Causal inference via implied interventions

TL;DR

This paper proposes a new causal inference approach that focuses on identifiable interventions implied by instruments, avoiding untestable assumptions and enabling transparent estimation of causal effects.

Contribution

It introduces a framework that characterizes causal effects through implied interventions and uses projections to approximate target effects without relying on traditional assumptions.

Findings

Provides explicit G-computation formula under hidden confounding.

Introduces a projection-based method for estimating causal effects.

Utilizes the Highly Adaptive Lasso for flexible estimation.

Abstract

In the context of having an instrumental variable, the standard practice in causal inference begins by targeting an effect of interest and proceeds by formulating assumptions enabling identification of this effect. We turn this around by simply not making assumptions anymore and just adhere to the interventions we can identify, rather than starting with a desired causal estimand and imposing untestable hypotheses. The randomization of an instrument and its exclusion restriction define a class of auxiliary stochastic interventions on the treatment that are implied by stochastic interventions on the instrument. This mapping effectively characterizes the identifiable causal effects of the treatment on the outcome given the observable probability distribution, leading to an explicit transparent G-computation formula under hidden confounding. Alternatively, searching for an intervention on the instrument whose implied one best approximates a desired target -- whose causal effect the user aims to estimate -- naturally leads to a projection on a function space representing the closest identifiable treatment effect. The generality of this projection allows to select different norms and indexing sets for the function class that turn optimization into different estimation procedures with the Highly Adaptive Lasso. This shift from identification under assumptions to identification under observation redefines how the problem of causal inference is approached.