Spatial Effect Research on Educational Output and Economic Growth in China

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1 Ope Joural of Statistics, 206, 6, Published Olie Jue 206 i SciRes. Spatial Effect Research o Educatioal Output ad Ecoomic Growth i Chia Wuyua Su, Jiayu Ma The College of Ecoomics, Jia Uiversity, Guagzhou, Chia Received 8 April 206; accepted Jue 206; published 4 Jue 206 Copyright 206 by authors ad Scietific Research Publishig Ic. This work is licesed uder the Creative Commos Attributio Iteratioal Licese (CC BY). Abstract This thesis is to study spatial effect of educatio output o ecoomic growth through the use of spatial measuremet techique. Accordig to the study: there s the presece of spatial spillover effects i huma capital, ecoomic growth, ad others; i previous years, huma capital depeded o maily the employers with juior school educatio or below; i recet years, with the reductio of employers with juior school educatio or below, employers with regular higher educatio ca best promote the ecoomic growth. However, it s very difficult for huma capital with vocatioal educatio to promote ecoomic growth, especially i recet years. Therefore, from the perspective of log-term ecoomic growth, Chia should focus o culturig professioal talets ad put more resources ito the developmet of vocatioal educatio while developig the higher educatio. Keywords Educatioal Output, Ecoomic Growth, Spatial Effect. Itroductio A large umber of Chia s labor forces i recet years are maily provided by two educatio systems of regular higher educatio, vocatioal ad techical educatio. The huma capital as a importat elemet affects ecoomic growth, ad the differet educatio levels of labor forces will also affect the ecoomic growth. Beeficiaries of higher educatio have stroger adaptio to ew techologies ad ability of creatio, the ecoomic growth rate of the ecoomies with rapid developmet of vocatioal educatio is lower tha that of the ecoomies takig the priority of developig the higher educatio. I recet years, Chia has bee i short supply of all kids of the skilled persoel, ad some people call such pheomeo as shortage of skilled workers. The experts assert that if the shortage situatio of the skilled persoel is left uresolved, it will ievitably become the bottleeck affectig sustaied ad healthy developmet of Chia s ecoomy. With Chia s great success i the 43rd World How to cite this paper: Su, W.Y. ad Ma, J.Y. (206) Spatial Effect Research o Educatioal Output ad Ecoomic Growth i Chia. Ope Joural of Statistics, 6,

2 Skills Competitio: 5 gold medals, 6 silver models, 3 broze medals ad 2 prizes for excellece, the atioal authorities have give a high priority to the skills educatio. Accordig to the Vice Miister of the Miistry of Educatio Lu Xi, the Miistry of Educatio will complete trasformatio of more tha 600 local udergraduate colleges to be applicatio techology ad vocatioal educatio types. This thesis used the pael data of 3 provices durig , ad spatial measuremet techology to uderstad the spatial effect of differet educatioal outputs o ecoomic growth. The educatioal output studied i this thesis refers to the umber of graduates provided by differet types of educatio. 2. Model Costructio ad Relevat Theory 2.. Desig of Ecoometric Model Cobb-Douglas productio fuctio has bee the most commo productio fuctio i the literature of aalyzig ecoomic growth, amely: Y = AK L α β it it it it Wherei, Y it represets ecoomic output, K it represets physical capital ivestmet, L it represets ivestmet i huma capital, α, β respectively represets the elasticity of physical capital ad huma capital to ecoomic output, A it represets total factor productivity. The author i this thesis takes a referece of improvemet of classic Cobb-Douglas productio fuctio made by A Xuehui (2002), Mao Shegyog (200) [] et al., ad believes that huma resources deped o ot oly the umber of employees, but also the quality of employmet, so the author divides the labor force ito labors with juior school educatio or below (L ), labors with vocatioal ad techical educatio (L 2 ) ad labors with regular higher educatio (L 3 ). Therefore, the fuctio becomes: Y = AK L L L β α β β 2 3 it it it it 2it 3it Select the logarithm from the above model to obtai the followig model: l Y = l A+ αl K + β l L + β l L + β l L 2.2. Idicator Selectio ad Data Descriptio it it it 2 2it 3 3it The author i this thesis adopts the classic Cobb-Douglas productio fuctio ad adds the iovatio efficiecy of the first stage for the spatial ecoometric