UQO Working Papers · WP19 · v1.0
The Endogenous Housing Liquidity Premium: Search Frictions, Seller Urgency, and Price Discovery
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
The housing liquidity discount is the price of seller urgency
In the illustrative baseline the most urgent seller concedes 5.6% relative to the most patient, identical houses show 3.5% price dispersion, and halving matching efficiency lowers prices by 4.8% while lengthening time on market from 2.2 to 3.4 months.
Abstract
This paper studies how search frictions, heterogeneous seller urgency, financing frictions and bargaining jointly determine the liquidity discount, transaction prices, sale hazards and price dispersion in a local housing market. In a continuous-time matching model with free entry of buyers, sellers differ in a permanent carrying cost, buyers draw match-specific valuations, and prices are set by Nash bargaining. The urgency discount, defined relative to the most patient seller, is nonnegative and increasing in the carrying cost, and the expected price falls by less than the reservation price.
A fall in buyer arrivals or in mortgage qualification lowers prices, lengthens time on market and widens the discount when the valuation distribution has an increasing failure rate; with heavy-tailed valuations a more liquid market can lengthen time on market, under an explicit condition on the carrying cost. Liquidity shocks move prices, volume, inventory and durations with no change in housing-service values, and buyer entry amplifies them. The gap between mortgage and cash prices decomposes into a delay-bargaining term that rises with urgency, an outside-option term, and a selection term that can be negative.
The composition of transactions shifts after a liquidity shock in a direction governed by the shape of the valuation distribution, and its effect on a transaction-price index is an order of magnitude smaller than the within-type liquidity effect, which no quality adjustment removes. The Walrasian free-entry price is shown not to be a liquidity-premium benchmark, since search prices exceed it in thick markets. Results are illustrated numerically with a documented parameterisation and reproducible code; no data are used.
Key findings
8
propositions on discounts, hazards, entry, shocks, selection and financing
5.6%
urgency discount of the most urgent seller
3.5%
price dispersion among identical houses in the baseline
−4.8%
price change after halving matching efficiency
≤ 0.15 log-%
sale-selection term in a transaction-price index
1.73%
cash–mortgage gap in the financing extension
Scientific contributions
- Urgency discount characterised relative to the most patient seller
- The discount is nonnegative and increasing in the carrying cost, the expected price falls by less than the reservation price, and the discount widens when buyers are scarce whenever the valuation distribution has an increasing failure rate.
- An exact condition under which liquidity lengthens time on market
- With heavy-tailed buyer valuations a more liquid market can lengthen the time on market of urgent sellers, under a condition that depends on the carrying cost but not on the arrival rate — with an explicit Pareto counterexample.
- Liquidity shocks without fundamentals, amplified by entry
- A fall in matching efficiency or in mortgage qualification moves prices, volume, inventory and durations together with no change in housing-service values; free entry amplifies arrival shocks (elasticity 1.10), and a permanent −20% arrival shock cuts sales by 13% on impact while inventory rises 13% with a half-life of 1.9 months.
- Sign condition for sale-selection bias in price indices
- The composition term depends on whether the product of the hazard function and the mean residual valuation rises or falls: exponential and Pareto valuations amplify measured price changes, truncated-normal and Weibull valuations dampen them, and the term stays at or below 0.15 log-% against within-type liquidity effects an order of magnitude larger.
- Three-term decomposition of the cash–mortgage gap
- Mortgage buyers pay 1.73% more than cash buyers in the extension — 0.49 from delay-bargaining, 1.61 from the outside option, −0.37 from selection — ranging from 1.1% for patient to 3.0% for urgent sellers; tighter approval and longer delays widen the gap.
- The Walrasian price is not a liquidity-premium benchmark
- A seller with the option to wait for a high-valuation buyer captures match-specific rents, so search prices exceed the Walrasian free-entry price in thick markets; the discount is therefore measured among sellers in the same market. The welfare-maximising bargaining weight is 0.55 against a Hosios value of 0.50.
Methodology
Methodology (4)
Analytical results
Eight propositions and supporting lemmas on the urgency discount, the arrival-rate comparative statics, free-entry equilibrium, liquidity shocks, dispersion, sale selection, the cash–mortgage gap and posted prices, with proofs in the appendix.
Numerical solution
Seller values by Brent's method on a strictly decreasing fixed-point map, free-entry tightness by sign scan and Brent with multiplicity reported, posted-price and financing variants as root problems, a steady-state planner's problem, and transitions by backward HJB, forward Kolmogorov and pointwise free entry.
Twelve pre-registered experiments
Comparative statics of arrivals, qualification, approval delay, bargaining power, entry costs and seller heterogeneity; transitions after permanent and temporary shocks; index decomposition across four valuation families; posted-price protocol; sensitivity of every result to the parameters.
Monte Carlo validation
Simulated markets cross-check the analytical moments, residuals and bounds; results are written with the configuration hash, seed, software versions and the pre-registered hypothesis.
Research data
- Model environment
- A continuous-time local housing market with exogenous listing inflow, withdrawals, free entry of buyers at cost k, a Cobb–Douglas contact technology, sellers heterogeneous in a permanent carrying cost drawn from a continuous distribution, buyers drawing match-specific valuations from truncated-normal, exponential, Pareto or Weibull families, Nash bargaining, and extensions with posted prices and a financing contingency (cash versus mortgage buyers).
- Illustrative parameterisation
- A single configuration file (config/baseline.yaml, hash 0a165f317815d76c, seed 20261020) in which a listing sells in about 2.2 months, a buyer searches about 10.8 months, tightness is 4.39 buyers per listing with contact rates of 8.0 and 1.8 per year, and the most urgent seller concedes 5.6%; no data are used and no empirical claim is made.
Reproducibility
- Makefile targets test, simulate (12 experiments, about 6 minutes), diagnostics (Monte Carlo, about 3 minutes), tables, figures and paper, all driven by the single config/baseline.yaml
- 24 pytest tests on closed forms, propositions, boundary cases, equilibrium and convergence (about 20 s)
- 14 figures and 23 LaTeX table fragments plus numbers.tex macros regenerated from stored CSVs only; literature matrix of 132 references cross-checked against Crossref
- Six falsifiable predictions stated in terms of listing-level data (time on market, withdrawals, financing type, seller circumstances) for the empirical follow-up
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.0current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 60 p. |