The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities

Gabor, Manuela Rozalia; Ştefănescu, Daniela; Conţiu, Lia Codrina Article The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic Journal Provided in Cooperation with: The Bucharest University of Economic Studies Suggested Citation: Gabor, Manuela Rozalia; Ştefănescu, Daniela; Conţiu, Lia Codrina (2010) : The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities, Amfiteatru Economic Journal, ISSN 2247-9104, The Bucharest University of Economic Studies, Bucharest, Vol. 12, Iss. 28, pp. 314-331 This Version is available at: https://hdl.handle.net/10419/168694 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 314 THE APPLICATION OF MAIN COMPONENT ANALYSIS METHOD ON INDICATORS OF ROMANIAN NATIONAL AUTHORITY FOR CONSUMERS PROTECTION ACTIVITIES Manuela Rozalia Gabor1∗, Daniela Ştefănescu2 and Lia Codrina Conţiu3 1) 2) 3) Petru Maior, University of Tîrgu Mureş, Romania Abstract The National Authority for Consumers Protection, Romania (NACP Romania) is the institution which records various trends from one development region to another as well as from one county to another. The indicators of NACP Romania activities are firmly correlated with other important macroeconomic indicators, even at the level of Romanian counties, hypothesis verified by the authors in a previous research. (Ştefănescu & Gabor, 2008) The paper tests the hypothesis that in the last decade there have been numerous structural changes regarding the economic indicators at county level and we will analyze the evolution of these structural changes in two different periods, respectively year 2000 and 2006, and especially the clustering of Romanian counties, taking into account the macroeconomic indicators and those recorded by NACP Romania, using a descriptive method of data analysis, the principal component analysis (PCA). By applying the PCA method, we can obtain useful information for NACP that, according to its specific tasks, cooperates with local government authorities regarding the development of consumer education strategy and the organization of control activities. In this regard, depending on the level of economic development of each county, the consumption characteristics of the population, the earnings level, as well as the GDP per capita, the NACP can develop differentiated strategies, adapted to the features of each county. Keywords: The National Authority for Consumers Protection from Romania, principal component analysis, macroeconomic indicators, counties, correlation JEL Classification: C02, C1, C19, D02, D03, D12, D18 Introduction Among the economic phenomena and processes there are interdependence relationships, under the influence of essential or non-essential factors that act either independently or grouped, forming another decisive factor in the development of these processes or phenomena. ∗ Corresponding author, Manuela Rozalia Gabor - [email protected] Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 315 Statistics, data analysis has, through descriptive methods of data analysis, powerful and effective tools of multidimensional analysis, tools by which derivative information can be gathered being important for market research, economic analysis, etc. Based on these methods the information can be ranked in terms of influence intensity and especially they can be analyzed as a whole and not independently. Less commonly used than the explanatory data analysis methods (regression, for example), descriptive methods provide additional benefits compared to them: the advantage of non-separation of variables into explanatory and explained ones, the advantage of being presented all these influences in a vector space that assembles and recommends these methods of data analysis. To analyze the data, the descriptive methods can be used successfully in the following cases: • to identify the basic dimensions or factors that explain correlations among multiple variables; • to identify a small set of new uncorrelated variables to replace the first set of correlated variables in multivariate analysis (regression analysis or discriminant analysis); • to identify a smaller set of basic variables starting with a larger body that can be applied to multivariate analysis; • seeking new concepts to reduce the number of variables that describe a situation (Petcu, 2003, p. 122); • testing assumptions on a set of variables (Petcu, 2003, p. 122). The study of many economic variables, which usually are correlated through descriptive analysis of data, is very important and it represents an useful piece of information for complex and detailed analyses, either for the company management and marketing or for local, regional or national characterizations. In economics, an individual - consumer, customer, organization, etc.