aalysis. Takig ito cosideratio of the meaig of each idex of the productio fuctio ad takig a referece to the idicator selectio coducted by Fa Gag (20) [2] et al i the study of ecoomic growth. This thesis cosiders the year 2004 as a costat price to select costat price GDP as the idicator of ecoomic output, ad the costat price physical capital stock K. Perpetual ivetory method is adopted for physical capital K, amely Kit = Iit + ( α ) Kit, I it is the ivestmet amout of fixed assets for each year, the processig approach of depreciatio rate α is the same to that of Wag Xiaolu, Fa Gag (2009) [3], amely to set α = 5%, ad take fixed asset ivestmet of 2004 as the iitial value to calculate physical capital stock durig , ad also treat 2004 as the costat price. Sice the educatio degree of the umber of employees i Chia Populatio ad Employmet Statistics Yearbook is divided ito several categories of o schoolig, elemetary educatio, juior school educatio, seior school educatio, college educatio, udergraduate ad graduate educatio, ad there s o umber of employees with vocatioal ad techical educatio. Through the calculatio of proportio M it of the umber of graduates i vocatioal ad techical colleges of provices each year ad the umber of graduates i regular higher schools, the author believes that the proportio of umber of graduates of the two educatio systems is approximately equal to the proportio of the umber of employees, ad therefore the approximate umber of employees with vocatioal ad techical educatio ca be obtaied i the way the proportio M it is multiplied by the umber of employees with regular higher school educatio. Wherei, L it is the sum of umber of employees with o schoolig, primary ad juior school educatio i t term of I provice; L 2it is for M it *L 3it ; L 3it is the umber of employees with college educatio, udergraduate ad graduate educatio Correlatio Test of Pael Data Space I practical applicatio study, the spatial autocorrelatio idex of Mora s I is ofte used to test whether there s 388

3 the spatial correlatio, ad the correspodig calculatio formula is show as follows: i= j= ( )( ) W Y Y Y Y ij i j Mora s I = () 2 S W i= j= Wherei, S 2 = ( Y i Y ); Y = Y i, Y i represets the observed value of the area i; is the total um i= i= ber of regios; W ij is a biary cotiguous spatial weight matrix, represetig ay of correspodig elemets, the purpose of usig cotiguity stadards or distace criterio is to defie mutual adjacecy of the spatial objects, thus to be easy to place the relevat attributio i the geographic iformatio system (GIS) database to the studied geographic space for cotrast. Geerally, the cotiguity stadard W ij is as follows: W ij =, whe the area i is adjacet to the area j. W ij = 0, whe the area i is ot adjacet to the area j. I the equatio, i =, 2,, ; j =, 2,, m; m= or m traditioally, all the diagoal elemets of W is ordered to be W ii = 0. Mroa s I idex [4] ca be cosidered as the product sum of observed values of each regio, which rages betwee ad, if the ecoomic behavior betwee each regio is positively correlated, the correspodig value should be larger; ad the value should be smaller if the ecoomic behavior is egatively correlated; the ull space autocorrelatio appears whe there s mutually idepedet betwee distributio of attributio value ad distributio of locatio data. Accordig to the calculatio results of Mora s I idex, the ormal distributio assumptio ca be used to test whether there s the presece of spatial autocorrelatio i N regios, ad the correspodig stadardized form is as follows: Mora s I E( I) Z( d) = (2) VAR I The expectatio value ad variace of the ormal distributio Mora s I idex ca be calculated accordig to the distributio of spatial data: E ( I) = 2 2 (3) w + w2 + 3w0 2 VAR( I ) = E ( ) 2 2 I w 2 0 ( ) ( ) I the equatio, ( ) 2 2 w0 = wij, w = wij + wji, w2 = ( wi. + wj.), wi. ad j. i= j= i= j= i= ij w is respectively the sum of row i ad colum j i spatial weight value matrix [2]. Formula (2) ad (3) ca be used to test whether there s the presece of the spatial autocorrelatio i N regios. If Z value of ormal statistics of Mroa s I idex is greater tha the critical value.96 of the ormal distributio fuctio at the 0.05 level, idicatig that there s a sigificat positive correlatio i the spatial distributio, the positive spatial correlatio represets that similar characteristic value of eighborig regios appears the cluster tred Spatial Lag Model (SLM) ad Spatial Error Model (SEM) Spatial lag model focuses o discussig whether variables have the pheomeo of diffusio (spillover effects) i a area, ad the correspodig expressio is [4]: Y = ρwy + X β + ε I the equatio, Y is the depedet variable; X is exogeous idepedet variable matrix; ρ is the relevat coefficiet of spatial regressio; reflectig the role of spatial depedece i observed value of the samples, 389

