UQO Working Paper No. 18· v1.1· November 2026· 86 pages

Housing, Leverage, and Intergenerational Wealth Inequality

A Dynamic General Equilibrium Theory

Real Estate & Urban Economics

On SSRN

Among equal-income households, transfers generate a mid-life owner–renter wealth gap of about 4.8 years of annual income, and the sign of the house-price response to surprise inflation depends on who receives the lender's revaluation gain.

A three-stage benchmark delivers nine closed-form propositions; a twelve-period overlapping-generations economy is solved in stationary general equilibrium and along perfect-foresight transitions. After a 10% price-level surprise the real house price moves by −0.47% when the lender's gain leaves the household sector, +0.34% under a uniform rebate and −0.18% when the old keep their houses. The calibration is illustrative, no moment is fitted, and intergenerational persistence without transfers is zero by design.

Simon-Pierre Boucher — contact@spboucher.ai

Paper PDF (revised)Read online SSRN Code & data repository

≈ 4.8 years

of annual income (0.95 average five-year incomes): owner–renter wealth gap at 40–44 among households with the same income process; 4.0 years when gift incidence is targeted to the Canadian figure

0.34

rank–rank slope of net worth between parents and children with transfers; zero by design without them, because child and parent incomes are independent; 0.16 with gift incidence targeted to the Canadian figure

0.54 vs 0.35

probability that a child owns at 35–39 when the parent is an owner versus a renter (a tenure-timing statistic)

64–66%

of the partial-equilibrium ownership response to the down-payment constraint absorbed by the price and the rent in stationary general equilibrium

−0.47%

impact response of the real house price to a 10% price-level surprise under fixed-rate contracts when the lender's revaluation gain leaves the household sector and the estate is liquid (seed standard deviation 0.047 percentage points); −1.88% when the surprise persists

+0.34% / +0.02% / +0.79%

the same impact response when the lender's gain is rebated to households uniformly, pro rata to deposits, or to entrants; −0.18% when the old keep their houses (a run above tolerance)

+0.63% vs −1.01%

change in lifetime consumption after the level surprise for owners with a mortgage and for renters; fixed-rate and renewable-term contracts give identical outcomes for a level surprise

Abstract

Under what conditions do inherited wealth, mortgage leverage, nominal debt, housing supply and down-payment constraints generate persistent owner–renter wealth gaps among households with the same labour-income process, and what does an unanticipated inflation change? A three-stage benchmark gives closed forms for the entry threshold, the leverage multiplier, intergenerational tenure persistence, uniqueness and the accounting of a price-level surprise under three mortgage contracts; a twelve-period overlapping-generations model with nominal mortgages, transfers and segmented housing markets is solved in stationary general equilibrium and along perfect-foresight transitions under an illustrative calibration. Transfers generate a mid-life wealth gap of 0.95 average five-year incomes (about 4.8 years of annual income) and a rank–rank wealth slope of 0.34 that is zero by design without transfers; prices absorb 64–66% of the partial-equilibrium ownership response to the down-payment constraint; excess demand has a single root in the scanned region. The sign of the real house price’s impact response to a 10% level surprise depends on who receives the lender’s revaluation gain and on the estate: −0.47% with the gain outside the household sector and a liquid estate, +0.34% under a uniform rebate, +0.02% under a rebate pro rata to deposits, −0.18% when the old keep their houses. Fixed-rate and renewable-term contracts coincide for a level surprise; only the persistent ordering, fixed rate above renewable term above a within-period-indexed contract, tests the accounting proposition.

JEL: R21, R31, D31, D91, E31, G51

Key Results

Ownership-entry threshold with a liquidity component

The transfer required to own equals the down-payment bound plus the stage-one consumption of the marginal buyer; the paper presents this as an incremental extension of existing ladder and credit-constraint models to transfers, a rental sector and nominal debt.

Leverage scales exposure, not the break-even

The leverage multiplier net of transaction costs raises the sensitivity of terminal wealth to the resale price while the break-even price growth is independent of the loan-to-value ratio.

