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\section{Related literature}
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The literature that bears on the question is large but fragmented along five mechanisms that are rarely combined in one general-equilibrium model: the collateral or down-payment constraint that gates entry into ownership; the leveraged return on housing and the resulting divergence of owner and renter balance sheets; the revaluation of nominal mortgage debt under surprise inflation; the supply side that converts demand shocks into prices rather than quantities; and the intergenerational transmission of wealth through transfers. This section reviews each mechanism, then the Canadian institutional setting, and closes with the gaps that the model is built to address. Only references whose metadata were verified are cited.

\subsection{Collateral, leverage and the price feedback}

The amplification mechanism descends from \citet{kiyotaki1997credit}: when durable assets serve as collateral, a shock that raises their price relaxes borrowing limits, which raises demand and the price again. \citet{iacoviello2005house} transplanted the mechanism into a monetary model with housing collateral and nominal debt, obtaining two results this paper inherits, that collateral constraints amplify demand shocks and that debt deflation transfers wealth from borrowers to lenders. Its limits are equally instructive: two representative households, no tenure choice, no wealth distribution and no inheritance, so that the redistribution it identifies is between two types rather than within a cross-section of households that differ in initial wealth.

The quantitative heterogeneous-household literature supplies the architecture. \citet{favilukis2017macroeconomic} build an overlapping-generations economy with aggregate and idiosyncratic risk, collateral constraints and heterogeneous bequest motives, and show that relaxing financing constraints produces a large price boom through a fall in the housing risk premium. \citet{kaplan2020housing} add a rental market, long-term mortgages and tenure choice and reach the conclusion that disciplines any claim about the collateral--price feedback: in their calibration, shifts in credit conditions move ownership, leverage and foreclosures but not prices, because the rental sector and long-term mortgages absorb the demand shift. \citet{greenwald2025do} resolve the apparent conflict with the credit-driven-boom literature by showing that everything hinges on the segmentation between the owner-occupied and rental stocks. \citet{sommer2013equilibrium} and \citet{sommer2018implications} provide the template for a rental equilibrium with landlords and an endogenous rent--price ratio; the latter is a standing warning that general-equilibrium price responses can reverse partial-equilibrium intuition. For the present paper this literature means that the strength of any price feedback is not a free parameter: it is governed by the segmentation parameter and the supply elasticity, both of which the model makes explicit, and Proposition~\ref{prop:noseg} restates the \citeauthor{kaplan2020housing} neutrality in the model's language while Remark~\ref{rem:noseg_scope} records the condition, unit demand, under which it holds.

The empirical side of the collateral channel is well established. \citet{mian2011house} document home-equity borrowing of 25--30 cents per dollar of house-price gain, concentrated among constrained owners; \citet{gete2018mortgage} show that tighter mortgage supply pushes households into renting and raises rents; \citet{cloyne2020monetary} show that the consumption response to interest rates is driven by mortgagors, with outright owners not responding. None of these speak to intergenerational persistence, but together they justify two modelling choices: owners must be allowed to be liquidity-constrained despite high net worth, and the rental market must be an explicit margin rather than an outside option.

The mortgage-contract literature is the second pillar. \citet{campbell2003household} formalise the household's choice between a nominal fixed-rate mortgage, which carries inflation risk, and an adjustable-rate mortgage, which carries income risk. \citet{chambers2009accounting} embed contract choice in an overlapping-generations economy with tenure choice and attribute a large share of the rise in US ownership to mortgage innovation: contract design changes who can own, which is the sense in which the present paper treats the contract. \citet{guren2021mortgage} and \citet{campbell2021structuring} study contract design for macroeconomic stabilisation in equilibrium life-cycle models; the latter prices mortgages off a risk-averse lender, a device that keeps lender wealth in the accounting of inflation redistribution, as the model here does with a simpler risk-neutral lender.

\subsection{Nominal debt and surprise inflation}

The Fisher channel \citep{fisher1933debt} is the oldest element of the paper. Its modern quantification is \citet{doepke2006inflation}, who revalue the nominal positions of US households by age and wealth and find that a moderate inflation episode transfers wealth from rich, old bondholders and from foreigners to young middle-class households with fixed-rate mortgages. \citet{adam2016price} replicate the exercise for the euro area and \citet{meh2011inflation} for Canada, finding that the main winners are young middle-class households with mortgage debt while the old, the rich and holders of non-indexed pensions lose. \citet{pallotti2024who} bring the accounting up to the 2021--2023 episode and add a nuance that matters for a model with renters: rigid rents acted as a hedge for lower-consumption households, so the episode worked like an age-dependent tax.

