# Step 205: a partial housing calibration for Israel

Two model inputs are set from Israeli data; everything else stays as in steps 96–101 (illustrative,
uncalibrated). Archived in `data/processed/israel_housing_v205.json`, generated by
`scripts/israel_housing_v205.py`.

**Source.** CBS, household expenditure survey 2024, first findings (release 315/2026, tables A-1
and A-2; SHA-256 `28e380fa…`): 62.5% of households own their dwelling, 32.7% rent and 4.8% live
rent-free; in the bottom income decile 35.5% own and 56.5% rent. Mean rent of renting households is
3,924 NIS a month (bottom decile 2,864). Mean net household income, derived from the release
(cash expenditure 15,370 = 68.1% of net income), is about 22,570 NIS; the bottom decile holds 2.8%
of net income, about 6,320 NIS per household. The share of owners paying a mortgage is not in the
release; the latest figure found is 39.3% (CBS 2012, as reported in the press), so it is varied
from 30% to 50%. The split between fixed-rate and rate-reset mortgages is unknown and shown as a range.

## A. Tenure mix

The grid weights the four tenure forms equally. Reweighting the v101 results (cases completed in
all seven variants) by the Israeli mix:

| Share of paths where both displaced groups kept 90% | pass-through 0 | 0.5 | full |
|---|---:|---:|---:|
| Equal weights (grid) | 46.9% | 39.2% | 26.4% |
| Israel, all households (central) | 48.5% | 43.6% | 28.8% |
| Israel, bottom income decile (central) | 49.1% | 44.2% | 22.9% |

Across the mortgage assumptions the full pass-through rate is 24.9–31.5% for all households and
20.7–24.4% for the bottom decile. The equal-weight grid is close to the Israeli average mix; for
low-income households, who rent more, the full pass-through rate is lower.

## B. Rent burden

In the model a renting household pays 12 against a reference disposable income of 48
(concentrated ownership) or 78 (broad): 25% or 15%. The Israeli average is about 17% and the bottom
decile about 45%. The 144 renter cases were rerun with rent set to 17%, 30% and 45% of the
reference income (no-credit variant), under the v98 benefit rule and the housing-indexed rule of
step 200. Cells show preserved / completed paths.

| Rent burden | Benefit rule | pass-through 0 | 0.5 | full |
|---|---|---:|---:|---:|
| Model (12) | goods | 8/16 | 8/18 | 2/18 |
| Israel mean, 17% | goods | 8/16 | 8/18 | 2/18 |
| 30% | goods | 8/16 | 8/18 | 0/18 |
| 30% | goods and housing | 8/16 | 8/18 | 4/20 |
| Bottom decile, 45% | goods | 4/16 | 0/18 | 0/18 |
| Bottom decile, 45% | goods and housing | 4/16 | 2/18 | 6/22 |

Reading:

1. At the Israeli average rent burden the results do not change: the model's rent level is close
   to the Israeli mean.
2. At the burdens of low-income renters the renter penalty widens: with 45% of income going to rent,
   no path preserves consumption once half the productivity gain reaches prices, and only 4 of 16
   without any pass-through.
3. Indexing the benefit to housing costs matters more as the burden rises: at 45% it turns 0 of 18
   into 6 of 22 at full pass-through. It also lets more paths complete, because the benefit follows
   the rent that landlord-owners receive.

## C. Mortgage burden

In the model a mortgage of 150 at 4% over 25 years costs 9.6 a year: 20% of the reference income
under concentrated ownership, 12% under broad. In Israel the average payment-to-income ratio of the
bank housing-credit portfolio was about 29% through 2024 (Bank of Israel banking supervision annual
survey, as reported in the press); it is varied from 25% to 35%. The mortgage and the home price
are scaled together, keeping loan-to-value at 75%, and the 144 cases of each mortgage form are
rerun. Preserved / completed:

| Mortgage | Payment-to-income | Benefit rule | pass-through 0 | 0.5 | full |
|---|---|---|---:|---:|---:|
| Fixed | model | goods | 8/16 | 6/16 | 6/18 |
| Fixed | 29% | goods | 4/12 | 6/16 | 4/20 |
| Fixed | 29% | goods and housing | 4/12 | 6/16 | 10/22 |
| Rate reset | model | goods | 6/16 | 4/16 | 3/18 |
| Rate reset | 29% | goods | 2/14 | 3/16 | 2/19 |
| Rate reset | 29% | goods and housing | 4/14 | 6/17 | 7/21 |

At the Israeli mortgage burden fewer paths preserve consumption at every pass-through level, and
indexing the benefit to housing costs again does most of the repair at full pass-through.

