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