The Application of Spatial Filtering Technique to the Economic Convergence of the European Regions between 1995 and 2007 Francesco Pecci, Nicola Pontarollo

The Application of Spatial Filtering Techniqueto the Economic Convergence of the

European Regions between 1995 and 2007

Francesco Pecci, Nicola Pontarollo

Department of Economics,

Univesity of Verona

Fifth International Workshop on

"Geographical Analysis, Urban Modeling, Spatial Statistics"

GEOG-AN-MOD 10

Aim of the work

Evaluate the convergence rates of European regions

by the application of the spatial filtering technique that is able to manage:

economies are structurally different

economies are not isolated islands

- Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions

•Economic etherogeneity

•Spatial dependence

F. Pecci & N. PontarolloSpatial Filtering & European Economic Convergence 2

Economic convergence: the beta-covergence model

• it correlates the initial stage of developement T-twith 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 thepameter;

• ε is the error term.



ZyT

yyTt

Ttt logloglog

The augmented model: the variables

• GVAEMP07 = log of the regional GVA per worker in region iin 2007;

• GVAEMP95 = log of regional GVA per worker in region i in1995;

• SCEMP03 = log of (δ + g + ni) where (δ + g) = 0.03,ni = average growth in employment between 1995 and 2007in each region;

• SAVEGVA = log of the average investment as a per cent ofGVA, a proxy for the saving rate in the region i between 1995and 2007;



• TECHEMPe = log of the average workers in high-tech sectorsas per cent of total employees in the region i between 1995and 2007 (Eurostat Regio);

• LONGUNEMPe = log of the average of long-termunemployment (more than 12 months) as per cent of thetotal unemployed in the region i between 1999 and 2007(Eurostat Regio), an indicator of the rigidity of the labourmarket;


(…continue) the variables


• EMPAGRIe = log of the average employees in agriculture asper cent of total employees in the region i between 1995and 2007 (Eurostat Regio);

• LNLIFLEARe = log of the participants in programs of long lifelearning as per cent of total employees in region i between1999 and 2007 (Eurostat Regio).

(…continue) the variables



The β-convergence augmented model

We expect that the coefficients of:

• GVAEMP95 would be negative (it means convergence);

• SCEMP03, LONGUNEMPe, EMPAGRIe would be negativebecause they give a negative contribution to the economicgrowth;

• SAVEGVA, TECHEMPe, LNLIFLEARe would be positivelycorrelatetd with the dependent variable.



iii

iii

iii

LNLIFLEAEMPAGRIeLONGUNEMPe

TECHEMPeSAVEGVASCEMP

GVAEMPGVAEMPGVAEMPT

Re

03

959507

654

321

13

n

1i

2

i

n

1i

n

1j

jiji

n

1i

n

1j

ij )y(y

)y(yc)y(y

c

nMC

• It uses of Moran’s measure of spatial autocorrelation (MC).

The better results are given by:• a Gabriel Graph contiguity matrix (1 if a contiguous neighbor,

0 if not);• globally standardized (C scheme).

The spatial filters



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

Spatial autocorrelation of the variables



Steps:1. Determine MCM matrix that corresponds with the

numerator of MC:

n-IC

n-I

TT 1111

The spatial filters

Where:

• 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 mappatterns for a given surface partitioning.



2. Decompose MCM matrix into series of uncorrelated matrixof 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 spatial filters


The eigenvectors can be used as predictive variables in aregression 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.


The spatial filters



The spatial filters



The spatial filters



The spatial model

Spatial filtering enables easier implementation of GWR, as well asproper assessment of its dfs.

intercept coefficientsof the variables

Variables

Elementper element

product

Iteraction terms


p

p

p

K

k

kk

K

k

kk

p

p

GWRppGWR

XEE

XY

p

p

pp

1 1

0

1

0

1

,,0

110

0

00


3. Compute all of the interactions terms XjEk for the P covariatestimes the 71 candidate eigenvectors with MC > 0.25;

4. select from the total set, including the individualeigenvectors, with stepwise regression;

5. the geographically varying intercept term is given by:

6. the geographically varying covariate coefficient is given byfactoring Xj out of its appropriate selected interaction terms:

K

1k

Eki,i ki,bEaa

The spatial model

j

K

1k

EXki,jjji, XbEbXbki,j



The spatial model



beta = − 0.01469− 0.06595*E6 + 0.03642*E18 − 0.06540*E26

+ 0.04771*E36 + 0.02629*E60 − 0.02146*E62 + 0.01071*E68

Coefficient of the variable Coefficient of the 6_th eigenvector

6_th eigenvector

Example: the computation of local beta

VariableSpatial Filtered Model OLS Model

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)


F. Pecci & N. PontarolloSpatial Filtering & European Economic Convergence

Sign.: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Results

18

Global (average) parameters values



Results

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

19

Local parameters values

Variable

Scale of the eigenvectors associated to every variable

Global(MC>0.75)

Regional(0.75>MC>0.50)

Local(0.50>MC>0.25)

Intercept E6, E18, E19 E26, E35, E36, E44 E60

GVAEMP95 E6, E18, E26 E36 E60, E62, E68

SCEMP03E5, E6, E9, E10,E18,

E19, E22E26, E36, E38 E44, E48

SAVEGVA E6, E12, E16, E18, E22 E30, E38, E43

TECHEMP E9, E10, E16, E19E26, E30, E36, E38,

E43E51, E69

LONGUNEMP E5, E12, E17E47, E51, E60,

E62,E69

EMPAGRI E1, E9, E11, E24 E27, E31, E38 E46, E50, E70

LNLIFLEAR E13, E17 E33E45, E48, E49,

E51,E65, E66, E69

ResultsSignificant eigenvectors of the model


Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 20

Results



Convergence rates of GVA per worker

Results

Regional convergence rates of GVA per worker in EU-15



Results

Regional convergence rates of GVA per worker in EU-NMS



ResultsCorrelation between convergence rates and initial GVA per worker





Conclusions

25

• in EU-27 the regional economies are structurally different,and, as a consequence, there are many different path ofgrowth;

• regional convergence rates (and the coefficient of the othervariables) differ within the same country;

• it exists some clusters of regions with similar structures;

• NMS and EU-15 countries does not have common economicstructure within them dummy variables or artificialspatial partitions are not able to manage this phenomenus;

• spatial filters give us the information about the scale ofinfluence of every variable useful information for policymakers.



Further research fields

26

• To deep the analysis of European regional economies in viewof these results;

• to build spatial clusters for identifying economies withcommon structural characteristics;

• to evaluate the effects of specific policies in relation to theirscale of intervention.



Documents

The Application of Spatial Filtering Technique to the Economic Convergence of the European Regions between 1995 and 2007 Francesco Pecci, Nicola Pontarollo