# Step 268: a government that returns surpluses, and tax reach as a level

**Why.** The second referee report raised three points about the government rule of step 248:

- **The rule is asymmetric.** Existing spending is always paid and benefits are cut first. Surpluses
  first redeem bonds and, once the bonds are gone, are hoarded as treasury cash. Step 266 found that
  all 93 failures under its firm closure occur while the government is a net creditor.
- **Tax reach is a phased cut.** In the grid, tax reach (κ) falls from 1 to 0.5 as automation
  advances, while spending stays at the year-0 budget. All 108 cap-breach cases of step 248 had
  κ = 0.5.
- **There is no risk premium on debt.**

Generated by `scripts/fiscal_rule_v268.py`, with the model in `scripts/closure_model_v268.py`
(a copy of step 266; archived files untouched). Archived in `data/processed/fiscal_rule_v268.json`.
The firm side is the step-266 main closure. Illustrative; not a forecast.

## Rules

| Variant | Surplus | When the 90% cap binds | Bond rate |
|---|---|---|---|
| Step 266 | redeems bonds, then hoarded | benefits rationed | 3% |
| **Central** | redeems bonds until net debt is 0, then returned to every household per person | benefits rationed | 3% + 0.05 × (net debt/output − 0.6) |
| Symmetric | as central | benefits **and existing spending** rationed by the same fraction | as central |
| Tax reach as a level | as central | as central | as central; κ applies from year 0 and existing spending is lowered by the lost base-year revenue, so year 0 still balances |

With the default settings the model reproduces step 266 exactly (tested). Money is conserved in every
run, including with the VAT option used in step 269.

## Results on the 432 distinct cases

| Variant | Completed | Preserved | Needed firm credit | Existing spending cut | Both displaced below control | Median gap, displaced |
|---|---:|---:|---:|---:|---:|---|
| Step 266 (surpluses hoarded) | 339 | 134 (31%) | 49 | – | 74% | −21% / −25% |
| **Central (surpluses returned)** | **432** | **211 (49%)** | **0** | – | 58% | −20% / −21% |
| Central, no risk premium | 432 | 216 | 0 | – | 57% | −21% / −21% |
| Central, surpluses returned above 60% net debt | 432 | 231 | 0 | – | 59% | −16% / −15% |
| Symmetric rationing | 432 | 244 (56%) | 0 | 187 cases, to a median 57% of its level | 56% | −9% / −10% |
| Tax reach as a level | 432 | 246 (57%) | 0 | – | 55% | −8% / −7% |

"Preserved" means that both displaced cohorts keep at least 90% of their initial consumption in every
year. The control keeps the status-quo tax policy and the same closure. Gaps are for the cohort without
debt and the cohort with debt.

**What changes.**

- **Hoarding was the binding constraint.** Once surpluses go back to households, every case runs to the end,
  no case needs firm credit, and preservation rises from 134 to 211. In 144 of the 211 preserved cases
  the government returns a surplus at some point. Returns are a median of 5% of output over the run,
  in the cases where they are paid.
- **Symmetric rationing raises preservation further, to 244, but at a large cost.** In 187 cases
  existing public spending falls to a median 57% of its level. Only 36 of those 187 cases preserve the
  displaced. Sharing the cut keeps the benefit higher where the budget binds. It does not create money.
- **The risk premium matters little** (211 against 216).
- **About 40% of the tax-reach effect was the phased cut.** With reach phased in, half reach preserves
  64 cases against 147 with full reach. Set as a base-year level with spending recalibrated, half reach
  preserves 99. Reach still matters, but less.

**Factors under the central rule** (preserved of 432):

| Factor | Values | Preserved |
|---|---|---|
| Pass-through | 0 / 0.5 / 1 | 85 / 76 / 50 of 144 |
| Productivity gain | 25% / 50% / 100% | 23 / 64 / 124 of 144 |
| Tax rate | 25% / 35% | 88 / 123 of 216 |
| Tax reach | 0.5 / 1 | 64 / 147 of 216 |
| Ownership | concentrated / broad | 87 / 124 of 216 |
| Tenure | renters / outright owners / fixed mortgage / reset mortgage | 35 / 40 of 72; 74 / 62 of 144 |

**Correction (step 271).** "Runs to the end" hides a fiscal failure. In 140 of the 432 cases under the
central rule, existing spending and interest alone push net debt past the 90% cap. In 110 of them peak
net debt is clearly above the cap (above 95% of output), and in 48 above twice output (the risk premium
compounds). None of the 140 preserves the displaced. They are fiscal crises, not completed paths. The
symmetric rule avoids them by cutting existing spending. See `CENTRAL_V271.md`.

## The gap to the control (Shapley, as in step 266)

Units are consumption-index points (year 0 = 100), averaged over the two displaced cohorts. The sample
is the cases where all eight combinations of the switches complete. Under the central rule, 87 cases
fail when the debt cap is removed: unlimited borrowing pushes demand above output, and investment, the
residual, runs real capital down to zero.

| Component (mean points) | Step 266 | Central | Symmetric | Reach as level |
|---|---:|---:|---:|---:|
| Cases | 339 | 345 | 345 | 401 |
| Baseline gap | −34.7 | −13.9 | −0.6 | −16.2 |
| Growth of the same cohorts in the control | +0.2 | +23.3 | +23.3 | +23.0 |
| R: rationing | +43.8 | +24.4 | +9.4 | +25.0 |
| D: claw-back on own dividends | +12.2 | +18.3 | +19.5 | +15.4 |
| H: housing indexation | +4.0 | +4.0 | +4.5 | +3.9 |

The control now grows: its government also returns its surpluses. In the step-266 rule those
surpluses were hoarded. Rationing and the claw-back are the two main components. Housing indexation
remains small.

## What it means for the thesis

The level result is sensitive to the government rule. Preservation ranges from 31% to 56% of all
cases depending on what the government does with surpluses and how it rations. The ordering of the
factors does not change: productivity, tax reach and rate, and ownership help; pass-through to prices
and reset mortgages hurt. The central rule is used from here on. Its results replace the step-248
figures in the text.

## Limits

- Returning surpluses per person is one choice among many. Spending them on goods would leave household
  incomes unchanged and raise investment less.
- The risk premium is assumed, not estimated.
- Without a debt cap, demand can exceed output. The model has no demand-constrained output or
  inflation to absorb it.