4 amely, the affectig directio ad extet of the observed value WY of the cotiguity area o the observed value Yy of the local regio; ad W is the spatial weight matrix of order, ad it is usually expressed by the cotiguity matrix; Wy is the spatial lag depedet variable, ad ε is the vector of a radom error term. Parameter β reflects the impact of idepedet variable X o depedet variable Y, ad the spatial lag depedet variable Wy is a edogeous variable, reflectig the effect of spatial distace o regioal behavior. The regioal behavior is affected by cost of migratio related to cultural eviromet ad the spatial distace, which is with strog regioal characteristics. Mathematical expressio of the spatial error model is: Y = Xβ + ε ε = λwε + µ I the equatio, ε is the vector of radom error term, λ is the spatial error coefficiet of the vector of cross-sectio depedet variable, ad µ is ormally distributed radom error vector. Parameter λ measures the spatial depedece role of sample observed value, amely, the affectig directio ad extet of observed value Y of the cotiguity regio o observed value Y of the local regio, the parameter β reflects the impact of the idepedet variable X o the depedet variable Y. The spatial depedece of SEM presets i disturbace error term, which measures the affectig extet of cotiguity area about the error impact of depedet variable o observed value of the local regio Direct Effect ad Idirect Effect Theories The measuremet method of priciple of direct effect ad idirect effect is coducted as follows by takig SLM model as a example [5]. First, SLM model i Equatio (4) is rewritte as follows: ( ) I ρw y = Xβ + ε (5) k r ( ) r ( ) (6) r= y = S W x + V W ε ( ) ( ) S W = V W I β (7) r r V ( W) ( I ) ρw I ρw 2 2 ρ W 3 3 ρ W The the total effect is S r (W), the average total effect is Sr ( W) = V ( W) Iβr. The partial derivatio of x ir is coducted accordig to the Equatio (8) to obtai: yi = S ( W ) = = (8) r ii, this value xir represets the impact of chages of a idepedet variable of the regio j o the depedet variable itself of the regio, ad this is direct effect [5]. yi The partial derivatio of x ir is coducted accordig to the Equatio (8) to obtai: = Sr ( Wij ). This value x represets the chages of a idepedet variable of the regio j will potetially affect the depedet variable of regio j, ad this is idirect effect. Thus the expressio of the average direct effect, average total effect ad average idirect effect required i the study is show as follows: M ( r) = trace ( S ( )), ( ) ( ), ( ) ( ) ( ) direct r W M r = S total r W M r = M r M r idirect total direct 3. Empirical Aalysis I order to make a dyamic compariso ad study of the effect of employees of various educatio systems o ecoomic growth, the author i this thesis respectively studies pael data samples of three time periods of , , ad First, Mroa s I is used to make the correlatio test of various educatioal outputs ad ecoomic growths year by year, to obtai: jr (4) 390

5 See from Mroa s I idex (Table ), GDP, labors with juior school educatio or below, labors with vocatioal ad techical educatio, labors with regular higher educatio of all regios show positive spatial correlatio, showig some spatial clusterig ad the spatial correlatio i recet years is more obvious. I additio, the labors with vocatioal ad techical educatio ad regular higher educatio show more obvious spatial clusterig. Obviously, it s reasoable ad ecessary to use spatial measuremet to build the model. It ca be see from Mroa s I scatter diagram of GDP (Figure ) that most cities are located i the first ad third quadrats, idicatig that most cities show high values surrouded by high values, Jiagsu ad Shadog are more sigificat, but also the situatio that low values are surrouded by low values. However, more sigificat situatio of Guagdog provice is about the high values surrouded by low values, Ahui is low values surrouded by high values, which is also i lie with the status quo. I additio, it ca be see from Mroa s I scatter diagram of the three kids of educatio (Figures 2-4) that most cities are located i the third quadrat, there are some cities located i the first ad secod quadrat, idicatig that there s more obvious situatio of