# 🏠 The Endogenous Housing Liquidity Premium **UQO Working Paper No. 19** — *Search Frictions, Seller Urgency, and Price Discovery* [-b31b1b?logo=latex&logoColor=white)](paper/main.pdf) [](requirements.txt) [](data/raw/README.md) [](Makefile) [](https://uqo.ca) [](mailto:simon-pierre.boucher@uqo.ca) > **TL;DR** — A continuous-time search model of a local housing market with free entry of buyers, a continuous distribution of > seller carrying costs (urgency), Nash bargaining, withdrawals, and a financing-contingency extension (cash vs mortgage buyers). > Eight propositions (urgency discount, arrival rate with an exact Pareto counterexample, free entry, liquidity shocks without > fundamentals, dispersion, sale selection in price indices with a distribution-dependent sign, the cash–mortgage gap in three > terms, posted prices) and twelve pre-registered numerical experiments. Baseline: 2.2 months on market, 5.6 % urgency discount, > 3.5 % price dispersion among identical houses; halving matching efficiency lowers prices 4.8 % and raises time on market to > 3.4 months; the composition (selection) term of the observed index is ≤ 0.15 log-% against 2–10 % within-type effects. > Theoretical paper: **no data are used**. --- ## 📌 Status | Item | Value | |---|---| | Version | 1.0 (October 2026) | | SSRN | not yet submitted | | Journal | — | | Code & data | fully reproducible from `config/baseline.yaml` (see Quick start); no data | ## 🎯 What this paper does The paper asks how market tightness, heterogeneous seller reservation values, financing frictions, time-on-market costs and bargaining power jointly determine an endogenous housing liquidity discount, transaction prices, sale hazards and price dispersion, and under which conditions a liquidity shock propagates when housing-service values are unchanged. Sellers of type $c$ (carrying cost) solve ``` (r+δ) V(c) = −c + δ w0 + Λ_s β H(V(c)+U), H(v) = E[(w−v)^+], Λ_s = φ A θ^α ``` with free entry of buyers ($U=k$), sale hazard $η(c)=Λ_s[1−G(V(c)+U)]$, Nash price $p=(1−β)V−βU+βw$, and stocks $n(c)=s f(c)/(η(c)+δ)$. The urgency discount is $D(c)=1−\bar p(c)/\bar p(c_L)$; the Walrasian free-entry price $p^*$ solves $H(p^*)=rk$. ## 🏆 Headline results | Object | Value (baseline, model-generated) | |---|---| | Tightness θ*, contact rates Λ_s / Λ_b | 4.39 buyers per listing; 8.0 / 1.8 per year | | Time on market of sales; buyer search | 2.2 months; 10.8 months | | Urgency discount, most urgent / transaction-weighted | 5.6 % / 2.0 % | | Price s.d. among identical houses; between-type share | 3.5 %; 13 % | | Halving matching efficiency (GE vs PE) | price −4.8 % vs −4.3 %; TOM 3.4 vs 3.2 months; θ 3.73 | | Entry amplification d ln Λ_s / d ln φ | 1.10 | | Transition, permanent −20 % A | price −1.46 % on impact; sales −13 % → −1.4 %; inventory +13 % (half-life 1.9 months) | | Index composition term (selection) | ≤ 0.15 log-%; dampens for truncated normal/Weibull, amplifies for exponential/Pareto | | Cash–mortgage gap (extension) | 1.73 % = 0.49 (delay-bargaining) + 1.61 (outside option) − 0.37 (selection); 1.1 % patient → 3.0 % urgent | | Welfare-maximising β (flow criterion) | 0.55 (Hosios 0.50); planner gain 0.30 % | ## 🗂 Repository layout ``` endogenous-housing-liquidity-premium/ (spbgit: wp19_uqo.git) ├── CLAUDE.md # research brief and execution protocol ├── config/baseline.yaml # the only input: parameters with units and justifications ├── src/ │ ├── model.py # distributions (truncnorm, exponential, Pareto, Weibull), type grid, Params │ ├── solver.py # seller block, free-entry equilibrium, posted prices, financing extension, planner, transition │ ├── simulation.py # the 12 pre-registered experiments → results/processed, results/raw (hypothesis + env + hash) │ ├── diagnostics.py # Monte Carlo cross-check, residuals, bounds → results/logs/validation.json │ ├── calibration.py # illustrative-parameterisation report (no data) │ ├── plotting.py # 14 figures (PDF + PNG) → results/figures, paper/figures │ ├── tables.py # 23 LaTeX fragments + numbers.tex macros → results/tables, paper/tables │ └── literature.py # merges the verified literature parts, cross-checks Crossref JSON, writes references.bib ├── tests/ # 24 pytest tests (closed forms, propositions, boundary cases, equilibrium, convergence) ├── research/ # wp_style_audit, literature_matrix.csv (132 refs), literature_review, novelty_matrix, │ # model_specification, proofs, validation, results_audit, limitations, progress, verification/ ├── results/{raw,processed,figures,tables,logs}/ ├── data/raw/README.md # no data └── paper/ # main.tex + sections/ + appendix/ + tables/ + figures/ + references.bib → main.pdf ``` ## 🚀 Quick start ```bash python3 -m pip install -r requirements.txt make test # pytest (24 tests, ~20 s) make simulate # 12 experiments (~6 min on an Apple-silicon laptop) make diagnostics # Monte Carlo validation (~3 min) make tables # LaTeX fragments + numbers.tex make figures # 14 figures make paper # cd paper && latexmk → main.pdf ``` `python -m src.simulation --exp 3,9` runs a subset. Every result file carries the configuration hash (`0a165f317815d76c`), seed (20261020), software versions and the pre-registered hypothesis. ## 🗃 Data None. The parameterisation is illustrative (Table 1 of the paper, `config/baseline.yaml`); see `data/raw/README.md`. ## 🔬 Methodology 1. Seller value by Brent's method on the strictly decreasing Φ(V) (`solver.seller_value`). 2. Free-entry tightness by sign scan + Brent, multiplicity reported (`solver.solve_equilibrium`). 3. Posted prices (`solve_equilibrium_posted`), financing extension as a 3-equation root (`solve_equilibrium_financing`), planner's flow optimum (`planner_optimum`), transition by backward HJB / forward KFE / pointwise free entry (`transition`). 4. Experiments E1–E12 (`simulation.py`), Monte Carlo validation (`diagnostics.py`), figures and tables from stored CSVs only. ## 🖼 Figures & tables inventory | Figure | Content | |---|---| | `fig01_equilibrium_matching` | free-entry residual and matching rates | | `fig02_urgency_reservation_price`, `fig03_urgency_sale_hazard` | urgency gradients for five arrival rates | | `fig04_liquidity_discount_vs_arrivals` | discount, price and Γ sign change | | `fig05_financing_counterfactual` | cash–mortgage gap decomposition, φ_m and delay | | `fig06_volume_vs_price`, `fig07_tom_survival`, `fig08_seller_type_price_distributions` | comovement, survival, mixture density | | `fig09_observed_vs_latent_index` | index decomposition by G family and the h_G·M sign condition | | `fig10_shock_impulse_responses` | transition paths | | `fig11_welfare_friction_contours`, `fig12_sensitivity_tornado`, `fig13_numerical_convergence`, `fig14_posted_vs_nash` | welfare, sensitivity, convergence, protocols | Tables: `tab01_parameters`, `tab02_baseline_moments`, `tab02b_baseline_types`, `tab03_comparative_statics`, `tab04a–e` (financing), `tab05`, `tab05b` (heterogeneity), `tab06`, `tab06b` (selection, dynamics), `tab07`, `tab07b–f` (robustness, convergence, entry, uniqueness), `tab08`, `tab08b` (welfare, planner), `tab09_protocols`, `numbers.tex` (macros). ## ⚠️ Limitations Theoretical, stationary, local; permanent nonnegative urgency; complete information; buyers never exit (financing extension inadmissible for φ_m ≤ 0.6); flow welfare criterion; unanticipated shocks with instantaneous entry; no data. See `research/limitations.md` and Section 10 of the paper. ## 📖 Citation ```bibtex @techreport{boucher2026liquidity, author = {Boucher, Simon-Pierre}, title = {The Endogenous Housing Liquidity Premium: Search Frictions, Seller Urgency, and Price Discovery}, institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives}, type = {UQO Working Paper}, number = {19}, year = {2026}, month = {October} } ``` ## 👤 Author & contact Simon-Pierre Boucher — simon-pierre.boucher@uqo.ca — Département des sciences administratives, Université du Québec en Outaouais. ## 📝 Notes - Deviations from the series standard: theoretical paper (no Data section; a numerical-solution section instead); extended amsthm environments; `src/*.py` + `Makefile` + `config/` instead of numbered `scripts/`; `research/` directory kept in git. - Pushed to spbgit `wp19_uqo.git` on 2026-10-20 (`origin`, branch `main`). - Process record: `research/progress.md`; novelty audit: `research/novelty_matrix.csv`; claim audit: `research/results_audit.md`.