מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 276: a tax response, benefit design, present-value equity and fiscal crises
Why. The third referee report raised four points:
- Only the benefit adjusts when the debt cap binds. No tax ever responds, although the research
question asks whether taxes can finance the benefit. The referee also found that "preserved" is almost the same as "never rationed": the two agree in 392 of 432 cases.
- The benefit design is fixed. It replaces 100% of reference income and is withdrawn one-for-one
against the recipients' own dividends. Both are design choices.
- Dividend yields are still 11%–16% with book-value equity. This inflates the claw-back and the
owners' gains.
- Paths with net debt of up to 8.6 times output count as completed and enter the gap statistics.
Generated by scripts/benefit_rules_v276.py, with the model in scripts/closure_model_v276.py (a copy of step 274; archived files untouched). Archived in data/processed/benefit_rules_v276.json. All 432 distinct cases, central specification of step 271 unless stated. Illustrative; not a forecast.
New options
| Option | What it does |
|---|---|
| Tax response | When the cap would ration benefits, the government first levies an extra tax on profits, up to 15% (or 30%) of profits, to close the gap. Firms pay it from cash, and their retention rule passes it on to dividends. |
| Present-value equity | Each unit is worth the net payout (after-tax profit less depreciation) divided by 4.5%, with a floor of half the replacement cost of capital. |
| Replacement rate | 60%, 80% or 100% of reference income. |
| Claw-back rate | 0%, 50% or 100% of the recipients' own dividends. |
Fiscal crisis: peak net debt above 95% of output. Severe crisis: above 150%. Gaps to the status-quo control are now measured as the mean of the last five years, because the final-year control jumps when its debt reaches zero (step 271).
With the defaults, the model reproduces step 274 exactly (tested).
Results
| Variant | Preserved | Fiscal crises | Severe | Final dividend yield | Gap to control, displaced (all cases) | Both displaced below control (no severe crisis) |
|---|---|---|---|---|---|---|
| Central (step 271) | 211 (49%) | 110 | 82 | 13.0% | −16% / −19% | 45% of 350 |
| Present-value equity | 214 | 110 | 82 | 4.4% | 46% of 350 | |
| Tax response 15% | 277 | 10 | 0 | 12.8% | 46% of 432 | |
| Tax response 30% | 332 | 56 | 0 | 13.3% | 41% of 432 | |
| Revised: present value + tax response 15% | 277 (64%) | 10 | 0 | 4.4% | +3% / +4% | 47% of 432 |
| Revised, tax response 30% | 338 (78%) | 56 | 0 | 4.4% | 43% of 432 |
With the tax response, debt never reaches 1.3 times output. The 10–56 "crises" are overshoots of a few points above the 90% cap.
Replacement and claw-back (revised specification; preserved cases, and median gap of the displaced to the control):
| Replacement \ claw-back | 0% | 50% | 100% |
|---|---|---|---|
| 60% | 173; −11% / −10% | 142; −20% / −18% | 71; −36% / −36% |
| 80% | 173; +4% / +3% | 174; −3% / −1% | 122; −21% / −20% |
| 100% | 289; +10% / +7% | 287; +10% / +10% | 277; +3% / +4% |
"Preserved" means at least 90% of initial consumption. With a replacement rate below 90%, a displaced household can reach that level only through its own savings and dividends, so the count falls by construction.
What it shows.
- The relative-position result rested on fiscal crises. - In the central specification, the displaced end below the control in 58% of cases (step 271). - Leaving out the 82 severe crises and averaging over the last five years, they end below it in 45%, with a median gap of +4% / +9%. - The large negative gaps were mostly cases in which the benefit was rationed to nothing while debt exploded.
- A tax that responds to the cap removes the crises and raises preservation. - With a profit levy of up to 15%, preservation rises from 49% to 64%. A 30% levy raises it to 78%. - This is the natural answer to the research question: the gain can be financed if the profit tax is allowed to rise when the budget binds. - The levy is used in 182 cases.
- The claw-back matters less once yields are realistic. - With present-value equity (yield 4.4%), removing the claw-back adds only 12 preserved cases (289 against 277). - The step-266/268 Shapley split, which gave it 12–18 points, came from high yields.
- The replacement rate is the real design lever. A benefit at 60% of reference income cannot keep the displaced near their level in most cases, whatever the claw-back.
Proposal. Use the revised specification (present-value equity plus a 15% tax response) as the new central specification, and keep the benefits-only rationing rule as an alternative. The summary, breakeven surfaces, Israel and demand runs are recomputed on it in the next steps.