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- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 3
- 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; Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 4
- 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; Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 5
- 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). Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 6
- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 7
- 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) j1 MC n n n cij i 1 j1 (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). Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 8
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 9
- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 10
- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 11
- 12. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions The spatial filters Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 12
- 13. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions The spatial filters Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 13
- 14. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions The spatial filters Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 14
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 15
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 16
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 17
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 18
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 19
- 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 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 20
- 21. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions Results Convergence rates of GVA per worker Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 21
- 22. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions Results Regional convergence rates of GVA per worker in EU-15 Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 22
- 23. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions Results Regional convergence rates of GVA per worker in EU-NMS Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 23
- 24. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions Results Correlation between convergence rates and initial GVA per worker Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 24
- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 25
- 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. Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 26
- 27. - Aim - Growth model - Spatial filters - Spatial model - Results - Conclusions Spatial Filtering & European Economic Convergence F. Pecci & N. Pontarollo 27

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