מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 250: what the gap to the control is made of
Why. The "relative position" result (displaced workers end below a matched control without automation) was challenged on three counts: the control keeps each case's tax policy, so only cases with the status-quo policy had a complete control; the gap mixes several mechanisms; and part of the grid is duplicated. Generated by scripts/gap_decomposition_v250.py; archived in data/processed/gap_decomposition_v250.json. Closures of step 248 (debt cap 90%, firm overdraft) unless stated.
1. Duplicate cells
The stress setting raises interest rates and housing costs for mortgage holders but does not change rent or outright owners' costs. All 144 renter and outright-owner pairs are identical across stress settings (checked). The grid has 432 distinct cases, not 576; counts below use the 432.
2. A control without policy change
| Closure | Control | Matched | Both displaced below | Retained workers above | Median gap, displaced (no debt / debt) |
|---|---|---|---|---|---|
| Strict | same policy (grid) | 21 | 100% | 100% | -25% / -21% |
| Strict | status-quo policy | 51 | 100% | 100% | -22% / -17% |
| Closures | same policy | 432 | 91% | 96% | -24% / -20% |
| Closures | status-quo policy | 432 | 93% | 94% | -23% / -20% |
The choice of control hardly matters. Under strict rules every matched pair has the displaced below the control; with closures 91%-93% do.
3. Decomposition (all 432 distinct cases)
Switches applied cumulatively; numbers are the change in the final consumption index of the displaced (average of the two cohorts, initial level = 100), mean over cases (median in brackets):
| Component | Mean | Median |
|---|---|---|
| Gap to the status-quo control, baseline | -39.2 | -25.4 |
| of which: growth of the same cohorts in the control (employed) | 13.7 | 10.3 |
| R: no rationing of the benefit (no debt cap) | +22.9 | 0.0 |
| D: no claw-back of dividends on the cohort's own savings | +31.9 | +28.8 |
| H: benefit indexed to goods and housing | +4.9 | +2.5 |
| Gap after all three switches | +20.5 | +15.1 |
After the three switches the displaced end above the control in 75% of cases.
What it means.
- Rationing matters in a minority of cases (median 0) but is large where the budget binds. Removing
it needs net debt above 90% of output in 37% of cases, up to 2.7 times output at the 90th percentile.
- The claw-back is the largest single component. The benefit tops income up to the reference and
subtracts the cohort's own dividends one-for-one. The displaced keep saving out of the benefit, buy equity, and in a growing, automating economy those dividends rise; the rule withdraws all of it, a 100% marginal tax on their capital income. Limiting the claw-back to the dividend already in the reference income lifts the displaced well above where they would otherwise end.
- Housing indexation adds a little on top, more under full pass-through (step 247: the housing
effect is a deflation effect).
- The control's growth is real but smaller than the gap.
So the relative-position result is a property of the benefit design, not a law of the model. A benefit set against today's standard, rationed when the budget binds and withdrawn against the recipient's own capital income, leaves the displaced behind. A benefit that lets them keep the returns on their own savings does not, if the budget can carry it.
Limits
- The switches are applied in one order; contributions in another order would differ.
- Removing rationing ignores the debt it requires; there is no interest premium in the model.
- The model's saving rule (90% of income consumed, the rest invested) drives the claw-back effect.