Overview

Purpose

This companion is designed to ensure transparency and reproducibility for the paper “Occupational Mobility Is Not One Thing: Evidence from the Canadian Labour Market”. It provides technical detail on distance metrics and normalization, specificity measures.

Skill distance: O*NET-based occupational skill vectors, dimensionality reduction via PCA, and the resulting continuous distance matrix.
Hierarchical distance: Taxonomy-based discrete distances derived from the NOC structure, resulting in labour market silos with internal TEER platforms.
Cost matrix normalization: percentile-based anchoring/normalization across distance metrics.
Occupation’s education specificity: A size-adjusted measure of concentration in educational inflows into occupations: how different is this occupation than the labour market as a whole in terms of educational pathways.
Education’s occupation specificity: A size-adjusted measure of concentration in occupational outcomes across educations (cross product of fields of study and attainment): how different is this education compared with education in general in terms of occupational pathways.

Skill Distance

Skill distance matrix

We use 161 occupational characteristics (Skills, Abilities, Knowledge, Work Activities) from ONET to measure the distance between occupations.
Because occupational skill vectors are high-dimensional and highly correlated, Euclidean distances computed in the full feature space may suffer from distance concentration.
We therefore project the data onto the 12 leading principal components, which achieve a 99% rank correlation of distance (pca vs raw).
This reduces noise from low-variance directions while preserving the dominant geometry of the skill space.
Diagonal is self distance (0).
Dark boxes along diagonal are clusters of occupations with similar skill profiles.
Yellow lines near the edge are “Other Performers”: they have the most distinct skill set.

Column

Rank Correlation

Column

Normalized ONET Skill Distance (left mouse button hold and drag to zoom)

Hierarchical distance

Column

Description

Hierarchical distances encode institutional and career-ladder barriers implied by occupational taxonomies:

All five digits match: distance = 0
First four digits match: distance = 1
First three digits match: distance = 2
First digit matches: distance = 3 + |ΔTEER|
Otherwise: distance = 9

These distances are then normalized by division by 4, as described on the page “Cost matrix normalization”.
The Spearman correlation is 0.289, indicating that institutional proximity and skill similarity are positively but only modestly related.
The two metrics encode overlapping yet distinct occupational geometries.

Distance counts

Column

Normalized hierarchical distances (left mouse button hold and drag to zoom)

Cost matrix normalization

Anchoring to the Informative Cost Region

The hierarchical distance contains a large mass of maximally distant pairs (distance = 9), which represent transitions the taxonomy treats as categorically distant. Because these pairs provide little information about substitution intensity among plausible transitions, we define the informative region as the set of non-maximal, non-zero hierarchical distances.

Within this region, we compute the 25th, 50th, and 75th percentiles of hierarchical cost. These conditional quantiles represent increasingly broad but still economically meaningful transition margins.

Each anchor value is then mapped to its unconditional percentile in the full hierarchical distribution. The skill distance matrix is calibrated by selecting cost values at these same unconditional percentiles. This procedure ensures that calibration aligns comparable substitution margins across metrics, rather than matching arbitrary numerical magnitudes.

Percentile-based anchoring is invariant to monotonic transformations of the cost scale and therefore preserves the rank ordering of transition costs in each metric.

Conditional Quantile	Hierarchical Anchor	Unconditional Percentile	Skill Anchor
Calibration Anchors Across Distance Metrics
0.25	3.000	0.040	7.145
0.50	4.000	0.081	8.590
0.75	5.000	0.105	9.253

The median non-maximal hierarchical transition lies at approximately the 8th percentile of the full hierarchical distribution; the skill anchor is defined at this same percentile to ensure comparable substitution intensity.

Occupation’s Education Specificity

Step 1 — Overall Educational Distribution

We compute the overall educational distribution across all NOCs. This represents the expected education mix for a worker drawn from the educated workforce without conditioning on occupation.

