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1% ============================================================================2% UQO Working Paper No. 18 — Housing, Leverage, and Intergenerational Wealth3% Inequality: A Dynamic General Equilibrium Theory (Simon-Pierre Boucher)4% Preamble = UQO template (HARMONISATION.md) + amsthm environments (WP18)5% ============================================================================6\documentclass[12pt,letterpaper]{article}78% --- Encoding & Language ---9\usepackage[utf8]{inputenc}10\usepackage[T1]{fontenc}11\usepackage[english]{babel}1213% --- Page Layout ---14\usepackage[15 letterpaper,16 top=1in,17 bottom=1in,18 left=1in,19 right=1in20]{geometry}2122% --- Typography ---23\usepackage{mathptmx} % Times-like font (text + math)24\usepackage{microtype} % Improved typographic refinements25\usepackage{setspace}26\onehalfspacing % 1.5 line spacing2728% --- Math ---29\usepackage{amsmath,amssymb,amsthm}3031% --- Theorem Environments (WP18; research/wp_style_audit.md, §6) ---32\theoremstyle{plain}33\newtheorem{proposition}{Proposition}34\newtheorem{lemma}{Lemma}35\newtheorem{corollary}{Corollary}36\newtheorem{theorem}{Theorem}37\theoremstyle{definition}38\newtheorem{assumption}{Assumption}39\newtheorem{definition}{Definition}40\theoremstyle{remark}41\newtheorem{remark}{Remark}4243% --- Tables ---44\usepackage{booktabs}45\usepackage{tabularx}46\usepackage{multirow}47\usepackage{threeparttable}48\usepackage{siunitx}49\sisetup{50 input-symbols = {()},51 table-format = -1.3,52 parse-numbers = false53}5455% --- Figures ---56\usepackage{graphicx}57\graphicspath{{figures/}}58\usepackage{subcaption}59\usepackage{float}6061% --- Colors & Links ---62\usepackage[dvipsnames]{xcolor}63\usepackage[64 colorlinks = true,65 linkcolor = NavyBlue,66 citecolor = NavyBlue,67 urlcolor = NavyBlue,68 breaklinks = true69]{hyperref}7071% --- Bibliography ---72\usepackage[authoryear,round,semicolon]{natbib}73\bibliographystyle{aer}7475% --- Captions ---76\usepackage[77 font = small,78 labelfont = bf,79 labelsep = period,80 justification = justified,81 singlelinecheck = false82]{caption}8384% --- Headers & Footers ---85\usepackage{fancyhdr}86\pagestyle{fancy}87\fancyhf{}88\renewcommand{\headrulewidth}{0pt}89\fancyfoot[C]{\thepage}9091% --- Section Formatting ---92\usepackage{titlesec}93\titleformat{\section}{\large\bfseries}{\thesection.}{0.5em}{}94\titleformat{\subsection}{\normalsize\bfseries}{\thesubsection.}{0.5em}{}95\titleformat{\subsubsection}{\normalsize\itshape}{\thesubsubsection.}{0.5em}{}9697% --- Appendix Support ---98\usepackage[toc,page]{appendix}99100% --- Misc ---101\usepackage{enumitem}102\setlist{nosep,leftmargin=*}103104% ============================================================================105% METADATA106% ============================================================================107\newcommand{\WPnumber}{18}108\newcommand{\WPtitle}{Housing, Leverage, and Intergenerational Wealth Inequality}109\newcommand{\WPsubtitle}{A Dynamic General Equilibrium Theory}110\newcommand{\WPdate}{October 2026}111\newcommand{\WPversion}{1.0}112\newcommand{\WPabstract}{%113 This paper asks under what conditions 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 an unanticipated inflation changes. A three-stage benchmark with two-period generations yields a closed-form ownership-entry threshold that adds a liquidity component to the down-payment bound, a leverage multiplier whose break-even price growth is independent of the loan-to-value ratio, a closed-form intergenerational tenure persistence that is positive only if the house is net wealth at the end of life, existence and a uniqueness condition for the stationary equilibrium, and the accounting of a price-level surprise under three mortgage contracts. A twelve-period overlapping-generations model with nominal annuity mortgages, gifts and estates, and segmented rental and construction sectors is solved in stationary general equilibrium and along perfect-foresight transitions under an illustrative calibration. Transfers generate a \GapAgeFour{} income-year wealth gap at mid-life and a rank--rank wealth slope of \RankRankNW{} that vanishes without transfers; price adjustment removes \AbsorbThetaFivePct{}--\AbsorbThetaFortyPct\% of the partial-equilibrium ownership response to the down-payment constraint; no multiple equilibria arise under near-fixed supply. Because households are net nominal creditors, a 10\% surprise moves the real house price by \FrmLevelPzero\%, a fall where the benchmark predicts a rise; the contract ordering, fixed-rate above renewable term above adjustable, is confirmed.%114}115\newcommand{\WPkeywords}{housing tenure, mortgage leverage, intergenerational wealth, bequests, down-payment constraint, surprise inflation, overlapping generations}116\newcommand{\WPjel}{R21, R31, D31, D91, E31, G51}117118% --- Author ---119\newcommand{\WPauthor}{Simon-Pierre Boucher}120\newcommand{\WPaffiliation}{%121 Département des sciences administratives\\122 Université du Québec en Outaouais%123}124\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}125\newcommand{\WPaddress}{%126 Gatineau -- Pavillon Alexandre-Taché\\127 283, boulevard Alexandre-Taché\\128 Gatineau, Québec, Canada J9A 1L8%129}130131\hypersetup{pdftitle={\WPtitle: \WPsubtitle}, pdfauthor={\WPauthor}}132133% --- Generated numbers (src/tables.py -> results/tables/numbers.tex -> paper/tables/) ---134\input{tables/numbers}135136% ============================================================================137% DOCUMENT138% ============================================================================139\begin{document}140141% --- Title Page ---142\input{sections/titlepage}143144% --- Main Body ---145\input{sections/introduction}146\input{sections/literature}147\input{sections/model}148\input{sections/equilibrium}149\input{sections/computation}150\input{sections/baseline}151\input{sections/inflation}152\input{sections/supply_policy_welfare}153\input{sections/sensitivity_conclusion}154155% --- References ---156\newpage157\bibliography{references}158159% --- Appendices ---160\newpage161\begin{appendices}162\renewcommand{\thetable}{\Alph{section}\arabic{table}}163\renewcommand{\thefigure}{\Alph{section}\arabic{figure}}164\input{appendix_proofs}165\input{appendix_computation}166\input{appendix/appendix}167\end{appendices}168169\end{document}170