Shocking Regions: Estimating the Temporal

and Spatial Effects of One-Time Events

Shocking Regions: Estimating the Temporal

and Spatial Effects of One-Time Events

Hebrew University of Jerusalem

Michael Beenstock

Daniel Felsenstein

2

The IssuesThe Issues

• Rising interest in the spatial dynamics of shocks and disasters (Katrina, Tsunami, acts of warfare and terrorism).

• Shocks have a spatial and temporal impact: one-time effect and cumulative effects

• Much interest in the temporal effects: can cities bounce back? how long does it take? is there a size threshold for shocks?

2

3

The MethodsThe Methods

• Control groups and trend analysis (Bram et al 2002, WTC 9/11).

• Expanded I-O models (SIM) (Okuyama, Hewings and Sonis 2004, Kobe earthquake 1995)

• CGE models (Rose et al 2004, electricity losses from Tennesse earthquake)

• NEG models- path dependence and temporary equilibria (Brakman et al 2004, Davis and Weinstein 2002, wars and bombing damage: Hiroshima, Dresden)

What about abrupt socio-econ processes and not just natural and man-made ‘disasters’?

3

The State of the LiteratureThe State of the Literature

• Static Spatial Panel Models:

Elhorst (2003) SAC and spatial lags

Elhorst (2004) SAC and TAC

• Spatial Panel Models:

Pfeifer & Deutsch (1980), univariate context

temporal lags, ‘lagged’ spatial lags

4

The State of the Literature (cont.)The State of the Literature (cont.)

• Dynamic Spatial Panel Models – joint estimation, multivariate

Spatial lags and spatial (auto)correlation estimated

jointly with temporal lags and temporalautocorrelation.

Beenstock and Felsenstein (2007)

• Dynamic Spatial Panel Models – 2 stage process1. spatial filtering2. estimate dynamic panel

Badinger, Muller and Tondl (2004)

5

The QuestionsThe Questions

• Method: can temporal and spatial dynamics of shocks be integrated (using spatial panel data)?

• Temporary or permanent effects: What are the impulse responses? How long do they last?

• Spatial issues: are shocks independent or spatially correlated?

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NotationNotation

Regions: n = 1, 2, ….., N

Time Periods: t = 1, 2, ..…, T

Endogenous Variables (Yk) k = 1, 2, ..…, K

Exogenous Variables (XP) p = 1, 2, ..…, P

Temporal Lag (Yt-q) q = 1, 2, ..…, Q

7

8

tttt uYXY 1

• Time Series (Temporal lag):

Integrating Temporal and Spatial Dynamics in Spatial Panel Data

Integrating Temporal and Spatial Dynamics in Spatial Panel Data

0

0

~

~

)(

sn

ns

NN

N

nssn

nnnn

w

w

W

YwY

uYXY

ns

• Cross Section (Spatial lag):

9

Identification ProblemIdentification Problem

• In Time Series (TS):

VARs under-identify the structural parameters.

0)~

( nnuYE

• In Cross Section (CS):Identification problem

Provided β = 0 MLIV

• SpVAR (CS + TS):

Structural identification remains a problem.

Temporal and Spatial Dynamics (‘Lagged’ spatial lag)Temporal and Spatial Dynamics (‘Lagged’ spatial lag)

Notation: – spatial lag – temporal lag – lagged spatial lag

Error Structure:

– spatial autocorrelation (SAC) – lagged SAC (LSAC) – temporal autocorrelation (TAC)nr – spatial correlation (SC = SUR)

10

ntntntntntnt uYYYXY 11

~~

1

1

)(~~ 211

sn

ns

ntntntntnt Euuuu

11

Weak Exogeneity (K=1)Weak Exogeneity (K=1)

ntntntntnt uYYYY 11

~~

Are Ynt-1 and instruments for ?1~

ntY

ntntntntnt uuuu 11~~

1. = = 0 Ynt-1 weakly exogenous

2. = = 0 Ynt-1 weakly exogenous

3. = θ = 0 unt-1 unt

Ynt-1

1~

ntY

1~

ntY

1~

ntY

1~

ntu

The SpVAR ModelThe SpVAR Model

K

ikntkikikikiknknt YYYYY

11intint1intint

~~

In Matrix Form:

where: ’s are region specific effects, • δ’s are temporal lag coefficients ’s are spatial lag coefficients ’s are lagged spatial lag coefficients

When = = 0, this equation reverts to an SVAR. 12

tttttt YYYBYAY 1**

1** ~~

tttt eYYY 12110

~

13

Data Sources

• 9 regions, 1987-2004

• 4 variables:Earnings:

