Mediation Analyses; Methodology

What These Analyses Do

Causal mediation analysis asks: when X affects Y, how much of that effect operates through a mediator M, and how much is direct?

For example: "Immigrants earn less than Australian-born workers. Is this because they have different education levels (indirect effect), or because they earn less even with the same education (direct effect)?"

Framework

We use the counterfactual decomposition framework (Imai et al. 2010), which defines effects in terms of potential outcomes. The Total Effect (TE) measures the full outcome gap between two groups. This decomposes into the Average Causal Mediation Effect (ACME), which captures the indirect pathway through the mediator, and the Average Direct Effect (ADE), which captures everything not operating through the mediator. The identity TE = ACME + ADE always holds exactly.

Effects are calculated directly from cross-tabulation tables rather than regression models, avoiding parametric assumptions and using empirical distributions. This approach is transparent, assumption-lean, and exactly reproducible.

Geographic Levels

Mediation analyses are available at LGA, GCCSA, State/Territory, and National levels. They are not available at suburb or postcode level because the required cross-tabulations are too sparse at these granular levels.

Pooled vs Stratified Analysis

Two modes are available when you select multiple geographies. Pooled combines all geographies into one analysis; useful for a single summary. Stratified runs analysis separately for each geography (maximum 5); useful for comparing patterns across regions, with forest plots for visual comparison.

Included Analyses

Six mediation pathways are pre-configured: (1) Migration → Education → Income, (2) Gender → Occupation → Income, (3) Education → Occupation → Income, (4) Gender → Industry → Income, (5) Migration → Occupation → Income, and (6) Family Composition → Labour Force → Family Income.

Income Dichotomisation

Income outcomes are dichotomised to above/below national median. The median bracket is computed from the national income distribution and the same threshold is applied across all geographies for comparability.

Bootstrap Intervals

AUSynth analyses are based on the full Census 2021 population (with WPI/CPI adjustments). Bootstrap intervals are reported but reflect variability in the cross-tabulation cell counts due to ABS suppression and rounding rather than sampling uncertainty in the traditional sense. They serve as a robustness check: stable estimates across resamples indicate that the effect is not driven by small-cell artefacts. Each resample produces a full set of effects; the 2.5th and 97.5th percentiles define the interval.

How To Read The Results

When both ACME and ADE have the same sign, the mediator partially explains the gap; the proportion mediated tells you how much. When they have opposite signs, the mediator partially compensates for the direct effect, which is often the most interesting finding. If a bootstrap interval crosses zero, the effect may not be robust to small perturbations in the data.

Required Assumptions

For causal interpretation, sequential ignorability (no unmeasured confounders), positivity (all exposure-mediator combinations observed), and consistency must hold. These are strong assumptions that cannot be verified with cross-sectional data. Findings should be interpreted as suggestive of causal structures consistent with the assumed model.

Data Source

ABS Census 2021 cross-tabulation tables, adjusted for wage growth (state-specific WPI) through Q4 2025. AUSynth v1.0.

Reference

Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15(4), 309-334.