## D. Combined

Israeli tenure weights (mortgage share 39.3%, half rate-reset), with the renter rate at the Israeli
rent burden (mean 17%; bottom decile 45%), the mortgage rates at 29% payment-to-income and the
owner rate from step 200 (same variant and rule):

| Population | Benefit rule | pass-through 0 | 0.5 | full |
|---|---|---:|---:|---:|
| All households | goods | 43.6% | 42.8% | 26.4% |
| All households | goods and housing | 45.3% | 39.5% | 32.3% |
| Bottom decile | goods | 32.2% | 18.7% | 15.3% |
| Bottom decile | goods and housing | 33.2% | 22.4% | 34.0% |

For the average Israeli household mix the full pass-through rate is the same as the uncalibrated
grid (26.4%). For the bottom decile it falls to 15.3%, and indexing the benefit to housing costs
more than doubles it (34.0%). Under the Israeli housing profile, the indexation rule matters most
for the households with the least room.

## E. Rent that follows prices

The renter penalty rests on rent being nominal. Here rent follows the goods price index with
elasticity e: rent_t = rent x (1 + e (P_t - 1)), e = 0, 0.5 or 1. The goods price path in v98 does
not depend on rent (checked for every case), so it is taken from a first run and fed to the ledger
copy. Renter cases, preserved / completed:

| Rent burden | e | Benefit rule | pass-through 0 | 0.5 | full |
|---|---:|---|---:|---:|---:|
| Model | 0 | goods | 8/16 | 8/18 | 2/18 |
| Model | 0.5 | goods | 8/16 | 8/18 | 2/18 |
| Model | 1 | goods | 8/16 | 8/18 | 6/18 |
| Bottom decile, 45% | 0 | goods | 4/16 | 0/18 | 0/18 |
| Bottom decile, 45% | 0.5 | goods | 4/16 | 6/18 | 0/18 |
| Bottom decile, 45% | 1 | goods | 4/16 | 8/18 | 2/18 |
| Bottom decile, 45% | 0 | goods and housing | 4/16 | 2/18 | 6/22 |

Reading:

1. Even if rent fell one-for-one with goods prices, renters at full pass-through would keep their
   consumption in 6 of 18 paths, not the 8 of 18 of outright owners. Sticky rent explains part of
   the penalty; the rest is the fiscal channel (the benefit budget shrinks with the tax base).
2. With half-elastic rent nothing changes at full pass-through. The result does not hinge on rent
   being perfectly rigid.
3. For high-burden renters, a fully price-indexed rent (2/18) does less than indexing the benefit
   to housing costs with rigid rent (6/22): the benefit rule is the stronger lever.

## G. Rent that rises with benefits

Housing allowances and cash transfers are partly captured by landlords. Here every renting household
pays an extra rent equal to a share phi of last year's total benefit spending per household (total
household mass is 1), so landlords collect about 0.9 phi of benefit spending. Rent and benefits now
depend on each other; each case is solved by iterating the yearly rent add-on to a fixed point (at
most 10 iterations, residual below 1e-9). Renter cases at the model rent level, preserved / completed:

| Capture phi | Benefit rule | pass-through 0 | 0.5 | full |
|---:|---|---:|---:|---:|
| 0 | goods | 8/16 | 8/18 | 2/18 |
| 0.3 | goods | 8/16 | 4/18 | 2/18 |
| 0.6 | goods | 4/16 | 2/18 | 0/18 |
| 0.3 | goods and housing | 8/16 | 6/18 | 4/20 |
| 0.6 | goods and housing | 8/16 | 4/18 | 4/20 |

Reading:

1. Capture worsens the renter result: at 60% renters lose even without pass-through (8 to 4 of 16)
   and no path survives full pass-through.
2. The housing-indexed benefit partly offsets capture (4 of 20 at full pass-through for both capture
   levels), even though indexing feeds back into rent; the loop converges.
3. Together with part E: sticky rent and rent that rises with benefits push in opposite directions,
   but in every variant tested renters stay behind outright owners at full pass-through.

Limits: rent responds to goods prices (E) and to benefits (G) in separate tests, not to local demand or both at once; rent and mortgage levels change for every household of that tenure, not only the displaced;
the payment-to-income figure is a portfolio average reported second-hand, at origination incomes;
the mortgage share is from 2012; tenure of displaced workers in
exposed occupations may differ from both the average and the bottom decile. Not a forecast.