Optimally weighted average derivative effects

TL;DR

This paper introduces a new class of optimal weighted average derivative effect estimators that improve efficiency and simplify estimation by relying only on conditional expectation estimation, with applications in causal inference.

Contribution

It proposes a novel class of Riesz representers for WADEs, deriving optimal weights that minimize the nonparametric efficiency bound, and connects these to partially linear models.

Findings

New class of RRs isomorphic to WADEs.

Optimal WADE estimators require only conditional expectation estimation.

Numerical experiment applied to Warfarin dose effect.

Abstract

Weighted average derivative effects (WADEs) are nonparametric estimands with uses in economics and causal inference. Debiased WADE estimators typically require learning the conditional mean outcome as well as a Riesz representer (RR) that characterises the requisite debiasing corrections. RR estimators for WADEs often rely on kernel estimators, introducing complicated bandwidth-dependant biases. In our work we propose a new class of RRs that are isomorphic to the class of WADEs and we derive the WADE weight that is optimal, in the sense of having minimum nonparametric efficiency bound. Our optimal WADE estimators require estimating conditional expectations only (e.g. using machine learning), thus overcoming the limitations of kernel estimators. Moreover, we connect our optimal WADE to projection parameters in partially linear models. We ascribe a causal interpretation to WADE and projection parameters in terms of so-called incremental effects. We propose efficient estimators for two WADE estimands in our class, which we evaluate in a numerical experiment and use to determine the effect of Warfarin dose on blood clotting function.