Shocking Regions: Estimating the Temporal
and Spatial Effects of One-Time Events
Michael Beenstock
Daniel Felsenstein
Hebrew University of Jerusalem
The 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: onetime 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
The 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 Literature
• Spatial Panel Models:
Pfeifer & Deutsch (1980), univariate context
temporal lags, ‘lagged’ spatial lags
• Static Spatial Panel Models:
Elhorst (2003) SAC and spatial lags
Elhorst (2004) SAC and TAC
4
The State of the Literature (cont.)
• Dynamic Spatial Panel Models – 2 stage process
1. spatial filtering
2. estimate dynamic panel
Badinger, Muller and Tondl (2004)
• Dynamic Spatial Panel Models – joint estimation,
multivariate
Spatial lags and spatial (auto)correlation estimated
jointly with temporal lags and temporal
autocorrelation.
Beenstock and Felsenstein (2007)
5
The 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?
6
Notation
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
Integrating Temporal and Spatial Dynamics
in Spatial Panel Data
• Cross Section (Spatial lag):
~
Yn     X n  Yn  u n
N
~
Yn   w ns Ys
sn
W
( N N )
 0
 
 wsn
wns 


0 
• Time Series (Temporal lag):
Yt      X t   Yt 1  ut
8
Identification Problem
• In Cross Section (CS):
~
E(Ynun )  0
Provided β = 0
Identification problem
ML
IV
• In Time Series (TS):
VARs under-identify the structural parameters.
• SpVAR (CS + TS):
Structural identification remains a problem.
9
Temporal and Spatial Dynamics (‘Lagged’ spatial lag)
~
~
Ynt    X nt  Ynt  Ynt 1  Ynt 1  unt
Notation:
 – spatial lag
 – temporal lag
 – lagged spatial lag
Error Structure:
unt   u~nt  unt 1  u~nt 1   nt
 1
  E (  )   2 
 sn
 – spatial autocorrelation (SAC)
 – lagged SAC (LSAC)
 – temporal autocorrelation (TAC)
nr – spatial correlation (SC = SUR)
 ns 


1 
10
Weak Exogeneity (K=1)
~
~
Ynt    Ynt  Ynt 1  Ynt 1  unt
~
Are Ynt-1 and Ynt 1 instruments for ?
unt  u~nt  unt1  u~nt1  nt
~
1.  =  = 0
Ynt-1 Ynt 1 weakly exogenous
2.  =  = 0
Ynt-1 Y~
weakly exogenous
nt 1
3.  = θ = 0
unt-1
Ynt-1

u~nt1 

~
Ynt 1
unt
11
The SpVAR Model

~
~ 
Yknt  kn    kiYint   kiYint 1   kiYint  kiYint 1    knt
i 1 

K
In Matrix Form:
~
*~
Yt    A Yt  B Yt 1   Yt   Yt 1  t
*
*
*
where:
• ’s are region specific effects,
• δ’s are temporal lag coefficients
• ’s are spatial lag coefficients
• ’s are lagged spatial lag coefficients
~
Yt  0  1Yt 1   2Yt 1  et
When  =  = 0, this equation reverts to an SVAR.
12
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)
13
Spatial Weights
Asymmetric spatial weights based on distance
and population size
wknit
Z it
1