Household Income Surveys (CBS)

Population:Central Bureau of Statistics

House Prices:Central Bureau of Statistics

Housing Stock:Housing Completions (CBS)

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Spatial Weights

Asymmetric spatial weights based on distance and population size

where:dni = distance between regions n and i,

Z= variable that captures scale effects.

itnt

it

niknit ZZ

Z

dw

1

15

Data

Housing Stock (th sq m) Real Earnings (1991 prices)

0

5000

10000

15000

20000

25000

30000

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

1500

2000

2500

3000

3500

4000

4500

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

0

5000

10000

15000

20000

25000

30000

Krayot

Jerusalem

Tel -Aviv

Haifa

Dan

Center

South

Sharon

North

16

Data (cont.)

House Prices (1991 prices) Population (th)

90

140

190

240

290

340

390

440

490

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 20040

200

400

600

800

1000

1200

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

0

5000

10000

15000

20000

25000

30000

Krayot

Jerusalem

Tel -Aviv

Haifa

Dan

Center

South

Sharon

North

17

Panel Unit Root Tests

• Auxiliary regression: dlnYknt = kn + knd-1lnYknt-1 + kndlnYknt-1 + knt.

• Critical values of t-bar with N = 9 and T = 18 are –2.28 at p = 0.01 and –2.17 at

p = 0.05.

• We estimate SpVAR in log first differences

Ln(Yj)d = 0d = 1d=2

Earnings-1.205-3.503-5.079

Population-2.707-2.531-6.603

House Prices-3.030-2.537-5.321

Housing Stock-0.092-2.227-3.410

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Estimating the SpVAR  EarningsPopulationHouse PricesHousing Stock

Temporal Lag(δ) Unrestricted

ModelRestricted

ModelUnrestricted

ModelRestricted

ModelUnrestricted

ModelRestricted

ModelUnrestricted

ModelRestricted

Model

Earnings-0.357-0.3320.0380.0370.1040.1020.006**-

Population-0.311*-0.112**-0.6780.6720.0590.060

House Prices-0.148-0.1040.0004**--0.006**-0.0160.018

Housing Stock0.9701.019-0.078**-0.0003-0.3960.389

Lagged Spatial Lag (λ)

Earnings0.131**-0.018**-0.2330.2350.0003**-

Population-0.314**-0.4970.037**--0.593*-0.605*-0.064-0.068

House Prices0.205**0.196**0.1040.1030.4930.4030.003**-

Housing Stock1.8362.174-0.359-0.458-0.790-0.8100.1720.170

R2 adjusted 0.1460.1480.2970.3120.0910.1070.4640.474

Panel DW2.2352.1762.1161.8661.8431.8611.6411.639

F statistic 0.847 0.393 0.000 0.019

SBC unrestricted -814.88SBC restricted -818.97

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Spatial Lag and Spatial Autocorrelation Coefficients

 EarningsPopulationHouse PricesHousing Stock

Spatial Lag ()

-0.426*-0.0100-0.0984-0.0215*

Error Parameters

TAC-0.147*-0.034**0.0094**0.0443**

SAC0.7940.8360.8530.952

LSAC0.118**-.0400**-0.0066**-0.0602**

(Determinant of correlation matrix)

0.00490.00030.0000910.0014

*Coefficients significant at 0.05<p<0.1** Coefficients significant at p>0.1

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Spatial Correlation (SC): SUR Estimates  JerusalemTel AvivHaifaKrayot DanCenterSouthSharonTel AvivEarningsPopulationHousingPrices

 0.46890.05920.46810.8367

       

HaifaEarningsPopulationHousingPrices

 0.52580.63950.44650.5760

 0.48850.37690.14430.7259

      

KrayotEarningsPopulationHousingPrices

 0.32610.35710.36280.1686

 -0.09860.7532

-0.09470.1560

 0.31230.66990.70050.4088

     

DanEarningsPopulationHousingPrices

 0.46240.43810.11880.9057

 0.63460.76620.24350.8092

 0.21500.68460.02750.7621

 -0.15960.6268

-0.00420.3445

    

CenterEarningsPopulationHousingPrices

 0.69400.31920.56930.4371

 0.77200.44500.50250.3631

 0.40290.65010.54100.2653

 -0.06720.63140.66750.1329

 0.75910.39450.40960.4384

   

SouthEarningsPopulationHousingPrices

 0.31800.2908

-0.38510.3490

 0.64750.2860

-0.23980.1425

 0.55100.2584

-0.47620.2024

 0.10600.5066

-0.28450.1480

 0.36800.2959

-0.49850.4834

 0.54940.2491

-0.47040.4808

  

