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דניאל פלזנשטיין, אייל אשבל וצבי וינוקור

אמידה סימולטנית של התנהגות היזם ומחירי קרקע - המקרה של

שינויים בשימושי קרקע במטרופולין תל אביב

אמידה סימולטנית של התנהגות היזם ומחירי קרקע - המקרה של

שינויים בשימושי קרקע במטרופולין תל אביב

28.11.10כנס האיגוד הישראלי למדע האזור, אוניברסיטת חיפה,

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The Motivation

The Motivation

• In land use models, developer behavior and land prices modeled independently

• In practice, the two occur simultaneously

• LU models treat land prices as exogenous. But, developer behavior depends on land prices and vice versa, therefore endogeneity issue.

• Prices also fixed by expectations of price (rational expectations world)

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TheoryTheory

Relative PriceRelative Price QuantityQuantity

itB

A

it

it

P

P L

LA

B

A

P

P

L

LA

AB

D

S' (π+1= π)

S'' (π+1> π)

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SupplySupply

itite1ititiit UλZγπβπασ

itititit VXπd

Z, X = vectors of variables that cause supply/demand curves to shift

general price is sum of parcel prices.

n

1iitittit w;θ

itit d

(–)

(+)DemandDemand

Equilibrium

Equilibrium

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Estimation StrategyEstimation Strategy

Maddala (1983): simultaneous equationsUse probit two-stage least squares (P2SLS)CDSIMEQ routine (STATA Journal 2003)

111

*211 uyy X

22212*2 uyy X

Land price model (OLS)

Developer model (probit)

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1. Simultaneous equations

2. y*2 is not observed,

rewrite, (1) and (2) as

3. Estimate reduced form

4. Extract predicted values

5. Plug-in fitted values and adjust covariance matrix

)2(

)1(

22212*2

111*211

uyy

uyy

X

X

)4(

)3(

2

22

2

21

2

2**2

111**

2211

u

yy

uyy

X

X

)6(

)5(

222**

2

1111

vy

vy

X

X

)8(ˆˆ

)7(ˆˆ

2**

2

11

X

X

y

y

)10(ˆ

)9(ˆ

22212**

2

111**

211

uyy

uyy

X

X

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Estimated Results – Example 1Estimated Results – Example 1

ln Land PricesDeveloper Behavior 2 -(-1), Residential – no

further developmentConstant 12.43**

Developer Behavior 0.541*

Travel time CBD -0.00253**

Percent water -0.00710 **

ln resid. units walking dist -0.0808**

ln resid. units 0.104**

ln distance highway 0.0468**

ln commercial sq. ft. 0.0199**

Mixed Use 1.477**

Residential -2.377 **

Constant 4.113*

ln land prices -0.1300Access to arterial hwy. -0.5499*

Recent transitions to resid. (walking dist) -0.58853Recent transitions to same type (walking dist) -1.4915**

Percent mixed use (walking dist) 0.5465*

Percent same type cells (walking dist)0.01518*

ln resid. units -0.8261**

-2log likelihood -N 2,919R2 0.73LR X2 -

-57.634238

-

214.5(p<0.000)

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Estimated Results – Example 2

Estimated Results – Example 2

ln Land PricesDeveloper Behavior (24-2):

Vacant developable – residential (low density)

Constant 11.56**

Developer Behavior 0.665**

Travel time CBD -0.0066**

Percent water -0.0015**

ln resid. units walking dist -0.0359*

ln resid. units 0.0337* 

Constant -2.766ln land prices 0.026Recent transitions to resid. (walking dist) 0.625*Recent transitions to same type (walking dist) -1.101**Percent residential (walking dist) 0.017Percent same type cells (walking dist) 0.018*ln resid. units 0.468**

-2log likelihood -N 2,696R2 0.25LR X2 -

-40.177315

-58.5

(p<0.000)

**p< 0.001; * P<0.05

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Residential Density (persons per grid cell), 2001-2020

Residential Density (persons per grid cell), 2001-2020

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Residential Land Values, 2001-2020

Residential Land Values, 2001-2020

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ResidentialResidential

• Simultaneous estimation predicts more population deconcentration.

