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1% ============================================================================2\section{Sensitivity, limitations and conclusion}3\label{sec:sensitivity}4% ============================================================================56\subsection{Sensitivity}7\label{subsec:sens}89Table~\ref{tab:mobility} and Table~\ref{tab:robustness} in Appendix~\ref{app:computation} report the sensitivity of the stationary equilibrium to rates, trend inflation, the rent wedge, earnings risk, the outside asset, preferences and transaction costs; every variant is a full re-solution of the general equilibrium. A real rate of 1 or 3\% gives prices of \RoneP{} and \RthreeP, ownership of \RoneOwn{} and \RthreeOwn, mean estates of \RoneEstate{} and \RthreeEstate, $\lambda_7$ of \RoneLamSeven{} and \RthreeLamSeven{} and rank--rank slopes of \RoneRR{} and \RthreeRR: a higher real rate raises saving, estates and persistence. Trend inflation of 0 or 4\% gives prices of \PiZeroP{} and \PiFourP{} and ownership of \PiZeroOwn{} and \PiFourOwn; at fixed prices, 4\% inflation lowers under-35 ownership by \PiFourPEDropUthirtyfivePP{} percentage points through the nominal tilt of the constant-payment mortgage and the nominal payment-to-income cap, which is Proposition~\ref{prop:tilt} in partial equilibrium, and the general-equilibrium price fall offsets \PiFourGEOffsetPct\% of it. A landlord wedge of 2 or 8\% gives ownership of \PhiLowOwn{} and \PhiHighOwn. Earnings risk with annual innovation standard deviations of 0.10 and 0.20 gives ownership of \SigLowOwn{} and \SigHighOwn, Ginis of \SigLowGini{} and \SigHighGini, mean gifts of \SigLowGift{} and \SigHighGift{} and $\lambda_7$ of \SigLowLamSeven{} and \SigHighLamSeven: more risk raises precautionary transfers and persistence while lowering ownership. A deposit premium of two percentage points, the renter's investment return, raises the age-1 threshold at the median state to \DepPremThr, estates to \DepPremEstate{} and the rank--rank slope to \DepPremRR: a better outside asset delays purchase but raises estates and persistence, which is the mechanism of \citet{nekoei2023how} in reverse. Annual discount factors of 0.94 and 0.98 give prices of \BetaLowP{} and \BetaHighP{} and ownership of \BetaLowOwn{} and \BetaHighOwn; $\gamma = 3$ gives \GammaThreeOwn; a housing share of 0.25 gives a price of \AlphaHighP; low and high transaction costs give prices of \KappaLowP{} and \KappaHighP; a 5\% ownership premium gives \ChiFiveOwn. None of these variants changes the qualitative results: persistence requires transfers, prices absorb credit shifts, the surprise lowers the real price.1011The numerical variants bound the precision of the statistics. Coarse grids move ownership by \DevCoarseOwnPP{} percentage points, the price by \DevCoarsePPct\%, the Gini by \DevCoarseGini, the age-1 threshold by \DevCoarseThr{} and $\lambda_7$ by \DevCoarseLamSeven; fine grids move ownership by \DevFineOwnPP{} points, the price by \DevFinePPct\% and the threshold by \DevFineThr. A tolerance of $10^{-5}$ returns the same best iterate; a panel of 240{,}000 dynasties and an alternative seed move ownership by \DevSampleLargeOwnPP{} and \DevSeedOwnPP{} points, the price by \DevSampleLargePPct{} and \DevSeedPPct\%, $\lambda_7$ by \DevSampleLargeLamSeven{} and \DevSeedLamSeven{} and the rank--rank slope by \DevSampleLargeRR{} and \DevSeedRR. The ownership rate, prices, the Gini and the rank--rank slope are robust; the age-1 threshold and $\lambda_7$ are the least robust statistics and are quoted accordingly. Mean Bellman residuals of owners lie between $\BellmanOwnerMinAll$ (fine grids) and $\BellmanOwnerMaxAll$ ($\gamma = 3$ and coarse grids) across the \NRobustnessRuns{} robustness runs.1213\subsection{Limitations}14\label{subsec:limitations}1516The calibration is illustrative, no moment is fitted and the supply elasticity has no verified Canadian source, so magnitudes are statements about this parameterisation. The ownership profile falls after 65 because the warm glow is defined over a liquid estate, whereas Canadian owners keep their houses; a bequest motive over housing, or the slow dissaving of \citet{nakajima2020home}, would keep the old in their houses, raise the housing share of estates and, since the house would then be inherited at a market price, strengthen the ladder channel that the multiplicity scan found weak. Seventy percent of entrants receive a gift, against 28\% in the Canadian data, because every parent has the same