# WP19 — Literature review and novelty audit (Phase 1)

Date: 2026-10-20. Basis: 132 references verified against Crossref (129 with a DOI resolved; 3 with a publisher/RePEc evidence file), merged from two independent searches (lit_part_A.csv, theory, 73 rows; lit_part_B.csv, evidence and measurement, 66 rows; 7 papers in both; 4 duplicate keys reconciled, see literature_merge_report.md). Raw Crossref records are in verification/. Unverified or deliberately excluded candidates are listed in lit_unverified_A.md and lit_unverified_B.md (notably: no formal theory of financing contingencies beyond bian2018bargaining; no verified Québec or Canadian time-on-market study). Detailed thematic notes: lit_notes_A.md, lit_notes_B.md. Model-design implications are collected in §8.

# 1. Housing search theory: from vacancies to liquidity

The matching approach to housing starts with arnott1989housing (idiosyncratic tastes generate equilibrium vacancies) and wheaton1990vacancy (a mismatched owner searches while carrying a vacant unit; the Nash-bargained price depends on the vacancy rate through expected time to sell and the cost of holding two houses). yavas1992simple adds two-sided search intensity; williams1995pricing prices heterogeneous real assets as optimal-stopping values under Poisson buyer arrivals, giving the first explicit search-induced discount. krainer2001theory is the reference theory of residential liquidity: buyers draw match values, sellers set reservation prices anticipating the aggregate state, and time on market lengthens in downturns because waiting is rational; krainer2002equilibrium values an illiquid asset relative to a liquid benchmark as a function of arrival intensity. han2015microstructure organises the field (one-sided search, random matching, directed search, bargaining and auctions, brokerage). WP19 is a random-matching, Nash-bargaining model with a posted-price robustness check and inherits from this strand the two objects it formalises: the sale hazard and a discount against a frictionless benchmark.

The important distinction for WP19 is that the "liquidity shock" of krainer2001theory is a shock to the dividend (housing services), whereas WP19 studies shocks to matching efficiency and buyer qualification with the dividend distribution fixed. ngai2014hot is the closest precedent for a non-fundamental driver: thick-market effects on match quality turn small seasonal drivers into large price and volume swings. novymarx2009hot shows that feedback between the buyer–seller ratio and bargaining positions amplifies demand shocks; diaz2013house (random matching, bargaining, entry) and head2014search (search with construction and buyer entry, momentum from time-varying time to sell) reproduce the cyclical comovements; ngai2020decision, ngai2024ins, moen2021buying, gabrovski2019beveridge, caplin2011trading, guren2018house, anenberg2016information, leung2017flipping and piazzesi2020segmented complete the aggregate-dynamics branch. WP19 is stationary and local in scope: it asks what a fall in $A$ or $\phi$ does to the cross-section of hazards and prices and to the composition of transactions.

# 2. Seller urgency and heterogeneity

The nearest antecedent of WP19's central device is albrecht2007opportunistic: buyers and sellers switch from a "relaxed" to a "desperate" flow value at a Poisson rate, and the bargained price depends on the pair's states; the expected price conditional on time on market falls with duration while its variance is hump-shaped. Other treatments of urgency are deadlines (salant1991sale), the seller's discount rate (arnold1999search), the endogenous cost of holding two homes (anenberg2020endogenous), debt overhang that raises asking prices (head2023default), and an estimated motivation parameter (carrillo2012empirical). The empirical call for heterogeneous-seller theory is explicit in glower1998motivation: planned-move sellers sell faster and motivation lowers the sale price but not the list markup; springer1996motivation finds lower prices for eager, relocated, vacant and foreclosed sellers; harding2003bargainingeffects finds weaker bargaining power for vacant sellers; levitt2008agents provides the marginal value of waiting (about 3.7% for about 9.5 extra days). Equity and reference dependence work in the opposite direction: high-LTV and loss-facing sellers set higher asking prices and sell more slowly (genesove1997equity, genesove2001lossaversion), and patient sellers sort into FSBO platforms (hendel2009fsbo).

In all theoretical treatments urgency is a two-state process, a deadline, a debt position or a nuisance parameter. None models a continuous, permanent carrying-cost type whose cross-sectional distribution determines the stock of listings, the composition of transactions and, through free entry, market tightness. That is WP19's modelling choice. The evidence on constrained sellers implies that the carrying-cost distribution should admit very patient types (low $c$) and that the model's predictions for "locked" sellers are limited to the case $c\ge0$ (Limitations).

