Step 200: indexing the benefit to housing costs

Question: step 198 traced the renter and mortgage penalty under full price pass-through to a rule in the model: housing payments are nominal, while the required benefit is indexed to the goods price only. If the housing part of the benefit followed actual housing costs, would the penalty go away?

Design: the full 576-case grid, no-credit variant (v98 model), actual paths, run under two rules. goods is the v98 rule. goods_and_housing indexes the housing part of each displaced cohort's reference income to that cohort's own housing cost in the previous year, and the rest to the goods price. The default model behaviour is unchanged (tested). Illustrative and uncalibrated.

Result: the penalty is a budget problem as much as an indexation problem

Full pass-through, by tenure (preserved / completed; last column = budget binding at year 10):

Reading:

1. Where the budget has room, the housing-inclusive rule removes every remaining failure (64 of 64 preserved). Under the goods rule, 10 slack-budget paths still failed. Some paths move between the slack and binding groups because the new rule raises the entitlement.
2. Renters with full pass-through stay at 2 of 18. In 16 of those 18 paths the budget binds at the unemployment peak, so the benefit is rationed. A higher entitlement then reallocates a fixed amount instead of adding to it. The median change in cumulative real benefit spending is 0.0.
3. The two channels of step 198 therefore work together. Nominal housing payments decide who is hurt first. The fiscal residual decides whether a better-designed benefit can be paid. Calling the fiscal channel "secondary" was too strong: it is secondary for explaining the tenure gap, but it is the binding constraint on fixing it.

Limits: the previous-year housing cost is an administrative simplification; the model has no rent response to benefits; budget binding is measured at year 10 only; no causal claim.