Simultaneous Modeling of Developer Behavior and Land Prices in UrbanSim

1. Simultaneous Modeling of Developer Behavior and Land Prices in UrbanSim Daniel Felsenstein Eyal Ashbel UrbanSim European Users Group meeting, ETH Zurich, 17-18th March 2008

2. The Motivation • In UrbanSim, interdependence between developer behavior and land prices is noted. • Interdependence between dev.behav/land prices and h’hold and job location choice, is also noted. • However, in the model developer behavior and land prices are modeled independently. • In practice, the two occur simultaneously

3. Motivation cont. • UrbanSim models assumes prices are exogenous to interaction between buyers and sellers (their individual transactions are too small to affect aggregate prices). • But much urban economics points to endogeneity issue: developer behavior depends on land prices and land prices depend on developer behavior • Issue of endogeneity means dealing with: • Correct identification of models (error structures) • Instrumentation • Dynamics

4. Motivation cont 2. • Dynamics in current land price model: cross-section simulation of end-of-the-year-prices based on updated cell characteristics (from developer model, h’hold and jobs location choices and transport model). • These land prices then influence h’holds, jobs, developer behavior in next year: back-door endogeneity? • Prices also fixed by expectations of price (rational expectations world)

5. S' (π+1= π) S'' (π+1> π) A B D Theory Relative Price Quantity

6. (–) (+) Supply Demand Z, X = vectors of variables that cause supply/demand curves to shift general price is sum of parcel prices. Equilibrium

7. Adding in future expectations (e) Rational Expectations Assumptions: expected price + error term E(vit+1)=0 people do not expect to err. E(vit+1it)=0  = current information factor – instrument for future relative prices.

8. Adding time factor to future expectations: yt=xt+[yt+1-vt+1]+ut E(vt+1,ut)=0 =xt+yt+1+ut- vt+1 E(yet+1)<0 IV: yt+1 , xt , vt+1

9. Estimation Strategy Maddala (1983): simultaneous equations Use probit two-stage least squares (P2SLS) CDSIMEQ routine (STATA Journal 2003) Land price model (OLS) Developer model (probit)

10. Simultaneous equations • y*2 is not observed, rewrite (1) and (2) as • Estimate reduced form • Extract predicted values • Plug-in fitted values and adjust covariance matrix

11. In our case:y1 observed (continuous)- land prices y2 dichotomous – developer behavior Simultaneous equations:

12. As is not observed (ie only observed as a dichotomous variable), equations (1) and (2) are re-written: This has implications for standard errors that will need to be corrected later on.

13. Two-stage Estimation Stage 1: (estimated by OLS and probit): models fitted using all exogenous variables. Predicted values obtained. X= matrix of all exogenous variables Π1’Π2,= vectors of parameters to be estimated From these reduced-form estimates, predicted values from each model are obtained for use in Stage 2.

14. Two-stage Estimation cont. Stage 2: (estimated by OLS and probit): original endogenous variables in (3) and (4) are replaced by their fitted values from (7) and (8). Finally, need correction for standard errors (adjustment of the variance- covariance matrix) as models based on and not on the appropriate

15. Estimated Results - Example

16. Tel Aviv Metropolitan Area • 1,683 sq km. • Three million inhabitants. • One million employees • 49 % National GNP. • 60 local authorities (city governments)

17. Commercial sq.m 2001-2020

18. Non- residential land values, 2001-2020

19. Non-residential • Non-resid sq m: development starts later but reaches more extreme values • Similar trends to individual model estimation. Accentuated suburban non-residential development • Simultaneous estimation makes for more extreme values in non- resid land prices. Less smooth price gradient

20. Density – persons per grid cell, 2001-2020

21. Residential Land Values, 2001-2020

22. Residential • Simultaneous estimation predicts more population deconcentration. • Residential land values are estimated to be higher in suburban locations than in CBD (using simultaneous estimation) • Individual estimation gives opposite picture: higher residential prices closer to CBD

23. Local Authorities within the Metro Area

24. Households Data

25. Grid Cells Data

26. Grid Cells Data

27. Grid Cells Data

28. Results for Individual Local Authorities • Results tend to stabilize over the longer term (2020) • Households data: simultaneous estimation generally yields higher outcomes (positive deltas) than individual estimation. • Changes in attributes of cells: estimates of changes in non-residential cells (units, area) much more volatile than for residential cells. Confirms results relating to land values. • Southern local authorities estimated gains much more in non-residential units than in residential (implications for fiscal independence).

29. Conclusions • Avoiding endogeneity in price fixing= the easy way out? • Explicit treatment of prices in UrbanSim- can this be improved? (Prices respond at the end of the year to grid cell characteristics of location, balance of supply an demand at each location) • Price expectations need to be included (need credible instrument) • Is this more suited to UrbanSim4?