confidence bands based on a multiplier bootstrap procedure. To demonstrate the effectiveness of our approach, we apply our estimators to the 1983 Medicare Prospective Payment System (PPS) reform studied by Acemoglu and Finkelstein (2008), reframing it as a DiD with continuous treatment and nonparametrically estimating its effects.
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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 | Acemoglu, D. and Finkelstein, A (2008) Input and technology choices in regulated industries: evidence from the health care sector | 1.000 | 16 | 3 | 100% |
| 2 | Callaway, B., Goodman-Bacon, A., and Sant'Anna, P. H (2024) Difference-in-differences with a continuous treatment | 1.000 | 11 | 3 | 100% |
| 3 | Fan, Q., Hsu, Y. C., Lieli, R. P., and Zhang, Y (2022) Estimation of conditional average treatment effects with high-dimensional data | 0.941 | 6 | 4 | 83% |
| 4 | Colangelo, K. and Lee, Y. Y (2025) Double debiased machine learning non-parametric inference with continuous treatments | 0.928 | 4 | 3 | 100% |
| 5 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.899 | 11 | 5 | 73% |
| 6 | Bibaut, A. F. and van der Laan, M. J (2017) Data-adaptive smoothing for optimal-rate estimation of possibly non-regular parameters, arXiv:1706.07408 | 0.843 | 3 | 3 | 100% |
| 7 | Su, L., Ura, T., and Zhang, Y (2019) Non-separable models with high-dimensional data | 0.843 | 3 | 3 | 100% |
| 8 | Chang, N. C (2020) Double/debiased machine learning for difference-in-differences models | 0.830 | 7 | 4 | 57% |
| 9 | Abadie, A (2005) Semiparametric difference-in-differences estimators | 0.811 | 4 | 2 | 100% |
| 10 | Chernozhukov, V., Chetverikov, D., and Kato, K (2014) Anti-concentration and honest, adaptive confidence bands | 0.811 | 4 | 2 | 100% |
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