Feature selection in stratification estimators of causal effects: lessons from potential outcomes, causal diagrams, and structural equations

TL;DR

This paper investigates the optimal regression methods for estimating average causal effects with discrete covariates, analyzing variance and integrating insights from potential outcomes, causal diagrams, and structural models.

Contribution

It provides a unified analysis of stratification estimators' variance, combining three causal inference frameworks to clarify fundamental statistical principles.

Findings

Derived expressions for finite-sample variance of stratification estimators

Clarified the statistical phenomena underlying causal effect estimation

Unified insights from potential outcomes, causal diagrams, and structural models

Abstract

What is the ideal regression (if any) for estimating average causal effects? We study this question in the setting of discrete covariates, deriving expressions for the finite-sample variance of various stratification estimators. This approach clarifies the fundamental statistical phenomena underlying many widely-cited results. Our exposition combines insights from three distinct methodological traditions for studying causal effect estimation: potential outcomes, causal diagrams, and structural models with additive errors.