Extreme Treatment Effect: Extrapolating Dose-Response Function into Extreme Treatment Domain

Juraj Bodik ()
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Juraj Bodik: Faculty of Business and Economics (HEC Lausanne), University of Lausanne, 1015 Lausanne, Switzerland

Mathematics, 2024, vol. 12, issue 10, 1-36

Abstract: The potential outcomes framework serves as a fundamental tool for quantifying causal effects. The average dose–response function μ ( t ) (also called the effect curve) is typically of interest when dealing with a continuous treatment variable (exposure). The focus of this work is to determine the impact of an extreme level of treatment, potentially beyond the range of observed values—that is, estimating μ ( t ) for very large t . Our approach is grounded in the field of statistics known as extreme value theory. We outline key assumptions for the identifiability of the extreme treatment effect. Additionally, we present a novel and consistent estimation procedure that can potentially reduce the dimension of the confounders to at most 3. This is a significant result since typically, the estimation of μ ( t ) is very challenging due to high-dimensional confounders. In practical applications, our framework proves valuable when assessing the effects of scenarios such as drug overdoses, extreme river discharges, or extremely high temperatures on a variable of interest.

Keywords: causal inference; potential outcomes; extreme value theory; extreme causal effect; dimension reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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