d ni Z nt  Z it
where:
dni = distance between regions n and i,
Z= variable that captures scale effects.
14
Data
Housing Stock (th sq m)
Real Earnings (1991 prices)
30000
4500
25000
4000
20000
3500
15000
3000
10000
2500
5000
2000
0
1500
Kray ot
Jerusalem
Tel-Av iv
Haif a
Dan
03
02
01
00
99
98
04
20
20
20
20
20
19
19
96
95
94
97
19
19
19
19
92
91
90
93
19
19
19
19
89
88
87
North
19
19
19
03
South
Sharon
04
20
02
20
01
20
00
20
98
97
96
95
99
20
19
19
19
19
94
19
93
19
92
19
91
19
90
19
89
19
88
19
19
19
87
Center
Kray ot
Jerusalem
Tel-Av iv
Haif a
Dan
Center
04
20
03
20
01
00
99
98
97
02
20
20
20
19
19
19
96
19
95
19
94
19
93
19
92
19
91
19
89
90
19
19
19
88
South
Sharon
North
15
Population (th)
1200
490
440
1000
390
800
340
600
290
240
400
190
200
140
0
90
20
04
20
03
20
02
20
01
20
00
19
99
19
98
19
97
19
96
19
95
19
94
19
93
19
92
19
91
19
90
19
89
19
88
19
87
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Kray ot
Jerusalem
Tel-Av iv
Haif a
Dan
Center
03
02
01
00
99
98
97
96
95
94
93
92
91
90
04
20
20
20
20
20
19
19
19
19
19
19
19
19
19
89
South
19
88
House Prices (1991 prices)
19
19
Data (cont.)
Sharon
North
16
Panel Unit Root Tests
Ln(Yj)
d=0
d=1
d=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
• Auxiliary regression: dlnYknt = kn + knd-1lnYknt-1 + kndlnYknt-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
17
Estimating the SpVAR
Earnings
Population
House Prices
Housing Stock
Temporal Lag(δ)
Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted Unrestricted Restricted
Model
Model
Model
Model
Model
Model
Model
Model
-0.357
Earnings
-0.311*
Population
-0.148
House Prices
0.970
Housing Stock
Lagged Spatial Lag (λ)
0.131**
Earnings
-0.314**
Population
0.205**
House Prices
1.836
Housing Stock
0.146
R2 adjusted
2.235
Panel DW
F statistic
SBC unrestricted
SBC restricted
-0.332
-0.104
1.019
0.038
0.112**
0.0004**
-0.078**
0.037
-
0.104
0.678
-0.006**
0.0003
-0.497
0.196**
2.174
0.148
2.176
0.847
0.018**
0.037**
0.104
-0.359
0.297
2.116
0.103
-0.458
0.312
1.866
0.393
0.233
-0.593*
0.493
-0.790
0.091
1.843
0.102
0.672
-
0.006**
0.059
0.016
0.396
0.060
0.018
0.389
0.235 0.0003**
-0.605* -0.064
-0.068
0.403 0.003**
-0.810
0.172
0.170
0.107
0.464
0.474
1.861
1.641
1.639
0.000
0.019
-814.88
-818.97
18
Spatial Lag and
Spatial Autocorrelation Coefficients
Earnings
Population
House Prices
Housing Stock
-0.426*
-0.0100
-0.0984
-0.0215*
TAC
-0.147*
-0.034**
0.0094**
0.0443**
SAC
0.794
0.836
0.853
0.952
 LSAC
0.118**
-.0400**
-0.0066**
-0.0602**
 (Determinant of
correlation matrix)
0.0049
0.0003
0.000091
0.0014
Spatial Lag ()
Error Parameters
*Coefficients significant at 0.05<p<0.1
** Coefficients significant at p>0.1
19
Spatial Correlation (SC): SUR Estimates
Jerusalem
Tel Aviv
Earnings
Population
Housing
Prices
Haifa
Earnings
Population
Housing
Prices
Krayot
Earnings
Population
Housing
Prices
Dan
Earnings
Population
Housing
Prices
Center
Earnings
Population
Housing
Prices
South
Earnings
Population
Housing
Prices
Sharon
Earnings
Population
Housing
Prices
North
Earnings
Population
Housing
Prices
Tel Aviv
Haifa
Krayot
Dan
Center
South
Sharon
0.4689
0.0592
0.4681
0.8367
0.5258
0.6395
0.4465
0.5760
0.4885
0.3769
0.1443
0.7259
0.3261
0.3571
0.3628
0.1686
-0.0986
0.7532
-0.0947
0.1560
0.3123
0.6699
0.7005
0.4088
0.4624
0.4381
0.1188
