Unlocking Hidden Paths: A Practical Guide to Mediation Analysis in Causal Inference

Introduction

In non‑AB causal inference we often only obtain a single overall effect of a variable X on Y, yet we may want to know through which pathway X influences Y. Mediation analysis helps reveal these indirect effect paths.

1. Mediation Effect Overview

1.1 Definition

According to Wen Zhonglin et al. (2004), if X influences Y through a variable M, then M is a mediator. For example, a father’s socioeconomic status affects a son’s education, which in turn affects the son’s socioeconomic status. The total effect (c) equals the direct effect (c') plus the indirect effect (a×b).

1.2 Significance of Testing Mediation

Testing mediation allows researchers to explore mechanisms behind causal relationships and to detect cases where competing mediators may cancel each other’s effects, explaining why a direct causal link appears insignificant.

1.3 Theoretical Models

Three common mediator structures are:

Simple mediation : a single mediator M links X to Y.

Parallel mediation : multiple mediators (M1, M2, …) operate independently.

Chain mediation : multiple mediators influence each other sequentially.

2. Selecting Mediators

Mediator selection relies on theory and empirical validation. Using the Uber causal inference case as an example, the process includes posing a research question, applying business knowledge to shortlist potential mediators, and confirming data availability for each candidate.

3. Testing Mediation Effects

3.1 Causal Stepwise Regression (Baron & Kenny, 1986)

The classic three‑step linear regression tests whether:

Path a: X significantly predicts mediator M.

Path b: M significantly predicts Y controlling for X.

Path c': The direct effect of X on Y becomes non‑significant after accounting for M.

3.2 Optimized Testing (Zhao 2010; Preacher & Hayes 2004)

Because the Baron‑Kenny method has limitations, modern approaches use bootstrap confidence intervals to assess the significance of the indirect effect a×b, providing more reliable inference.

4. Research Workflow

The overall mediation analysis process includes:

Define research question and hypothesized mediator.

Select mediators based on theory and data availability.

Estimate the three regression equations (or use structural equation modeling).

Test indirect effect with bootstrap or Sobel test.

Interpret results (full vs. partial mediation).

4.1 Example: Leverage Ratio → Social Financing → Economic Growth

Using the causal stepwise regression, the study finds that leverage negatively affects social financing, which in turn positively influences GDP growth. Social financing acts as a mediator linking financial conditions to macro‑economic performance.

Regression results show a significant negative coefficient from leverage to social financing and a significant positive coefficient from social financing to GDP growth, confirming a partial mediation effect.

Summary

The article introduces the concept of mediation effects, outlines how to choose mediators, presents classic and modern testing procedures, and demonstrates the full workflow with a concrete economic case, offering deeper insight into causal mechanisms between variables.