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

ASSESS 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

APPLICATIONS 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 (H h ) Transport (acc hi, att i ) 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 (S vi, q h vi ) Allocation (H hvi ) Rents (r vi ) Consumers and producers surpluses Results and notation The Equilibrium Model

Auction Location Rents Auction Location Rents Equilibrium: all find a location Supply Land lots Real estate Supply Land lots Real estate Willingness to pay Households and firms Willingness to pay Households and firms Regulations Incentives Subsidies Taxes Incentives Subsidies Taxes (3) b (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 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 Consumer’s income

Externalities Location Externalities Attribute defined by allocation of consumers and supply in zone i Endogenous Attributes Example: Average income of residents Mathematic Formulation Bids depend on endogenous variables: land use and built environment

Allocation by auctions Constraints Income budget. Location bid: Deterministic term Auction fixed-point Adjusts externalities (1) H h : Number of agents in cluster h Mathematic Formulation Theoretical obs. Theoretical obs.: !max bidder implies max utility¡ Auction probability

Cut-off factors Mathematic Formulation Composite cut-off

Real estate rents Real estate rents: depends on amenities/externalities and utility level Expected max bid for real estate v located at zone i Mathematic Formulation

(2) Real estate supply Supply: Total Nr of real estate units Regulations Rents Subsidies or taxes Production Cost with scale/scope economies Supply MNL fixed-point Mathematic Formulation

(3) Equilibrium Condition: every agents is allocated 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 Equilibrium logsum fixed-point Adjusts utility levels Mathematic Formulation

(1) (2) (3) Resume of equilibrium equations Allocation w/ externalities... Supply w/ econ. scale Equilibrium System of fixed point Mathematic Formulation

Parameters Calibration Calibration

Santiago supply model Calibration supply

Data collection Sources 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 (m 2 ) Data collection Calibration supply

Total housing floor space (m 2 ) Data collection Calibration supply

Total floor space of buildings (m 2 ) Data collection Calibration supply

Average residents income Data collection Calibration supply

Supply vs. Real estate (houses) Data Analysis Rents per month Number of real estate units Calibration supply

Number of real estate (house) units vs. built houses floor space Number of real estate units Built floor space Data Analysis Calibration supply

Number of real estate units Number of real estate (house) units vs. average residents’ income Average income Data Analysis Calibration supply

Santiago supply model Classic profit: rent minus direct costs (building and land) Additional explaining variables Calibration supply

Supply model calibration: by type Estimated parameter Estimated parameter Standard error Standard error 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 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 Industry Retail Service Education Other Segments by: Commercial type Business size MUSSA Santiago: 5 types of firms Calibration demand Typology

REAL ESTATE SUPPLY Types by: 700 Zones 12 Real estate building type Calibration demand MUSSA Santiago: location options Typology

Accessibility attributes 1.Use balancing factors A npi : 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 Calibration demand

Calibration Methodology: Bids Bid functions: linear-in-parameters multi-variate functional form Parameters per income level n Examples of variables regarding their sub-index: Household x h : Household Income Zonex i : Residents average income, zone sevices Household-zonex hi : accessibility Real estate-zonex vi : Built floor space of real estate type v in zone i Calibration demand

Maximum likelihood estimators of the parameters set  Calibration demand Calibration Methodology: Bids With d obtained from the observed data:

Linear least squared regression r vi 0 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 (m 2 of land use/zone area) Income level Industry land use density Retail land use density Service land use density Education land use density 10,014 0,0090,007 20,0130,0170,0150,007 30,0150,0250,0230,010 40,0170,0360,0390,012 50,0060,0320,0400,011 Calibration demand Data Analysis

Floor space pattern Average floor space by income level and household size (m2) Income level Household size Calibration demand Data Analysis

Zone average of residents income Average zone income compared with the household income in the same zone (Ch$ 2001) Calibration demand Data Analysis

Accessibility Average accessibility by income level and car ownership Income level Car ownership ,010,510,3 210,911,611,2 311,311,6 410,111,811,5 58,611,512,0 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 (m 2 ) Average floor space (m 2 ) Attractiveness (tips attracted by zone) Average residents’ income by zone (Ch$ 2001) Education Industry Services Retail Other Calibration demand NON-Residential Data

Parameter estimates Residential BIDS Model Income level Constantln(zone_inco me) Accessib.Dummy apartm ent Industry density Education density ln(floor_s pace) 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 Constantln(floor_spa ce) ln(land lot size) ln(attractive ness) ln(zone income) Education _0,424 (1,549) 0,570 (4,400) 0,441 (5,348) 0,116 (0,544) * Industry 3,321 (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) _ Retail 6,505 (1,769) _0,512 (5,087) 0,163 (2,031) 0,035 (0,379) * Other 3,128 (0,782) * 0,500 (3,384) _0,044 (0,524) * 0,337 (1,353) Calibration demand Parameter estimates

Residential RENTS Model VariableEstimateTest T Constant Logsum Land lot size (houses) Floor space (houses) Floor space (apartments) Family size (houses) Ln(Family size) (apartments) Income (houses) Income (apartments) Floor Industry/ Nr of households Floor Education/ Nr of households Calibration demand Parameter estimates