Paciorek (2013) showed that regulation- and geography-driven supply constraints amplify house-price volatility across U.S. metropolitan areas: simulations of a dynamic structural model holding demand shocks identical across cities reproduce roughly 45 percent of the San Francisco-Atlanta volatility gap. Yet the paper itself acknowledges that the model 'does a very poor job' of replicating the absolute level of price volatility (house-price volatility far exceeds rent volatility), that regulation is observed once (2005) and treated as exogenous and time-invariant, that persistent parcel-level heterogeneity is omitted because estimation with it is intractable, that the option-value-of-delay channel cannot be separated from cost effects, and that the benefits of regulation needed for a net welfare assessment are unquantified. This problem asks for the completion of that program: a structural account of housing market dynamics that simultaneously matches the cross-city dispersion and the absolute levels of observed house-price volatility with explicitly identified additional mechanisms, treats regulation as time-varying and endogenous, quantifies parcel-level heterogeneity and option values as independent channels, and supports a net, distribution-aware welfare evaluation of housing supply regulation. Each of these components has been advanced by later work in isolation, but no study delivers them jointly, so the integrated question remains open.

Background

House prices in the United States fluctuate far more in some metropolitan statistical areas (MSAs — city-plus-suburb labor-market regions, the standard unit for U.S. housing-market data) than in others: over 1984-2008 the standard deviation of detrended log house prices was roughly 0.16 in San Francisco versus 0.08 in Atlanta. A leading explanation is constraints on housing supply, summarized across cities by two measures: the Wharton Residential Land Use Regulatory Index (WRLURI), a survey-based summary of the stringency of local land-use regulation built by Gyourko, Saiz and Summers (2008), and the geographic land-availability measure of Saiz (2010), computed from satellite terrain data (steep slopes and water bodies reduce the buildable land around a city). Paciorek (2013) documents the strong raw relationship between regulation and price volatility and then builds a dynamic structural model of housing investment — that is, a model estimated equation-by-equation from an explicit optimization problem rather than a reduced-form regression — to examine the mechanism. Owners of undeveloped land choose when to convert parcels into houses; construction takes LL periods, where the lag LL is longer in more regulated cities; landowners hold rational expectations (their subjective forecasts equal the true conditional expectations of future prices); regulation raises marginal costs and lengthens permitting lags, and geographic constraints lower average investment relative to the existing housing stock. Estimating the model's supply parameters across MSAs, Paciorek finds that both channels reduce the elasticity of housing supply (the percentage change in new construction per percent change in price) and that simulations holding demand shocks identical across cities reproduce about 45 percent of the San Francisco-Atlanta volatility gap, establishing supply constraints as quantitatively important amplifiers of demand shocks. Related earlier work (Glaeser, Gyourko and Saiz 2008) had shown that inelastic supply accentuates price bubbles. The model nevertheless falls short in specific, author-acknowledged ways that jointly define what remains open. First, it underpredicts the average level of price volatility across cities — the model explains relative differences between cities, not absolute magnitudes — and it inherits an excess-volatility puzzle analogous to the classic equity-market finding that prices move more than the fundamentals they discount: house prices are substantially more volatile than rents, which the standard user-cost relation (the identity tying a house's purchase price to the expected discounted stream of its housing services, with an interest rate, depreciation and a risk premium) makes hard to reconcile, since transitorily high prices should induce construction that lowers future rents. Second, regulation is observed in a single cross-section (the 2005 Wharton survey), so the model must treat it as exogenous and time-invariant, precluding analysis of how regulation evolves and responds to local market conditions. Third, parcels differ persistently in their construction costs (cities build first on flat, desirable land), but the metropolitan-level model admits only transient parcel shocks, because combining individual-level shocks with persistent individual heterogeneity makes estimation intractable with available data. Fourth, although the timing decision embodies the option value of waiting to build (the value of keeping the choice to develop later rather than committing now, a 'real option'), the model cannot separate this timing channel from marginal-cost effects. Finally, the paper quantifies only the costs of regulation; without measuring benefits (for example, protection from neighboring land uses, the traditional justification for zoning), no net welfare evaluation — including distributional effects that operate through volatility itself, which harms both current owners cashing out and first-time buyers — is possible. How the purchase price of housing can respond much more to supply constraints than the price of housing services was later formalized by Molloy, Nathanson and Paciorek (2022), sharpening why the volatility-level and welfare questions remain intertwined.

Problem Statement

Complete the quantitative account of U.S. housing market dynamics that Paciorek (2013) left unfinished, under one overarching objective: determine the extent to which regulation- and geography-driven supply constraints — together with explicitly identified additional mechanisms — generate observed house-price volatility, and what the net welfare consequences of housing supply regulation are. This objective comprises four jointly supporting components: (1) a structural housing-market model that matches the data on both margins simultaneously — the cross-city dispersion of volatility (e.g., the roughly twofold San Francisco-Atlanta gap, observed 1984-2008 standard deviations of detrended log house prices of roughly 0.16 in San Francisco versus 0.08 in Atlanta) and its absolute level, i.e. the level and not merely the cross-city ratio, matched to within the estimation uncertainty of those observed statistics — with a decomposition attributing the level gap that a rational-expectations supply-constraint model underpredicts to named, quantified mechanisms (such as time-varying risk premia, higher-variance or spatially heterogeneous demand shocks, belief heterogeneity, or supply-side speculation — developers buying and holding undeveloped land in expectation of future price gains — or others), where the decomposition must quantify the share of the gap it explains but need not close it exactly, and must confront the related fact that house-price volatility exceeds rent volatility; (2) treatment of regulation as time-varying and potentially endogenous to local housing-market conditions, replacing the single 2005 cross-section, with an assessment of how this changes the estimated supply channel; (3) quantification of persistent parcel-level heterogeneity and the option value of delaying construction as independent channels, separated from marginal-cost effects; and (4) a net welfare evaluation of housing supply regulation that quantifies benefits (e.g., amenity and environmental protections) alongside the established costs, including distributional consequences operating through volatility as well as through price levels. The components are jointly required: (1) is the scientific core; (2) and (3) are the measurement and modeling ingredients without which the attribution in (1) is confounded by an exogenous, time-invariant, aggregated treatment of the supply side; and (4) is the welfare conclusion the whole program exists to answer.

References

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