# 3. Forced sales and the size of liquidity discounts

campbell2011forced (foreclosure discount about 27% in Massachusetts, smaller discounts for death and bankruptcy sales, about 1% spillover per nearby foreclosure), clauretie2009foreclosure (naive discounts above 20% overstated by about one third once condition, endogenous marketing time and spatial dependence are controlled), penningtoncross2006reo, mayer1998auctions (price of immediacy 0–9% in a boom versus 9–21% in a bust) and andersen2017firesales (sudden-death forced sales: discounts rising with urgency, poor market conditions and seller constraints, with demand held fixed) establish the empirical range of the urgency discount and its state dependence. Spillovers (harding2009contagion, anenberg2014foreclosures, mian2015foreclosures) show that a larger mass of urgent sellers lowers prices for all sellers without a change in fundamentals, the empirical content of WP19's liquidity-shock proposition. What this literature does not provide is the decomposition the model delivers: how much of the discount is bargaining under high carrying cost and how much is selection of which houses transact.

# 4. Credit, qualification and the cash–mortgage gap

On the theory side, hedlund2016illiquidity, hedlund2016cyclical and garriga2020mortgage make search-based illiquidity a state variable interacting with long-term defaultable mortgages; guren2020foreclosures show how foreclosures freeze the non-distressed market; eerola2018borrowing find that a moderate credit tightening raises time on market and idiosyncratic price dispersion; gabrovski2021search open a channel from credit to liquidity with multiplicity; diaz2024housing has wealthier buyers paying to transact faster under competitive search; stein1995prices and ortalomagne2006housing are the frictionless-with-credit benchmarks. On the evidence side, qualification is elastic and delays are measurable (anenberg2019creditavailability, bhutta2021insurance, defusco2020leverage, fuster2019technology); allen2019searchfrictions is the only verified Canadian structural evidence (insured mortgages as a search market).

The cash–mortgage gap is the empirical object WP19's financing extension speaks to. reher2024mortgage estimate an 11% mortgage premium (1980–2017) against about 3% from a representative-seller model and find that heterogeneity in selling conditions closes half of the gap; han2024cash estimate a 2–3.9% cash discount with 29% faster closing and show, with a calibrated search model, that closing risk alone is insufficient — the risk that a relisted property fails to sell is needed, so the discount is smaller in booms and larger markets. asabere1992cash, jauregui2019fundingprice, aroul2023cashdiscount, lin2025contingencies and buchak2026ibuyers (about 5% immediacy spread) add magnitudes and selection caveats. The only formal bargaining theory with financing is bian2018bargaining. No verified paper decomposes the measured gap into a bargaining component (compensation for delay and failure risk, which depends on seller urgency) and a selection component (mortgage deals require a better match), with the buyer's outside option differing by financing type. That decomposition is WP19's Proposition 7.

# 5. Selection, indices and volume–price comovement

The measurement literature establishes that sold houses are not a random sample of the stock and that the bias co-moves with the cycle: jud1994selection, gatzlaff1997selection, gatzlaff1998selection, hwang2004selectivity, and above all goetzmann2006reservation, where heterogeneous reservation prices make falling volume bias index returns upward and rising volume bias them downward. In commercial real estate, fisher2003controlling, fisher2007tbi and clayton2008liquidity build constant-liquidity indices that lead transaction indices and are more volatile; lin2007illiquidity, bond2007marketing, cheng2010illiquidity, lin2008real and cheng2013liquidityrisk show that ignoring the uncertain marketing period biases returns upward and risk downward, and that risk is seller-specific. The classical index tools (bailey1963repeatsales, case1989efficiency, clapp1992assessed) assume random sampling. Bargaining and information confounders are documented by harding2003bargainingpower, kurlat2015asymmetries, garmaise2004asymmetries; volume leads prices in berkovec1996turnover, hort2000turnover, clayton2010pricevolume, andrew2003transactions, leamer2007businesscycle; dachis2012transfertax is the Canadian transfer-tax experiment.

The literature recognises the bias but no verified paper derives its sign from primitives in a search equilibrium. WP19's Proposition 6 does so and finds that the sign is not a general law: it depends on whether the elasticity of the sale hazard to the arrival rate rises or falls with urgency, which is governed by the product of the hazard function and the mean residual valuation of the match-value distribution. This nuance is new relative to goetzmann2006reservation and fisher2003controlling.

