Post on 16-Aug-2021
Modeling the Causes of Urban Expansion
Stephen SheppardWilliams College
Presentation for Lincoln Institute of Land Policy, February 16, 2006
Presentations and papers available at http://www.williams.edu/Economics/UrbanGrowth/HomePage.htm
Urban ExpansionUrban expansion taking place world wide• Rich
• Evolving from transportation choices - “car culture”• Failure of planning system?
• Poor• Rural to urban migration• Urban bias?
Policy challenges• Environmental impact from transportation• Preservation of open space• Pressure for housing and infrastructure provision
Policy response• Land use planning• Public transport subsidies & private transport taxes• Rural development
Surprisingly few global studies of this global phenomenonLimited data availability
Data
3.0%12019.6%415,605,6243,9432,120,319,475Total
4.3%819.9%18,360,01218792,142,320Western Asia
3.6%1211.5%16,733,386335145,840,985Sub-Saharan Africa
4.6%1233.1%36,507,583260110,279,412Southeast Asia
2.5%1621.3%70,900,333641332,207,361South & Central Asia
3.0%1621.2%77,841,364534367,040,756Other Developed Countries
6.4%841.9%22,517,63612553,744,935Northern Africa
2.9%1624.4%70,402,342547288,937,443Latin America & the Caribbean
2.1%1614.1%45,147,989764319,222,933Europe
2.9%1613.9%57,194,979550410,903,331East Asia & the Pacific
%N%Populationin 2000in 2000Region
Sample CitiesSample PopulationCitiesUrban Pop.
To address the lack of data, we construct a sample of urban areasThe sample is representative of the global urban population in cities with population over 100,000Random sub-sample of UN Habitat sampleStratified by region, city size and income level
Data – a global sample of cities
< $3,000 $3,000 - $5,200 $5,200 - $17,000 > $17,000
100,000 to 528,000528,000 to 1,490,0001,490,000 and 4,180,000> 4,180,001
East Asia & the Pacific Europe Latin America & the Caribbean Northern Africa Other Developed Countries South & Central Asia Southeast Asia Sub-Saharan Africa Western Asia
Classcapita GNP)
Income (annual per
Size ClassPopulationRegions
Remote Sensing
0
10
20
30
40
50
60
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Wavelength (micrometers)
% R
efle
ctan
ce
Agricultural Soil Bare Soil Aged ConcreteFresh Concrete Water GrassDry Vegetation Sand Asphalt
Satellite (Landsat TM) data measure – for pixels that are 28.5 meters on each side – reflectance in different frequency bands
The relative brightness in different portions of the spectrum identify different types of ground cover.
Measuring Urban Land Use
EarthSat Geocover Our Analysis
1986
2000
Contrasting Approaches:
1. Open space within the urban area
2. Development at the urban periphery
3. Fragmented nature of development
4. Roadways in “rural” areas
Change in urban land use
Display in Google Earth
Google Earth Ground View
Change in urban land use: Jaipur, India
Google Earth view of Jaipur
Households:• L households • Income y• Preferences v(c,q)
• composite good c• housing q.
• Household located at x pays annual transportation costs In equilibrium, household optimization implies:
for all locations xHousing q for consumption is produced by a housing production sector
Modeling urban land use
( )( )max ,q
v y t x q p x q u− ⋅ − ⋅ =
Households:• L households • Income y• Preferences v(c,q)
• composite good c• housing q.
• Household located at x pays annual transportation costs In equilibrium, household optimization implies:
for all locations xHousing q for consumption is produced by a housing production sector
( )( )max ,q
v y t x q p x q u− ⋅ − ⋅ =
Modeling urban land useHousing producers• Production function H(N, l) to produce square meters of housing
• N = capital input, l=land input
• Constant returns to scale and free entry determines an equilibrium land rent function r(x) and a capital-land ratio (building density) S(x)
• Land value and building density decline with distance • Combining the S(x) with housing demand q(x) provides a solution
for the population density D(x,t,y,u) as a function of distance t and utility level u
The extent of urban land use is determined by the condition:
( ) ( )0r x S x
andx x
∂ ∂<
∂ ∂
( ) Ar x r=
Modeling urban land useEquilibrium requires:
The model provides a solution for the extent of urban land use as a function of
Generalize the model to include an export sector and obtain comparative statics with respect to:• MP of land in goods production• World price of the export good
( )0
2 , , ,x
x D x t y u dx Lπ θ⋅ ⋅ ⋅ =∫
Land made available for housingTransport costsMP of land in housing productionIncomeAgricultural land valuesPopulation
Hypotheses
An increase in the world price of the export good will increase urban extent and urban expansion.8.
