Choosing the Right Approach at the Right Time: A Comparative Analysis of Causal Effect Estimation using Confounder Adjustment and Instrumental Variables

TL;DR

This paper compares confounder adjustment and instrumental variable methods for causal effect estimation, providing theoretical insights, a sensitivity framework, and practical guidance for observational studies with unobserved confounding.

Contribution

It offers a theoretical comparison of CAC and IVAC approaches under assumption violations and introduces a sensitivity framework to guide method choice.

Findings

Analytical comparison of inconsistency under various assumption violations.

A sensitivity framework to assess method suitability for specific datasets.

Demonstration through simulation and real data revisiting educational attainment effects.

Abstract

In observational studies, potential unobserved confounding is a major barrier in isolating the average causal effect (ACE). In these scenarios, two main approaches are often used: confounder adjustment for causality (CAC) and instrumental variable analysis for causation (IVAC). Nevertheless, both are subject to untestable assumptions and, therefore, it may be unclear which assumption violation scenarios one method is superior in terms of mitigating inconsistency for the ACE. Although general guidelines exist, direct theoretical comparisons of the trade-offs between CAC and the IVAC assumptions are limited. Using ordinary least squares (OLS) for CAC and two-stage least squares (2SLS) for IVAC, we analytically compare the relative inconsistency for the ACE of each approach under a variety of assumption violation scenarios and discuss rules of thumb for practice. Additionally, a sensitivity framework is proposed to guide analysts in determining which approach may result in less inconsistency for estimating the ACE with a given dataset. We demonstrate our findings both through simulation and by revisiting Card's analysis of the effect of educational attainment on earnings, which has been the subject of previous discussion on instrument validity. The implications of our findings on causal inference practice are discussed, providing guidance for analysts to judge whether CAC or IVAC may be more appropriate for a given situation.