low values surrouded by low values. Followed by is the situatio of low values surrouded by high values, icludig the more sigificat situatio of labors with vocatioal ad techical educatio i Shadog ad Zhejiag, which is the situatio of high values surrouded by high values, ad Ahui is the situatio of low values surrouded by high values. However, amog the labors with regular higher educatio, Beijig shows the situatio of high values surrouded by low values; Jiagsu is the situatio of high values surrouded by high values. It s visible that there s spatial heterogeeity for labor outputs of various educatios. Ulike the ordiary pael regressio, the parameter estimatio of spatial pael model is usually coducted by usig maximum likelihood ad momet estimatio method. SLM ad SEM model described i previous sectio are used to make SLM ad SEM fittig of pael data of the three time periods respectively. Fially is to select the oe with better fittig effects for aalysis, the selectio is made maily based o checkig which model has larger log-likelihood, ad better variable sigificace, the models of various time periods obtaied through fittig are better SEM models. The estimatio results of various models calculated by usig R laguage are show Table. Correlatio test. Mroa s I GDP *** 0.99 *** 0.2 *** 0.20 *** *** 0.27 *** 0.29 *** 0.29 *** 0.22 *** L ** ** ** ** 0.03 *** 0.0 *** 0.3 *** 0.39 *** 0.6 *** L ** ** ** ** 0.83 *** 0.66 *** 0.9 *** *** *** L ** ** 0.08 ** 0.3 *** 0.45 *** 0.87 *** *** *** *** Note: *, **, *** represet to pass the sigificace test at respective level of 0%, 5% ad %. Figure. Mroa s I scatter diagram of GDP. 39

6 Figure 2. Mroa s I scatter diagram of juior school ad educatio below. Figure 3. Scatter diagram of vocatioal ad techical educatio output. as follows, ad P values of parameters are icluded i paretheses. It ca be see from estimatio results of time period durig (Table 2), λ is greater tha zero, idicatig that there s the spatial spillover effect of labors with various educatio levels, which has the obvious clusterig effect. This may be related to the strog mobility of labors, the chages of urba labor iput variables ca affect GDP level of cities earby. I this time period, labors with juior school educatio or below have the largest cotributio to ecoomic growth, its role i promotig the ecoomy eve more tha physical capital ivestmet. While labors with vocatioal ad techical educatio ad labors with regular higher educatio i this period have played similar roles i promotig the ecoomy, but their role is far less tha the labors with juior school educatio or below. It ca be kow from the estimatio results of the latest time period durig (Table 3) that the role of labors with juior school educatio or below i promotig ecoomic growth is chaged from positive to egative. This is also related to uiversal icreased educatio level of Chia s labors i recet years, ad the sharp declie of umber of labors with juior school educatio or below. The role of labors with vocatioal ad 392

7 Figure 4. Educatio output Mora s I diagram of regular higher educatio. Table 2. SEM model estimatio result table durig Parameter Radom effect Fixed space Fixed time Fixed space ad time C.6635 *** *** *** (2.68E 5) (2.20E 6) (0.6658) (.39E 2) λ.9286 ** *** * 0.94 (0.0055) (7.65E 08) (0.057) (0.20) lk *** *** *** *** (2.20E 6) (2.20E 6) (2.20E 6) (3.6E 08) ll *** 0.79 * *** 0.64 * (2.20E 6) (0.0982) (.3E 09) (0.028) ll ** ** *** ** (0.057) (0.045) (0.000) (0.0330) ll *** *** (0.0002) (0.4224) (7.7E 0) ( ) Hausma test chisq = 4.897, p-value = 6.8e 08 Note: *, **, *** represet to pass the sigificace test at respective level of 0%, 5% ad %. techical educatio i promotig the ecoomic growth is also chaged from positive to egative, which is also cosistet with the actual situatio of Chia s shortage of skilled workers i recet years. Sice most of educated childre of this geeratio are from the oly oe child families, those families attach great importace to higher educatio of their childre, ad they are ot too willig to sed their childre to vocatioal ad techical schools, coupled with elarged erollmet policy i regular higher colleges ad uiversities, ad therefore, regular higher educatio has played the strogest role i promotig ecoomic growth. However, there s o substatial cotributio accordig to the coefficiet, substatially GDP is icreased by more tha 20% per icrease of % labors with regular higher educatio. 393

