Step 302: does the profit levy still protect the displaced when wages respond?

Why. Referees argued that the levy's success follows from four assumptions. Step 301 tested three of them: a tax base that does not respond, investment that ignores the levy, and a uniform propensity to consume. This step tests the fourth: the fixed nominal wage. In every earlier specification, the whole efficiency gain and the whole return to capital accumulation went to profits, which keeps the levy's base large. Here wages respond in two ways, separately and together with the step-301 costs.

The runner is scripts/wages_v302.py, tested in scripts/test_wages_v302.py, with results in data/processed/wages_v302.json. No change to the closure model was needed: the wage responses sit in the macro feedback and the source inputs. With both responses off, every run reproduces step 301 exactly (tested). Money is conserved in every run. Illustrative; not a forecast.

The two wage responses

• Wage share of the gain, ω (0.25 and 0.5). A share ω of the productivity gain goes to the wages of the employed. It

applies to both sources of the gain: - The efficiency gain, through the existing wage_gain switch of the source model. The wage per worker rises by ω·g as automation progresses. With pass-through, the price level falls less. - The return to capital accumulation. A share ω of the extra output from capital is paid as wages.

• Wage curve, β_w (0.07 and 0.1). Every employed worker's nominal wage falls with unemployment:

w × ((u0 + u)/u0)^(−β_w), with u0 = 4%. At 20% scenario unemployment this cuts wages by 12% (β_w = 0.07) or 16% (β_w = 0.1). The saving goes to profits, and prices are not changed by it. - β_w = 0.1 is the long-run elasticity of pay with respect to unemployment that Blanchflower and Oswald (2005) report for the United States, "consistent with … more than 40 other countries". - β_w = 0.07 is the unbiased mean of 208 estimates in the meta-analysis of Nijkamp and Poot (2005). - These are cross-regional relations, applied here to an aggregate shock.

• What follows in the model. Wage-tax revenue moves with the wage bill, and the profit and levy base move

the other way. Retained workers' income follows the wage bill.

• The benefit rule does not change. The benefit tops income up to pre-automation disposable income in real

goods terms, and it is not indexed to wages.

Results: central specification (432 cases)

"Levy's own effect" is preservation with the levy minus preservation with present-value equity and no levy. The last column gives the median gap to the status-quo control over the last five years, for retained workers and for the two displaced cohorts.

The step-301 costs are erosion 0.5, owners consuming 0.4, and q after the levy.

Results: demand closure with the interest-rate rule

This uses step-301 conventions: autonomous investment is recalibrated when owners consume less, and the slump is held at the same size in GDP points. Each cell gives cases preserved, then fiscal crises.

What it shows

• A wage curve appears to strengthen the levy. When unemployment pushes wages down, the saving goes to profits

and so into the levy's base. Step 304 shows this is a redistribution from retained workers to owners: when the saving passes to prices, the levy's effect returns to its fixed-wage size. Preservation rises to 292–298 and the breakeven gain falls. The retained workers' advantage over the control shrinks from 29% to 14%–17%.

• Sharing the gain with wages changes who gains, not whether the levy helps. With ω = 0.5:

- The levy's own effect stays about the same (+67). - The breakeven gain rises from 0.325 to 0.40, because less of the gain lands in the taxable profit base. - The relative positions diverge sharply. Retained workers end about 49% above the control. The displaced end 9%–11% below it: their benefit is fixed in real terms and no longer shares in a gain that now goes to the wages of the employed.

• The levy's margin is smallest when wage sharing and the step-301 costs combine. In the central

specification its own effect falls from +63 to +35. In the demand closure with investment responding to the tax (ξ = 1), the levy beats no levy by only 10–14 cases out of 432. In that combination it is also associated with more fiscal crises than no levy at strengths 0–1.27.

• The levy still preserves more cases than no levy in every specification tested. But with wage sharing and

costs together the margin is small and comes with more fiscal crises: a trade-off between preservation and crises, not a free gain. Step 304 finds the erosion threshold at which the effect reaches zero (about 2.4).

• Levy-financed demand support helps without costs in the stress case, as in step 285, and harms with costs,

as step 301 found. Responsive wages do not change that. Step 304 shows the reversal comes mainly from owners' lower consumption together with the investment response, not from the levy lowering investment alone.

Limits

• The wage curve is a level relation estimated across regions. Applying it to an aggregate 20-point rise in

unemployment is an extrapolation.

• Wage cuts do not pass through to prices here, and the wage curve ignores Okun lay-offs. Step 304 adds both:

with full pass-through the levy's effect returns to its fixed-wage size, and the apparent strengthening of the levy by the wage curve turns out to be a redistribution from retained workers to owners.

• ω is a sharing rule, not a bargaining model. The displaced do not re-enter employment.
• The benefit reference is not indexed to wages. A benefit indexed to the wages of the employed would cost more

when ω > 0, and would narrow the gap to the employed.

Sources

• Blanchflower, D. G., & Oswald, A. J. (2005). The wage curve reloaded. NBER Working Paper 11338.
• Nijkamp, P., & Poot, J. (2005). The last word on the wage curve? Journal of Economic Surveys, 19(3), 421–450.