The dispersion of house prices across U.S. metropolitan areas roughly tripled between 1975 and 2007. Van Nieuwerburgh and Weill (2010) showed that a calibrated spatial equilibrium model driven by the observed rise in cross-city wage dispersion reproduces this increase, but the model overpredicts the growth of rent dispersion roughly tenfold (its CV of rents rises to 0.515 against a measured rise from only 0.153 to 0.190), explains only one-third of the rise in the average house price level, and rests on simplifications - quasi-linear utility, frictionless mobility, uniform construction costs - that create further documented tensions; the authors themselves call for a model with an explicit choice between renting and owning and segmented markets that can be confronted with price and rent data simultaneously. Later work supplies the components - spatial interest-rate capitalization (Amaral et al. 2024), rent-income quantification and a rents-prices model (Howard and Liebersohn 2021, 2023), tenure-choice spatial equilibrium (Parkhomenko 2026), rational bubbles (Tang, Zeng, and Zhu 2020), frictional migration (Nenov 2015), endogenous regulation (Parkhomenko 2023), and improved price-rent measurement (Miles 2026) - but no published model is documented to match the cross-city dispersion of house prices and rents jointly in the segmented-markets framework the source proposes. The problem is open: build and calibrate such a unified quantitative account.

Background

Between 1975 and 2007 the dispersion of house prices across U.S. metropolitan areas rose dramatically: the population-weighted coefficient of variation (CV, the standard deviation divided by the mean, a scale-free measure of dispersion) of real, de-trended house prices rose from 0.154 to 0.536, while the dispersion of real wages per job rose far less. Van Nieuwerburgh and Weill (2010) asked whether the second fact could explain the first, in the spatial-equilibrium tradition of urban economics in which households and firms locate across cities until utility and profits are equalized, so that wages and housing costs compensate for differences in local productivity and amenities. They built a dynamic general-equilibrium island model - each metropolitan area is an island hit by persistent local productivity shocks, and households with heterogeneous earnings ability migrate in response to wage differences - with two key frictions: housing supply cannot adjust instantly because of regulatory constraints on building, and houses must be held by households. In equilibrium, house prices compensate for cross-sectional productivity differences: as productivity dispersion widens, workers want to move to high-wage cities, bidding up house prices there. Calibrating the productivity process so that the model matches the observed 30-year increase in cross-city wage dispersion (an 8.8-point increase in the population-weighted CV of wages), the model reproduces the increase in house price dispersion (the model CV rising from 0.022 in the initial steady state to 0.532 on the transition, against 0.154 to 0.536 in the data) and the increasing cross-sectional sensitivity of house prices to wages. A central finding is that tightening housing supply regulation alone has small price effects, because households move out of newly restricted areas; rising wage dispersion is the essential driver.

The model nevertheless fails in ways the authors themselves enumerate as unfinished business. First, and most quantitatively severe: the model prices houses as the present discounted value of rents (the rent being the per-period user cost, or implicit rental price, of housing services), so the same forces that raise price dispersion should raise rent dispersion - and in the model they do, far too much. The model's CV of rents rises to 0.515, while in the rent data the CV rose only from 0.153 to 0.190. The authors conclude that measured rents are probably not the relevant cash flows for owner-occupied housing, that the ownership and rental markets are segmented (they serve different housing types and populations), and that a model with an explicit choice between renting and owning is needed - one that could confront price and rent data simultaneously rather than explaining one market by construction of the other. Second, the model accounts for only about one-third of the observed increase in the average house price level (11 percent in the model against 33 percent in the data), leaving falling interest rates, demographics, and expectations of future price growth as candidate explanations outside the framework. Third, several auxiliary tensions: calibrating the model to match the 1975 level of price dispersion instead worsens the initial sensitivity of prices to wages; the calibrated productivity process implies a counterfactual initial drop in the fraction of jobs in the highest wage quintile and low rank correlation of wages across the transition; construction costs are assumed equal across regions (Davis and Palumbo (2008) show this is a reasonable approximation, but regional variation may interact with regulation in important ways); and households are assumed fully mobile with no moving costs or search frictions, which may overstate the equilibrating response of migration to shocks. Finally, utility is quasi-linear - linear in consumption, so that the marginal utility of consumption is equalized across cities, equivalent to full insurance against local risk - which rules out risk aversion and asset-pricing premia; the paper sketches but does not solve the general concave-utility case, and points to spatial asset pricing (Ortalo-Magné and Prat (2016)) as the natural extension.

Adjacent results frame why these gaps matter. Gyourko, Mayer, and Sinai (2013) document that long-run differences in house price appreciation across metropolitan areas can be driven by an inelastic supply of land in unique locations combined with growth in the number of high-income households nationally - an aggregate-demand mechanism rather than rising local productivity. Määttänen and Terviö (2014) show in an assignment framework (matching heterogeneous households to a fixed hierarchy of houses by willingness to pay) that changes in the income distribution can move house prices. Hsieh and Moretti (2019) quantify the aggregate output cost of housing supply constraints in a static spatial equilibrium across 220 U.S. metropolitan areas. None of these confronts prices and rents jointly, and each abstracts from at least one margin that the Van Nieuwerburgh-Weill benchmark quantifies.

Problem Statement

Construct and quantitatively evaluate a spatial equilibrium model of the U.S. housing market with segmented rental and ownership markets and an explicit choice between renting and owning - the extension Van Nieuwerburgh and Weill (2010, Section 4.7) explicitly propose as beyond the scope of their paper - that can confront price and rent data simultaneously and thereby account for the measured cross-city distributions of both. The common objective is a single calibrated framework in which the forces behind the joint price-rent distribution are identified and quantified; the core requirements, which trace to the source's own framing, are the following.

(1) An explicit choice between renting and owning, with segmented rental and ownership markets, so that measured rents are not forced to be the cash flows that price owner-occupied houses - resolving the benchmark's central quantitative failure, in which a model that matches the rise of house price dispersion (from 0.154 to 0.536 in the data) simultaneously implies a rise in rent dispersion to 0.515 against only 0.153 to 0.190 in the rent data.

(2) Preferences and pricing beyond the quasi-linear benchmark - general concave (risk-averse) utility and spatial asset-pricing features of the kind the source sketches - insofar as they are needed to fit the joint distribution.

Beyond this core objective, the benchmark documents limitations that a completing model should engage with as context rather than as mandated joint completion requirements:

(3) The benchmark accounts for only about one-third of the observed increase in the average house price level (11 percent in the model against 33 percent in the data), leaving falling interest rates, demographics, and expectations of future price growth as candidate explanations outside the framework; a completing model may quantify their contributions insofar as they bear on the joint price-rent fit.

(4) The benchmark's auxiliary tensions are documented limitations to be engaged with insofar as they bear on the central moments: the trade-off between matching the initial (1975) price dispersion and the initial sensitivity of prices to wages; a productivity process whose implied wage rank correlations and wage-quintile dynamics match the data rather than the counterfactual initial drop in the top wage quintile; regional variation in construction costs and its interaction with regulation; and impediments to labor mobility such as moving costs or search frictions.

The calibrated model's simulated cross-sectional moments - the population-weighted CVs of house prices and of rents - should reproduce the measured increase in house price dispersion (CV 0.154 to 0.536) under comparable measurement conventions (real, de-trended series; population weighting; the same metropolitan sample), without implying the far larger increase in rent dispersion the benchmark generates (model CV 0.515 against 0.153 to 0.190 in the data).

References

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