מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 281: the revised central specification
Why. After the third referee round the central specification changes. It is now the revised specification of step 276:
- Firms (step 266): retained earnings, depreciation 5%, overdraft capped at 50% of output.
- Government (step 268): a debt cap of 90% of output, surpluses returned to households once net
debt is zero, and a risk premium.
- Equity: priced at the present value of the net payout, at 4.5%.
- Tax response: a profit levy of up to 15% of profits when the cap would otherwise ration benefits.
Every number and figure the text uses for this specification comes from scripts/central_v281.py. The model is closure_model_v279, with all later options off. Results are archived in data/processed/central_v281.json and figures/*_v281*. Gaps to the status-quo control are means of the last five years. Illustrative; not a forecast.
Preservation (432 distinct cases)
| Threshold | 80% | 85% | 90% | 95% |
|---|---|---|---|---|
| Both displaced cohorts preserved | 320 | 300 | 277 (64%) | 257 |
With a 120% debt cap, 251 cases are preserved. A higher cap means a larger risk premium, and the levy starts later.
| Factor | Values | Preserved |
|---|---|---|
| Productivity gain | 25% / 50% / 100% | 32% / 75% / 85% |
| Tax reach | 0.5 / 1 | 50% / 78% |
| Tax rate | 25% / 35% | 55% / 73% |
| Ownership | concentrated / broad | 49% / 80% |
| Pass-through | 0 / 0.5 / 1 | 73% / 69% / 51% |
| Tenure | renters / outright owners / fixed / reset mortgage | 64% / 72% / 68% / 56% |
The breakeven productivity gains of step 277 summarise the same information without the coarse grid. The median breakeven gain is 0.33, at which output is about 9% below the no-automation path.
Debt and the levy
- No severe fiscal crisis. Peak net debt never exceeds 1.2 times output. In 10 cases it overshoots
the cap by more than 5 points.
- The levy is used in 182 cases, and 65 of them preserve the displaced.
- The benefit is still rationed in 129 cases, where the levy cap is not enough.
- The final dividend yield is 4.4% at the median.
Relative position (mean of the last five years, vs status-quo control)
| Cohort | Median | IQR | Range |
|---|---|---|---|
| Retained workers | +28.9% | +4.6% to +56.2% | −12.7% to +158.5% |
| Capital owners | +43.4% | +20.9% to +94.8% | −4.8% to +281.6% |
| Displaced, no debt | +2.8% | −23.6% to +29.7% | −100% to +83.9% |
| Displaced, with debt | +4.0% | −28.0% to +33.2% | −100% to +109.0% |
Both displaced cohorts end below the control in 47% of cases, and retained workers above it in 80%. Measured in the final year alone, the median for the displaced without debt is −2.1%.
The displaced fall behind the employed, but not, in the median case, behind their own position without automation. The earlier headline, "below the control in 58%–93% of cases", came from fiscal crises in which the benefit was rationed to nothing, and from the timing of the control's rebates.
Shapley split of the gap (index points, mean of the last five years)
The sample is the 293 cases in which all eight combinations complete. In 139 cases, removing the debt cap lets demand outrun output and runs the capital stock down, so those cases are left out.
| Component | Mean | Median |
|---|---|---|
| Gap to the control, baseline | +16.7 | +18.2 |
| Growth of the same cohorts in the control | +16.3 | +14.5 |
| R: no debt cap | +3.2 | 0.0 |
| D: no claw-back on own dividends | +41.3 | +10.0 |
| H: housing-indexed benefit | +4.6 | +2.4 |
With the levy, R is small, although the benefit is still rationed in 129 cases. Removing the claw-back lets the displaced keep the dividends on everything they save, so their consumption keeps rising (mean +41, median +10). That is a level effect, not protection: the claw-back adds only 12 preserved cases (step 276).
Wage regimes (144 distinct cases each)
| Regime | Preserved | Renters / outright owners (of 24) | Room for benefits at year 10 vs profits regime (points of output) |
|---|---|---|---|
| Gain stays in profits | 105 | 18 / 18 | – |
| Gain to wages | 91 | 15 / 15 | −1.40 (revenue −1.13, interest −0.27) |
| Half and half | 92 | 15 / 16 | −0.86 |
| Gain to prices (deflation) | 73 | 11 / 17 | −0.25 (revenue +0.52, interest −0.78) |
Passing the gain to wages costs revenue: 14 cases fewer than keeping it in taxed profits. Deflation costs more cases, mostly among renters and mortgage holders. With 2% inflation or indexed rent, that extra loss disappears (step 278).
Israel (144 cases, 108 distinct; revised specification)
| Opening budget balance | Consumption share 0.90: distinct preserved | 0.76 | g = 0.25 / 0.5 / 1 (0.90, of 48) |
|---|---|---|---|
| Primary deficit 2% (central for Israel) | 62 of 108 (57%) | 95 | 0 / 45 / 40 |
| Balanced | 91 (84%) | 99 | 37 / 45 / 40 |
| Primary surplus 1% | 98 (91%) | 100 | 45 / 45 / 43 |
Israel ran primary deficits in 2021–2024, so the deficit opening is now the central Israeli case. Even with the levy, a 25% productivity gain preserves no case from a 2% deficit.