Development and Application of a Land Use Model for Santiago de Chile

Development and Application of a Land Use Model for Santiago de Chile

Universidad de Chile

Francisco MartínezFrancisco MartínezUniversidad de ChileUniversidad de Chile

www.citilabs.comwww.citilabs.comwww.mussa.clwww.mussa.cl

ASSESS URBAN POLICIESASSESS URBAN POLICIES

• Evaluation of Zone Regulation Plans– Max or min lot sizes– Building density – Land use banned (residential, indust.,

commercial)

– Max height of buildings

• Incentives: subsidies or taxes

• Sensitive to transport policies

• Optimal regulation plans

Introduction

APPLICATIONSAPPLICATIONS

• Equilibrium predictions– Create scenarios for transport studies– Evaluation of mega projects (Transatiago

BRT, Cerillos Airport, Central Ring)

• Optimal Location (subsidies)– Land use under externalities– Schools: minimum transport cost – Emissions: minimum emission and

tradable CO2 permits

Introduction

Model structure

Model inputs

• Growth: N° households and firms (Hh)

• Transport (acchi, atti)

• Regulations on supply and land use• Incentives or taxes for allocation of residential

and commercial activities

The Equilibrium Model

The model problem

Predict location, rents and supply with:

• Land Market: auction

• Agents (households and firms h ): rational, diverse tastes, competing for land, externalities.

• Space (zones i ): heterogeneous attributes, limited space and regulated.

• Real State Industry (v) variety of options, maximize profit

The Equilibrium Model

• Land use (Svi, qhvi)• Allocation (Hhvi)• Rents (rvi) • Consumers and producers

surpluses

Results and notation

The Equilibrium Model

Auction

LocationRents

Auction

LocationRents

Equilibrium: all find a locationEquilibrium: all find a location

SupplyLand lots

Real estate

SupplyLand lots

Real estate

Willingness to pay

Households and firms

Willingness to pay

Households and firms

RegulationsRegulations

Incentives

Subsidies

Taxes

Incentives

Subsidies

Taxes

(3) b(3) b

(1) externalities(1) externalities

Population

HH & firms

Population

HH & firms

Current land use

Transport

Current land use

Transport

The Equilibrium Model

(2) economies of scale(2) economies of scale

Demand and Supply models

Mathematic Formulation

The Bid function

( , , )v hi iD acc att

( , ) ( , )vihvi h h hvi hvi i hvi v i hviB I b F X Z Sub B D Z

Subsidy or Tax:

To consumer type h for locationg at dewlling

type v in zone i

Consumer’s

utility level

Attributes

Dwelling

Accesibility,

Attractivenes.

Zonal (externalities)

Supply specific bid

Mathematic Formulation

hh

h

Ub

Consumer’s

income

Externalities

( , )i i i iZ Z S H h H v V

Location Externalities

Attribute defined by allocation of consumers

and supply in zone i

Endogenous Attributes

Example: h hvih HH v V

ihvi

h HH v V

I HI

H

Average income of residents

Mathematic Formulation

/( , ) ,hvi h i iB B S P h H v V

Bids depend on endogenous variables: land use and built environment

Allocation by auctions

//

/

exp( ( ))

exp( ( ) )

hvi vi hvi

h hvi hvi ih vi

g gvi gvi ig H

H S P

H B PP

H B P

Constraints

Income budget.Location bid:

Deterministic term

),,( SPbPP Auction fixed-pointAdjusts externalities

(1)

Hh: Number of agents in cluster h

Mathematic Formulation

Theoretical obs.Theoretical obs.: !max bidder implies max utility¡

Auction probability

Cut-off factors

K

k

Unki

Lnkini

1

11

11

n i

hi

n ii n

if C Z

if C Zexp Z C

Mathematic Formulation

0

0.2

0.4

0.6

0.8

1

1.2

Serie1

Serie2

nkbnka

kiZ

Lnki

Unki

Composite cut-off

0 1( , )

Real estate rents

1ln exp( ) ( , )vi g gvi gvi vi v i

g H

r H B G D Z

Real estate rents: depends on amenities/externalities and utility level

Expected max bid for real estate v located at zone i

vi h H hvir E(max B )

),,( SPbrr

Mathematic Formulation

(2)

Real estate supply

.

' ' ' ' . ' ' ' ' '' '

exp ( ( ) ( ))

exp ( ( ) ( ))vi vi i vi v vi

vi viv i v i i v i v v i

v i

r S s C SS HP H

r S s C S

Supply:

Total Nr of real estate units Regulations

Rents

Subsidies or taxes

SCrmaxargHS tvvivivi ,,

ProductionCost with

scale/scope economies

),,( SPbSS Supply MNL fixed-point

Mathematic Formulation

(3)

Equilibrium Condition: every agents is allocated

vi

hvihvi hHbPS )(/

Supply:

Nr of real estate type v available in zona i

Allocation probability:

Probability that consumidor type h is best bidder on real

estate type v in zone i

Nr agents type h to be allocated

),,( SPbbb Equilibrium logsum fixed-pointAdjusts utility levels

Mathematic Formulation

(1)

(2)

(3)

Resume of equilibrium equations

Allocation w/ externalities...Allocation w/ externalities...