8 Table 3. SEM model estimatio result table durig Parameter Radom effect Fixed space Fixed time Fixed space ad time C *** *** *** (2.20E 6) (2.20E 6) (0.975) (2.20E 6) λ.9286 ** (0.0055) (0.4030) (0.2658) (0.7568) lk *** *** *** *** (0.0000) (0.0000) (0.0000) (0.0000) ll 0.66 *** * *** * (0.0000) (0.0253) (0.0000) (0.094) ll *** (0.8298) (0.6295) (0.0092) (0.3573) ll *** ** *** (0.0039) (0.0623) (0.0000) (0.734) Hausma test chisq = 4.897, p-value = 6.8e 08 Note: *, **, *** represet to pass the sigificace test at respective level of 0%, 5% ad %. See from (Table 4), the labors with juior school educatio or below have overall the largest elastic coefficiet i promotig ecoomic growth, but elastic coefficiet i promotig ecoomic growth becomes much smaller compared to the time period durig With the social progress ad improvemet of educatio level, it s ideed ufeasible to drive the ecoomic growth by log-term relyig o the labors with juior school educatio or below; there s a more rapid icrease of the umber of labors with regular higher educatio i recet years, but o the whole it does ot have played large role i promotig the ecoomic growth; i geeral, the elasticity of the vocatioal ad techical educatio is egative, which i fact is ot optimistic for Chia. It s essetial to ecourage the vocatioal ad techical educatio, ad expad the umber of erollmet of vocatioal ad techical educatio, ad also focus o culturig the vocatioal ad techical persoel. It ca be see from Hausma test results of estimatio tables of the three time periods above that P value of the test is far less tha 0.0, idicatig that ull hypothesis of radom selectio effect ca be rejected, ad three models are with better fixed effects. Accordig to the foregoig presetatio o priciple of the spatial effects, the tables of direct ad idirect effects of models with better fixed effects obtaied through calculatio are show as follows. It ca be see from spatial effect of various variables durig (Table 5) that direct effect is always greater tha the idirect effect, idicatig that the huma capital of local regio plays a greater role i promotig the ecoomic growth of the regio. However, idirect effect of huma capital whe there s fixed spatial is greater tha the idirect effect whe time is fixed, idicatig that a certai time is required for the spillover effects of huma capital, the huma capital of some area will affect the ecoomic growth of the cotiguity regios with the passage of time. It ca be kow from spatial effect of variables durig (Table 6) that direct effect is always greater tha the idirect effect, but the spatial effects of labors with juior school educatio or below, ad also labors with vocatioal ad techical educatio are egative, idicatig that the educatio level of huma capital i recet years is i favor of regular higher educatio. With the upgradig of the educatio level, it s reasoable for the reductio of labors with the juior school educatio or below. However, the huma capital with vocatioal ad techical educatio has played a role that is irreplaceable for huma capital of regular higher educatio i promotig the social developmet, the youth are blidly biased to the regular higher educatio, which is actually uecoomical ad ureasoable o matter for idividuals or the coutry. It ca be see from spatial effect of various variables durig (Table 7) as a whole that direct effect is always greater tha the idirect effect, where the spatial effect of the labors with juior school educatio or 394

9 Table 4. SEM model estimatio result table durig Parameter Radom effect Fixed space Fixed time Fixed space ad time C *** *** *** (2.20E 6) (2.20E 6) (0.2844) (2.20E 6) λ.9286 *** *** * (0.0055) (2.00E 6) ( ) (0.0258) lk 0.56 *** *** *** (2.20E 6) (2.00E 6) (2.20E 6) (2.00E 6) ll *** * *** * (0.0002) (0.0247) (3.6E 07) (0.07) ll * (0.90) (0.808) (0.060) (0.695) ll ** *** (0.0648) (0.9685) (2.20E 6) (0.962) Hausma test chisq = 4.897, p-value = 6.8e 08 Note: *, **, *** represet to pass the sigificace test at respective level of 0%, 5% ad %. Table 5. Spatial effect of fixed effect model durig Fixed space Fixed time Fixed time ad space Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect K E L E L E L E Table 6. Spatial effect of fixed effect model durig Fixed space Fixed time Fixed space ad time Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect K L L L Table 7. Spatial effect of fixed effect model durig Fixed space Fixed time Fixed space ad time Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect Direct effect Idirect effect Total effect K E L E L E L E

