Structural Change, Land Use and Urban Expansion

This paper asks how cities grow in the process of structural transformation — specifically, whether urban expansion occurs at the intensive margin (higher density within a fixed area) or the extensive margin (larger area). The authors document and explain a persistent decline in urban density in France since 1870, and develop a spatial general equilibrium model in which endogenous land use — land allocated either to agriculture or housing — is the key mechanism linking structural change to urban sprawl.

The central empirical fact is striking: between 1870 and 2015, the area of the 100 largest French cities increased by a factor of roughly 30, while their population grew by only a factor of about 4, implying that average urban density fell by a factor of roughly 8. This density decline was fastest over 1950–1975, coinciding with the acceleration of structural change (France’s rural exodus). Since the mid-nineteenth century, approximately 15% of French land has been reallocated away from agricultural use — more than the total artificially-used land in France today (about 9%).

The theoretical mechanism operates through the opportunity cost of urban expansion. Agricultural land at the urban fringe must earn its marginal product in the rural sector; this agricultural rent pins down the cost of converting land to urban use. When agricultural productivity is low, farmland is expensive relative to income (the “food problem”), households devote large shares of resources to food, and cities remain small in area and very dense. As agricultural productivity rises — the engine of structural change — workers leave rural areas, farmland values fall relative to income, and cities can expand cheaply at their fringes. Simultaneously, richer households spend more on housing. Both forces cause urban area to grow faster than urban population, generating a sustained decline in average density.

The model also predicts a “hockey-stick” path for housing prices: during structural change, the extensive margin expansion of cities limits the rise in urban land rents despite growing housing demand. Once the reallocation of workers and land out of agriculture slows, urban land values must adjust upward rapidly, producing the pattern documented by Knoll et al. (2017) — relatively flat housing prices until roughly the 1950s, then steep increases.

The model is a multi-city, multi-sector spatial equilibrium framework with non-homothetic CES preferences (including a subsistence requirement for the agricultural good), endogenous city fringes determined by land market clearing between agricultural and residential uses, and a monocentric commuting structure with endogenous commuting speed (workers adopt faster modes as wages rise). The model is calibrated to French historical data spanning 1840–2015, with 20 regions whose sectoral productivities are estimated to match regional urban populations and local farmland prices.

Quantitatively, the calibrated model accounts for approximately 70% of the increase in urban area since 1870, most of the decline in average urban density (the factor-of-8 fall), about half of the rise in real housing prices, and most of the reallocation of land values from agricultural to urban. Cross-sectional evidence confirms a core prediction: cities surrounded by more expensive farmland are denser, with an IV-estimated elasticity of urban density with respect to farmland prices of approximately 0.3 (a 10% increase in farmland prices raises urban density by about 3%), consistent with the model’s counterpart. Scope conditions include the focus on France as a single country case, reliance on a monocentric urban structure, and the abstraction from within-urban-sector reallocation (manufacturing to services).

Q: What is the central stylized fact motivating the paper? A: Between 1870 and 2015, the area of the 100 largest French cities increased by a factor of roughly 30, while their total population grew by a factor of about 4, so average urban density fell by a factor of roughly 8. This density decline was most rapid over 1950–1975, coinciding with France’s peak rural exodus, and has barely fallen since — tracking the slowdown of structural change. This pattern is not unique to France; Angel et al. (2010) document persistent urban density decline on a global scale.

Q: What is the paper’s key theoretical mechanism linking structural change to urban sprawl? A: The rental price of agricultural land at the urban fringe is the opportunity cost of expanding the city into surrounding farmland. When agricultural productivity is low, farmland is expensive relative to income, keeping cities small and dense. As productivity rises and workers migrate to cities, the value of agricultural land falls relative to income, reducing the cost of urban expansion at the fringe. Richer households also devote a larger share of spending to housing, reinforcing the demand for space. These two channels together cause city area to grow faster than city population, generating a sustained decline in average density — even without any improvement in commuting technology.

Q: How does the paper distinguish between the structural change channel and the commuting cost channel? A: The model contains both channels: structural change (falling agricultural land values at the fringe) and falling effective commuting costs (rising wages lead workers to adopt faster commuting modes, a wage elasticity of commuting speed calibrated from survey data). Counterfactuals show that without structural change (rural productivity growth set to 4% of baseline), the model cannot replicate the observed density decline. Without faster commutes (setting the income elasticity of commuting speed to unity), the model predicts only about 30% of the baseline density decline. Both channels are necessary; their combined effect exceeds the sum of parts because structural change raises wages, which in turn amplifies the commuting speed mechanism.

Q: How do the two channels differ in their spatial imprint within cities? A: Structural change adds new low-density settlements at the urban fringe, so suburban density falls more than average density — the center is relatively less affected. Faster commuting modes, by contrast, induce suburbanization: workers relocate from the center outward, so central density falls more than average density. For Paris, historical data show that central density fell less than average urban density, which is consistent with both mechanisms operating simultaneously — the commuting channel pushing central density down more, but the structural change channel adding fringe expansion that affects suburban density more.

Q: What is the empirical evidence on the cross-sectional farmland price prediction? A: Using data on local farmland transaction prices from the French Ministry of Agriculture at the “Petite Region Agricole” level (over 700 areas), the authors show that cities surrounded by more expensive farmland are denser. A binned scatter plot across 200 French cities shows that moving from the first to last decile of farmland prices raises density by about one third — an effect comparable in magnitude to an increase in population from roughly 25,000 (3rd decile) to 150,000 (9th decile). To address endogeneity (productive cities may inflate nearby farmland prices), the authors instrument farmland prices with soil quality characteristics; the IV elasticity of urban density with respect to farmland prices is approximately 0.3, consistent with the model’s predicted counterpart.