Intergenerational tenure persistence in closed form

Persistence is the second eigenvalue of the dynasty chain and is positive only if the house is net wealth at the end of life. In the quantitative economy transfers are, by design, the whole of the persistence, which disappears when the bequest motive is removed.

Prices absorb most of what credit constraints would do

Lowering the minimum down payment from 20% to 5% raises ownership under 35 from 0.38 to 0.429 at fixed prices, but general equilibrium removes 64% of the aggregate ownership effect; the search for multiple stationary equilibria finds a monotone excess-demand function with a single root in the scanned region, including under near-fixed supply.

The inflation sign is a property of incidence and of the estate

The general-equilibrium sign of the house-price response is decomposed by who receives the lender's revaluation gain, and tied to a density-weighted net nominal position of the parents whose children are at the tenure margin (computed at −0.323, standard error 0.008).

Negative results reported as results

Surprise inflation lowers rather than raises the real house price in the economy of record, and price neutrality without segmentation does not carry over to an economy with an intensive housing margin; in each case the responsible benchmark assumption is identified and the proposition restated under it.

Quality control

This paper went through a multi-stage quality control: 7 quality-control reports and 85 points checked. The version presented on this page is the revised manuscript. Scores are on a 0–100 scale and are a diagnostic of the manuscript, not an acceptance probability.

Score after revision

69.2/100

62.0 before quality control · +7.2

Quality control dated November 7, 2026

Quality-control decision: claims not supported as written → reframed and revised
Scientific integrity: PASS
Reproducibility: R1reproduced from documented analysis data
Maturity: Bone revision cycle from submission
Quality-control reports: 7
Points checked: 85

Scores by dimension

Before quality controlAfter revision

Originality & contribution58.4 → 62.0
Scientific rigor63.9 → 71.0
Identification & methodology57.3 → 68.0
Data & reproducibility69.6 → 76.0
Robustness & validation61.7 → 70.0
Writing67.7 → 70.0
Figures & tables59.0 → 72.0
Literature positioning62.9 → 70.0

Revised manuscript86 pages15 figures14 tables25 equations83 references39,020 words

What quality control changed

Quality control concluded that the original inflation result, a fall in the real house price explained by households being net nominal creditors, could not stand as written. The revised paper shows that the sign depends on who receives the lender's revaluation gain and on the estate specification, and states the transfer results with their design limits.

Inflation headline: ‘a 10% surprise moves the real house price by −0.45% because households are net nominal creditors’ → −0.47% only when the lender's gain accrues outside the household sector and the estate is liquid; +0.34%, +0.02% or +0.79% when the gain is rebated uniformly, pro rata to deposits or to entrants; −0.18% when the old keep their houses.
Wealth gap: ‘0.95 income-year’ → 0.95 average five-year incomes, about 4.8 years of annual income; 4.0 years when gift incidence is targeted to the Canadian figure.
Persistence: rank–rank slope of 0.34 that ‘vanishes without transfers’ → zero by design without transfers, because child and parent incomes are independent; with an intergenerational income correlation of 0.4 the slope is 0.41.
Multiplicity: ‘no multiple equilibria arise under near-fixed supply’ → excess demand has a single root in the scanned region.
Contract ordering: ‘fixed-rate above renewable term above adjustable is confirmed’ → fixed-rate and renewable-term contracts coincide for a level surprise; only the persistent surprise tests the ordering, and the third contract is a within-period-indexed contract.
Added: Monte-Carlo resolution for every transition statistic, a grid-convergence study, and a full re-run of the simulation layer on a second machine.