- is characterized by more than one variable, and the other statistical methods (such as correlations) allow the analysis of each variable, but separately, while the descriptive analysis of data - and in particular the Main Component Analysis - allows addressing the multidimensional nature of data / variables that characterize an individual. In the present research, using the PCA method, we aimed at verifying the hypothesis regarding the Romanian counties distribution change and the way of NACP and macroeconomic indicators clustering, respectively, which of these groups of indicators characterize better the market conditions in each county. Another hypothesis aims to verify the extent to which the population of the more economically developed counties, i.e. with a higher level of GDP, would lead to a strengthening of the NACP control activity. Starting from the correlations already tested in a previous research, for which we obtained results which were statistically significant, we aim at identifying the NACP indicators that are combined with macroeconomic indicators and which influence the dispersion of the Romanian counties. From the correlations highlighted among the NACP indicators and the macroeconomic ones analyzed previously, we preserve the following: the Value of payments from fines to the budget and GDP (Spearman correlation coefficient: 0.62), Total AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 316 value of applied fines and GDP (Spearman correlation coefficient: 0.45), GDP and Number of trade firms (Spearman correlation coefficient: 0.67), Value of products infringement and Number of trade firms (Spearman correlation coefficient: 0.50), population and GDP (Spearman correlation coefficient: - 0.65). Results are guaranteed with a significance level of 0.01 and all show an average level of correlations intensity. By applying the PCA method, we aim at testing the hypothesis that the NACP indicators together with the macroeconomic indicators will form one of the main components and that this cluster follows the previously tested correlations. 1. Methodology – The description of the principal component analysis method (PCA) The basic of this method is to extract the smallest number of components to recover as much of the total information contained in the original data as possible, these new components expressing new attributes of individuals and built to be uncorrelated among them, each is a linear combination of original variables. (Giannelloni & Vernette, 2001, p. 382) This method provides a graphical view of the counties distribution map of the study, according to the similarities among them and the variables map, respectively the NACP and macroeconomic indicators according to their correlations. Although this method is based on the same principle as the factorial analysis (being a linear factorial method), the main component analysis differs with the factorial analysis through the way it defines the elements of the original data table and the calculation of distances among points. As a descriptive method of data analysis it only applies to quantitative variables and large tables that contain information about more than 15 individuals and 4 variables. Another feature that distinguishes it from the factorial analysis is given by the way it transforms the terms (Pintilescu, 2003, p. 24), such as in the main component analysis is used the relation (1), while in the factorial analysis is used the relation (2). j jij ij n xx x σ ∗ − = " (1) j jij ij xx x σ − = ' (2) PCA phases are illustrated in Figure no. 1. The stages shown above are followed by the interpretation of analysis results, Saporta and Stefanescu (1996, pp. 76-80) showing two kinds of interpretations to be made for PCA, respectively the "internal" interpretation the correlations among components resulted based on the principal component analysis and original variables (represented by the circle of correlations) and the "external" interpretation among variables and additional individuals, the counties, the explanation of the results being made based on data that were used to obtain them. Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 317 Figure no. 1: Stages of the Principal Components Analysis Source: Pintilescu, C., 2003. Analiza datelor. Iaşi: Editura Junimea, p. 37 In the main component analysis, in choosing the number of factorial axis to be analyzed, the components, the following criteria are used: • Kaiser's criterion (the criterion of supra-unitary value) which consists in choosing the number of axis for which the eigenvalues correspond to values greater than one (Saporta & Stefanescu, 1996, p. 507). • Evrard's criterion (the criterion of slope or “granularity“) based on the graphical representation of the eigenvalues and tracing the sudden failure of inertia explained by them. • Benzecri's criterion (the criterion of coverage percentage) that infers the choice of that amount of axis that explained more than 70% of the total variation of the cloud of points. • parallel analysis method (developed by Horn) is applicable to standardized data and requires generating random samples, the variables characteristic to population are presumed to be uncorrelated two by two. (Saporta & Stefanescu, 1996, pp. 508-509) • regression method is similar to parallel analysis but it does not involve generating random samples and the PCA does not have to be performed on each sample. (Saporta & Stefanescu, 1996, p. 511) In this paper, to ensure a higher degree of objectivity of data processing we used a cumulative number of the specified criteria: Kaiser, Evrard and Benzecri criteria. When selecting the number of main components, the standard linear combinations are used. They have as a starting point, instead of the R correlation matrix, the covariance matrix, and it is the choice of standard linear combinations having the biggest variance. Unlike factorial analysis - where the X variables variations are shaped through linear transformations of a fixed, limited number of factors called "hidden" or latent - PCA seeks linear combinations among variables, ordering them by their own values of covariance matrix. For the PCA method application we used SPSS program, and in detailing the internal and external interpretations we used Excel program for the descriptive statistics of the PCA results. Calculation of standardized eigenvectors of XTX or XXT correlations matrix Calculation of XTX or XXT matrix elements Calculation of XTX or XXT matrix eigenvalues Calculation of coordinates and contributions of statistical units and variables on the factorial axis Projection and representation of points in the factorial axis plan AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 318 2. Results obtained through PCA method The applicable approach of this method is based on the statistical data presented in Annexes 1 and 2, for both periods, respectively year 2000 and 2006 using the following groups of variables: • Variables specific to the activity carried on by NACP Romania: the total number of controls accomplished, the value of products infringement O.G. 21/1992 per total and for imported products, total value of applied fines and value of payments from fines to the budget; • Macroeconomic variables at the county level: population by county at 1 July, GDP per county, number of trade firms, turnover of trade firms, average net nominal monthly earnings per total economy. Based on the stages of PCA application, in the first stage we got the results illustrated in annexes 3 and 4 where the correlation matrices of the analyzed variables for the two periods are illustrated, Pearson correlation coefficients where it is noticed high values for many variables. It is a sign of information redundancy and therefore we try to reduce the dimensionality applying the PCA method both for year 2000 and 2006, and further on we will analyze if during these two periods there were significant structural changes regarding the clustering of Romanian counties based on these variables . The only variable that has changed is the average net nominal monthly earnings (ANNME) which recorded an increase of the correlation intensity with other variables of component 1, as well as with the variable the total number of products infringement, from a weak negative correlation in 2000 to an average positive correlation in 2006. For the second phase of the PCA method application, respectively the calculation of their correlation matrix values, the SPSS program has generated results for the two periods considered which are illustrated in Tables 1 and 2. It can therefore be noticed that both for year 2000 and 2006, only two main components can be retained, Romania’s counties will be represented by two factorial axis formed by the combination of original variables, since only two components obtained values greater than 1 (Kraiser criterion). Another criterion was taken into account in choosing the two factorial axes, respectively two main components, the Benzecri criterion, and according to data from Tables no. 1 and no. 2 these components explain together more than 70% of the total variance of the cloud of points. Table no. 1: Total Variance and Eigenvalues Explained for year 2000 Initial Eigenvalues Extraction Sums of Squared Loadings Component Total % of Variance Cumulative % Total % of Variance Cumulative % 1 6,595 65,949 65,949 6,595 65,949 65,949 2 1,311 13,108 79,058 1,311 13,108 79,058 3 ,761 7,611 86,669 … … … … 10 ,006 ,058 100,000 Extraction Method: Principal Component Analysis. Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 319 Table no. 2: Total Variance and Eigenvalues Explained for year 2006 Initial Eigenvalues Extraction Sums of Squared Loadings Component Total % of Variance Cumulative % Total % of Variance Cumulative % 1 6,885 68,846 68,846 6,885 68,846 68,846 2 1,900 18,995 87,842 1,900 18,995 87,842 3 ,514 5,138 92,980 … … … … 10 0,007 0,067 100,000 Extraction Method: Principal Component Analysis. Based on the results shown in Tables no. 1 and no. 2, we deduced that only two components have eigenvalues greater than 1, expressing 79% of the total variance in year 2000 and 88% in year 2006, which means that we can use them to represent the cloud of points in the main plan. The increase of the total variation proportion explained by the two components is the result of the increased correlation intensity, from low to medium level, of the average net nominal monthly earnings variable with other variables of component 1. The graphical representation specific to PCA method, the screen plot obtained, identical for the two periods analyzed, confirmed the two main components resulted from the application of the method, illustrated in Figure no. 2. Scree Plot Component Number 10987654321 Eigenvalue 8 7 6 5 4 3 2 1 0 Figure no. 2: Graph Eigenvalues Analyzing the graphical representation of eigenvalues, and following the Evrard criterion in obtaining the number of main components, we can choose 2 components. If we want to reduce the amount of information and that only the first 2 components bring additional information compared to a variable in the original form, then we preserve only the latter. Also, we should note that a proportion of 79% of the initial information for year 2000 and 88% for year 2006 is extracted from the new variables. We notice that the variables (according to the two correlations matrices from Annexes 3 and 4) value of products infringement O.G. 21/1992 _total and value of products infringement O.G. 21/1992_import AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 320 do not correlate strongly with any of the variables of component 1. In Figures no. 3 and no. 4 are illustrated the components through axes rotation by Varimax method for the two periods. The values of the correlation coefficients from annexes 3 and 4 serve as coordinates of the initial variables in the vector plan of the two main components. Figure no. 3: Year 2000 Figure no. 4: Year2006 Analyzing the two graphical representations from Figures no. 3 and no. 4, it becomes clear that the first main component is close to the variables that describe both the measurement indicators of the activity of NACP Romania and the macroeconomic indicators, while the second main component is close to the value of products infringement O.G. 21/1992 both per total value and imported products. But there are recorded changes of variables clustering on the two components from one year to another as such: • transition from negative values of the first component of the average net nominal monthly earnings variable to positive values far from the OX axis formed by the components 2, so its contribution grows in year 2006 compared to 2000 to the component formation; • OX axis distancing, axis that describes the main component 2 of the total value of products infringement variable that forms component 2 and the proximity of the value of the imported products infringement variable, these two variables forming component 2. The results generated by SPSS program for the main component matrix after Varimax rotation in normalizing the eigenvectors according to the third stage of the method, as well as the coordinates of the statistical units contributions and the variables on the factor axes, according to the fourth stage of the PCA method, are presented in Tables no. 3 and no. 4. Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 321 Table no. 3: Rotated Principal Component Matrix – year 2000 Component Initial Variables 1 2 GDP per county ,956 ,084 Number of trade firms ,955 ,098 Population by county at 1 July ,936 ,059 Total value of applied fines ,933 ,199 Value of payments from fines to the budget ,899 ,257 Total number of controls effected ,888 ,172 Turnover of trade firms ,873 ,186 Average net nominal monthly earnings ,638 -,069 Value of products infringement O.G. 21/1992 _total ,028 ,859 Value of products infringement O.G. 21/1992_import ,163 ,777 Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations Table no. 4: Rotated Principal Component Matrix – year 2006 Component Initial Variables 1 2 N umber of trade firms ,973 ,061 GDP per county ,966 ,098 Turnover of trade firms ,934 ,125 Population by county at 1 July ,930 -,007 Total value of applied fines ,919 ,206 Value of payments from fines to the budget ,916 ,197 Total number of controls effected ,842 ,200 Average net nominal monthly earnings ,682 ,470 Value of products infringement O.G. 21/1992_import ,091 ,982 Value of products infringement O.G. 21/1992 _total ,124 ,974 Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations. To represent the counties distribution on the map, respectively the counties of Romania, we used their coordinates which can be found in the variables of main component 1 and main component 2, the phases 3 and 4 of the methodological approach, by calculating the standardised eigenvectors of the correlation matrix. In Tables no. 3 and no. 4 can be noticed the clustering of the ten initial variables on the two new main components related to variables of the two periods analyzed. It is also noticed that the two variables describing specific indicators of NACP Romania explains only 13% of total variance for year 2000 and 19% for year 2006. Regarding the initial variables clustering around the two main components it is their ranking that has changed in year 2006 compared to year 2000, respectively: AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 328 ANNEX 1 Statistical data used - 2000 Value of products infringement O.G. 21/1992 (thou RON) County Total number of controls effected Total Of which: from imports Total value of applied fines ( thou RON) Value of payments from fines to the budget (thou RON) GDP per county (thou RON) Population by county at 1 July Number of trade firms Turnover of trade firms (thou RON) Average net nominal monthly earnings (thou RON) Alba 1826 2035 124 67 44 1322,1 395941 2264 11753 188,45 Arad 1713 439 308 100 66 1838,8 476272 3211 29499 191,99 Arges 2173 561 205 103 86 2451,0 671514 5415 35831 203,24 Bacau 2477 1669 495 148 102 2154,8 752761 4946 32586 204,69 Bihor 1622 9510 520 90 78 2146,3 620517 6598 37653 184,84 Bistrita Nasaud 1434 435 77 51 43 944,5 326278 2050 10502 189,99 Botosani 1904 439 130 74 46 925,8 463808 1869 8375 171,02 Brasov 1917 865 323 165 106 2734,7 628643 6536 54510 217,63 Braila 1199 667 509 44 27 1041,2 385749 3175 14215 187,19 Buzau 1569 782 200 71 41 1317,8 504540 4281 17096 195,8 Caras Severin 851 119 99 66 36 1070,7 353209 1789 7957 185,05 Calarasi 859 136 16 56 30 709,1 331843 2021 8124 167,36 Cluj 1909 2747 373 95 77 3241,5 719864 7461 53981 209,71 Constanta 3339 1310 863 234 191 3187,5 746041 7192 53885 241,7 Covasna 937 172 78 66 45 885,7 230537 1553 10587 178,69 Dambovita 837 113 30 33 20 1403,0 551414 2562 12311 210,17 Dolj 1765 622 254 121 85 2147,3 744243 6522 34279 219,48 Galati 1342 566 169 68 42 1995,1 644077 5958 28902 240,5 Giurgiu 1318 551 35 85 54 564,5 294000 1600 14794 192,95 Gorj 1155 55 2 63 39 1668,1 394809 2895 12163 264,58 Harghita 669 1676 1621 38 16 1239,5 341570 2215 16009 175,69 Hunedoara 1191 462 285 78 38 1703,2 523073 3906 19998 238,25 Ialomita 1128 595 147 72 63 836,6 304327 1680 10122 194,46 Iasi 1412 447 166 71 26 2469,1 836751 6246 34139 185,83 Ilfov 1203 3348 1566 135 111 1521,5 275482 2683 12111 247,5 Maramures 946 429 144 53 30 1355,5 530955 3517 16484 181,26 Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 329 Mehedinti 952 480 225 40 35 779,5 321853 2000 7414 223,68 Mures 1709 308 161 111 98 2403,0 601558 4052 23564 195,91 Neamt 1629 1864 1240 74 49 1483,8 586229 3210 16723 175,53 Olt 1052 188 81 45 36 1387,7 508213 2906 8751 223,62 Prahova 2170 679 245 150 85 2794,1 855539 7030 45145 226,77 Satu Mare 714 404 81 43 42 1134,3 390121 2300 16757 176,99 Salaj 820 656 277 41 39 678,9 256307 1489 7759 185,87 Sibiu 1496 523 180 89 56 1592,5 443993 3120 24114 198,34 Suceava 1929 762 108 76 45 1802,5 717224 4213 21744 177,4 Teleorman 1464 353 128 83 35 1048,8 456831 2857 40307 201,83 Timis 1687 1048 308 127 100 2914,1 688575 6379 49266 194,33 Tulcea 