An increase in marginal productivity of land in production of the export good will increase urban extent and urban expansion.7.
An increase in the share of land available for housing development will increase urban extent and urban expansion. 6.
An increase in the marginal productivity of land in housing production will cause urban expansion. 5.
An increase in the opportunity cost of non-urban land will reduce urban extent and limit urban expansion.4.
An increase in transportation costs will reduce urban extent and limit urban expansion.3.
An increase in household income will increase urban extent and urban expansion.2.
An increase in population will increase urban extent and urban expansion.1.
DescriptionResult
0xL∂
>∂
0xy∂
>∂
0xt
∂<
∂
0xw∂
>∂
0l
xf∂
>∂
0xθ∂
>∂
0l
xH∂
>∂
0A
xr∂
<∂
Model estimationWe consider three classes of empirical models• Linear models of urban land cover
• “Models 1-3”• Linear models of the change in urban land cover
• “Models 4-6”• Log-linear models of urban land cover
• “Models 7-11”
Each approach has different relative merits• Linear models – simplicity and sample size• Change in urban land use – endogeneity• Log linear – interaction and capture of non-linear impact
Linear model variables
0.0681740.0008340.0105420.011168Sampling Weight100.1305150.017234Mediterranean Cold Climate100.0714990.005109Mediterranean Warm Climate100.2679790.077395Temperate Humid Climate100.4510220.281518Ground Water (1=shallow aquifer)
558.50.39191.4476144.7495Cars per 1000 persons1.560.020.3286730.581498Cost of fuel ($/liter)
19,442.168.83723,140.5961,641.608Agricultural Rent ($/Hectare)72.784.1614.5528925.34515Maximum Slope (percent)
6590117.671688.78808Air Linkages0.5936723.50E-060.1936960.085741National share of IP addresses32,636.5562.9829,916.3179,550.217Per Capita GDP (PPP 1995 $)
1.70E+07105,4684,179,0503,287,357Total Population2328.878.91769533.7343400.6871Urban Land Use (km2)
MaxMinσMeanVariable
Linear model estimatesModel 3Model 2Model 1Variable
BiomeBiomeBiomeFixed Effects82.310385.389983.5832Shallow Ground Water
-0.4750Cars/100064.0541Fuel Cost
-0.0190-0.0207-0.0182Agricultural Rent
-0.8658-0.3551-0.7247Maximum Slope
0.40400.36330.3207Air Link639.3068606.6442529.3747IP Share
0.02600.03550.0295Income0.0000730.0000750.000077Population
Models of change in urban land
0.0681740.0008340.0105730.011168Sampling Weight
489.20.39182.7599130.7622Cars per 1000 in 1990
1.180.020.2479240.436883Fuel Cost in 1990
19442.184.90033396.4541589.797Agricultural Rent in 1990
70.634.1614.330925.03812Maximum Slope in 1990
6590124.180188.03663Air Links in 1990
6722.88-4552.332156.8121566.28Change in Per Capita GDP
5.40E+06-4705861474634751827.3Change in Total Population
527.368-322.559163.3169125.8202Change in Built-Up Area
MaxMinσMeanVariable
Change in urban land model estimates
20.837810.636424.2468Constant
74.15474.03573.515Root MSE0.81540.8160.8207R-squared
909088Number of observationsBiomeBiomeBiomeFixed Effects
36.559135.802536.0570Shallow Ground Water-0.0199T1 Cars/1,000
21.0234T1 Fuel Cost-0.0011T1 Agricultural Rent
-1.2267-1.1688-1.2954T1 Maximum Slope0.13010.11540.1383T1 Airlink
270.6102279.7229237.1614IP Share0.0201290.018130.02169Income Change0.0000840.0000850.000083Population Change
Model 6Model 5Model 4
Log-linear models
0.0681740.0008340.0105420.011168Sampling Weight
6.32525-0.9416092.16093.399618Ln(Cars Per 1,000)
0.444686-3.912020.640135-0.71369Ln(Fuel Cost)
9.87524.231740.9805556.757474Ln(Agricultural Rent)
4.287441.425520.5955723.065746Ln(Maximum Slope)
6.4922402.213412.923513Ln(Air Links+1)