motive; heterogeneous motives would concentrate transfers and raise the dispersion the model understates. There is no aggregate risk, no default, no survival risk and no endogenous real rate; the estate is anticipated as an unconditional lottery and held at its stationary value along transitions; the adjustable-rate contract is a stylised within-period repricing; and the five-year period understates peak leverage, so that no household is ever underwater and the leverage channel operates through consumption and entry rather than foreclosure. Monte-Carlo noise bounds market clearing to about $5\times10^{-4}$ in stationary equilibria and $10^{-3}$ along transitions, and four of the \NTransitions{} transitions are reported with residuals above tolerance. On the theory side, single crossing of the tenure decision is proved only on the hand-to-mouth region, the comparative statics in the down payment hold for a once-and-for-all tenure decision, price neutrality without segmentation holds under unit demand, and the impact proposition covers one period under static expectations and pure debtor positions. The general-equilibrium sign of the inflation response is governed by a density-weighted net nominal position that the quantitative model computes but that no verified Canadian source pins down; \citet{meh2011inflation} report net nominal positions by age and tenure, and a calibration that targeted them would be the natural next step.1718\subsection{Conclusion}19\label{sec:conclusion}2021The paper asked under what conditions inherited wealth, mortgage leverage, nominal debt, housing supply and down-payment constraints generate persistent owner--renter wealth inequality among households with the same income process, and what an unanticipated inflation changes. The benchmark answers the first part analytically. Ownership requires a transfer above a threshold that exceeds the down-payment bound by the consumption of the marginal buyer; leverage multiplies the exposure of terminal wealth to the resale price without changing the break-even; the parent's housing equity is pivotal for the child's tenure over an interval of income draws whose probability mass is the intergenerational persistence, positive only if the house is net wealth at the end of life, and a half-life rather than a trap; the stationary equilibrium exists and is unique when the entry-threshold channel dominates the ladder channel; and with a fixed stock, credit and transfers move prices and composition, not the ownership rate. The quantitative economy supports these statements in their stated scope. Transfers generate a mid-life wealth gap of about one year of income among equal-income households and are the whole of the model's intergenerational persistence, which disappears when the bequest motive is removed; prices absorb two thirds to nine tenths of what credit constraints would do to ownership at fixed prices; and no multiplicity appears, even under near-fixed supply.2223For the second part the benchmark was wrong in sign and the paper says so. A surprise erodes mortgages and deposits alike, and households in this economy hold more of the latter: the real house price falls, aggregate welfare falls, and the gains of mortgaged owners under fixed-rate and renewable-term contracts come from debt-free owners, renters and, through the lender, from rentiers. The benchmark's prediction of a price rise is restored only under the assumption that the mortgage is the households' sole nominal position, and the corollary that replaces it ties the sign of the price response to a density-weighted net nominal position of the parents whose children are at the tenure margin. Two further benchmark results fail outside their premises, price neutrality without segmentation under unit demand and the monotonicity of the entry threshold in the down payment for a once-and-for-all tenure decision, and both have been restated under those premises. What survives of the inflation analysis in general equilibrium is the accounting and the contract ordering: fixed-rate at least as good as the renewable term and both better than the adjustable contract for the indebted, with the term losing its advantage exactly when the surprise is persistent and the real rate responds, which is the Canadian case. The natural continuation is a calibration that targets the net nominal positions of Canadian households by age and tenure and a bequest motive over housing, since the sign of the general-equilibrium response and the strength of the ladder channel both turn on them.24