Step 303: a benefit indexed to wages

Why. Step 302 found a cost of wage sharing that the levy cannot fix. When a share ω of the automation gain goes to the wages of the employed, the levy still protects the displaced against a fall in their own living standard. But the benefit reference is fixed in goods. At ω = 0.5 the displaced end 9%–11% below the status-quo control, while the employed end about 49% above it. This step asks whether indexing the benefit to wages closes that gap, what it costs the budget, and whether it changes the levy conclusion.

The model is scripts/closure_model_v303.py, a copy of step 301. With its new option off it reproduces steps 301 and 302 exactly (tested). The runner is scripts/wage_index_v303.py, with output in data/processed/wage_index_v303.json. Money is conserved in every run. Illustrative; not a forecast.

The rule

The benefit tops displaced workers' income up to a reference. Until now the reference was their pre-automation disposable income, fixed in goods. Here it follows the real net wage per employed worker:

reference_t = reference_0 × (1 + θ × (W_t / W_0 − 1))

• W is the wage net of wage tax, deflated by the goods price.
• θ is the degree of indexation: 0 is the old rule, 0.5 is half indexation, 1 is full indexation.
• With a wage curve (β_w, step 302), wages fall with unemployment, so full indexation also lowers the

benefit. A variant with an upward-only floor (the factor never goes below 1) is reported for that case.

Two measures of preservation.

• Original reference (the thesis measure): consumption of both displaced cohorts stays at or above 90% of its

pre-automation level in every year.

• Indexed reference: consumption stays at or above 90% of the pre-automation level times the indexation

factor. It asks whether the indexed promise is kept. For θ = 0 the two measures are the same.

Fiscal cost.

• Total benefit cost and total levy as shares of total output over the 20 years (medians across cases).
• Cases using the levy and cases in which the benefit is rationed.

Results: central specification, 432 cases

The "gap" columns are the median gap to the status-quo control (mean of the last five years). "Levy's effect" is preservation with the levy (up to 15%) minus preservation with present-value equity and no levy.

Under the step-301 costs (erosion 0.5, owners consume 0.4, q after the levy), at ω 0.5:

There are no fiscal crises under the step-301 costs. Without them there are 10–14 crises at every θ. In the cases that use the levy, the median peak levy rate is at the 15% ceiling whatever θ (slightly below it only under the wage curve with the step-301 costs).

Demand closure with the step-283 rate rule (preserved, original / indexed; fiscal crises in brackets):

What it shows.

• Indexation closes the gap, and half indexation is enough.

- At ω 0.5, half indexation turns the displaced's −9% / −11% into +10% / +8% against the control. - Full indexation overshoots to +21% / +17%. The employed still end higher (+38% to +44%). - The same holds under the step-301 costs.

• It roughly doubles the cost of the benefit when wages rise. At ω 0.5 the benefit costs 3.9% of output

with no indexation, 5.6% with half and 7.1% with full. The levy is used in more cases (204 → 230 → 284), and the benefit is rationed in more cases (162 → 200 → 229), because the levy hits its 15% ceiling.

• The indexed promise is harder to keep than the old one. Preservation against the original reference

rises slightly (279 → 292 → 289). Against the indexed reference it falls (279 → 273 → 247): the benefit is promised more than the budget can always pay.

• The levy matters more, not less, against the original reference. Its effect grows from +67 to +85 and +116

cases. Against the indexed reference the increase is much smaller (step 304: +63 to +71 with half indexation). Without the levy, indexation in the demand closure leaves 139 cases instead of 218 at decay 0. A promise that grows with wages needs a revenue source that grows with the gain.

• With a falling wage, full indexation backfires. The benefit falls with wages: 245 cases preserved instead

of 298, and the displaced end about 5% below the control. An upward-only floor avoids that (322 cases).

• In a demand slump, indexation helps demand but raises crises. At decay 1.27 and ω 0.5, preservation

against the original reference rises from 129 to 252. Fiscal crises rise from 276 to 342.

Limits

• The wage index is the model's average real net wage of the employed, with no lag and no distinction

between occupations. A real index would follow a published wage statistic with a lag.

• The replacement rate stays at 100%. Indexation on top of full replacement is generous by construction.

Half indexation with a lower replacement rate was not tested here. Step 304 tests half indexation with an upward-only floor and an 80% replacement rate, and reports both preservation measures.

• No behavioural response of the displaced to a more generous benefit: employment is imposed, as everywhere

in the thesis.

• The levy ceiling stays at 15%, so the extra cost shows up as rationing. A higher ceiling would trade

rationing for a larger levy (step 276: up to 30%).