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Identification and Estimation of Optimal Continuous Treatment Effects

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  • Fangzhou Yu

Abstract

Estimating continuous treatment effects is hard because average-derivative estimators rely on an ill-posed conditional-density score. Recent work makes a bounded outcome weight the primitive, characterizing a class of weighted average derivative effects without density estimation. In this paper, we develop the identification and estimation theory for the optimally efficient estimands of this class under homoskedasticity and heteroskedasticity. On identification, we show that these estimands relax standard conditions, remaining valid at sharp boundaries and at interior treatment deserts that the strict overlap and density-smoothness conditions of classical theory rule out. On estimation, we derive the efficient influence function, and develop Debiased Machine Learning estimators.

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  • Fangzhou Yu, 2026. "Identification and Estimation of Optimal Continuous Treatment Effects," Papers 2609.19031, arXiv.org.
    • Handle: RePEc:arx:papers:2609.19031
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    References listed on IDEAS

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    1. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.
    2. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
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