Supply w/ econ. scale...................Supply w/ econ. scale...................

Equilibrium ...............................Equilibrium ...............................

),,,,( SPbSS

),,,,( SPbbb

),,,,( SPbPP

System of fixed point

Mathematic Formulation

Parameters Calibration

Calibration

Santiago supply model

Calibration supply

Data collectionSources of data:

– OD trips household survey 2001– Real estate rents– Household income

– Tax records– Supply by real estate type and zone– Real estate attributes

Calibration Supply

Residential land use (m2)

Data collectionCalibration supply

Total housing floor space (m2)

Data collectionCalibration supply

Total floor space of buildings (m2)

Data collectionCalibration supply

Average residents income

Data collectionCalibration supply

Supply vs. Real estate (houses)

Data Analysis

0

500

1000

1500

2000

2500

3000

0 100000 200000 300000 400000 500000 600000 700000

arriendo

ofe

rta

.

Rents per month

Nu

mb

er

of

rea

l e

sta

te u

nit

s

Calibration supply

Number of real estate (house) units vs. built houses floor space

0

500

1000

1500

2000

2500

3000

0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0

superficie construida

ofe

rta

.N

um

be

r o

f re

al

es

tate

un

its

Built floor space

Data AnalysisCalibration supply

0

500

1000

1500

2000

2500

3000

0.0 50.0 100.0 150.0 200.0 250.0

ingreso zonal (UF)

ofe

rta

.N

um

be

r o

f re

al

es

tate

un

its

Number of real estate (house) units vs. average residents’ income

Average income

Data AnalysisCalibration supply

Santiago supply model

cons terrvi v vi v vi v i vi v i v i ir q p q ing _ zon Q

Classic profit: rent minus direct costs (building and land)

Additional explaining variables

iviv

vinnvi HHS

,

00

)exp(

)exp(

Calibration supply

Resultados modelo Casa

Variable Parámetro estimado

Error Estándar Test-T

vir 0.069 0.019 3.739 consviq -0.004 0.002 -2.644

terrvii qp -0.006 0.002 -3.052

izoning _ 0.009 0.003 3.516

iQ -1.700 0.317 -5.365

Resultados modelo Depto

Variable Parámetro estimado

Error Estándar Test-T

vir 0.129 0.027 4.851 consviq -0.003 0.002 -1.470

terrvii qp -0.025 0.004 -6.934

izoning _ -0.006 0.003 -1.860

iQ -0.417 0.498 -0.837

Supply model calibration: by typeEstimatedparameter

Estimatedparameter

Standarderror

Standarderror

Houses

Departments buildings

Rents

Floor space

Land price x floor space

Residents Income

Available zone land

Rents

Floor space

Land price x floor space

Residents Income

Available zone land

Calibration supply

Santiago demand model

Calibration demand

HOUSEHOLDS CLUSTERSHOUSEHOLDS CLUSTERS

5 income levels

3 levels of car ownership

5 Levels of household size

Socioconomic segments:

MUSSA Santiago: 65 household types; 16 million inhabitants

Calibration demand

Typology

FIRMS FIRMS

Industry Retail

Service Education

Other

Segments by:

Commercial type

Business size

MUSSA Santiago: 5 types of firms

Calibration demand

Typology

REAL ESTATE SUPPLYREAL ESTATE SUPPLY

Types by:

700 Zones

12 Real estate building type

Calibration demand

MUSSA Santiago: 8.400 location options

Typology

Accessibility attributes

1. Use balancing factors Anpi: from trip distribution model, by agent n, time

period p and residential zone i:

2. Interpolate missing values: spatially for each agent type

3. Aggregate on periods

4. Normalize between 0-1

1npi npi

np

acc ln( A )

ni npi npp

acc acc * ( t )

ni

nj

njj

accacc'

max acc

Calibration demand

Calibration Methodology: BidsBid functions: linear-in-parameters multi-variate

functional form

k

hviknknhvi xB 0

Parameters per income level n

Examples of variables regarding their sub-index:

Household xh : Household Income

Zone xi : Residents average income, zone sevices

Household-zone xhi : accessibility

Real estate-zone xvi : Built floor space of real estate type v in zone i

Calibration demand

Maximum likelihood estimators of the parameters set

h/vihvih,v ,i

Máx d ln ( ) P

0 1

0hvi

if h is located at ( v,i )d

if not

Calibration demand

Calibration Methodology: Bids

With d obtained from the observed data:

Linear least squared regression

2

00

1vikvi vi k

,v ,i k

MIN r E( B ) x

rvi0 is the observed value of rents

E(B)vi is the expected maximum bid obtained as the logsum of bids

Calibration demand

Calibration Methodology: Rents

Residential Data• Data sources 2001:

– OD survey: residents location, socioeconomics, rents and trips

– Tax records: land use– Transport model ESTRAUS: trip balancing factors

• Variables collected• Household characteristics (size, income, car ownership, age

of household’s main adult)• Real estate attributes (type, land lot size, floor space, height)• Zone attributes (land use, average residents income, land

use densities, accessibility)

Calibration demand

Land use pattern

Average land use density by residents income level

(m2 of land use/zone area)

Income levelIndustry land use density

Retail land use density

Service land use density

Education land use density

1 0,014 0,014 0,009 0,007

2 0,013 0,017 0,015 0,007

3 0,015 0,025 0,023 0,010

4 0,017 0,036 0,039 0,012

5 0,006 0,032 0,040 0,011

Calibration demand

Data Analysis

Floor space pattern

Average floor space by income level and household size (m2)

Income level

Household size

1 2 3

1 62 53 49

2 67 59 53

3 71 65 60

4 89 84 79

5 115 123 150

Calibration demand

Data Analysis

Zone average of residents income

Average zone income compared with the household income in the same zone (Ch$ 2001)

0

500000

1000000

1500000

1 2 3 4 5

Calibration demand

Data Analysis

Accessibility

Average accessibility by income level and car ownership

Income level

Car ownership

0 1 2+

1 10,0 10,5 10,3

2 10,9 11,6 11,2

3 11,3 11,6 11,6

4 10,1 11,8 11,5

5 8,6 11,5 12,0

Calibration demand

Data Analysis

NON-Residential Data• Data sources 2001:

– Tax records: land use– Transport model ESTRAUS: trip balancing

factors

• Variables collected• Firms características (business type)• Real estate (type, land lot size, floor space, height)• Zone attributes (land use, zone average income,

density, attractiveness)

Calibration demand

Attributes by business type

Business category

Average land lot size (m2)

Average floor space (m2)

Attractiveness (tips attracted by

zone)

Average residents’

income by zone (Ch$ 2001)

Education 841 352 4.256 550.790

Industry 380 227 3.746 540.064

Services 191 152 11.118 733.262

Retail 181 121 5.820 572.514

Other 417 166 3.400 608.527

Calibration demand

NON-Residential Data

Parameter estimates

Residential BIDS Model

Income level

Constant ln(zone_income)

Accessib. Dummy apartm

ent

Industrydensity

Education density

ln(floor_space)

Houses

1-2 -9,284(-5,317)

2,642(2,678)

1,287(4,356)

35,366(13,343)

1,198(0,912) *

0,293(0,925) *

_

3 -15,984(-9,769)

0,758(2,420)

3,090(2,541)

12,821(1,454)

36,748(17,071)

2,750(2,056)

2,438(5,951)

4 -21,340(12,588)

3,769(2,323)

0,962(2,590)

-2,152(-5,867)

-6,093(-0,704) *

36,471(17,651)

4,732(3,347)

5 -35,475(-4,593)

36,746(13,727)

13,063(10,221)

-8,547(-6,627)

-1,015(-3,528)

_ 2,888(11,019)

Calibration demand

NON Residential BIDS Models

Business category

Constant ln(floor_space)

ln(land lot size)

ln(attractiveness)

ln(zone income)

Education_ 0,424

(1,549)0,570

(4,400)0,441

(5,348)0,116

(0,544) *

Industry3,321

(1,113)1,028

(3,917)0,170

(1,485)0,403

(1,894)0,422

(3,602)

Services-1,559

(-0,421)0,310

(1,462)_ 0,142

(1,252)_

Retail6,505

(1,769)_ 0,512

(5,087)0,163

(2,031)0,035

(0,379) *

Other3,128

(0,782) *0,500

(3,384)_ 0,044

(0,524) *0,337

(1,353)

Calibration demand

Parameter estimates

Residential RENTS ModelVariable Estimate Test T

Constant 3.847 0.148

Logsum 7.386 2.511

Land lot size (houses) 0.233 8.484

Floor space (houses) 0.274 3.115

Floor space (apartments) 1.117 8.305

Family size (houses) 21.922 4.690

Ln(Family size) (apartments) 44.906 6.230

Income (houses) 0.000 21.990

Income (apartments) 0.000 6.921

Floor Industry/ Nr of households -0.526 -2.799

Floor Education/ Nr of households 0.559 1.645

Calibration demand

Parameter estimates