# Hayashi Germany Länder data extraction note

Immutable repository commit: `0546db331aa8e3bad671cc2ff997359216103233`.

## Canonical source products

- Annual panel: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-preanalysis-b86a097d5159fb29/laender_annual_preanalysis.csv`
- Window panel: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-preanalysis-b86a097d5159fb29/laender_window_preanalysis.csv`
- Preanalysis manifest: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-preanalysis-b86a097d5159fb29/release_manifest.json`
- Annual real-output source product: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-pilot-9054b7aeace8575e/laender_real_output.csv`
- Execution registry: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-results-e03dd8e13726e7b4/laender_execution_registry.csv`
- Target estimates: `Hayashi_Germany_Research_Package/Hayashi_Germany_Research_Package/outputs/releases/laender-results-e03dd8e13726e7b4/laender_target_estimates.csv`

The frozen preanalysis manifest reports 544 annual observations (16 Länder × 34 years, 1991–2024), 80 window observations, twelve passed validation checks, no warnings, and no missing core age-ratio or real-output-per-denominator values.

## Definitions

- Old-to-young ratio = resident population aged 50–79 / resident population aged 20–49.
- “Older per 100 younger” = 100 × that ratio.
- It is an adult-composition measure, not the conventional old-age dependency ratio.
- Real GDP per adult aged 20–79 divides workplace real GDP by resident population, so it is explicitly commuting-sensitive and is not a welfare or resident-productivity measure.
- Real GDP per employed person is a workplace/workplace labor-productivity proxy.

## Regional grouping used in the scratch extracts

- East: Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt, Thüringen.
- West: Baden-Württemberg, Bayern, Hessen, Niedersachsen, Nordrhein-Westfalen, Rheinland-Pfalz, Schleswig-Holstein, Saarland.
- City States: Berlin, Bremen, Hamburg.

Berlin is kept in the mutually exclusive City State group, not duplicated in East.

## Growth calculations added to the scratch annual file

- Annual aging change: 100 × [ln(ratio_t) − ln(ratio_{t−1})].
- Annual real GDP-per-adult growth: 100 × [ln(level_t) − ln(level_{t−1})].
- Annual real GDP-per-employed growth: same log-difference convention.
- The official total-real-GDP growth rate is retained separately as `gdp_real_growth_pct_official`.
- Group ratios are ratios of summed age-group populations, not averages of Länder ratios.

## Convergence correction

The paper's canonical adjacent-window primary unweighted model already performs a standard conditional-convergence correction. It regresses annualized real workplace GDP-per-resident-aged-20–79 growth on the period-average log old-to-young ratio and controls for:

1. initial log GDP per resident aged 20–79,
2. period-average log child dependency, and
3. window fixed effects.

The frozen execution registry reports N = 48 and 16 Länder clusters. Frisch–Waugh–Lovell residualization in the scratch file reproduces the treatment coefficient `−3.32608630069268` to numerical precision (difference below 8e−15). A 10% higher period-average ratio implies:

`−3.3260863 × ln(1.10) = −0.3170099` percentage points of annual growth.

This means a comparable Land/window with an average old-to-young ratio 10% higher is associated with about 0.317 percentage point lower annual growth. If sustained mechanically for ten years, that annual gap compounds to roughly 3.1% lower output per resident aged 20–79. This is conditional association, not a causal effect, and the treatment is the average composition level—not the realized change in the ratio.

The separate realized-aging-change estimate is a different estimand and is not statistically resolved. Do not describe the composition coefficient as “aging 10% faster.”

The common-X accounting decomposition is not convergence-adjusted in the same way: it uses initial sector share and a period dummy, not initial log outcome. Do not transfer the canonical model's convergence interpretation to the common-X mechanism coefficients.

## Data discontinuities and interpretation caveats

- All Länder carry `census_basis_change` flags in 2011 and 2022. Mark both vintages in annual charts and avoid interpreting one-year movements through those breaks as pure demographic change.
- The 2022 census-vintage stabilization is still on the research roadmap; the current annual panel is frozen but not a fully harmonized single-census-vintage historical series.
- Eastern Länder exhibit large post-reunification catch-up. A single linear initial-income control is a basic convergence correction, not a complete reunification counterfactual. A stronger article diagnostic should add East × window fixed effects and/or East/West-specific convergence slopes, clearly labeled as sensitivity analysis.
- Chain-linked real measures are revision-sensitive, and workplace GDP per resident mixes workplace output with resident denominators.

## Scratch products

- `SCRATCH_HAYASHI_LAENDER_ANNUAL_1991_2024_FINAL_0546DB3.csv`: all 544 annual observations plus exact group labels, ratios, official GDP growth, derived per-denominator log growth, census and pandemic flags.
- `SCRATCH_HAYASHI_LAENDER_GROUP_AGGREGATES_1991_2024_0546DB3.csv`: aggregate age ratios for East, West, City States, and Germany.
- `SCRATCH_HAYASHI_LAENDER_SUMMARY_1991_2024_CONVERGENCE_0546DB3.csv`: Länder endpoints and a clearly descriptive 1991–2024 cross-sectional convergence residual.
- `SCRATCH_HAYASHI_CANONICAL_ADJACENT_FWL_CONVERGENCE_0546DB3.csv`: exact 48-observation residualized data surface reproducing the canonical convergence-adjusted coefficient.

