Step 301: does the profit levy still protect the displaced when it has costs?

Why. Referees argued that the thesis's central conclusion, that a profit levy protects the displaced, follows largely by construction. In the model the levy cost nothing:

• the tax base did not respond to it;
• investment did not depend on after-tax returns. In the central specification investment is a residual;

in the demand version Tobin's q was computed before the levy;

• owners consumed 90% of their income, like every other group;
• the nominal wage is fixed, so the whole return to automation goes to profits.

This step gives the levy costs through the first three channels and checks whether the conclusion survives. The fourth assumption is not changed here and stays a stated limit.

The model is scripts/closure_model_v301.py, a copy of step 285. With the new options off it reproduces step 285 exactly (tested). The runs are in scripts/levy_cost_v301.py, with output in data/processed/levy_cost_v301.json. Money is conserved in every run (maximum error below 1e-7). Illustrative; not a forecast.

The four channels

• Tax-base erosion (ε). When a levy is charged, reported profit shrinks with the net-of-tax rate:

f = ((1 − τ − λ)/(1 − τ))^ε. Here τ is the year's base profit-tax rate and λ the levy rate. - The levy and the base tax on the eroded part are not collected. The amount stays with firms. - The government knows this: it raises the gross levy so that the net amount equals what it needed, up to the same ceiling. Only what it cannot reach is rationed. - Values are 0.2 and 0.5. Estimates of the elasticity of the corporate tax base with respect to the net-of-tax rate include 0.2 for the United States (Gruber and Rauh, 2007), 0.58 for Germany (Dwenger and Steiner, 2012) and 0.13–0.17 at the highest UK kink (Devereux, Liu and Loretz, 2014). These values are as summarised by the Congressional Research Service (2026). Some studies find larger values, up to about 0.9 for US private corporations and 3.5 across Swiss cantons. So 0.5 is a middle value, not an upper bound.

• Owners' propensity to consume. Owners consume 0.6 or 0.4 of their income; the other groups keep 0.9.

- In the central specification the extra saving becomes investment, because investment is a residual. - In the demand closure, the autonomous investment that keeps the status-quo control at full use is recalibrated: 0.061 at 0.6 and 0.079 at 0.4, against 0.034 at 0.9. - The slump strength is rescaled so that the slump is the same size in points of GDP.

• q after the levy. The equity quote, and with it Tobin's q, is computed from the payout net of the

expected levy, taken as last year's levy share of profit.

• Investment tax elasticity (ξ), demand closure only. Planned investment is multiplied by

((1 − τ_t − λ_(t−1))/(1 − τ_0))^ξ. - Values are 0.5 and 1.0. Zwick and Mahon (2017) estimate a user-cost elasticity of about −1.6 and note that earlier estimates surveyed by Hassett and Hubbard (2002) range from −0.5 to −1. - Ohrn (2018) finds that a 1-point cut in the tax rate raises investment by 4.7% of capital. - ξ applies to the net-of-tax share, so it is only an approximate counterpart of the user-cost elasticity.

Results A: central specification (432 cases, investment as residual)

Each cell gives preserved cases, with fiscal crises in brackets.

At ε = 0.5 erosion takes 20% of the gross levy at the median (27% with a 30% ceiling).

Breakeven productivity gain g\*: medians over 144 combinations, quartiles in brackets.

Results B: demand closure with the interest-rate rule

The interest-rate rule is the central rule of step 283. Each cell gives preserved cases with fiscal crises in brackets; the "Gap" columns give the levy's advantage over no levy.

Levy-financed support for demand. This is the step 285 rule: support at any gap, φ = 1, with a shared 15% levy ceiling. Preserved cases with and without the support:

What it shows

• The levy still beats no levy under every cost channel tested, but tax-base erosion cuts its

advantage. - In the central specification, the levy's own effect (against present-value equity without a levy) falls from 63 cases to 46 at ε = 0.5. - The gap in breakeven gain narrows from 0.14 to 0.11. - Fiscal crises rise from 10 to 16. - At ε = 0.2, the size most often estimated for the United States, little changes (+60 cases).

• A lower propensity to consume among owners does not weaken the levy; it strengthens the results.

- In the central specification, the extra saving becomes investment. - In the demand closure, a transfer from low-spending owners to the displaced adds demand. - The uniform 0.9 was therefore not what made the levy look good. But level comparisons across this channel also reflect a recalibrated economy that invests more.

• q after the levy hardly matters. The equity price falls, but in these closures that does not move

much.

• Investment that responds to the tax cuts the levy's advantage in the demand closure, from 71 to 52–53

cases in the OECD stress case. With all channels at once and ξ = 1.0, the advantage is 4 cases with no slump, 37 in the full slump and 39 in the stress case.

• Levy-financed support for demand is fragile.

- Without costs it helps in the stress case: 131 to 147. - Once owners save more and investment responds to the tax, it hurts. With all channels and ξ = 0.5 or 1.0, preservation falls by 71–74 cases in the stress case and by 72–91 in the full slump. - So the step 285 result, that support financed from profits works best, holds only in the stress case and only while owners do not save more and investment does not respond strongly to the tax. - Correction (step 304). An earlier version said support stops helping because the levy that finances it lowers investment. A Shapley decomposition in step 304 shows that the reversal comes mainly from owners' lower consumption (in the recalibrated economy) together with the investment response, which reinforce each other; erosion contributes little. See ROBUSTNESS_V304.md, section 1.

Verdict. The conclusion that a profit levy protects the displaced survives the cost channels tested, with a smaller margin. The narrower claim that levy-financed public spending supports demand in a slump does not survive once owners save more and investment responds to the tax. Step 304 finds that the levy's effect reaches zero only at an erosion elasticity of about 2.4, but that with combined costs in the demand closure it comes with more fiscal crises than no levy: a trade-off, not a free gain.

Limits

• The fixed nominal wage is not changed. The whole return to automation still goes to profits, which

keeps the base the levy draws on large.

• Erosion is static, applied within the year. It does not move profits abroad (step 304 adds a leakage

variant) and does not lower investment in the central specification, where investment remains a residual.

• Elasticities larger than 0.5, found in some studies, are not run here. Step 304 runs ε up to 5 and ξ

up to 10 and reports the thresholds.

• The owners' channel changes the calibration of the demand closure, so levels across it are not like

for like.

• The investment elasticity is applied to the net-of-tax share, an approximation to the user cost.

Sources

• Congressional Research Service (2026). Corporate Taxation: The Revenue-Maximizing Tax Rate, R48913.

Summarises Gruber and Rauh (2007), Dwenger and Steiner (2012), Devereux, Liu and Loretz (2014) and others.

• Gruber, J., & Rauh, J. (2007). How elastic is the corporate income tax base? In A. Auerbach, J. Hines and

J. Slemrod (Eds.), Taxing Corporate Income in the 21st Century. Cambridge University Press.

• Dwenger, N., & Steiner, V. (2012). Profit taxation and the elasticity of the corporate income tax base:

evidence from German corporate tax return data. National Tax Journal, 65(1), 118–150.

• Zwick, E., & Mahon, J. (2017). Tax policy and heterogeneous investment behavior. *American Economic

Review*, 107(1), 217–248.

• Ohrn, E. (2018). The effect of corporate taxation on investment and financial policy: evidence from the

DPAD. American Economic Journal: Economic Policy, 10(2), 272–301.