• Residential land values are estimated to be higher in suburban locations than in CBD (using sim. estimation).

• Indiv. estimation gives opposite picture: higher residential prices closer to CBD: opposite trend.

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Density of Commercial Development (sq.m.) 2001-2020

Density of Commercial Development (sq.m.) 2001-2020

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Non-Residential Land Values, 2001-2020

Non-Residential Land Values, 2001-2020

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Non-residentialNon-residential

• Non-resid sq m: development starts later but reaches more extreme values

• Similar trends to indiv model estimation. Accentuated suburban non-residential development

• Simultaneous estimation makes for more extreme values in non- resid land prices. Less smooth price gradient

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Differences in Households Attributes due to the Two

Methods of Estimation

Differences in Households Attributes due to the Two

Methods of Estimation Average

Household Income

Number of Households

City NameΔ 2001

Δ 2010

Δ 2020

Δ 2001

Δ 2010

Δ 2020

Ra'anana0%1%1%1%5%5%

Petah Tikva12%-2%1%0%2%2%

Netanya2%-4%2%2%1%1%

Rehovot10%2%-1%-1%2%2%

Rishon Leziyon

20%2%0%0%1%1%

Ashdod9%11%1%1%2%2%

Tel Aviv5%1%3%3%1%1%

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Differences in Grid Cells Attributes: Estimated Commercial

Land Use (sq m)

Differences in Grid Cells Attributes: Estimated Commercial

Land Use (sq m)

Commercial Land Use (sq.m.)

City NameΔ 2001Δ 2010Δ 2020

Ra'anana-18%-4%0%

Petah Tikva27%39%43%

Netanya3%18%20%

Rehovot37%38%37%

Rishon Leziyon

25%45%52%

Ashdod31%52%65%

Tel Aviv9%16%15%

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Differences in Grid Cells Attributes: Number of Estimated

Residential Units

Differences in Grid Cells Attributes: Number of Estimated

Residential Units

Residential Units

City NameΔ 2001Δ 2010Δ 2020

Ra'anana-2%2%4%

Petah Tikva0%1%3%

Netanya0%1%2%

Rehovot-1%0%0%

Rishon Leziyon

-2%0%0%

Ashdod0%1%1%

Tel Aviv0%1%1%

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Differences in Grid Cells Attributes: Change in Share of

Residential Land Use

Differences in Grid Cells Attributes: Change in Share of

Residential Land Use

Fraction Residential

City NameΔ 2001Δ 2010Δ 2020

Ra'anana-23%5%5%

Petah Tikva-9%5%5%

Netanya-6%2%2%

Rehovot-17%-2%-2%

Rishon Leziyon

-19%-1%-2%

Ashdod-8%-3%-4%

Tel Aviv0%1%1%

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ConclusionsConclusions

• Why is simultaneous estimation more volatile? Technical reason: more noise in estimation due to use of fitted values. No true BLUE estimation- goodness of fit is less robust.

• But forecasts less likely to be biased; therefore consistently above or below individ. est. (Table).

• Behavioral focus on land users not land uses. Therefore, endogenity becomes an issue.

• Past behav and future expectations affect the current. Neighbors behavior- another source of endogeneity.

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Comparison of Estimated Coefficients for Land Price Model (land conversion from residential

to no further development)

Comparison of Estimated Coefficients for Land Price Model (land conversion from residential

to no further development)

Estimation Method

VariableSimultaneousIndividualΔ

Constant12.43310.9331.500

Travel time CBD-0.002-0.026-0.024

ln resid.units0.1040.0260.078

ln commercial sq m.0.0190.0070.012

Mixed use1.4770.1701.307

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Actual versus Estimated Population, 2002, 2003, select

cities

Actual versus Estimated Population, 2002, 2003, select

cities

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Actual versus Estimated Residential Units, 2002, 2003

select cities

Actual versus Estimated Residential Units, 2002, 2003

select cities

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Actual versus Estimated Employment 2002, 2003, select

cities

Actual versus Estimated Employment 2002, 2003, select

cities

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Actual versus Estimated Commercial Floor Space, 2002,

select cities

Actual versus Estimated Commercial Floor Space, 2002,

select cities