# 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- **The benefit design is fixed.** It replaces 100% of reference income and is withdrawn one-for-one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.**

1. **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.
2. **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.
3. **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.
4. **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.