Step 2 — Distribution Within Each NOC

For each NOC:

Compute total workers \(T\)
Compute occupation-specific education shares \(p\)
Compare to the baseline distribution \(p_0\)

Step 3 — Remove Size Effect

Finite samples mechanically inflate divergence for small occupations. We remove this statistical artifact by modeling expected divergence as a function of occupation size.

fit_kl <- lm(log(KL) ~ log(T), data = noc_specificity)

noc_specificity <- noc_specificity |>
  mutate(
    specificity = log(KL) - predict(fit_kl),
    TEER = str_sub(noc, 2, 2)
  )

The resulting specificity index measures how distinct an occupation’s education mix is relative to what is statistically expected given its size. As expected, higher-credential occupations tend to exhibit greater specificity, but the relationship is far from deterministic.

Key Insight:

Occupational education distributions are estimated from finite counts, and small cells are imprecisely measured or suppressed.
Traditional concentration measures (HHI, entropy, support size) therefore scale mechanically with occupation size and tail thickness.
KL divergence captures where probability mass is concentrated relative to the aggregate baseline, rather than how much mass lies in very small cells.
Residualizing KL with respect to \(T\) removes predictable finite-sample divergence, isolating economically meaningful concentration.
Crucially, this construction yields a measure of destination gating intensity that is orthogonal to occupation size by construction. The index therefore captures how narrowly educational pipelines feed into an occupation, not how large the occupation happens to be.
In the equilibrium transport framework, this matters because:
1. Size affects marginal constraints (the mass that must be absorbed).
2. Specificity affects the effective cost landscape faced by workers.
By separating these components, we ensure that occupation’s education specificity reflects structural concentration in educational pathways rather than equilibrium scale effects. This allows education specificity to enter as heterogeneity in frictions within the same general equilibrium mobility model, rather than as a mechanical artifact of occupational size.

Column

High specificity indicates few educational pathways into the occupation; residualized specificity is not correlated with log occupation size (Pearson=-0.03, Spearman=0.03).

Column

Education’s Occupation specificity

Education’s Occupation Specificity

We construct education’s occupation specificity symmetrically to occupation’s education specificity, conditioning on education rather than occupation.

Step 1 — Overall Occupational Distribution

We compute the aggregate occupational distribution across all educated workers. This serves as the baseline allocation of workers across destinations absent conditioning on field of study.

Step 2 — Distribution Within Each Education

For each Education:

Compute total graduates \(T\)
Compute occupation shares \(p\)
Compare to the aggregate occupational distribution \(p_0\)
Measure divergence using KL distance

Step 3 — Remove Size Effect

As with occupations, small cohorts mechanically inflate divergence. We therefore residualize \(\log KL\) with respect to \(\log T\), isolating concentration beyond what is statistically expected given field size.

fit_kl <- lm(log(KL) ~ log(T), data = educ_specificity)

educ_specificity <- educ_specificity |>
  mutate(
    specificity = log(KL) - predict(fit_kl)
  )

The resulting index measures how narrowly a field of study feeds into occupations, independent of cohort size.

Interpretation

Professional and doctoral fields exhibit consistently high occupational concentration. Below that threshold, specificity varies substantially within attainment levels. Educational level alone does not determine pipeline concentration.

Column

High specificity indicates few occupational pathways from the education; residualized specificity is not correlated with log occupation size (Pearson=0.07, Spearman=-0.01).

Overview

Purpose

Contents

Skill Distance

Inputs

Skill distance matrix

Column

Rank Correlation

Column

Normalized ONET Skill Distance (left mouse button hold and drag to zoom)

Hierarchical distance

Column

Description

Distance counts

Column

Normalized hierarchical distances (left mouse button hold and drag to zoom)

Cost matrix normalization

Anchoring to the Informative Cost Region

Occupation’s Education Specificity

Inputs

Occupation’s Education Specificity

Step 1 — Overall Educational Distribution

Step 2 — Distribution Within Each NOC

Step 3 — Remove Size Effect

Key Insight:

Column

High specificity indicates few educational pathways into the occupation; residualized specificity is not correlated with log occupation size (Pearson=-0.03, Spearman=0.03).

Column

Education’s Occupation specificity

Inputs

Education’s Occupation Specificity

Step 1 — Overall Occupational Distribution

Step 2 — Distribution Within Each Education

Step 3 — Remove Size Effect

Interpretation

Column

High specificity indicates few occupational pathways from the education; residualized specificity is not correlated with log occupation size (Pearson=0.07, Spearman=-0.01).

Column