Efficient least squares for estimating total effects under linearity and causal sufficiency

TL;DR

This paper introduces an efficient recursive least squares estimator for total causal effects in linear structural equation models, applicable under known causal structures with no unobserved confounding, and proves its optimality among covariance-based estimators.

Contribution

It presents a simple, consistent, and most efficient estimator for total causal effects in linear SEMs under partial causal knowledge, without requiring Gaussian errors.

Findings

Estimator is consistent for total causal effects.

It is the most efficient among covariance-based estimators.

Works under non-Gaussian error distributions.

Abstract

Recursive linear structural equation models are widely used to postulate causal mechanisms underlying observational data. In these models, each variable equals a linear combination of a subset of the remaining variables plus an error term. When there is no unobserved confounding or selection bias, the error terms are assumed to be independent. We consider estimating a total causal effect in this setting. The causal structure is assumed to be known only up to a maximally oriented partially directed acyclic graph (MPDAG), a general class of graphs that can represent a Markov equivalence class of directed acyclic graphs (DAGs) with added background knowledge. We propose a simple estimator based on recursive least squares, which can consistently estimate any identified total causal effect, under point or joint intervention. We show that this estimator is the most efficient among all regular estimators that are based on the sample covariance, which includes covariate adjustment and the estimators employed by the joint-IDA algorithm. Notably, our result holds without assuming Gaussian errors.