ANALISYS OF THE INTERREGIONAL
MOBILITY FLOWS - USE OF THE
ECONOMETRIC LINEAR MODEL
PhD. Univ. Lecturer Aniela B L CESCU PhD. Candidate Assistant Irina CHIRTOC “Constantin Brâncuşi” University from Targu-Jiu
Abstract
The phenomenon of labour’s mobility is extremely complex, multidimensional, plurivalent, diffi cult to decipher in structure and amplitude. Although unfolds amid and in the conditions of the economies’ globalization, free labour circulation run against the institutional, national and international constraints, of the behavioural constraints of the population from the areas and regions of destination as well as constraints that are the results of the diffi culties of adaptations of the new arrivals.
The labour’s mobility is approached both in theory and in practice in relation with the necessity of a balanced social and economic development in regional plan combining the aspects of structural order with the ones of functional order.
Key words: mobility fl ows; interregional mobility; multifactor model; dependent variable; independent variable.
***
By using the multifactorial regression model was analyzed the interdependence between the interregional mobility fl ows and a series of independent variables.
The set of data includes the dependent variable - considered the interregional mobility fl ows and the independent variables: the number of the unemployed persons, the number of employees, the monthly wage, the payments made for the stimulation of the labour’s mobility, the scholar population from the higher education system.
Evolution of the dependent and independent variable in each county and Bucharest Municipality
Counties
Inter-regional mobility
fl ows
yi Number of un-employed x1 Number of employees x2 Net monthly earnings of the
average wage x3 Payments to encourage labour mobility x4 School population in higher education x5
Alba 12029 12827 91854 1128 401254 5395
Arad 15461 6549 124410 1143 209757 20477
Argeş 25453 13131 146835 1269 85370 15666
Bac u 25573 12411 121996 1254 80780 7512
Bihor 20104 8596 167334 1004 74190 21013
Bistriţa –N s ud 9552 3614 60868 1085 232670 1473
Botoşani 13804 5519 56570 1036 125970 361
Braşov 20036 10655 169429 1226 108480 60519
Br ila 9542 6026 75845 1125 61310 2021
Buz u 17087 10854 87004 1106 230010 222
Caraş-Severin 13371 7698 63672 1054 336697 3845
C l raşi 11423 5463 47498 1058 26500 499
Cluj 21271 9998 199066 1315 16769 61487
Constanţa 29168 9612 193725 1291 22010 40093
Covasna 5341 6786 50998 987 23730 1215
Dâmboviţa 19941 11715 84077 1184 109230 8037
Dolj 23771 24310 136003 1216 161620 37650
Galaţi 17647 14538 128334 1219 89890 20363
Giurgiu 9121 4181 34199 1161 13000 0
Gorj 16712 10994 79329 1503 225830 6307
Harghita 7681 9280 67335 998 99387 1796
Hunedoara 16272 13826 128927 1157 246790 6697
Ialomiţa 10644 5204 47748 1087 42740 0
Iaşi 28759 16905 164886 1257 36097 60226
Ilfov 18927 2098 103552 1560 0 236
Maramureş 12836 7577 94097 1018 107680 6282
Mehedinţi 12318 11429 49028 1261 225830 3176
Mureş 18452 11607 130740 1133 139470 11456
Neamţ 20063 8223 86530 1040 178940 845
Olt 18251 9463 74595 1192 199300 730
Prahova 23884 12122 182610 1323 245894 8262
Satu Mare 10596 4600 77060 1041 23780 1348
S laj 7632 5845 47650 1076 148850 425
Sibiu 14892 5794 122491 1230 69030 25221
Suceava 19688 10963 101602 1091 170260 10090
Teleorman 14865 13702 57809 1100 112210 686
Timiş 29207 5568 216731 1319 59430 48433
Tulcea 9404 4005 46386 1112 50740 0
Vaslui 15432 16458 60815 1060 123600 0
Vâlcea 17430 8344 84940 1162 1019686 2709
Vrancea 14423 6677 59505 1064 45010 164
Bucharest
Municipality 100445 18274 922234 1838 75644 388161
The fi rst unifactorial model built is:
and explains
the variation of the interregional mobility fl ows in accordance with the unemployed persons. After processing, the data using this model the following theoretical values were obtained: y=1,489x+4228 and the multiple correlation coeffi cients whose value is 0,220.
Another unifactorial model refl ects the variation of the dependent variable according to the number of employees and has the following the form: . The chart between the two variables was made with the help of the Excel software and following linear function resulted: y = 0,102 x 6244. Because the multiple correlation coeffi cient has the value 0,942, it results that labour mobility fl ows at level of regions are strongly infl uenced by the number of employees.
By analyzing the interdependence between the dependent variable and the monthly wage another model can be obtained: Linear function which was obtained from the analysis is as following: y=66,38x-59676, and the multiple correlation coeffi cient is 0,576. The value that tends to 1 demonstrates a good relationship between variables.
