www mussa cl www citilabs com Development and

www. mussa. cl www. citilabs. com Development and Application of a Land Use Model for Santiago de Chile Francisco Martínez Universidad de Chile

Introduction 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 CO 2 permits

Model structure

The Equilibrium 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 Results and notation • • Land use (Svi, qhvi) Allocation (Hhvi) Rents (rvi) Consumers and producers surpluses

The Equilibrium Model Current land use Transport Willingness to pay Households and firms Incentives Subsidies Taxes Auction Location Rents (1) externalities (3) Regulations Supply Land lots Real estate (2) economies of scale Population HH & firms Equilibrium: all find a location b

Mathematic Formulation Demand Supply models

Mathematic Formulation The Bid function Supply specific bid Consumer’s income Attributes Consumer’s Dwelling utility level Accesibility, Attractivenes. Zonal (externalities) Subsidy or Tax: To consumer type h for locationg at dewlling type v in zone i

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

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

Mathematic Formulation Cut-off factors Composite cut-off

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

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

Mathematic Formulation Equilibrium Condition: every agents is allocated Supply: Allocation probability: Nr of real estate type v available in zona i Probability that consumidor type h is best bidder on real estate type v in zone i (3) Equilibrium logsum fixed-point Adjusts utility levels Nr agents type h to be allocated

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

Calibration Parameters Calibration

Calibration supply 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 Data collection Residential land use (m 2)

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

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

Calibration supply Data collection Average residents income

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

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

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

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

Calibration supply Supply model calibration: by type Houses Estimated parameter Standard error Rents Floor space Land price x floor space Residents Income Available zone land Departments buildings Estimated parameter Rents Floor space Land price x floor space Residents Income Available zone land Standard error

Calibration demand Santiago demand model

Calibration demand Typology HOUSEHOLDS CLUSTERS Socioconomic segments: 5 income levels 3 levels of car ownership 5 Levels of household size MUSSA Santiago: 65 household types; 16 million inhabitants

Calibration demand Typology FIRMS Segments by: Commercial type Business size Industry MUSSA Santiago: 5 types of firms Retail Service Education Other

Calibration demand Typology REAL ESTATE SUPPLY Types by: 700 Zones 12 Real estate building type MUSSA Santiago: 8. 400 location options

Calibration demand 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

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

Calibration demand Calibration Methodology: Rents Linear least squared regression rvi 0 is the observed value of rents E(B)vi is the expected maximum bid obtained as the logsum of bids

Calibration demand 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 Data Analysis Land use pattern Average land use density by residents income level (m 2 of land use/zone area) Industry land Income level use density Retail land use density Service land use density Education land use density 1 0, 014 0, 009 0, 007 2 0, 013 0, 017 0, 015 0, 007 3 0, 015 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 (m 2) 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)

Calibration demand Data Analysis Accessibility Average accessibility by income level and car ownership Car ownership Income level 0 1 2+ 1 10, 0 10, 5 10, 3 2 10, 9 11, 6 11, 2 3 11, 6 4 10, 1 11, 8 11, 5 5 8, 6 11, 5 12, 0

Calibration demand 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 NON-Residential Data Attributes by business type Average residents’ income by zone (Ch$ 2001) Business category Average land lot size (m 2) Average floor space (m 2) Attractiveness (tips attracted by zone) 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 Parameter estimates Residential BIDS Model Income level Constant ln(zone_inco me) Accessib. 1 -2 -9, 284 (-5, 317) 2, 642 (2, 678) 1, 287 (4, 356) 3 -15, 984 (-9, 769) 0, 758 (2, 420) 4 -21, 340 (12, 588) 5 -35, 475 (-4, 593) Dummy apartm ent Industry density Education density ln(floor_s pace) Houses 35, 366 (13, 343) 1, 198 (0, 912) * 0, 293 (0, 925) * _ 3, 090 (2, 541) 12, 821 (1, 454) 36, 748 (17, 071) 2, 750 (2, 056) 2, 438 (5, 951) 3, 769 (2, 323) 0, 962 (2, 590) -2, 152 (-5, 867) -6, 093 (-0, 704) * 36, 471 (17, 651) 4, 732 (3, 347) 36, 746 (13, 727) 13, 063 (10, 221) -8, 547 (-6, 627) -1, 015 (-3, 528) _ 2, 888 (11, 019)

Calibration demand Parameter estimates NON Residential BIDS Models Constant ln(floor_spa ce) ln(land lot size) ln(attractive ness) ln(zone income) _ 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) 0, 310 (1, 462) _ 0, 142 (1, 252) _ Services -1, 559 (-0, 421) _ Retail 6, 505 (1, 769) 0, 512 (5, 087) 0, 163 (2, 031) 0, 035 (0, 379) * 0, 500 (3, 384) _ Other 3, 128 (0, 782) * 0, 044 (0, 524) * 0, 337 (1, 353) Business category Education

Calibration demand Parameter estimates Residential RENTS Model Variable 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