Bid-auction framework for microsimulation of location choice with endogenous real estate prices

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1 Bd-aucton framework for mcrosmulaton of locaton choce wth endogenous real estate prces Rcardo Hurtuba Mchel Berlare Francsco Martínez Urbancs Termas de Chllán, Chle March 28 th 2012

2 Outlne 1) Motvaton 2) The bd-aucton approach to locaton choce modelng 3) Estmaton of bd-rent functons 4) Bd-aucton framework for mcrosmulaton of locaton choce

3 Motvaton Land use models Spatal dstrbuton of agents and actvtes n a cty affects: Travel demand Energy consumpton, polluton Socal welfare Ctes are complex systems: Interacton of dfferent markets Many heterogeneous agents Externaltes Land use models allow to understand and forecast (?) the evoluton of ctes Locaton choce models are a fundamental element of land use models Mcrosmulaton / agent based models are flexble and detaled, makng possble to evaluate complex scenaros

4 Motvaton Approaches to locaton choce modelng Choce: agents (households and frms) select locaton of maxmum utlty as prce takers Most usual mplemented approach n mcrosmulaton Requres prces/rents to be gven (usually modeled wth a hedonc prce model and/or exogenous adjustments) Bd-aucton: real estate goods are traded n auctons where prces and locatons are determned by the best bdders Usually mplemented n equlbrum models (bds are adjusted so everyone s located somewhere) Prces are endogenous (expected maxmum bd)

5 Motvaton Bd-aucton advantages Real estate goods (housng, land) are quas-unque and usually scarce competton between agents Explct explanaton of the prce formaton process (best bd n an aucton) Bd prces can be senstve to scenaros of demand or supply surplus Estmaton: no prce endogenety (spatal autocorrelaton) But: Estmates of bd functon must reproduce both prces and locaton dstrbuton Bd-aucton s not straghtforward to mplement n mcrosmulaton framework Detaled data s usually not avalable

6 Bd-aucton approach to locaton choce B h : wllngness to pay of agent h for locaton. B h f ( x, z, ) h x h : characterstcs of agent h (household, frm, ) z : attrbutes of locaton (housng unt, parcel of land, ) Probablty of agent h beng the best bdder for a locaton (Ellckson, 1981): P h/ H: set of bddng agents exp( B gh h exp( B ) g )

7 Bd-aucton approach to locaton choce Prce or rent for one locaton: Determnstc: bd of the wnner of the aucton Stochastc: expected maxmum bd r : rent/prce of = expected value of the maxmum bd: H: set of bddng agents C: unknown constant r 1 ln gh exp( B g ) C

8 Estmaton of bd-rent functons

9 Estmaton of bd-rent functons Rosen (1974): Prces as a functon of locaton attrbutes (hedonc rent model) Ellckson (1981): stochastc bd approach, undetermned model relatve prces Lerman & Kern (1983): bd approach + observed prce s maxmum bd absolute prces Very detaled data s requred (ndvdual transacton prces) Assumpton: groups of homogeneous bddng agents Valdaton only regardng rent and margnal wllngness to pay for locaton attrbutes, not agent locaton dstrbuton or prce forecastng (Gross, 1988; Gross et al 1990; Gn and Sonstele, 1992; McMllen 1996; Chattopadhyay 1998; Muto, 2006)

10 Estmaton of bd-rent functons Idea: Assume structural relatonshp between expected outcome of the aucton and observed (average) prces Estmate locaton choce model and prce model smultaneously, usng observed prces as ndcators Assumptons: Aucton prce s a latent varable (the aucton tself s a latent process) All agents are potental bdders for all locatons

11 Model wth prce ndcator Explanatory varables (x h, z ) (latent) aucton prces (r ) Observed prces (R ) Aucton prce measurement model Bd functon (B h ) Observed locatons (choces) Standard Logt choce model * Inspred by the Generalzed Random Utlty Model (Walker and Ben-Akva, 2002)

12 Model wth prce ndcator Structural equaton for prces: 1 r ln exp( B g ) gh Measurement equaton for prces: R a r ~ N(0, ) f ( R r ) 1 a r R exp Lkelhood: L Ph / f ( R r ) h y h

13 Case study: Brussels Data collected for a FP7 European Unon project (SustanCty) Census 2001 (aggregated nformaton by zone) Household survey 1999 (~1300 observatons), no detal on housng attrbutes Average transacton prces by commune and 2 types of dwellng (house or apartment) from 1985 to 2008 Other geographcal, land use databases households, dwellngs 157 communes 4975 zones 4 types of dwellng (wth average attrbutes per zone) Isolated house Sem-solated house Jont house Apartment

14 Case study: Brussels Bd functon specfcaton for locaton (bd) choce model (Ellckson):

15 Case study: Brussels Estmaton performed wth PythonBogeme (Berlare and Fetarson,2010)

16 Case study: Brussels Estmaton performed wth PythonBogeme (Berlare and Fetarson,2010)

17 Case study: Brussels Prces per commune and type (% error) (over estmaton dataset)

18 Case study: Brussels Prces (over estmaton dataset)

19 Case study: Brussels Prces (over estmaton dataset)

20 Case study: Brussels Prces (over estmaton dataset)

21 Case study: Brussels (forecastng/valdaton) Prces per commune and type (% error) (over full supply for 2001)

22 Case study: Brussels (forecastng/valdaton) Number of people per commune (% error)

23 Case study: Brussels (forecastng/valdaton) Number of people wth unv degree per commune (% error)

24 Case study: Brussels (forecastng/valdaton) Number of households wth 2+ cars (% error)

25 Case study: Brussels (forecastng/valdaton) Number of households wth 0 cars (% error)

26 Dscusson The proposed estmaton method fnds estmates that reproduce the locaton dstrbuton of agents and the average market prces of dwellngs better than other methods Proposed method requres less detaled data more sutable for extensve land use models Well estmated bd functons (wllngness to pay) allow to generate a good forecast of the transacton prces, wthout the need of hedonc prce models ths helps f we want to mcrosmulate usng a bd approach