Another factor, we considered important for the analysis proposed in this paper, was the payment for the labour’s stimulation. The unifactorial
model has the form: , and linear function
obtained presents the following theoretical values: y=0,223x+13805. The correlation coeffi cient obtained has the value 0,896, this proving a very strong link between the two variables analyzed.
The last unifactorial model has the following form:
and refl ects the infl uence of the employers from higher education on the fl ows of interregional mobility. From the linear form of model y=-0,005x+19389, and from the value of multiple correlation coeffi cient (0,004), results that the relationship between the variables analyzed is very weak.
Taking into consideration the linear trends for the models presented above, we can construct the following multifactor model:
where are the model’s parameters and y the aleatory variable.
Analysis based on the relationships of ANOVA table
ANOVA
df SS MS F Signifi cance
F
Regression 5 =k-1 8,01E+09 = 1,6E+09 = 158,8427 1,75E-23
36 =n-k 3,63E+08 = 10082016 =
Total 41 =n-1 8,37E+09 =
As the result of the comparisons made between the data presented by the used procedure and the values of Ftabelar it results that Ftabelar = 158,8427 > F0,05;5;36 = 2,477 (the meaning factor is α= 0,05 ). Note that the null hypostasis is rejected in favour of the alternative one and so the model is signifi cant from statistic point of view.
For a more detailed analysis of the constructed econometric model it was used the test t. In this analysis the same procedure of calculation REGRESSION from the EXCEL application was applied.
The regression results
Coeffi cients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -6886,17 4932,865 -1,39598 0,171271 -16890,5 3118,14 X Variable 1 0,307976 0,121253 2,539938 0,015546 0,062063 0,553889 X Variable 2 0,093313 0,019083 4,889827 2,1E-05 0,054611 0,132015
X Variable 3 9,578881 4,44548 2,154746 0,037947 0,563031 18,59473
X Variable 4 0,000899 0,003065 0,293459 0,770856 -0,00532 0,007116
X Variable 5 -0,00768 0,040863 -0,18803 0,851913 -0,09056 0,07519
Regression Statistics Semnifi cation
Multiple R 0,978079
R Square 0,956638
Adjusted R Square 0,950615
Standard Error 3175,219
The data obtained:
where 3175,219 is the standard error ( ).
The calculated values of the coeffi cients are the results of normal repartitions, in this way are available statistic checks of the coeffi cients.
The interpretation of the model’s coeffi cients by occurred changes, if: - at the number of unemployed people with a unit, a modifi cation occurs to the interregional mobility fl ow with 0,307976 units.
- at the number of employees people with a unit, a modifi cation occurs to the interregional mobility fl ow with 0,093313 units.
- at the monthly earnings of the average wage with a unit, a modifi cation occurs to the interregional mobility fl ow with 9,578881 units.
- at the value of the payments made to encourage labour mobility with a unit, a modifi cation occurs to the interregional mobility fl ow with 0,000899 units.
- at the number of the higher education’s staff with a unit, a modifi cation occurs to the interregional mobility fl ow with -0,00768 units.
Next it was calculated the multiple correlation coeffi cient to measure the intensity between a resultant variable and the factorial variables as well as the coeffi cient of determination for the determination of the weighting with which the independent variables infl uence the dependent variable.
The coeffi cient of multiple correlation has a value of 0,956638 resulting a strong connection between the interregional mobility fl ow and the variables x: the number of the unemployed persons, the number of employees, the monthly wage, the payments made for the stimulation of the labour’s mobility, the scholar population from the higher education. It resulted that 95, 66% from the interregional mobility fl ow is infl uenced by the fi ve dependent variables.
Another testing of the model was made with the test t. It was taken into consideration the statistic certitude and were compared the data presented by the application with the theoretic ones. The following conclusion detached: for the variable , , , is not rejected the null hypothesis because > ( ) but for the variables
, is rejected the null hypothesis ( < ).
Note that certain coeffi cients and are not statistically important but only random.
, , ,
Whereas some intervals do not include the value zero, it results that for these variables the null hypothesis is rejected.
