Incremental causal effects

TL;DR

This paper investigates the identification and estimation of incremental causal effects, showing they can be estimated under local assumptions and may be easier to estimate than average treatment effects, especially in high-dimensional settings.

Contribution

It introduces methods for identifying and estimating incremental causal effects under local assumptions, including a feature transformation for high-dimensional data and comparisons with average treatment effects.

Findings

Incremental effects are identifiable under local ignorability and overlap.

Estimating incremental effects can be statistically easier than average effects in some settings.

A feature transformation enables doubly-robust estimation in high-dimensional scenarios.

Abstract

Causal evidence is needed to act and it is often enough for the evidence to point towards a direction of the effect of an action. For example, policymakers might be interested in estimating the effect of slightly increasing taxes on private spending across the whole population. We study identifiability and estimation of causal effects, where a continuous treatment is slightly shifted across the whole population (termed average partial effect or incremental causal effect). We show that incremental effects are identified under local ignorability and local overlap assumptions, where exchangeability and positivity only hold in a neighborhood of units. Average treatment effects are not identified under these assumptions. In this case, and under a smoothness condition, the incremental effect can be estimated via the average derivative. Moreover, we prove that in certain finite-sample observational settings, estimating the incremental effect is easier than estimating the average treatment effect in terms of asymptotic variance. For high-dimensional settings, we develop a simple feature transformation that allows for doubly-robust estimation and inference of incremental causal effects. Finally, we compare the behaviour of estimators of the incremental treatment effect and average treatment effect in experiments including data-inspired simulations.