# Step 203: a benefit that keeps a fixed share of output

Question: the discussion chapter argued that a benefit indexed to today's living standard protects a
floor but not relative position, and that only a benefit keeping a fixed share of what the economy
produces would prevent the gap to the matched control. This step tests that claim.

Design: the 576-case grid, no-credit variant (v98 model). Rule `goods` is the v98 rule. Rule
`output_share` scales each displaced cohort's reference income by nominal output relative to year 0.
Control paths have no displacement and no benefits, so they are identical under both rules (asserted).
The default model behaviour is unchanged. Illustrative and uncalibrated.

## Result: the gap narrows, but the budget decides whether it closes

Same 42 cases that have a complete matched control under both rules:

| | goods rule | output-share rule |
|---|---:|---:|
| Displaced, no consumer debt: median gap to control | -25.3% | -20.0% |
| Displaced, with consumer debt: median gap to control | -20.7% | -20.8% |
| Displaced (no debt) at or above control | 0 of 42 | 18 of 42 |
| Displaced (with debt) at or above control | 0 of 42 | 18 of 42 |
| Retained workers: median gap to control | +16.5% | +16.5% |

Whole grid:

| | goods rule | output-share rule |
|---|---:|---:|
| Paths completed | 202 | 285 |
| Both displaced cohorts preserved (90% floor) | 75 | 163 |
| Budget binding at year 10 (completed paths) | 131 | 256 |
| Median change in cumulative real benefit spending (202 cases complete under both) | — | +10.7% |

Under the output-share rule, every paired case where the budget still has room at year 10 ends at or
above the control (4 of 4; median gap +35.1%). Where the budget binds, 20 of 44 reach it (these 48 paired cases include 6 that complete only under the output-share rule) (median gap -18.5%).

Reading:
1. The claim is supported in direction, not in full. Tying the benefit to output lets displaced workers
   reach the control path in 18 of 42 matched cases instead of none, and in every case
   with budget room. But in the same 42 cases the budget binds at year 10 in all of them, so the median
   gap stays large.
2. The rule also raises completion (202 to 285 paths) and joint preservation (75 to 163): in the model investment is the residual
   of output after consumption, so higher transfers lower the investment firms must finance and fewer paths
   stop on corporate liquidity. This is a property of the closure, not evidence that transfers pay for themselves. Government cash failures are unchanged (144).
3. As in step 200, the binding constraint is fiscal. Benefit design changes who is protected and how far;
   the budget at the unemployment peak decides whether the design can be paid for.

Limits: same model assumptions as steps 101 and 200; the output-share reference is one of many possible
formulas; no causal claim.