The document summarizes research applying spatial filtering techniques to analyze economic convergence across European regions from 1995 to 2007. Spatial filters were used to account for heterogeneity and spatial dependence among economies. A regression model was estimated to examine the relationship between regional growth rates and variables like initial GDP, investment, technology, unemployment, agriculture, and education. The model found evidence of conditional beta-convergence across regions. Local parameter estimates varied spatially according to eigenvectors representing different geographic scales.

1. Fifth International Workshop on
"Geographical Analysis, Urban Modeling, Spatial Statistics"
GEOG-AN-MOD 10
The Application of Spatial Filtering Technique
to the Economic Convergence of the
European Regions
between 1995 and 2007
Francesco Pecci, Nicola Pontarollo
Department of Economics,
Univesity of Verona

2. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Aim of the work
Evaluate the convergence rates of European regions
by the application of the spatial filtering technique that
is able to manage:
•Economic etherogeneity economies are structurally
different
economies are not isolated
•Spatial dependence islands
Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 2

3. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Economic convergence:
the beta-covergence model
log yt  log yt T      log y  Z  
t T
T
• it correlates the initial stage of developement T-t
with the mean growth rate for a chosen period T;
• α is the intercept;
• β is the so-called convergence rate;
• Z represents the explanatory variable and ϕ the
pameter;
• ε is the error term.
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4. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The augmented model: the variables
• GVAEMP07 = log of the regional GVA per worker in region i
in 2007;
• GVAEMP95 = log of regional GVA per worker in region i in
1995;
• SCEMP03 = log of (δ + g + ni) where (δ + g) = 0.03,
ni = average growth in employment between 1995 and 2007
in each region;
• SAVEGVA = log of the average investment as a per cent of
GVA, a proxy for the saving rate in the region i between 1995
and 2007;
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5. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
(…continue) the variables
• TECHEMPe = log of the average workers in high-tech sectors
as per cent of total employees in the region i between 1995
and 2007 (Eurostat Regio);
• LONGUNEMPe = log of the average of long-term
unemployment (more than 12 months) as per cent of the
total unemployed in the region i between 1999 and 2007
(Eurostat Regio), an indicator of the rigidity of the labour
market;
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6. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
(…continue) the variables
• EMPAGRIe = log of the average employees in agriculture as
per cent of total employees in the region i between 1995
and 2007 (Eurostat Regio);
• LNLIFLEARe = log of the participants in programs of long life
learning as per cent of total employees in region i between
1999 and 2007 (Eurostat Regio).
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7. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The β-convergence augmented model
T 13 GVAEMP 07i  GVAEMP 95i     GVAEMP 95i
 1SCEMP 03i  2 SAVEGVAi  3TECHEMPei 
 4 LONGUNEMPei  5 EMPAGRIei  6 LNLIFLEA Rei  
We expect that the coefficients of:
• GVAEMP95 would be negative (it means convergence);
• SCEMP03, LONGUNEMPe, EMPAGRIe would be negative
because they give a negative contribution to the economic
growth;
• SAVEGVA, TECHEMPe, LNLIFLEARe would be positively
correlatetd with the dependent variable.
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8. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
• It uses of Moran’s measure of spatial autocorrelation (MC).
n n
n
 (y
i 1
i  y) c ij (y j  y)
j1
MC n n n
  cij
i 1 j1
 (y i  y) 2
i 1
The better results are given by:
• a Gabriel Graph contiguity matrix (1 if a contiguous neighbor,
0 if not);
• globally standardized (C scheme).
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9. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Spatial autocorrelation of the variables
Variable Moran’s Coefficient
GVAEMP95 0.8916
SCEMP03 0.1115
SAVEGVA 0.5684
TECHEMPe 0.4124
LONGUNEMP 0.6774
EMPAGRI 0.7248
LNLIFLEAR 0.7477
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10. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
Steps:
1. Determine MCM matrix that corresponds with the
numerator of MC:
 11T   11T 
I -
 C I -
  

Where:  n   n 
• I is a n-by-n identity matrix and 1 is a n-by-1 vector of ones;
• (I – 11T/n) = M ensures that the eigenvector means are 0;
• symmetry ensures that the eigenvectors are orthogonal;
• M ensures that the eigenvectors are uncorrelated;
• thus, the eigenvectors represent all possible distinct (i.e.,
orthogonal and uncorrelated) spatial autocorrelation map
patterns for a given surface partitioning.
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11. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
2. Decompose MCM matrix into series of uncorrelated matrix
of variables.
- First eigenvector (E1) of matrix is the set of values that
has the largest MC achievable.
- Second eigenvector (E2) is the set of values that has the
largest MC achievable for values not correlated with E1.
And so on.
The eigenvectors can be used as predictive variables in a
regression and the ones associated with:
• the largest MC have global geographic scale,
• the ones whith the medium MC values a regional scale,
• and the ones with lower MC values a local scale.
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12. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
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13. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
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14. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial filters
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15. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial model
Spatial filtering enables easier implementation of GWR, as well as
proper assessment of its dfs.
p
Y   0,GWR   X p   p ,GWR 
p 1 Element
per element
 K0
 p  Kp