27 Bd-aucton framework for mcrosmulaton of locaton choce

28 Mcrosmulaton wth a bd approach When bds are smulated and we get: Spatal dstrbuton of agents Real estate prces But, n order to account for competton between agents for scarce goods, we need market clearng Through hedonc prce models (UrbanSm) Smple but not real market clearng Indvdual auctons (ILUTE) Expensve n computatonal terms Equlbrum (MUSSA) Aggregated approach

29 The market clearng problem Jont probablty of household h occupyng locaton :, h P hph Ph P P P h P h P P h Maxmum bd probablty Maxmum surplus (utlty) probablty Sellng probablty Locatng probablty 29

30 Re-vstng Equlbrum In equlbrum models t s usually assumed that supply (S) equals demand (H) P h P 1 h, H S Possble equlbrum condtons:, h P hph P P 1 h h, h Ph P Ph h P 1 (everythng s sold) (everyone s located) 30

31 Re-vstng Equlbrum Market clearng can be acheved by mposng one of the equlbrum condtons and fndng prces/bds that produce them h r : P 1 h h h b : P 1 h (prces clear the market) (bds clear the market) Due to nterdependence, these are usually fxed pont problems 31

32 Re-vstng Equlbrum If we have an aucton market and the best bdder rule s observed, adjustng prces or bds s equvalent n equlbrum When market condtons change (supply, demand, etc) utlty levels of the decson makers have to be adjusted, ths s reflected n the level of the prces or bds dea: quas-equlbrum 32

33 Quas-equlbrum Perodcal locaton of new and re-locatng agents, gven exogenous supply Assumpton: all households lookng for a locaton are located somewhere Ph 1 h Total supply must be greater or equal than total demand H S Not all locatons are necessarly used P 1 33

34 Quas-equlbrum No equlbrum no perfect nformaton (aggregate supply, prevous prces) No teratve negotaton/bddng No absolute adjustment of bds/prces Instead, adjustment of percepton of agents that goes n the drecton of an equlbrum but does not solve t. 34

35 Quas-equlbrum Algorthm (n each perod): t t All agents H observe the market: prces and supply r 1, z 1, S All gents (smultaneously) adjust ther bds, attemptng to make ther expected number of wnnng auctons equal to one: S q( h ) 1 h q(h ): perceved probablty of beng the best bdder for All agents bd at the same tme for all locatons prces and locaton dstrbutons are defned The assgnment mechansm s an aucton for each locaton a best bdder and a prce s determned 35

36 Quas-equlbrum Bd functon: Perceved probablty: 1 ) ( exp ) exp( ) ( exp t t h t h H g t g t h t h r b z V B b z V h q h h h h h h b z V z V U I B ) ( ) ( S t t h t h r z V b 1 ) ( exp ln S h q 1 ) ( Advantage: no fxed pont, just evaluaton of equaton t s possble to apply to large populatons wthout excessve computatonal cost 36

37 General framework Re-locaton models Transport model Travel tmes, congeston, level of servce Re-locatng agents, vacated real estate New real estate Supply model Market clearng New agents Located agents Real estate prces Frmographcs t=t+1 Externaltes, market condtons (prces, demand/supply surplus, etc) Gven for t=0 Demographcs 37

38 Market clearng Externaltes, prces and market condtons (t-1) t=t+1 Demographcs(t) Adjustment of utlty level (b h ) Re-calculaton of hedonc WP (V h ) Smulaton of locaton choce Supply (t) t=t+1 Empty unts Relocaton Locaton probablty dstrbuton (P h/ ) Located ndvdual agents and prces New and Relocatng agents Transacton prces (R ) Aucton

39 Some prelmnary results Average prces per year Average prce growth: BID: 50%, HEDONIC: 7%

40 Observed average prces per commune Average prce growth :108%

41 Advantages Agents have an ndvdual behavor but they relate to a hgher level market mechansm through the utlty level adjustment and the smultaneous aucton. Quas-equlbrum : Demand s not cleared: utlty adjustment does NOT assure allocaton Supply s not cleared System tends to equlbrum but does not clear Adjustment of utlty levels nstead of prces allow to Explan prce formaton (no need for hedonc prce models) Detect all agents utlty levels, ncludng those not actve n the market, trggerng future re-locaton 41

42 Thank you 42/38

43 Man assumptons of the general framework Aucton market Agents adjust ther utlty level (ndvdually n each perod) to ensure locaton (ex-ante expectatons) gven market condtons: prevous perod rents, current supply Tme lag: In producton of real estate goods: In percepton of attrbutes of locatons (non-nstantaneous) Smultaneous (macro level) bd of all agents for all locatons Locaton (best bdder) dstrbutons and expected rents (R). No teratve transactons. Computatonally smpler than transacton-specfc prce clearng Mcrosmulaton: Actual allocaton followng macro dstrbutons (smulaton of auctons) Rents at mcro level (r) 43

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