940 110 38 60 29 627,6 262692 2138 7898 187,87 Vaslui 1592 3271 66 147 125 798,8 466719 2027 7888 180,97 Valcea 1184 312 51 67 31 1506,3 430713 3111 15978 200,25 Vrancea 2554 1651 323 146 116 1117,6 391220 2589 11416 179,83 Municipiul Bucureşti 4896 1395 773 451 351 15357,7 2009200 34535 93669 277,45 ANNEX 2 Statistical data used - 2006 Value of products infringement O.G. 21/1992 (thou RON) County Total number of controls effected Total from which: from imports Total value of applied fines ( thou RON) Value of payments from fines to the budget (thou RON) GDP per county (thou RON) Population by county at 1 July Number of trade firms Turnover of trade firms (thou RON) Average net nominal monthly earnings (thou RON) Alba 2578 2828 2222 161 147 5974.1 378614 2745 2564 756 Arad 3775 9727 8486 748 798 8406.7 458847 4286 5015 790 Arges 2754 1960 1326 969 838 11770.9 644590 6329 7388 882 Bacau 2129 3485 3019 367 277 8506,0 721411 5623 5043 845 Bihor 5515 5970 2600 932 714 9475.4 594982 7230 6818 692 Bistrita Nasaud 3432 1736 1140 526 415 4086.3 317685 2499 1845 727 Botosani 2061 491 161 313 191 3561.3 456765 1968 1490 715 Brasov 4397 12823 8498 963 771 11261.3 595758 7310 9354 815 Braila 2249 2680 2262 247 137 4156,0 367661 3580 2651 730 Buzau 3260 1247 712 467 420 5334.2 490981 4909 3192 724 Caras Severin 2082 1032 742 346 254 4445.2 330517 2144 1314 732 AE The Application of Main Component Analysis Method on Indicators of Romanian National Authority for Consumers Protection Activities Amfiteatru Economic 330 Calarasi 1294 598 391 305 259 2686.8 316294 2331 1254 681 Cluj 4807 18941 15371 699 448 13558.6 689523 8500 10284 905 Constanta 5863 6461 5245 1542 1200 14653.3 716576 8736 9438 914 Covasna 1598 458 390 175 164 2779.7 223770 1761 1721 656 Dambovita 2038 1475 936 318 230 6402.5 535087 3132 2479 860 Dolj 3435 2317 1573 740 666 8839.4 715989 7510 6111 855 Galati 1741 3555 1972 364 340 7159.3 617979 6673 5319 834 Giurgiu 1987 1086 469 407 368 2477.6 284501 1739 2792 763 Gorj 3125 4072 1713 593 398 5984.1 383557 3032 2068 965 Harghita 1777 896 543 215 195 4464.5 326347 2861 2375 704 Hunedoara 3125 2994 2279 828 751 6867.1 477259 4490 3497 813 Ialomita 1804 2407 737 601 422 3341.3 291178 1874 1943 735 Iasi 2698 13290 1165 623 556 10040.6 824083 7317 6518 792 Ilfov 3173 41292 39882 797 682 8696.9 288296 3849 13833 1012 Maramures 2240 5182 3736 356 280 5932.2 515313 3814 3256 702 Mehedinti 2457 2106 1429 415 286 3246.6 301515 2113 1263 876 Mures 3247 599 377 487 424 8174.1 583210 5142 4492 784 Neamt 1794 3357 2299 231 198 5852.7 567908 4057 2845 710 Olt 2464 1114 749 290 259 4560.4 479323 3190 1805 804 Prahova 3592 12860 11247 944 804 13775.3 823509 7514 7558 889 Satu Mare 1413 14318 14022 277 215 4699.7 367677 2786 2759 778 Salaj 1985 1902 1134 148 134 3054,0 244952 1876 1371 781 Sibiu 2584 1503 753 530 392 7637.5 423119 3677 5073 834 Suceava 3118 1082 461 395 252 7054.5 705730 4662 4191 726 Teleorman 2429 572 351 290 294 3847,0 417183 2869 1665 760 Timis 1882 8387 7235 329 287 16069.9 660966 7768 8594 858 Tulcea 1593 774 250 343 198 3027.3 251614 2095 1220 763 Vaslui 2433 1552 710 519 485 5958.7 413511 3367 2559 768 Valcea 2832 1604 1046 325 337 3414.8 456686 2449 1479 717 Vrancea 3024 22395 20581 428 335 4178.6 393023 3055 2121 768 Municipiul Bucureşti 8158 10288 9038 2462 2097 69013.9 1931236 38766 89441 1142 Protection of Consumers’ Rights and Interests AE Vol XII • No. 28 • June 2010 331 ANNEX 3 Correlation Matrix for the variables of year 2000 No_controls Value_total Value _imports Fines Payment_budget GDP per county Population No trade firms Turnover ANNME No_controls 1,000 ,174 ,221 ,912 ,892 ,799 ,823 ,800 ,781 ,435 Value_total 1,000 ,382 ,171 ,233 ,096 ,113 ,135 ,213 -,044 Value _imports 1,000 ,298 ,314 ,242 ,171 ,225 ,248 ,185 Fines 1,000 ,980 ,876 ,823 ,870 ,797 ,541 Payment_budget 1,000 ,851 ,776 ,838 ,762 ,519 GDP per county 1,000 ,928 ,991 ,824 ,559 Population 1,000 ,942 ,867 ,499 No trade firms 1,000 ,840 ,553 Turnover 1,000 ,496 ANNME 1,000 ANNEX 4 Correlation Matrix for the variables of year 2006 No_controls Value_total Value _imports Fines Payment_budget GDP per county Population No trade firms Turnover ANNME No_controls 1,000 ,300 ,260 ,890 ,866 ,755 ,727 ,772 ,719 ,577 Value_total 1,000 ,969 ,302 ,295 ,223 ,145 ,198 ,243 ,476 Value _imports 1,000 ,266 ,262 ,2045 ,086 ,167 ,237 ,474 Fines 1,000 ,987 ,845 ,784 ,846 ,815 ,705 Payment_budget 1,000 ,846 ,786 ,847 ,818 ,687 GDP per county 1,000 ,918 ,989 ,981 ,697 Population 1,000 ,940 ,861 ,613 No trade firms 1,000 ,972 ,662 Turnover 1,000 ,668 ANNME 1,000