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# CLAUDE.md — UQO Working Paper 18

(Spécification de l'auteur, 2026-10-20. Conventions de forme : ~/Desktop/Recherche-UQO/HARMONISATION.md ; ce dossier s'appelle immobilier/housing-leverage-intergenerational-inequality et correspond au dépôt spbgit wp18_uqo.git — le nom wp18_uqo/ du plan ci-dessous désigne ce dossier.)

# Mission

Act as an autonomous team of housing economists, macro-finance theorists, mathematical economists, computational scientists, research librarians, and LaTeX editors. Develop a rigorous, reproducible English-language theoretical research paper:

WP18 — Housing, Leverage, and Intergenerational Wealth Inequality: A Dynamic General Equilibrium Theory

Author: Simon-Pierre Boucher. Verify institutional affiliation and contact details against prior UQO papers. Do not invent coauthors or acknowledgments.

Central question: Under what conditions do inherited wealth, mortgage leverage, nominal debt, housing supply and down-payment constraints generate persistent owner-renter wealth inequality among households with similar labor income? What changes under unexpected inflation?

Mandatory order: inspect previous UQO WPs and review literature → specify mathematical model → derive propositions → implement and validate numerical model → run simulations and robustness checks → generate all figures and tables → audit results → only then write and compile the LaTeX paper. Literature review must be expanded before drafting. Never invent results, citations, proofs, or data.

# Phase 0 — Reproduce UQO WP conventions

  1. Inspect current repository and accessible WP1–WP17 sources (all available locally in ~/Desktop/Recherche-UQO/{immobilier,finance}/*/paper/, notably WP2, WP5, WP10, WP16). Log unavailable files rather than claiming to have read them.
  2. Document observed series conventions in research/wp_style_audit.md: cover, number, typography, title/author block, abstract, keywords/JEL, section structure, theorem environments, figures, tables, citations, appendices, compilation. Follow them for WP18.
  3. Preserve paper/main.tex and paper/main.pdf naming conventions. Never overwrite earlier WPs.

# Phase 1 — Deep verified literature review and novelty

Search scholarly literature and authoritative working papers on: OLG/lifecycle housing, tenure choice, housing wealth inequality, bequests, down-payment/LTV constraints, nominal mortgage debt, surprise inflation and redistribution, housing collateral, monetary transmission, land scarcity/supply elasticity, rental equilibrium, incomplete markets, household heterogeneity, welfare and policy. Investigate relevant foundational work by Kiyotaki–Moore, Iacoviello, Ortalo-Magné–Rady, Glaeser, Gyourko, Saiz, Kaplan–Mitman–Violante, Doepke–Schneider, and other relevant researchers; verify actual paper metadata and contributions rather than assuming relevance.

Deliver research/literature_matrix.csv with a target of 50–80 verified references if genuinely relevant and accessible (never pad), including DOI/URL, model, method, findings, limitations, relevance and overlap with WP18. Produce a substantial critical synthesis in research/literature_review.md and verified paper/references.bib. Record inaccessible sources and uncertainty. Produce research/novelty_matrix.csv comparing each claimed contribution with the closest prior papers. Redesign weak contributions. Do not assert novelty before verifying it.

Candidate contributions: (i) an endogenous ownership-entry wealth threshold jointly shaped by bequests, collateral and price feedback; (ii) conditions for persistent ownership/wealth gaps and path dependence; (iii) conditional inflation redistribution through fixed nominal mortgages in general equilibrium; (iv) supply elasticity and mortgage-contract effects on intergenerational mobility. Treat each as a hypothesis, not a preordained result.

# Phase 2 — Complete theoretical model

Start with a tractable discrete-time overlapping-generations/lifecycle heterogeneous-household housing economy. Model owners and renters, consumption, housing services, liquid assets, income risk, bequests, mortgage debt, endogenous tenure choice, down-payment/LTV restrictions, transaction costs, maintenance, rents, housing supply and market clearing. Add features only when solvable and relevant.

Write explicit household Bellman problems, full owner/renter budgets, initial/terminal conditions, inheritance process, timing of choices and shocks, mortgage amortization and refinancing, collateral constraints, competitive equilibrium definition, aggregate consistency, rental market and housing market clearing. State units and notation precisely.

Distinguish nominal mortgage principal B_nom from real debt B_nom / CPI; distinguish CPI from house-price index. Separate expected from unexpected inflation and fixed-rate from variable-rate mortgages. Account for interest payments, inflation effects on wages/rents/interest rates, lender wealth, housing supply, and renter investment returns. Do not assume inflation necessarily raises real house prices or enriches every owner.

Seek rigorous analytical results: leverage amplification with costs; surprise-inflation redistribution under stated assumptions; ownership threshold; conditions for persistence/multiple equilibria (only if established); comparative statics of LTV, bequests, supply elasticity and mortgage structure. For every proposition provide exact assumptions, statement, proof or clearly labeled proof gap. Save proofs in paper/appendix_proofs.tex and failed conjectures in research/failed_hypotheses.md. Do not call simulation findings theorems.

# Phase 3 — Numerical implementation BEFORE writing

Use Python with NumPy/SciPy/pandas/matplotlib, optionally Numba/JAX. Write reproducible modules src/model.py, household_solver.py, equilibrium.py, distributions.py, simulation.py, calibration.py, robustness.py, figures.py, tables.py. Use configs/YAML, pinned dependencies, fixed seeds, tests, structured experiment logs, raw CSV/Parquet outputs, and a Makefile.

