מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 266: a firm sector that keeps earnings, pays for credit and is valued at its capital
Why. The second referee report found three weaknesses in the firm side of steps 248 and 250:
- Firms paid out all profit and borrowed without limit at 3%, with the interest paid to the owners on
top of their dividends. 136 of the 217 preserved cases in step 248 relied on that overdraft.
- Equity was priced at a constant real 200 per unit with no depreciation, so dividend yields ran at
15–30%.
- The step-250 decomposition applied its switches in a fixed order, so the claw-back component was
measured under unlimited government debt.
Generated by scripts/firm_closure_v266.py, with the model in scripts/closure_model_v266.py (a copy of step 248; archived files untouched). Results are archived in data/processed/firm_closure_v266.json. Illustrative; not a forecast.
The new firm closure
| Element | Step 248 | Step 266 (main) |
|---|---|---|
| Dividends | all after-tax profit | after-tax profit less depreciation and overdraft interest, less retained earnings |
| Retained earnings | none | enough to hold cash equal to 50% of last year's investment (repaying any overdraft first) |
| Depreciation | none | 5% of real capital a year; investment is gross |
| Overdraft | unlimited at 3%, interest paid to owners on top of dividends | up to 50% of output; rate 3% + 0.1 × overdraft/output; interest comes out of dividends |
| Equity price | 200 × price level per unit | replacement cost: price × real capital (q = 1) |
With the default settings, the new model reproduces step 248 exactly, and with the strict settings it reproduces v98 (tested). Money is conserved in every run.
Profit tax is unchanged. We treat the interest deduction and the tax on the lender's interest income as offsetting, and depreciation is not deducted for tax.
Results on the 432 distinct cases (government debt cap 90%)
| Firm variant | Completed | Preserved | of which used overdraft | Final dividend yield (median) |
|---|---|---|---|---|
| Step 248 (unlimited credit, no retention) | 432 | 217 (50%) | 136 | 17.7% |
| Main | 339 | 134 (31%) | 49 | 11.0% |
| Main, no credit at all | 282 | 85 (20%) | 0 | 12.1% |
| Main, unlimited credit | 432 | 208 (48%) | 123 | 9.3% |
| Main, credit limit 25% of output | 321 | 118 | 33 | 11.4% |
| Main, no depreciation | 329 | 138 | 57 | 14.8% |
| Main, depreciation 10% | 356 | 132 | 41 | 7.2% |
| Main, constant real price | 339 | 134 | 49 | 11.2% |
| Main, no retention target | 342 | 134 | 54 | 11.5% |
"Preserved" means that both displaced cohorts keep at least 90% of their initial consumption in every year. All other cases count as not preserved, including paths that stop.
What changes.
- Half of step 248's preserved cases depended on free credit. With a limit on the overdraft and a
rising rate, 134 of 432 cases are preserved. 85 of them need no credit at all.
- **All 93 failures in the main variant come from a cap on credit while the government runs a
surplus.** In every one of them the government is a net creditor when the path stops: the tax keeps collecting cash that is never spent. Household demand falls, and since output does not adjust, unsold output becomes investment that firms must finance. 72 of the 93 are the cases with the largest productivity gain. This is a closure artefact, the fiscal mirror of "saving becomes investment." Step 268 gives the government a symmetric rule that returns surpluses.
- The direction of the factors does not change. A higher tax rate (76 of 159 completed vs 58 of
180), full tax reach (70 of 123 vs 64 of 216) and broad ownership (85 vs 49) still help. Full pass-through still hurts, but less than before: 36 preserved vs 50 with no pass-through.
- Equity yields. In the no-automation control, the final dividend yield falls from 10.7% to 4.4%.
In the automation paths it stays high (11%) because profits rise faster than the capital stock. Pricing equity at the value of its future dividends would lower it further. That is not done here.
- Control growth disappears. Capital still roughly doubles in the control, because household
saving still becomes investment. But with realistic dividends, the employed displaced cohorts in the control end where they started: control growth is 0.2 index points on average, against 13.7 before.
The gap to the control, split with Shapley values
The baseline is the main closure with a 90% debt cap. The control keeps the status-quo tax policy and the same firm closure. The switches are:
- R: no rationing (no debt cap).
- D: the claw-back is limited to the dividend already in the reference income.
- H: the benefit is indexed to goods and housing.
Each switch is credited with its average contribution over all orders (Shapley value), so the result does not depend on order. Units are consumption-index points, year 0 = 100, averaged over the two displaced cohorts. The sample is the 339 cases where all eight combinations complete.
| Component | Main closure | Step-248 closure |
|---|---|---|
| Gap to the status-quo control, baseline (mean) | −34.7 | −39.2 |
| Growth of the same cohorts in the control | +0.2 | +13.7 |
| R: rationing (Shapley) | +43.8 | +26.8 |
| D: claw-back (Shapley) | +12.2 | +28.9 |
| H: housing indexation (Shapley) | +4.0 | +4.0 |
| D alone, at the 90% cap | +10.1 (median 0) | +25.6 |
| Gap after all three switches | +25.3 | +20.5 |
What changes. Under step 248, the claw-back on the cohort's own dividends looked like the largest component. Most of it came from the high dividend yield. With realistic dividends the claw-back still matters (12 points), but rationing is now the main component (44 of the 60 points). The gap is mostly a budget question: the displaced fall behind when the benefit is cut because the debt cap binds. The step-250 text, "the relative-position result is a property of the benefit design", needs qualification: it is mostly a property of how the benefit is financed.
Limits
- Investment is still the residual of output less consumption and government purchases, so saving
becomes capital. A demand-constrained model is beyond this project.
- The equity price follows the capital stock, not expected dividends.
- The government rule is unchanged from step 248 and is asymmetric: existing spending is always paid,
benefits are cut first, and surpluses are hoarded. Step 268 addresses this.