# 6. Duration dependence, censoring and withdrawals

zuehlke1987duration, haurin1988duration, jud1996brokerage, anglin2003tradeoff, knight2002listing, haurin2010listprices, huang2001withdrawal, benefield2015measurement, carrillo2012potatoes and anglin2006liquidity document the price–time tradeoff, positive duration dependence in parametric hazards without heterogeneity, and the sensitivity of results to withdrawals and relistings. taylor1999time (stigma) and anenberg2016information (learning) are competing explanations of duration effects. WP19's observed hazard is a mixture over urgency types with a competing withdrawal risk (Lemma 3), which predicts spurious negative duration dependence; the paper must state that positive dependence in the data requires list-price revisions, learning or stigma, which are outside the model.

# 7. Foundations and tools

Diamond–Mortensen–Pissarides architecture (diamond1982aggregate, mortensen1994job, pissarides2000equilibrium, mortensen1999new, rogerson2005search, petrongolo2001looking, shimer2005cyclical); efficiency (hosios1990efficiency, with the two-sided-entry caveat of gabrovski2025note); reservation values (lippman1976economics); log-concavity (bagnoli2005logconcave); bargaining (nash1950bargaining, rubinstein1982perfect); directed search (moen1997competitive, wright2021directed, albrecht2016directed); price dispersion (burdett1983equilibrium, maury2014search, sagi2021asset); OTC asset-market liquidity premia (duffie2005over, lagos2009liquidity, rocheteau2011liquidity), from which WP19 differs by the indivisibility and match-specificity of the housing unit; matching evidence (genesove2012search: contact-hazard elasticity 0.84 with respect to the buyer–seller ratio under CRS; carrillo2013heat, carrillo2015tightness, han2014biddingwars, han2016askingprice, merlo2004bargaining, merlo2015home, horowitz1992role, yavas1995strategic).

# 8. What is known, what is open, and the model-design implications

Known: urgency lowers reservation and transaction prices and shortens duration; liquidity is state dependent; credit tightening lengthens time on market and raises dispersion; cash buyers obtain discounts; transaction indices are selection-biased; tightness amplifies shocks. Open: (i) a stationary equilibrium with a continuous urgency distribution, free entry and an explicit frictionless benchmark; (ii) analytical conditions under which a lower arrival or qualification rate lengthens time on market (monotone hazard) and widens dispersion; (iii) the sign and size of the index selection bias from primitives; (iv) the decomposition of the cash–mortgage gap into bargaining, outside-option and selection terms; (v) the welfare role of bargaining power with heterogeneous sellers and one-sided entry.

Design implications adopted in model_specification.md: carrying cost $c$ is a continuous permanent type with a right-skewed distribution (most sellers patient, a minority urgent, as in the motivation and forced-sale evidence); an exogenous withdrawal hazard with a positive own-use value $w_0$ (withdrawals and relistings matter empirically); free entry of buyers pins the buyer value, which both isolates the seller-side comparative statics and generates tightness feedback; the baseline qualification screen is nested in a financing-contingency extension with a pending state, cash and mortgage buyers, so that $A$ and $\phi$ are observationally distinct only in the extension; the frictionless benchmark is defined as the Walrasian free-entry price and the urgency discount relative to the most patient seller is the primary liquidity-discount object, because the forced-sale literature measures exactly that comparison; match-value distributions include IFR cases (truncated normal, Weibull), the exponential boundary and a heavy-tailed Pareto case to display the conditions of Propositions 2 and 6; listing inflow is exogenous (one-sided entry) so that the Hosios benchmark applies in the homogeneous case and heterogeneity is the only wedge.

# 9. Novelty gate decision

Propositions 1 and the directional content of 2–4 restate known comparative statics in a new setting and are labelled as benchmarks in the manuscript, with albrecht2007opportunistic, krainer2001theory, lippman1976economics, eerola2018borrowing, ngai2014hot and novymarx2009hot credited as antecedents. The contributions that survive the audit are the joint treatment (continuous urgency × free entry × pending financing), the Pareto counterexample to monotone hazards with its exact condition, the index-selection proposition with its sign condition, the three-term decomposition of the cash–mortgage gap, and the numerical welfare analysis with heterogeneous sellers. The gate is passed with these labels; see novelty_matrix.csv.