First solve a two-/three-period benchmark with known behavior; unit-test budget identities, debt evolution, feasibility and terminal conditions. Then implement household dynamic programming (VFI/EGM or justified method), stationary distribution/OLG transitions, bequests, endogenous price iteration and housing/rental market clearing. Report Bellman residuals, equilibrium residuals, numerical tolerances, convergence, grid sensitivity and computational failures. If general equilibrium does not solve, never label partial equilibrium as GE.

Calibrate from traceable Canada/Québec sources when justified, or use clearly marked illustrative parameters. Record units, observation dates, transformations and sources. No fabricated calibration targets or empirical validation.

Run at least these experiments:

  1. Baseline wealth and ownership by age, income and inheritance quantile.
  2. Equal-income owner/renter wealth paths with differing initial endowments.
  3. Down-payment constraint and ownership-entry threshold sweeps.
  4. Surprise inflation with fixed versus adjustable nominal mortgages.
  5. Leverage/LTV sensitivity including negative house-price shocks.
  6. Bequests on/off and alternative inheritance transfers/tax scenarios.
  7. Housing supply elasticity, including near-fixed supply.
  8. Interest rates, rent growth, earnings risk and expectations sensitivity.
  9. Welfare changes using a defined consumption-equivalent measure.
  10. Robustness to discounting, preferences, transaction costs, grid resolution, solver tolerance and simulation sample size.

Produce 10–14 meaningful publication-quality figures and 6–9 substantive tables, adjusted to genuine findings rather than padded. Candidate figures: model timing, policy functions, ownership thresholds, wealth-age profiles, owner/renter divergence, inheritance quantile trajectories, inequality evolution, inflation impulse responses, mortgage comparison, supply-elasticity heatmap, welfare distribution and solver diagnostics. Candidate tables: notation, calibrated parameters/sources, baseline moments, convergence, scenario effects, inflation redistribution, inequality/mobility, welfare and robustness. Save vector PDFs + PNG previews in results/figures/, auto-generated LaTeX tables in results/tables/, and raw data in results/data/. Every paper number must map to a result file.

# Phase 4 — Integrity audit, then write the manuscript

Before writing the paper, complete research/results_audit.md: experiment, hypotheses, parameters, algorithm, convergence, results, limitations, robustness, and claims actually supported. Distinguish mathematical identities, theoretical comparative statics, illustrative simulations and empirical findings. Investigate contrary outcomes. Never manipulate assumptions to force a preferred conclusion.

Gate: do not start manuscript drafting until the baseline model is validated, claimed GE equilibria clear markets, principal simulations and exhibits reproduce, bibliography is verified, and theoretical claims have proofs or appropriate qualifications. If blocked, document the issue honestly and deliver a scoped partial result.

Then write a polished 30–45-page English main text, plus appendices as warranted, in paper/main.tex:

  1. UQO WP18 title page, author, verified affiliation.
  2. Abstract (150–220 words, actual results only), 5–7 keywords, verified JEL choices (consider R21, R31, D31, D91, E31, E44, G51).
  3. Introduction: question, precise contribution relative to closest work, preview of real results.
  4. Extensive critical literature review, organized by mechanisms and open gaps.
  5. Environment, timing, optimization, constraints and markets.
  6. Equilibrium and mathematical propositions.
  7. Numerical algorithm, calibration and verification.
  8. Baseline simulations, inheritance and inequality.
  9. Inflation/mortgage-contract counterfactuals.
  10. Supply elasticity, policy and welfare.
  11. Sensitivity, limitations and conclusion.
  12. References and appendices: full proofs, numerical algorithms, additional tables/figures.

Use amsmath, amssymb, amsthm, booktabs, graphicx, hyperref and a bibliography system compatible with observed UQO style. Maintain clean notation, labeled equations, real cross-references, readable figures and academic prose. Avoid inflated rhetoric or unsupported claims.

# Required directory layout

text
<dossier>/
  CLAUDE.md
  README.md
  Makefile
  requirements.txt
  configs/{baseline.yaml,scenarios.yaml}
  src/{model,household_solver,equilibrium,distributions,simulation,calibration,robustness,figures,tables}.py
  tests/
  research/{progress.md,wp_style_audit.md,novelty_matrix.csv,literature_matrix.csv,literature_review.md,model_specification.md,failed_hypotheses.md,results_audit.md}
  results/{data,figures,tables,logs}/
  paper/{main.tex,main.pdf,references.bib,appendix_proofs.tex,appendix_computation.tex}

# Final reproducibility and QA

Provide make setup, make test, make simulate, make figures, make tables, make paper, and make all targets, or equivalently documented commands. Rerun from a clean environment; verify no LaTeX compilation errors, undefined references, missing bibliography entries, broken paths, inconsistent numbers, unreported failures, or placeholder results. Check PDFs visually and inspect logs. Deliver final paper/main.pdf, source LaTeX, Python code, raw results, figures, tables, verified BibTeX, research audit, and a concise README explaining replication.

Maintain research/progress.md after every phase with completed work, evidence, blockers and next steps. Work autonomously, but ask for essential permissions or missing credentials rather than pretending access. Priority: scientific correctness, originality and reproducibility over speed, page count or positive findings.