0.9057
0.6346
0.7662
0.2435
0.8092
0.2150
0.6846
0.0275
0.7621
-0.1596
0.6268
-0.0042
0.3445
0.6940
0.3192
0.5693
0.4371
0.7720
0.4450
0.5025
0.3631
0.4029
0.6501
0.5410
0.2653
-0.0672
0.6314
0.6675
0.1329
0.7591
0.3945
0.4096
0.4384
0.3180
0.2908
-0.3851
0.3490
0.6475
0.2860
-0.2398
0.1425
0.5510
0.2584
-0.4762
0.2024
0.1060
0.5066
-0.2845
0.1480
0.3680
0.2959
-0.4985
0.4834
0.5494
0.2491
-0.4704
0.4808
0.1975
0.3651
-0.1399
0.6307
0.0748
0.6995
0.1156
0.5167
0.2110
0.7510
0.2709
0.6013
0.1117
0.7970
0.4803
0.4715
0.0491
0.7944
0.3213
0.7682
0.2969
0.4116
0.5398
0.5781
0.6222
0.3496
-0.2150
0.3371
0.4529
0.6555
0.6104
0.1364
0.2913
0.4359
0.5999
-0.0331
0.3333
0.8813
0.4791
0.3159
0.1053
0.7927
0.4058
0.5648
0.2991
0.6439
-0.0860
0.1499
0.4946
0.5445
0.5896
-0.1297
0.2078
0.5638
-0.2150
0.1607
0.2438
0.7686
0.0463
0.1653 20
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
21
Simulated Impulse Responses:
2% Earnings Shock in Jerusalem
W age
Price
2.5%
2.0%
J erus alem
Sout h
1.5%
0.01%
0.25%
0.00%
0.20%
0.00%
D an
1.0%
0.08%
J erus alem
0.07%
Sout h
0.06%
D an
0.15%
0.00%
0.05%
0.04%
0.10%
0.5%
0.00%
0.0%
0.00%
0.03%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
0.05%
0.01%
0.00%
0.00%
-1.0%
0.00%
-0.05%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
-0.5%
Populat ion
0.01%
J erus alem
0.01%
Sout h
D an
0.00%
0.00%
0.0%
0.00%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
0.0%
0.00%
0.0%
0.00%
0.0%
0.00%
0.009%
-0.01%
0.001%
0.008%
J erus alem
0.001%
0.007%
Sout h
0.001%
0.006%
D an
0.005%
0.004%
0.003%
0.001%
0.000%
0.000%
0.002%
0.000%
0.001%
0.000%
0.000%
0.000%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
0.0%
0.00%
Area
0.1%
0.1%
0.02%
22
Simulated Impulse Responses:
2% Population Shock in Tel Aviv
W age
Populat ion
0.4%
0.08%
2.5%
0.2%
0.06%
2.0%
0.0%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
0.04%
-0.2%
0.02%
Tel-Av iv
D an
Kray ot
1.5%
0.01%
0.02%
-0.4%
0.01%
1.0%
0.00%
-0.6%
-0.02%
D an
-1.0%
Kray ot
-1.2%
-0.04%
0.0%
-0.06%
-0.5%
-0.01%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
Tel-Av iv
-0.8%
0.00%
0.5%
Price
Area
1.60%
1.40%
0.05%
0.140%
0.00%
0.120%
1.20%
-0.05%
0.60%
Tel-Av iv
D an
Kray ot
0.40%
0.20%
-0.10%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
-0.40%
Tel-Av iv
-0.005%
D an
Kray ot
-0.010%
0.080%
-0.015%
0.060%
-0.15%
-0.020%
0.040%
-0.20%
0.00%
-0.20%
0.100%
0.000%
0.020%
-0.25%
0.000%
-0.30%
-0.020%
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
1.00%
0.80%
-0.01%
-0.025%
-0.030%
-0.035%
23
Impulses 1991 With and Without SC
(a) 2% Earnings Shock in Jerusalem
(a)
Jerusalem
Dan
South
Earnings
-0.00664
-0.00664
-0.00307
0.00000
-0.00211
0.00000
Population
0.00073
0.00073
0.00043
0.00000
0.00023
0.00000
Prices
0.00421
0.00203
0.00370
0.00021
0.00328
0.00071
Housing Stock
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
Prices
0.01968
0.01345
-0.00801
-0.00272
0.00083
-0.00078
Housing Stock
0.00155
0.00119
-0.00053
-0.00031
0.00004
-0.00008
(b) 2% Population Shock in Tel Aviv
(b)
Tel Aviv
Dan
Krayot
Earnings
-0.00994
-0.00993
0.00630
0.00000
-0.00098
0.00000
Population
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
24
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
25
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
26