The theoretical value of labour mobility fl ows and deviation from real value
Observation Predicted Y Residuals
( ) ( )
Standard Residuals
1 16759,81 -4730,81 - - -1,59001932
2 17719,79 -2258,79 -4730,81 6110883 -0,759176284 3 22971,45 2481,554 -2258,79 22470861 0,83404736 4 20346,75 5226,253 2481,554 7533373 1,756537465 5 20898,05 -794,051 5226,253 36244060 -0,266879709 6 10497,65 -945,651 -794,051 22982,56 -0,317832227 7 10126,49 3677,505 -945,651 21373571 1,236005205 8 23581,48 -3545,48 3677,505 52171512 -1,191632701 9 12862,85 -3320,85 -3545,48 50458,64 -1,116133246 10 15374,59 1712,408 -3320,85 25333686 0,575538419 11 11795,47 1575,53 1712,408 18735,59 0,529533923 12 9382,922 2040,078 1575,53 215804,8 0,685667669 13 26907,25 -5636,25 2040,078 58926012 -1,894335395 14 26229,18 2938,82 -5636,25 73531826 0,987734021 15 9428,875 -4087,88 2938,82 49374513 -1,373930082 16 15945,11 3995,894 -4087,88 65347402 1,343015358 17 24795,54 -1024,54 3995,894 25204758 -0,344345768 18 21167,42 -3520,42 -1024,54 6229417 -1,183209975 19 8725,448 395,5518 -3520,42 15334835 0,132944494 20 18453,84 -1741,84 395,5518 4568444 -0,585429373 21 11890,37 -4209,37 -1741,84 6088704 -1,414764093 22 20655,71 -4383,71 -4209,37 30394,44 -1,473359806 23 9622,713 1021,287 -4383,71 29213993 0,343253234 24 25316,5 3442,496 1021,287 5862253 1,157018884 25 18363,92 563,0824 3442,496 8291023 0,189251316 26 14027,69 -1191,69 563,0824 3079226 -0,400525892 27 13466,31 -1148,31 -1191,69 1881,824 -0,385944113 28 19778,5 -1326,5 -1148,31 31751,68 -0,445835671 29 13837,15 6225,85 -1326,5 57037991 2,092500883 30 14580,54 3670,461 6225,85 6530013 1,233637613 31 26717,49 -2833,49 3670,461 42301379 -0,952332314 32 11703,84 -1107,84 -2833,49 2977868 -0,372343245 33 9797,788 -2165,79 -1107,84 1119258 -0,72791888 34 17978,54 -3086,54 -2165,79 847780,6 -1,037381508 35 16497,1 3190,904 -3086,54 39406303 1,07245892 36 13360,45 1504,551 3190,904 2843786 0,505677696 37 27368,27 1838,735 1504,551 111678,9 0,617996496 38 9373,026 30,97383 1838,735 3268000 0,010410269 39 14122,09 1309,911 30,97383 1635680 0,440259698 40 15636,56 1793,445 1309,911 233805,1 0,602774576 41 10953,91 3469,094 1793,445 2807800 1,165958264 42 99489,6 955,3971 3469,094 6318672 0,321107841
To verify the hypothesis of error’s independence, the value of the variable Durbin-Watson was calculated:
For a threshold of signifi cance from the table of distribution Durbin-Watson were taken over the values for the case n=42, k=5, resulting The results of the analysis revealed that there is a positive autocorrelation.
The quality of the model is also the result of the graphics automatically constructed by the procedure REGRESSION of the EXCEL application. The following diagrams produce automatically and refl ect the waste for each independent variable.
The shape of uniform band shown above refl ects the constancy of the residues dispersion for all the independent variables, resulting in a “better” situation in which the hypostasis of normality applied to errors do not contradict.
The normal probabilitychart
The application also displays the normal probability chart from which results a roughly linear distribution.
Conclusion
Along history, man was characterized by territorial mobility more or less intense, depending, at the beginning, on the natural conditions and later on, on social and economic conditions, due to some rejection factors in his area or point of origin as well as to some attraction factors in the area or destination.
Interregional mobility plays an important role in the redistribution of labour offering. The internal mobility of workers and their families between localities and regions with different conditions of labour market is an important component of population growth at the county level and for the fl exibility of labour market. This phenomenon represents the way through which the regions can adapt to economic changes, and, in the same time, is ensured the economic growth. Mobility fl ows act as an “automatic stabilizer” for regions and give people the opportunity to improve the living standards by moving to areas with better employment and living conditions.
The phenomenon of mobility is a generator of economic development, on the one side, but, on the other side, it has regional agglomeration effects.
From the analysis made for a series of years, it results that the size of the interregional mobility fl ows is infl uenced in different proportions by the factors taken into consideration.
The rarity of the studies based on econometric methods represents a common feature of the macroeconomic literature. The econometric models can give important results only if the number of observations made for the variables included in the model is suffi ciently numerous. The econometric modelling is based on the hypothesis that the variables of interests are rendom, that is their future values are uncertain.
Bibliography:
- SEBER G.A.F. (1970), Linear Regression Analysis, J. Willey, New York;
- VASILE V., ZAMAN G. (2006), Migraţia forţei de muncă şi dezvoltarea durabilă
a României, Editura Expert;
- VOINEAGU V. (2007), Teorie şi practică econometrică, Editura Meteor Press; - VOINEAGU V. (2007), Analiză macroeconomică: sinteze şi studii de caz, Editura Meteor Press;