These are accounting exercises. They hold prices, rents, interest rates and behaviour fixed and therefore cannot answer whether the direct revaluation survives once rents, house prices and lender wealth respond. Three papers go further. \citet{meh2010aggregate} compute the general-equilibrium response to an unexpected price-level increase in an overlapping-generations economy with nominal positions calibrated for Canada and find that the young, the poor and the government gain and that the policy regime matters; the model has no housing market, so the owner--renter dimension is absent. \citet{auclert2019monetary} provides the sufficient-statistic language of unhedged interest-rate exposure and the Fisher channel but has no tenure structure or intergenerational dynamics. \citet{garriga2017mortgages} is the closest precedent for the inflation results: in a general-equilibrium model with long-term nominal mortgages they show that persistent inflation benefits fixed-rate borrowers over time but hurts adjustable-rate borrowers immediately. Their borrowers and lenders are two representative types; there is no renter priced out when nominal rates rise, no ownership-entry margin and no inheritance. The lesson this paper draws is that the sign of the general-equilibrium effect of a surprise cannot be assumed: \citeauthor{garriga2017mortgages} show that it is negative for adjustable-rate borrowers, \citeauthor{pallotti2024who} that rent rigidity can protect renters, and \citeauthor{kaplan2020housing} that the rental sector can absorb demand. Proposition~\ref{prop:impact} and Corollary~\ref{cor:creditor} therefore state conditions rather than a sign, and Section~\ref{sec:inflation} finds the sign that the brief expected to be positive to be negative.

\subsection{Land scarcity, supply elasticity and the rent--price ratio}

The case for treating land as a scarce factor is strong. \citet{knoll2017no} show that real house prices in fourteen countries were roughly flat until the mid-twentieth century and then tripled, with most of the rise attributable to land; \citet{davis2007price} show that the land share of US house value rose and drives price volatility; \citet{rognlie2015deciphering} shows that the post-war rise in the net capital share comes from housing; \citet{piketty2014capital} document the rise of wealth--income ratios in which housing is the main component. In the cross-section, \citet{saiz2010geographic} and \citet{glaeser2018economic} establish that geography and regulation determine supply elasticities, and \citet{gyourko2013superstar} show that inelastic supply with rising high-income demand produces persistent price divergence and sorting.

Two theoretical papers connect supply scarcity to the owner--renter distribution. \citet{kiyotaki2011winners} build a life-cycle production economy in which land and capital produce real estate and find that when the land share is large, prices react strongly to productivity and world-interest-rate shocks, redistributing between net buyers and net sellers, while financing constraints have limited price effects. \citet{grossmann2021distributional} model land as a fixed factor in a growing economy and show that surging rents redistribute from renters to landowners. \citet{borri2021optimal} analyse optimal taxation when appreciation widens the owner--renter gap, and \citet{favilukis2023affordable} offer the most complete architecture, owners, renters, construction and endogenous wealth inequality, for evaluating affordability policies. What is missing is the interaction of supply elasticity with the other mechanisms: \citeauthor{kiyotaki2011winners} have no bequests and no nominal debt, \citeauthor{grossmann2021distributional} have representative owner and renter types, and neither models the entry threshold. The conjecture that lower supply elasticity raises the price response to any demand shift and therefore both the leveraged return of incumbents and the entry threshold of renters is plausible but, as Section~\ref{sec:supply} shows, quantitatively weak when the demand shift itself is small and when the stock is durable.

\subsection{Tenure choice, the down-payment constraint and the property ladder}

The microeconomics of tenure choice begins with \citet{henderson1983model}, whose rental externality rationalises an ownership premium, and with \citet{linneman1989impacts}, who show that it is the wealth constraint rather than the income constraint that blocks ownership. \citet{stein1995prices} shows that down-payment effects generate multiple equilibria and price--volume comovement in a static setting. The paper closest to the threshold result is \citet{ortalomagne2006housing}: in a life-cycle model with a property ladder and a down-payment constraint, the ability of young households to finance the down payment on a starter home drives prices, and capital gains on starter homes relax the constraints of existing owners. It has no bequests, no nominal debt, no inflation and no supply side, and the distribution of wealth across households of equal income is not an object of analysis.

The quantitative life-cycle literature fills in the behavioural detail: \citet{gervais2002housing}, \citet{iacoviello2013housing}, \citet{halket2014saving}, \citet{diaz2010wealth}, \citet{kaas2021low}, \citet{floetotto2016government} and \citet{halket2015homeownership}. \citet{pazpardo2024homeownership} is especially relevant because it identifies a competing explanation for falling young ownership and wealth, riskier and more unequal earnings for later cohorts; the claim that inheritance generates gaps among households with similar labour income must therefore be isolated from the earnings channel, which is why the earnings process is held fixed across inheritance groups in the baseline and varied separately. \citet{nakajima2020home} close the life cycle: retired owners dissave slowly, so housing is the main asset bequeathed, which ties the tenure block to the bequest block. The quantitative model here departs from that finding in one respect that Section~\ref{sec:baseline} flags: with a warm glow over a liquid estate, old households sell their house before death.

