  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.