-0.52143-12.55923.012159-5.249607Ln(Share IP Addresses)
10.39326.333251.0997588.596582Ln(Per Capita GDP)
16.668211.56621.24390114.26064Ln(Total Population)
7.753142.188041.3024095.217764Ln(Urban Area)
MaxMinσMeanVariable
Log-linear modelsModel 11Model 10Model 9Model 8Model 7
BiomeBiomeBiomeBiomeBiomeFixed Effects
0.21630.26000.21830.27290.2920Shallow Ground Water0.26710.2907Cars/1000
0.06800.1670Fuel Cost
-0.2165-0.2693-0.2069-0.2578-0.2323Agricultural Rent
-0.1074-0.0519-0.1127-0.0492-0.0568Maximum Slope
0.04310.07900.03850.07540.0880Air Links
-0.0220-0.0219-0.0261-0.0364IP Share
0.09310.55520.07070.61660.5674Income
0.79190.74530.80400.76670.7412Population
Note: all variables except Ground Water enter as natural log
Hypotheses tested
8.
Confirmed – increased accessibility to global markets increases urban land use in all models – doubling the share of global IP addresses increases urban land use in linear and differenced models– increasing the number of direct international flights increases urban land use in all models
7.
Confirmed – less steeply sloped land increases the share of urban land available for development and increases urban land use6.
Confirmed – less steeply sloped land and easy access to well water increases urban land use in all models5.
Strongly confirmed – doubling the value added per hectare in agriculture decreases urban land use by 20 to 26 percent 4.
Unclear – increasing fuel cost associated with increased urban land use; doubling cars per capita increases urban land use by about 26 to 29 percent in log-linear model, but decreases urban expansion in linear model – colinearity and endogeneity?
3.
Confirmed – doubling national income increases urban land use by 55 to 60 percent –further investigation warranted on income and transport mode2.
Strongly confirmed – doubling population increases urban land cover by 74 to 80 percent.1.
Result of TestExpected
0xL∂
>∂
0xy∂
>∂
0xt
∂<
∂
0xw∂
>∂
0l
xf∂
>∂
0xθ∂
>∂
0l
xH∂
>∂
0A
xr∂
<∂
Policy ImplicationsPolicies designed to limit urban expansion tend to focus on a few variables• Transportation costs and modal choice
• Combat “car culture”• Provide mass transit alternatives• Limit road building
• Rural to urban migration and population growth• Enhance economic opportunity in rural areas• Residence permits for cities
Considerable urban expansion occurs naturally as a result of economic growthLimiting migration could be effective but ...• Economic misallocation costs• Problems where free mobility considered an important right
Land use planning policies?Land taxation?
Need for improved dataTo improve model estimates tests we require more dataField researchers• Local planning data• Local taxation data• House prices and land values• Transport congestion and fuel prices
Income data at local level• Big problem – explore alternative data sources
Conclusions and future directionsContinuing progress• Field research to collect data on planning
policies, taxes, housing conditions and prices• Evaluation of classification accuracy• Separate modeling of infill versus peripheral
expansion• Modeling at micro-scale –
• transition from non-urban to urban state• Interaction with nearby local development
Conclusions and future directionsIssues to address going forward• Endogeneity issues
• Income• Transport costs• Links to global economy
• Effect of planning and tax policies• Impact on housing conditions and affordability• Availability of housing finance• Evaluation of impacts of urban expansion
With global data we are developing a deeper understanding of the urban expansion that affects virtually every local area