Counterfactual Reasoning in Linear Structural Equation Models

TL;DR

This paper develops a framework for counterfactual reasoning in Gaussian linear structural equation models, extending previous formulas to interval and conditional observations to better understand causal effects.

Contribution

It reformulates counterfactual distribution formulas using total effects and covariance matrices, extending them to interval and conditional plans.

Findings

Formulated counterfactual distributions using total effects and covariance matrices.

Extended the framework to interval observations and conditional plans.

Clarified properties and established an optimal counterfactual plan.

Abstract

Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a treatment variable were assigned to some value (counterfactually), given that a set of variables is observed (actually). In order to achieve this aim, we reformulate the formulas of the counterfactual distribution proposed by Balke and Pearl (1995) through both the total effects and a covariance matrix of observed variables. We further extend the framework of Balke and Pearl (1995) from point observations to interval observations, and from an unconditional plan to a conditional plan. The results of this paper enable us to clarify the properties of counterfactual distribution and establish an optimal plan.