26.2 Establishing Mechanisms
Estimating a credible causal effect is a fundamental goal of quasi-experimental research. However, understanding how and why that effect arises is equally essential—especially for designing effective interventions, generalizing findings, and informing theoretical models.
This section discusses two critical approaches to uncovering mechanisms: mediation and moderation analysis. These strategies help unpack the “black box” of causal inference by identifying intermediate processes and subgroup heterogeneity.
26.2.1 Mediation Analysis: Explaining the Causal Pathway
Mediation analysis seeks to identify intermediate variables—known as mediators—through which the treatment influences the outcome. This allows researchers to distinguish between direct effects (from treatment to outcome) and indirect effects (those that operate through a mediator).
Let:
\(T\) = Treatment
\(M\) = Mediator
\(Y\) = Outcome
The goal is to decompose the total effect of \(T\) on \(Y\) into:
Direct Effect: \(T \rightarrow Y\)
Indirect Effect: \(T \rightarrow M \rightarrow Y\)
To identify mediated effects causally, the following assumptions are typically needed:
- Sequential Ignorability: Treatment is as good as random, and the mediator is as good as random conditional on treatment and observed covariates.
- No Unmeasured Mediator-Outcomes Confounders: A strong assumption, often violated in observational settings.
Estimation Strategies
- Causal Mediation Analysis (Imai, Keele, and Tingley 2010): Provides nonparametric estimators for direct and indirect effects under the assumptions above.
- Two-Stage Regression Approach:
- Estimate the effect of treatment on mediator: \(M_i = \alpha + \tau T_i + \varepsilon_i\)
- Estimate outcome as function of treatment and mediator: \(Y_i = \beta + \gamma T_i + \delta M_i + \eta_i\)
- Instrumental Variable Mediation: In the presence of endogeneity, use IV methods where the instrument affects \(M\) only through \(T\).
Practical Use Cases
- In marketing: Does an ad increase sales because it raises brand awareness (mediator)?
- In education: Does a tutoring program work by improving attendance (mediator), or student motivation?
Caution: Mediation analysis is often misused in quasi-experimental contexts; without strong assumptions or experimental variation in the mediator, estimates may not be causal.
26.2.2 Moderation Analysis: For Whom or Under What Conditions?
Moderation analysis investigates heterogeneity in treatment effects across subgroups or conditional on covariates. Rather than explaining why an effect occurs, moderation reveals when and for whom it is stronger or weaker.
Motivating Questions
- Do effects differ by gender, income, region, or baseline status?
- Is the treatment more effective for high-need individuals or early adopters?
Estimation Approaches
Subgroup Analysis: Estimate effects separately by subgroup (e.g., men vs. women).
Interaction Models: Include interactions between the treatment and moderator:
\[ Y_{it} = \alpha + \beta_1 T_{it} + \beta_2 Z_i + \beta_3 T_{it} \times Z_i + \varepsilon_{it} \]
where \(Z_i\) is a moderating variable (e.g., high vs. low income).
Difference-in-Differences (DiD) with Moderation: Extend Difference-in-Differences to test three-way interactions:
\[ Y_{it} = \alpha + \beta_1 \text{Post}_t + \beta_2 \text{Treat}_i + \beta_3 Z_i + \beta_4 \text{Post}_t \times \text{Treat}_i + \beta_5 \text{Post}_t \times \text{Treat}_i \times Z_i + \varepsilon_{it} \]
Here, \(\beta_5\) captures whether the treatment effect varies by \(Z_i\).
Visualization Tools
- Marginal Effects Plots: Show how the treatment effect varies across values of the moderator.
- Interaction Plots: Plot estimated means or regression lines by group and condition.
| Approach | Goal | Key Assumptions | Common Pitfalls |
|---|---|---|---|
| Mediation | Identify intermediate variables | Sequential ignorability, no omitted confounders | Mediators may be endogenous |
| Subgroup Analysis | Estimate effects by group | Sufficient sample size, balanced covariates | Spurious differences due to imbalance |
| Interaction Terms | Estimate conditional effects | Correct model specification | Misinterpretation of non-significant terms |
Both mediation and moderation analyses serve as bridges between empirical estimates and theoretical models:
- Mediation links to process theories: How does a treatment bring about change?
- Moderation links to contingency theories: Under what conditions does the treatment work?
In applied business research, understanding mechanisms is crucial for policy targeting, personalization strategies, and model refinement. For example:
- In customer retention programs, mediation might show that satisfaction explains retention gains.
- Moderation might reveal that effects are stronger for new customers than loyal ones.