  0 1   Ek  k      0 1   Ek  k   X p product
 0   p 
 
0 p
k 0 1 p 1  k p 1 
intercept coefficients Variables
of the variables
Iteraction terms
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16. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial model
3. Compute all of the interactions terms XjEk for the P covariates
times the 71 candidate eigenvectors with MC > 0.25;
4. select from the total set, including the individual
eigenvectors, with stepwise regression;
5. the geographically varying intercept term is given by:
K
a i  a   E i, k b E i, k
k 1
6. the geographically varying covariate coefficient is given by
factoring Xj out of its appropriate selected interaction terms:
 
bi, j X j   b j   E i,k b X jEi, k X j
K
 k 1 
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17. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
The spatial model
Example: the computation of local beta
Coefficient of the variable Coefficient of the 6_th eigenvector
6_th eigenvector
beta = − 0.01469− 0.06595*E6 + 0.03642*E18 − 0.06540*E26
+ 0.04771*E36 + 0.02629*E60 − 0.02146*E62 + 0.01071*E68
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18. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Global (average) parameters values
Spatial Filtered Model OLS Model
Variable
Coefficient Std. Error Coefficient Std. Error
Intercept 0.0767*** 0.0057 0.0998*** 0.0099
GVAEMP9 -0.0147*** 0.0009 -0.0107*** 0.0012
SCEMP03 -0.0003 0.0004 -0.001 0.0007
SAVEGVA 0.0069*** 0.0019 0.0181*** 0.0024
TECHEMP 0.0019 . 0.0010 0.0064*** 0.0019
LONGUNEMP -0.0015* 0.0006 -0.0004 0.0009
EMPAGRI -0.0201* 0.0084 0.0147 0.0107
LNLIFLEAR 0.0089 0.0091 0.0304** 0.0111
R sqr. (adj.) 0.9613 (0.9352) 0.5194 (0.506)
Sign.: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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19. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Local parameters values
Variable Min. 1st Qu. Median Mean 3rd Qu. Max.
Intercept -0.0651 0.0409 0.0696 0.0767 0.1061 0.3345
GVAEMP95 -0.0423 -0.0192 -0.0142 -0.0147 -0.0092 0.0008
SCEMP03 -0.0118 -0.0029 -0.0004 -0.0003 0.0021 0.0146
SAVEGVA -0.0226 -0.0009 0.0072 0.0069 0.0147 0.0403
TECHEMP -0.0294 -0.0028 0.0013 0.0019 0.0077 0.0247
LONGUNEMP -0.0106 -0.0043 -0.0019 -0.0015 0.0011 0.0096
EMPAGRI -0.2401 -0.0680 -0.0211 -0.0201 0.0227 0.3705
LNLIFLEAR -0.2153 -0.0392 0.0129 0.0089 0.0598 0.1861
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20. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Significant eigenvectors of the model
Scale of the eigenvectors associated to every variable
Variable Global Regional Local
(MC>0.75) (0.75>MC>0.50) (0.50>MC>0.25)
Intercept E6, E18, E19 E26, E35, E36, E44 E60
GVAEMP95 E6, E18, E26 E36 E60, E62, E68
E5, E6, E9, E10,E18,
SCEMP03 E26, E36, E38 E44, E48
E19, E22
SAVEGVA E6, E12, E16, E18, E22 E30, E38, E43
E26, E30, E36, E38,
TECHEMP E9, E10, E16, E19 E51, E69
E43
E47, E51, E60,
LONGUNEMP E5, E12, E17
E62,E69
EMPAGRI E1, E9, E11, E24 E27, E31, E38 E46, E50, E70
E45, E48, E49,
LNLIFLEAR E13, E17 E33
E51,E65, E66, E69
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21. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Convergence rates of GVA per worker
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22. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Regional convergence rates of GVA per worker in EU-15
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23. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Regional convergence rates of GVA per worker in EU-NMS
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24. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Results
Correlation between convergence rates and initial GVA per worker
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25. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Conclusions
• in EU-27 the regional economies are structurally different,
and, as a consequence, there are many different path of
growth;
• regional convergence rates (and the coefficient of the other
variables) differ within the same country;
• it exists some clusters of regions with similar structures;
• NMS and EU-15 countries does not have common economic
structure within them dummy variables or artificial
spatial partitions are not able to manage this phenomenus;
• spatial filters give us the information about the scale of
influence of every variable useful information for policy
makers.
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26. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Further research fields
• To deep the analysis of European regional economies in view
of these results;
• to build spatial clusters for identifying economies with
common structural characteristics;
• to evaluate the effects of specific policies in relation to their
scale of intervention.
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27. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions
Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 27