SharonEarningsPopulationHousingPrices

 0.19750.3651

-0.13990.6307

 0.07480.69950.11560.5167

 0.21100.75100.27090.6013

 0.11170.79700.48030.4715

 0.04910.79440.32130.7682

 0.29690.41160.53980.5781

 0.62220.3496

-0.21500.3371

 

NorthEarningsPopulationHousingPrices

 0.45290.65550.61040.1364

 0.29130.43590.5999

-0.0331

 0.33330.88130.47910.3159

 0.10530.79270.40580.5648

 0.29910.6439

-0.08600.1499

 0.49460.54450.5896

-0.1297

 0.20780.5638

-0.21500.1607

 0.24380.76860.04630.1653

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SpVAR Impulse Response Simulations:SpVAR Impulse Response Simulations:

The effect of shocks to variable k in region n on:

• The shocked variable in the region in which the shock occurred

• Other variables in which the shock occurred• The shocked variable in other regions• Other variables in other regions

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Simulated Impulse Responses: 2% Earnings Shock in Jerusalem

Wage

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

199019911992199319941995199619971998199920002001200220032004

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.01%

Jerusalem

South

Dan

Population

0.0%

0.0%

0.0%

0.0%

0.0%

0.1%

0.1%

199019911992199319941995199619971998199920002001200220032004

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.01%

0.01%

Jerusalem

South

Dan

Price

-0.05%

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

199019911992199319941995199619971998199920002001200220032004

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

0.07%

0.08%

Jerusalem

South

Dan

Area

0.000%

0.001%

0.002%

0.003%

0.004%

0.005%

0.006%

0.007%

0.008%

0.009%

199019911992199319941995199619971998199920002001200220032004

0.000%

0.000%

0.000%

0.000%

0.000%

0.001%

0.001%

0.001%

0.001%

Jerusalem

South

Dan

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Simulated Impulse Responses:2% Population Shock in Tel Aviv

Wage

-1.2%

-1.0%

-0.8%

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

199019911992199319941995199619971998199920002001200220032004

-0.06%

-0.04%

-0.02%

0.00%

0.02%

0.04%

0.06%

0.08%

Tel-Aviv

Dan

Krayot

Price

-0.40%

-0.20%

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

199019911992199319941995199619971998199920002001200220032004

-0.30%

-0.25%

-0.20%

-0.15%

-0.10%

-0.05%

0.00%

0.05%

Tel-Aviv

Dan

Krayot

Population

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

199019911992199319941995199619971998199920002001200220032004

-0.01%

-0.01%

0.00%

0.01%

0.01%

0.02%

Tel-Aviv

Dan

Krayot

Area

-0.020%

0.000%

0.020%

0.040%

0.060%

0.080%

0.100%

0.120%

0.140%

199019911992199319941995199619971998199920002001200220032004 -0.035%

-0.030%

-0.025%

-0.020%

-0.015%

-0.010%

-0.005%

0.000%

Tel-Aviv

Dan

Krayot

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Impulses 1991 With and Without SC (a) 2% Earnings Shock in Jerusalem

(b) 2% Population Shock in Tel Aviv

(a)EarningsPopulationPricesHousing StockJerusalem-0.006640.000730.004210.00000

-0.006640.000730.002030.00000Dan-0.003070.000430.003700.00000

0.000000.000000.000210.00000South-0.002110.000230.003280.00000

0.000000.000000.000710.00000

(b)EarningsPopulationPricesHousing StockTel Aviv-0.009940.00000 0.01968 0.00155

-0.009930.00000 0.01345 0.00119Dan 0.006300.00000-0.00801-0.00053

0.000000.00000-0.00272-0.00031Krayot-0.000980.00000 0.00083 0.00004

0.000000.00000-0.00078-0.00008

Main Results

• Evidence of temporal lags, spatially autocorrelated errors and ‘lagged’ spatial lags.

• Impulses: reverberate across space and time, feedback effects. But die out quite quickly

• Impulse response across regions: dictated by spatial weighting system, eg Jerusalem has greater spillover effect on South than on Dan region

• Spillover effects from Tel Aviv: reflects spatial lag coefficients in magnitude and sign

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Conclusions

• Integration of time series and spatial econometrics

• Joint estimation in SpVAR (not 2-stage estimation)

• Difference between spatially correlated errors (SC) and spatially autocorrelated errors (SAC) and lagged SAC

• Impulse responses – ripple-through effect within and between regions

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