Identification and Estimation of Optimal Continuous Treatment Effects

Fangzhou Yu

Papers from arXiv.org

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.

Date: 2026-07
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