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

arXiv: https://arxiv.org/abs/2008.03481 · HTML: https://mlsanity.com/paper/2008.03481/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [Efficient learning of nonlinear prediction models with time-series privileged information](https://mlsanity.com/paper/2209.07067/) (2022)
- [Linear Causal Discovery with Interventional Constraints](https://mlsanity.com/paper/2510.26342/) (2025)
- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)

## Abstract (arXiv)

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.