Transcript Simultaneous Model of Land Developer Behavior and Land Prices

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
1
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
2
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
3
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)
4
Theory
Relative Price
Quantity
PAit
  it
PBit
LA

L
S' (π+1= π)
PA

PB
S'' (π+1> π)
A
B
D
LA

L
5
Supply
(–)
σit  αi  βπit  γπite 1  λ Zit  Uit
Demand
(+)
dit  πit  X it  Vit
Z, X = vectors of variables that cause supply/demand curves to shift
θit  t ;  t   w i it
n
general price is sum of parcel prices.
i 1
Equilibrium
 it  dit
6
Adding in future expectations (e)
y1 ( y2 , x1 )  ui
y2*
( y1 , x2 , y1e )  u2
y1 ( x1 , x2 , y1e )
Rational Expectations Assumptions:
 it1   ite1  vit1
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.
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Adding time factor to future expectations:
y t  x t  y
e
t 1
 ut
y t 1  y et 1  v t 1
yt=xt+[yt+1-vt+1]+ut
=xt+yt+1+ut- vt+1
E(vt+1,ut)=0
E(yet+1)<0
IV: yt+1 , xt , vt+1
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Estimation Strategy
Maddala (1983): simultaneous equations
Use probit two-stage least squares (P2SLS)
CDSIMEQ routine (STATA Journal 2003)
y1   1 y2*  1 X1  u1
y2*   2 y1   2 X 2  u2
Land price model
(OLS)
Developer model
(probit)
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1. Simultaneous equations
2.
y*
is not observed, rewrite
(1) and (2) as
2
y1   1 y2*  1 X 1  u1
(1)
y2*   2 y1   2 X 2  u2
(2)
y1   1  2 y2**  1 X1  u1
(3)
2

u
y1  2  X 2 2
2
2
2
(4)
y2** 
3. Estimate reduced form
4. Extract predicted values
5. Plug-in fitted values and
adjust covariance matrix
y1  1 X1  v1
(5)
y2**   2 X 2  v2
(6)
yˆ1  ˆ 1X
(7 )
yˆ 2**  ˆ 2 X
(8)
y1   1 yˆ 2**  1 X1  u1
(9)
y2**   2 yˆ1   2 X 2  u2
(10)
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In our case:
y1 observed (continuous)- land prices
y2 dichotomous – developer behavior
Simultaneous equations:
y1   1 y2*  1 X 1  u1
(1)
y2*   2 y1   2 X 2  u2
(2)
y1  y1*
y2  1 if y2*  0
y2  0 otherwise
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*
y
As 2 is not observed (ie only observed as a dichotomous
variable), equations (1) and (2) are re-written:
y1   1  2 y2**  1 X1  u1
2
 2
u2
y 
y1 
 X2
2
2
2
**
2
(3)
( 4)
This has implications for standard errors that will need to be
corrected later on.
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Two-stage Estimation
Stage 1: (estimated by OLS and probit): models fitted using all
exogenous variables. Predicted values obtained.
y1  1 X1  v1
(5)
y2**   2 X2  v2
(6)
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.
ˆ X
yˆ1  
1
ˆ X
yˆ 2**  
2
(7 )
(8)
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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).
y1   1 yˆ 2**  1 X1  u1
(9)
y2**   2 yˆ1   2 X 2  u2
(10)
Finally, need correction for standard errors (adjustment of the variancecovariance matrix) as models based on yˆ ** , yˆ
2
1
**
and not on the appropriate y2 , y1
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Estimated Results - Example
Developer Behavior 2 -(-1),
Residential – no further
development
Land Prices
Constant
Developer Behavior
Travel time CBD
Percent water
ln resid. units walking dist
ln resid. units
ln distance highway
ln commercial sq. ft.
Mixed Use
Residential
-2log likelihood
N
R2
LR X2
12.43**
0.541*
-0.00253**
-0.00710 **
-0.0808**
0.104**
0.0468**
0.0199**
1.477**
-2.377 **
2,919
0.73
-
Constant
ln land prices
Access to arterial hwy.
Recent transitions to resid.
(walking dist)
Recent transitions to same
type (walking dist)
Percent mixed use
(walking dist)
Percent same type cells
(walking dist)
ln resid. units
4.113*
-0.1300
-0.5499*
-0.58853
-1.4915**
0.5465*
0.01518*
-0.8261**
-57.634
238
15
214.5(p<0.000)
Tel Aviv Metropolitan Area
•
•
•
•
•
1,683 sq km.
Three million inhabitants.
One million employees
49 % National GNP.
60 local authorities (city
governments)
16
Commercial sq.m 2001-2020
17
Non- residential land values, 2001-2020
18
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
19
Density – persons per grid cell, 2001-2020
20
Residential Land Values, 2001-2020
21
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
22
Local Authorities within the Metro Area
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Households Data
Average Income
Households
City Name
Delta 2001 Delta 2010 Delta 2020 Delta 2001 Delta 2010 Delta 2020
Ra'anana
17%
0%
1%
4%
1%
5%
Petah Tikva
-3%
11%
-2%
1%
1%
2%
Netanya
5%
2%
-4%
1%
2%
1%
Rehovot
0%
9%
2%
1%
-1%
2%
Rishon Leziyon
-6%
17%
2%
1%
0%
1%
Ashdod
2%
8%
10%
3%
1%
2%
Tel Aviv
5%
5%
1%
2%
3%
1%
Delta=(new-old)/new
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Grid Cells Data
Commercial Sqm
City Name
Delta 2001 Delta 2010 Delta 2020
Ra'anana
-22%
-4%
0%
Petah Tikva
21%
28%
30%
Netanya
3%
15%
17%
Rehovot
27%
27%
27%
Rishon Leziyon
20%
31%
34%
Ashdod
24%
34%
40%
Tel Aviv
8%
14%
13%
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Grid Cells Data
Residential Units
City Name
Delta 2001
Ra'anana
Delta 2010
Delta 2020
2%-
2%
4%
Petah Tikva
0%
1%
2%
Netanya
0%
1%
2%
Rehovot
1%-
0%
0%
Rishon Leziyon
2%-
0%
0%
Ashdod
0%
1%
1%
Tel Aviv
0%
1%
1%
Delta=(new-old)/new
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Grid Cells Data
Fraction Residential
City Name
Delta 2001
Delta 2010
Delta 2020
Ra'anana
30%-
5%
5%
Petah Tikva
10%-
5%
5%
Netanya
7%-
2%
2%
Rehovot
20%-
2%-
2%-
Rishon Leziyon
23%-
1%-
2%-
Ashdod
9%-
3%-
4%-
Tel Aviv
0%
1%
1%
Delta=(new-old)/new
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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).
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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?
29