Q: What does the model predict about the time path of housing prices? A: The model predicts a “hockey-stick” pattern: housing prices remain relatively flat for decades while structural change is ongoing, because cities expand cheaply at the extensive margin, absorbing growing housing demand without large rent increases. Once the reallocation of workers and land out of agriculture slows, the extensive margin ceases to buffer demand, and urban land values must rise sharply. The calibrated model accounts for about half of the observed rise in real housing prices since the mid-nineteenth century; it matches the qualitative hockey-stick pattern documented by Knoll et al. (2017) and Piketty and Zucman (2014) for France and advanced economies more broadly.

Q: What happens to the relative values of agricultural versus urban land over the period? A: Agricultural land values relative to income fall dramatically: the average value of a French agricultural field per unit of land, as a share of per capita income, was divided by a factor of 15 between 1850 and 2015. Meanwhile, urban land values rise. In 1820, agricultural land accounted for more than 70% of total housing and land wealth in France; by 2010 this share had fallen to about 3%. This reallocation of land values from rural to urban is a central prediction the model accounts for, driven by structural change reducing the scarcity premium on farmland.

Q: How is the model parameterized and calibrated? A: Preferences are non-homothetic CES with housing preference parameter gamma = 0.22, subsistence consumption for the rural good calibrated to match the 1840 agricultural employment share (about 60%), and substitution elasticity between urban and rural goods sigma = 0.8. The labor share in agriculture is alpha = 0.6. Commuting cost parameters (elasticities to wages and distance) are estimated from the French Labor Force Survey (Enquete Emploi). Region-specific sectoral productivity parameters for 20 regions (40 parameters total) are estimated to match the cross-section of urban populations and local farmland values in the base year 1870. The model is then simulated forward to 2015.

Q: What share of French land has been reallocated away from agriculture, and how does this relate to urban expansion? A: About two-thirds of French land was used for agriculture in 1840; by 2015 this fell to 52%, implying roughly 15 percentage points of French territory reallocated away from agricultural use. This 15% exceeds the total land currently under artificial use in France (about 9%). Over the more precisely measured period 1982–2015, artificialized soil increased by about 2 million hectares (3.7% of French territory), representing roughly 70% of the land converted away from agriculture over the same period. Two-thirds of land surrounding French cities is agricultural, confirming that urban expansion occurs at the expense of farmland.

Q: What are the limitations and directions for future research acknowledged by the authors? A: The model relies on a monocentric urban structure where all workers commute to a single city center, which is an approximation — commuting distance increases with residential distance to the center but less than one-for-one, suggesting workers sort into nearby jobs. The model also abstracts from within-urban-sector reallocation (the manufacturing-to-services transition), which the authors conjecture matters for the cross-section of cities in recent times. Finally, the model cannot fully replicate the steep recent rise in housing prices, which the authors attribute partly to land-use regulations constraining extensive margin growth — a policy counterfactual the general equilibrium structure is well-suited to analyze.

Q: How does the paper relate to the Ricardo/Nichols view that land values should rise with economic development? A: The traditional Ricardian view predicts that a fixed factor like land must rise in value with economic development — counterfactual given the historical data showing farmland values falling sharply relative to income. The authors reconcile this with the data by emphasizing that structural change and agricultural productivity growth reduce the scarcity of farmland even as total income grows, so farmland values fall. Urban land values do rise, but the structural change channel initially dampens this increase by facilitating extensive-margin city growth. The paper thus reconciles the Ricardian fixed-factor view with the commuting technology view (Miles and Sefton, 2020) within a unified spatial structural change framework.

Endogenous land use: In this paper’s framework, land in each region is allocated either to agricultural production or to residential use, with the margin between the two determined in equilibrium by the equality of the rental price of land at the urban fringe and the marginal product of land in the rural sector. This makes the urban-rural land boundary an endogenous object that responds to structural change.

Urban fringe (phi_k): The furthest residential location of an urban worker in city k, determined endogenously as the commuting distance at which the opportunity cost of further expansion (the agricultural land rent) equals the willingness of urban workers to pay for land. All workers beyond this fringe produce rural goods without commuting.

Structural change (in the paper’s sense): The reallocation of workers and land away from agriculture driven jointly by non-homothetic preferences with a subsistence consumption requirement for the agricultural good (demand side) and rising sectoral productivity (supply side). Structural change is the primary driver of falling farmland values and urban sprawl in the model.

Non-homothetic CES preferences: Household preferences over rural and urban goods that are not homogeneous of degree one in income, specified as a CES aggregate with a subsistence floor for the rural (agricultural) good. At low income levels, households devote large budget shares to food; as income rises, spending shifts toward urban goods and housing. This demand-side non-homotheticity is the channel through which rising income generates structural change.

Food problem (Schultz, 1953): The condition in which low agricultural productivity forces households to devote a large fraction of resources to meeting subsistence food needs, leaving little for housing expenditure. In the paper’s model, the food problem makes cities initially small and very dense; as agricultural productivity rises and the food problem relaxes, cities can expand in area.

Commuting cost function tau(l_k): Spatial frictions proportional to the worker’s distance from the city center and the urban wage, of the functional form tau(l_k) = a * w_{u,k}^{xi_w} * l_k^{xi_l}, where xi_w in (0,1) captures the endogenous adoption of faster commuting modes as wages rise. Concavity in both arguments is micro-founded by an optimizing commuting mode choice model, ensuring that the share of resources devoted to commuting falls as incomes rise.

Hockey-stick housing price path: The model’s prediction that real housing prices remain relatively flat over the period of active structural change — because city expansion at the extensive margin absorbs rising housing demand without large rent increases — before rising steeply once structural change slows and the extensive margin is exhausted. This prediction matches the empirical pattern documented by Knoll et al. (2017) for France and other advanced economies.