10 below, ad the labors with regular higher educatio are positive, while the employees with vocatioal ad techical educatio is egative, various huma capitals i promotig the ecoomic growth i cotiguity regio is with time delay, which ca t be igored. 4. Mai Coclusios ad Recommedatios It could be kow through the ecoometric model aalysis of the three time periods of , ad that because of the high mobility of huma resources, the labors of various educatio outputs of each time period were with the spatial spillover characteristics. Although the spatial direct effect of each time period is greater tha the idirect effect, the idirect effect ca t be igored, ad the huma capital betwee cotiguity regios will affect ecoomic growth of the regio. The proportio of Chia s labors with juior school educatio or below durig was relatively large, which was more obvious i drivig the ecoomic growth. The scale of labors with regular higher educatio at the time period is ot too large, the drivig effect o ecoomic growth is ot obvious eough; the effect of labors with vocatioal ad techical educatio o ecoomic growth of the time period is positive. However, with the cotiuous improvemet of Chia s educatio level i recet years, ad the expasio of higher educatio scale, there s a relatively large scale of reductio of labors with juior school educatio or below, ad some part of labors with vocatioal ad techical educatio is also trasformed to the higher educatio. Therefore, the effect of labors with vocatioal ad techical educatio o ecoomic growth is trasformed from positive to egative, which is actually ureasoable but also ot coducive to Chia s sustaiable developmet for the log-term. Because first of all the labors with vocatioal ad techical educatio have strog professioal skills, ad they play the role that is irreplaceable for labors with regular higher educatio, especially for maufacturig, costructio ad other idustries focusig more o the operatig ability, ad practice ability of labors. Secodly, the labors require more time for achievig the higher educatio, ad they also cosume more social resources, ad therefore the efficiecy of educatioal output is ot high. I additio, may labors with vocatioal ad techical educatio do ot require the seior school educatio, they ot oly lear the durig the required courses of seior high school durig the school educatio period, ad also lear a highly professioal vocatioal skill, so as to effectively participate ito the correspodig social work after graduatio. Fially, the curret society has a very large demad for skilled persoel with the vocatioal ad techical educatio, ad with Chia s great success i the 43 th WorldSkills, Chia begis to attach great importace to vocatioal ad techical educatio. Therefore, the followed educatio for Chia s studets with juior school educatio or above should: First, Chia should pay more attetio to vocatioal ad techical educatio, ad focus o the labors with vocatioal ad techical educatio, improvig their social status, broadeig their developmet prospects. I the process of developig the higher educatio, Chia should apply some certai resources to the developmet of the vocatioal ad techical educatio, so as to cultivate more professioal ad techical persoel, skilled persoel, ad good players of the WorldSkills, thereby improvig Chia s iteratioal status i terms of skills. Secod, Chia should ot eglect the spatial idirect effect while payig attetio to the spatial direct effect, ad Chia should stregthe huma capital flow, arrowig the gap betwee huma capital quality ad quatity betwee regios. Cities below first tier should pay more attetio to the idirect effect of such space, itroducig the appropriate talet itroductio policies to attract ad retai more persoel, so as to arrow the gap betwee cities i Chia to ease populatio pressure i some first-tier cities ad populatio agig issues of some cities, thereby achievig the commo developmet ad sustaiable developmet throughout the coutry. Refereces [] Mao, S.Y. ad Liu, Y.Y. (200) Labor Force of Higher Educatio ad Ecoomic Growth of Chia Aalysis o the Pael Data of [2] Fag, G. ad Wag, X.L. (20) Study o the Cotributio of Chiese Marketizatio to Ecoomic Growth. Ecoomic Research, No. 9, 4-6. [3] Wag, X.L., Fag, G. ad Liu, P. (2009) Study o the Trasformatio of Ecoomic Growth Mode ad Sustaiable Growth of Chia. Ecoomy, No., [4] Wag, X.Z. (204) Research Methods of Applicatio of Regioal Ecoomics: Applicatio Based o Arcgis, Geoda ad R. [5] Elhorst, J.P. (2009) Spatial Pael Data Models. I: Fischer, M.M. ad Getis, A., Eds., Hadbook of Applied Spatial Aalysis, Spriger, Berli,