Limitations stated in the paper

The calibration is illustrative: no moment is fitted and the supply elasticity has no Canadian source, so magnitudes are statements about this parameterisation.
The choice of closure is a choice of result for the inflation experiments; the runs in which the old keep their houses are above tolerance, a warm glow over housing wealth was not implemented, and the model's net nominal position is not compared with a measured Canadian profile.
In the baseline 72% of first-time buyers receive a gift against 28% in the Canadian source, so the gift channel is an upper bound; persistence without transfers is zero by design and the rank–rank slope is not an estimate.
The mortgage block is not converged on the committed loan grid, so mortgage moments and the welfare of mortgaged owners are quoted as bands; there is no aggregate risk, no default and no endogenous real rate, and the transfer rebate is counted twice in the two transfer-tax experiments.

Read online (interactive reader)Revised PDF Revised branch on spbgit

Data

Benchmark economy

A household lives three stages, buys or rents once, repays a nominal mortgage, sells, and transfers part of the proceeds to a child; closed forms yield nine propositions on entry, leverage, persistence, existence and uniqueness, price neutrality and the accounting of a price-level surprise under fixed-rate, renewable-term and adjustable-rate contracts.

Quantitative overlapping-generations economy

Twelve five-year periods, four house sizes and continuous rented services, persistent income risk, nominal constant-payment mortgages amortised over 25 years under three contract types with loan-to-value and payment-to-income constraints, a gift at the child's entry and an estate at the parent's death, segmented rental and construction sectors with durable stocks and a lender with a balance sheet; simulated on a Monte-Carlo panel of 96,000 dynasty slots.

Illustrative calibration, no microdata

No moment is fitted. Canadian comparison points from public sources are reported next to the model's moments without being targeted, and the housing-supply elasticity, for which no Canadian estimate was found, is swept from 0.05 to 2.

Methodology

Closed-form benchmark theory

Nine propositions with corollaries and scoping remarks, proved in an appendix; each quantitative result that departs from the benchmark is traced to the assumption responsible.

Stationary general equilibrium

The owner and rental markets clear to a stated tolerance, with the estate lottery re-solved; 45 stationary equilibria are computed, and every result at fixed prices is labelled as such.

Perfect-foresight transitions

Sixteen transitions after an unanticipated inflation or a real-rate shock, 13 within tolerance; the inflation experiments are re-solved under three rules that rebate the lender's gain to households and under a specification in which the old keep their houses.

Monte-Carlo resolution

Every transition statistic is accompanied by its resolution measured from a placebo transition, repeated seeds and a paired dynasty-slot bootstrap; a grid-convergence study reports mortgage moments as bands.

Welfare

Consumption-equivalent variations for households alive at the shock by tenure and for entrants; because of nearest-grid error in the warm-glow terms they are reported as bounds.

Reproducibility

The repository contains all code (Python 3.14, pinned requirements), configuration files, simulation outputs (45 stationary general equilibria, 16 transitions and the welfare computations) and the scripts that generate every table, figure and the macro file of numbers, under the MIT licence.

The simulation layer is reproduced with one command (59.8 minutes on an 18-CPU Apple-silicon machine, seed 20261020 with common random numbers) and the exhibits in under two minutes; a reduced-scale run with 24,000 dynasties is also provided.

The full simulation layer was re-run from the unmodified tree on a second machine and its 22,660 numeric fields compared with the committed results: no impact response changes sign, and the impact price responses of the 16 transitions agree within 0.065 percentage points.

The convergence flags of 4 of the 16 transitions flip at the noise floor between the two machines, none of which changes a conclusion; both readings of this outcome are stated in the replication package.

The paper uses no microdata; the Canadian comparison points are typed from public sources and listed with their sources, URLs and access dates.

Cite this paper

Boucher, S.-P. (2026). Housing, Leverage, and Intergenerational Wealth Inequality. UQO Working Paper No. 18, Université du Québec en Outaouais.

@techreport{boucher2026wp18,
  author      = {Simon-Pierre Boucher},
  title       = {Housing, Leverage, and Intergenerational Wealth Inequality},
  institution = {Université du Québec en Outaouais, Département des sciences administratives},
  number      = {18},
  type        = {UQO Working Paper},
  year        = {2026},
  month       = {nov},
  url         = {https://www.spboucher.ai/research/wp18},
}