# Step 274: when a demand shortfall costs jobs

**Why.** In step 273 output could fall short of capacity, but employment stayed on the scenario path.
A shortfall reached households only through profits, dividends and taxes. Here it also costs jobs.

Generated by `scripts/okun_v274.py`, with the model in `scripts/closure_model_v274.py` (a copy of
step 273; archived files untouched). Archived in `data/processed/okun_v274.json`. All 432 distinct
cases, central specification with the step-273 demand closure. Illustrative; not a forecast.

## The employment channel

- **Extra unemployment.** Last year's shortfall, relative to capacity, raises unemployment by an
  Okun-type coefficient: 0, 0.3, 0.5 (main) or 1. The job losses fall on the retained workers, capped
  at half of them.
- **Unemployment insurance.** Laid-off workers receive 60% of the net wage. It is paid by the
  government and rationed with the other benefits when the debt cap binds.
- **Who gains and who loses.** Firms save the gross wage, and the government loses the wage tax on it.
- **Loop.** Lower wage income lowers consumption and demand the next year.

With the coefficient at 0, the model reproduces step 273 exactly (tested). Money is conserved.

## Results (432 cases)

| Investment | Okun coefficient | Displaced preserved | Retained workers keep 90% | Fiscal crises | Use of capacity, median / 10th pct | Peak extra unemployment, median / 90th pct |
|---|---:|---:|---:|---:|---|---|
| Calibrated | 0 | 210 | 423 | 110 | 100% / 99% | 0 / 0 points |
| Calibrated | 0.5 | 210 | 423 | 110 | 100% / 99% | 0.3 / 2.6 |
| Calibrated | 1 | 210 | 423 | 110 | 100% / 99% | 0.7 / 5.5 |
| Slump | 0 | 174 | 420 | 190 | 95% / 91% | 0 / 0 |
| Slump | 0.3 | 167 | 418 | 210 | 94% / 90% | 3.5 / 5.6 |
| **Slump** | **0.5** | **159 (37%)** | **415** | **218** | **94% / 89%** | **6.4 / 9.9** |
| Slump | 1 | 132 | 352 | 250 | 93% / 87% | 15.3 / 27.5 |

**What it shows.**

- **With investment demand intact, the employment channel changes nothing.** Shortfalls are small,
  extra unemployment stays below a point in the median case, and preservation is 210 at every
  coefficient.
- **In an investment slump, it amplifies the damage.** Lost jobs cut wage income and wage-tax revenue
  and add unemployment insurance to the budget. With a coefficient of 0.5, the median peak adds about
  6 points of unemployment on top of the scenario's 20%. Preservation falls from 174 to 159 cases.
  Fiscal crises rise from 190 to 218.
- **At a coefficient of 1 the loop becomes severe.** Unemployment rises by a median 15 points, and
  even the retained workers lose 10% of their consumption in almost a fifth of the cases (80 of 432).
- **The productivity gain matters even more.** In the slump with a coefficient of 0.5, a 25% gain
  preserves nothing, a 50% gain 36 of 144, and a doubling 123.

## What this means for the thesis

The results of steps 266–272 do not depend on the assumption that saving becomes investment, provided
firms keep investing. The new risk the demand model reveals is an investment slump: firms invest less
as displacement rises, demand falls short, and the shortfall costs jobs. In that case preservation
falls from 49% to 37%, and fiscal crises affect half of the cases.

## Limits

- **The coefficient is assumed, not estimated.** Okun's law is usually estimated at 0.3–0.5 for
  unemployment per point of output gap.
- **Prices do not fall with slack, and no monetary policy responds.** With either, the slump would be
  smaller.
- **Only the retained workers lose jobs.** The displaced cohorts are already out of work in the
  scenario.