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

2. 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

3. 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

4. Model structure

5. 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

6. 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

7. Land use (S vi, q h vi ) Allocation (H hvi ) Rents (r vi ) Consumers and producers surpluses Results and notation The Equilibrium Model

8. 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

9. Demand and Supply models Mathematic Formulation

10. 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

11. 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

12. 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

13. Cut-off factors Mathematic Formulation Composite cut-off

14. 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

15. (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

16. (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

17. (1) (2) (3) Resume of equilibrium equations Allocation w/ externalities... Supply w/ econ. scale................... Equilibrium............................... System of fixed point Mathematic Formulation

18. Parameters Calibration Calibration

19. Santiago supply model Calibration supply

20. 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

21. Residential land use (m 2 ) Data collection Calibration supply

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

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

24. Average residents income Data collection Calibration supply

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

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

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

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

29. 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

30. Santiago demand model Calibration demand

31. 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

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

33. REAL ESTATE SUPPLY Types by: 700 Zones 12 Real estate building type Calibration demand MUSSA Santiago: 8.400 location options Typology

34. 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

35. 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

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

37. 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

38. 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

39. 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

40. Floor space pattern Average floor space by income level and household size (m2) Income level Household size 123 1625349 2675953 3716560 4898479 5115123150 Calibration demand Data Analysis

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

42. Accessibility Average accessibility by income level and car ownership Income level Car ownership 012+ 110,010,510,3 210,911,611,2 311,311,6 410,111,811,5 58,611,512,0 Calibration demand Data Analysis

43. 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

44. 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) Education8413524.256550.790 Industry3802273.746540.064 Services19115211.118733.262 Retail1811215.820572.514 Other4171663.400608.527 Calibration demand NON-Residential Data

45. 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

46. 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

47. Residential RENTS Model VariableEstimateTest T Constant3.8470.148 Logsum7.3862.511 Land lot size (houses)0.2338.484 Floor space (houses)0.2743.115 Floor space (apartments)1.1178.305 Family size (houses)21.9224.690 Ln(Family size) (apartments)44.9066.230 Income (houses)0.00021.990 Income (apartments)0.0006.921 Floor Industry/ Nr of households-0.526-2.799 Floor Education/ Nr of households0.5591.645 Calibration demand Parameter estimates