\subsection{Incomplete markets, bequests and intergenerational wealth}

The incomplete-markets tradition \citep{samuelson1958exact,diamond1965national,aiyagari1994uninsured,huggett1996wealth} provides the equilibrium concept. \citet{denardi2004wealth} is the canonical bequest specification, voluntary bequests as a luxury good, which the model adopts and extends to housing. \citet{benhabib2011distribution} and \citet{gabaix2016dynamics} supply analytical benchmarks for persistence, Pareto tails from capital-income risk and the slow convergence of random-growth processes; they concern the tail of the wealth distribution rather than a tenure-based structure, and the half-life statements of Proposition~\ref{prop:persist} are the model's counterpart. \citet{kuhn2020income} provide the macro-historical motivation: over 1949--2016 the portfolio composition of US households, leveraged housing for the middle class and equity for the top, makes asset-price movements the main driver of wealth-inequality dynamics.

The empirical literature on intergenerational wealth has converged on three findings the model must respect. Parental transfers at the time of purchase are a first-order determinant of entry: \citet{engelhardt1998intergenerational} find that about a fifth of US first-time buyers receive transfers, \citet{guiso2002private} that transfers advance first purchase in Italy, \citet{blickle2019borrowing} that a transfer raises the renter-to-owner transition probability through relaxed constraints rather than wealth effects, and \citet{charles2002transition} that parental wealth and transfers explain much of the Black--White ownership gap at equal income. Parental housing wealth specifically transmits to children: \citet{daysal2023intergenerational} estimate on Danish registers that about a quarter of a parental housing-wealth gain in early childhood passes through to the child's adult housing wealth, with earnings and education explaining only a fraction; \citet{benetton2022dynastic} study the US parent--child link through home equity. And transfers are not the whole story: \citet{fagereng2021why} show with adoptees that family environment raises child wealth causally and not mainly through gifts, \citet{nekoei2023how} show that inheritances reduce inequality on receipt but raise it within a decade because wealthy heirs earn higher returns, and \citet{boar2021dynastic} show that parents save to insure their children's income risk. The implication is that the inheritance channel formalised here is real and measurable but is not claimed to be the dominant source of intergenerational wealth persistence; the model isolates one mechanism, transfers interacting with the down-payment constraint and leveraged housing returns, while holding preferences, financial literacy and earnings transmission fixed. The \citeauthor{nekoei2023how} finding that returns on inherited wealth drive the reversal from equalising to disequalising is exactly what the ownership threshold does: it is a discontinuity in the return to the first dollar of transfer.

\subsection{The Canadian institutional setting}

Canada differs from the United States in ways that matter for every mechanism above. Mortgages are amortised over 25 years but renewed every five years or less at the prevailing rate, so the fixed-rate contract is fixed only for the term: \citet{kartashova2020how} exploit scheduled resets to show asymmetric spending and deleveraging responses; \citet{bounajm2024modelling} document how the Bank of Canada's projection model represents the term structure of mortgage debt; \citet{godbout2025how} estimate that a majority of outstanding mortgages renew in 2025--2026 at higher payments; and \citet{cmhc2026residential} show that traditional five-year fixed contracts were a small minority of new extensions in early 2026. The consequence for the inflation results is that the Canadian contract is intermediate between the US 30-year fixed-rate mortgage of \citeauthor{doepke2006inflation} and the adjustable contract of \citeauthor{garriga2017mortgages}: the inflation gain accrues only for the remaining term and is partly clawed back at renewal unless the surprise is transitory. \citet{allen2019search} document search frictions and rate dispersion in the insured segment, which are noted but not modelled. On the household side, \citet{meh2011inflation} provide nominal-exposure profiles by age and tenure, \citet{hou2010homeownership} the age profile of ownership, \citet{mirdamadi2023parents} the parental-ownership channel and the share of first-time buyers receiving family gifts, and \citet{statcan2024survey} the owner--renter wealth gaps quoted in the introduction. No Canadian analogue of the \citeauthor{saiz2010geographic} elasticity estimates was found among verified sources, so supply elasticity is treated as an illustrative parameter with a range.

\subsection{Gaps}

Reading the five strands together, four gaps are not filled by any verified paper. No general-equilibrium model combines bequest heterogeneity, a down-payment-gated ownership margin, an explicit rental sector and price feedback, and characterises the entry threshold analytically: \citeauthor{ortalomagne2006housing} have the threshold and the feedback but not bequests or a rental sector, \citeauthor{favilukis2017macroeconomic} have bequest heterogeneity and feedback but no tenure margin, \citeauthor{kaplan2020housing} have everything except inheritance heterogeneity and do not characterise the threshold. Persistence of the ownership gap across generations is documented empirically but not derived; the theoretical persistence results that exist concern the tail of the wealth distribution. Surprise inflation with fixed nominal mortgages has been studied in general equilibrium but never with renters, an entry margin and inheritance, and never with the Canadian renewable term placed between the long fixed-rate and the adjustable contract. And supply elasticity has been linked to owner--renter redistribution and contracts to ownership rates, but neither to intergenerational mobility in tenure or wealth. The model of Section~\ref{sec:model} is built to fill these gaps in a form that can be proved where possible and simulated where not; the verdicts on which results are new and which are incremental are given in the introduction and are not revisited in the conclusion.