# Methods — The labour market is not collapsing. It is freezing.

## Scope and definitions

The analysis covers Germany, France, the Netherlands, the United Kingdom and the United States. The empirical window begins in 2019 for stock–flow baselines and in 2021 for post-pandemic vacancy peaks. The latest observation depends on source availability and is labelled in each figure.

- **Employment stock:** persons employed under the relevant official national or harmonised definition.
- **Opportunity:** job vacancies or LinkedIn job postings per applicant, based on the figure.
- **Movement:** hires, quits or LinkedIn’s hiring rate. A fully harmonised current job-to-job transition measure is unavailable across all five countries.
- **Search intensity:** LinkedIn applications per applicant.
- **First rung:** LinkedIn hiring into entry-level roles requiring an advanced degree.

LinkedIn defines its hiring rate as members who add a new job divided by membership in the country, seasonally adjusted. Its postings-per-applicant measure divides active job listings that receive at least one application by applicants to those listings. Applications per applicant is the average number of applications submitted by each applicant within the same country.

## Acquisition and versions

Official data were retrieved on 30 August 2026.

1. The BLS public API supplied monthly CES employment, household employment, unemployment, JOLTS openings, hires and quits series for 2019–2026.
2. Eurostat’s dissemination API supplied quarterly job vacancy rates (`jvs_q_r21`), quarterly employment (`namq_10_pe`) and monthly unemployment (`une_rt_m`).
3. ONS VACS01 supplied the rolling three-month UK vacancy history through May–July 2026.
4. LinkedIn Economic Graph values were transcribed from its March and June 2026 EMEA–LATAM tables, June 2026 US labour-market publications and its 2026 graduate-market article. The PDFs are linked but not redistributed.

Raw acquisitions, derived extracts, checksums and executable code appear in `04_research/`.

## Cleaning and transformations

### Figure 1 — Freeze matrix

For Germany, France, the Netherlands and the UK, February and May 2026 values are connected using LinkedIn’s year-on-year change in postings per applicant on the horizontal axis and hiring rate on the vertical axis. The US is a May-only reference. Employment stock controls bubble **area** using the latest compatible official observation; it does not affect position.

### Figure 2 — US stock–flow wedge

For series \(s\) and month \(t\):

\[
I_{s,t} = 100 \times \frac{x_{s,t}}{x_{s,2019\text{-}12}}.
\]

June 2026 is the latest common month across employment, openings, hires and quits. Later employment observations are not used in the displayed endpoint comparison.

### Figure 3 — Vacancy retreat

For country \(c\):

\[
P_{c,t} = 100 \times \frac{v_{c,t}}{\max(v_{c,2021:2026})}.
\]

Eurostat vacancy rates, ONS vacancy counts and the BLS JOLTS openings rate are intentionally kept in separate panels. Normalisation permits comparison of each country’s retreat from its own peak; it does not make the underlying levels equivalent. The latest Netherlands observation available in the extracted Eurostat series is 2025 Q4.

### Figure 4 — Application fatigue

May 2026 year-on-year changes are used as published. Zero lines distinguish expansion from contraction. No regression, causal model or population weighting is applied.

### Figure 5 — Sector retreat

Within each country and NACE sector, the latest vacancy rate is compared with the maximum observed since 2021 Q1:

\[
\Delta_{c,k} = 100 \times \left(\frac{v_{c,k,latest}}{\max(v_{c,k,2021:2026})} - 1\right).
\]

Sixteen of twenty-four intended business-sector cells are available. Missing cells remain blank. Public administration is excluded from the displayed business-sector comparison.

### Figure 6 — First-rung gap

LinkedIn’s pre-pandemic hiring comparisons are used as published. The extra first-rung shortfall is entry-level hiring change minus overall hiring change, expressed in percentage points.

### Figure 7 — Remote-work mismatch

Posting and application shares are used as published. The audit table also reports the ratio of application share to posting share, but the chart retains both original shares to avoid reducing the evidence to a single score.

## Validation and robustness

- All required extracts passed minimum row-count and common-period checks.
- US index endpoints were independently recomputed from the raw BLS response.
- European employment series use seasonally-and-calendar-adjusted national-concept employment where published; France uses the available seasonally adjusted series.
- Every chart has an exact-value CSV and paired light/dark 1600 × 1000 export generated from the same data.
- The chart plan passed the strict Schym chart-contract validator with zero errors and zero warnings.
- The acquisition manifest records SHA-256 checksums for every raw and derived file.

## Limitations and use boundary

1. LinkedIn measures describe activity observed on its platform. Coverage differs by country, occupation and worker type; these are timely proxies, not population estimates.
2. “Movement” is not one harmonised statistic across the package. Figure 1 uses LinkedIn hiring, while Figure 2 uses BLS hires and quits. The terms are defined adjacent to each figure.
3. The vacancy retreat panels compare relative paths, not absolute tightness across countries.
4. Sector coverage is incomplete and no missing value is imputed.
5. Stable employment cannot establish that staying is involuntary; declining search cannot distinguish discouragement from selectivity, delay or a change in platform behaviour.
6. The evidence is descriptive. It does not identify the causal contribution of AI, interest rates, macro uncertainty, labour policy or employer strategy.

## Reproduction

From the package root, run:

```bash
python3 04_research/code/fetch_and_prepare_data.py
python3 04_research/code/validate_and_summarize.py
python3 04_research/code/render_figures.py
```

Network retrieval is only required for a refresh. The distributed extracts are sufficient to reproduce all published transformations and figures offline.