EFFICIENCY OF BROADBAND INTERNET ADOPTION IN EUROPEAN UNION MEMBER STATES

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1 he 11 th Iteratioal Coferece RELIABILIY ad SAISICS i RANSPORAION ad COMMUNICAION -011 Proceedigs of the 11 th Iteratioal Coferece Reliability ad Statistics i rasportatio ad Commuicatio (RelStat 11), 19 October 011, Riga, Latvia, p ISBN rasport ad elecommuicatio Istitute, Lomoosova 1, LV-1019, Riga, Latvia EFFICIENCY OF BROADBAND INERNE ADOPION IN EUROPEAN UNION MEMBER SAES Pavlyuk Dmitry rasport ad elecommuicatio Istitute Lomoosova str. 1, Riga, LV-1019, Latvia Phoe: (371) Dmitry.Pavlyuk@tsi.lv his paper is devoted to ecoometric aalysis of broadbad adoptio efficiecy i EU member states. Stochastic frotier models are widely used for efficiecy estimatio. We ehaced the stochastic frotier model by addig a spatial compoet ito the model specificatio to reflect possible depedecies betwee eighbour coutries. A maximum likelihood estimator for the model was developed. he proposed spatial autoregressive stochastic frotier model is used for estimatio of broadbad adoptio efficiecy. We cofirmed a egative impact of average prices of broadbad services o broadbad adoptio i a coutry ad also discovered a sigificat egative ifluece of a level of populatio icome iequality. Sigificat positive spatial effects also have bee revealed, so higher broadbad peetratio rates i eighbour coutries have a positive impact o broadbad adoptio i a give coutry. Keywords: spatial stochastic frotier, broadbad adoptio, efficiecy 1. Itroductio Iteret techologies are widely used by compaies, govermet bodies ad idividuals. hey support iformatio flows i the ecoomy, ad provide people with access to iformatio ad services for work, schoolig, ad leisure time. A sigificat positive impact of Iteret spreadig is ackowledged by researchers. here are a sigificat umber of studies dedicated to aalysis of broadbad Iteret impact o ecoomic developmet [1,, 3]. Nowadays Iteret is a essetial part of ecoomics ad prevalece of up-to-date Iteret coectios becomes oe of key factors of sustaiable ecoomic growth. Availability of broadbad services sigificatly improves geeral productivity of populatio ad coutry s GDP, employmet situatio ad almost all sectors of the atioal ecoomy. Accordig to [3], availability of broadbad gives competitive advatages to a coutry ad stimulates busiess ad overall ecoomy growth. A level of broadbad access is usually estimated usig a broadbad peetratio rate a umber of broadbad coectios per capita. his idicator is widely used as a key statistics of iformatio society. Efficiecy of broadbad Iteret adoptio is a subject of some recet researches [4]. Usually authors cosider a broadbad peetratio rate as a product of coutry-specific ecoomic ad demographic factors. Ford et al. [4] successfully applied a moder stochastic frotier model [5] for estimatio of broadbad efficiecy idex i OECD coutries. Based o previous researches, we ca assume that a distributio of broadbad i Europe has sigificat spatial patters [6] adoptio of broadbad services i a give couty is closely related with the same process i eighbour coutries. hese spatial effects are supported both from supply ad demad sides. For suppliers it is easier ad cheaper to provide broadbad coectio i adjacet areas, ad for customers the etwork effect icreases the utility of broadbad coectios. Despite its importace, there are o researches of broadbad efficiecy takig a spatial structure ito cosideratio (to the best of our kowledge), which ca lead to biased estimates of model parameters ad icorrect coclusios. here are two separate ecoometric tools for aalysis of efficiecy ad spatial depedecies. Stochastic frotier models are widely used by researchers for estimatio of uits efficiecy, while spatial autoregressive models are takig spatial depedecies ito cosideratio. I this research we develop a spatial autoregressive stochastic frotier model, which allows estimatig efficiecy levels i case of spatial depedecies betwee objects i a data set. here are some recet researches related to this issue. Schmidt et al. (009) [7] proposed a stochastic frotier model with latet spatial compoets i the iefficiecy term ad a Bayesia approach to its estimatio. Barrios ad Lavado (010) [8] exteded the stochastic frotier model with a spatial compoet ad suggested a back fittig algorithm for its estimatio. Affuso (010) [9] formulated maximum likelihood estimator for the spatial autoregressive stochastic frotier model with a half-ormal iefficiecy term, ad used it for estimatio of farmers productivity growth. 19

2 Sessio 1. Statistic Methods ad heir Applicatios he article icludes a formulatio of the spatial autoregressive stochastic frotier model, a proposed maximum likelihood estimator for this model, ad a empirical applicatio of this model to aalysis of broadbad adoptio i EU member states.. he Spatial Autoregressive Stochastic Frotier (SARSF) Model I this sectio we preset a sequetial formulatio of the spatial autoregressive stochastic frotier model ad describe its mai features..1. he classical regressio model ad spatial depedece he classical regressio model is widely used for aalysis of a stochastic relatioship betwee a depedet variable ad a set of determiats: y = Xβ v, (1) y is a ( x 1) vector of a depedet variable ( is a size of the sample); X is a ( x k1) matrix of explaatory variables (k is a umber of explaatory variables); β is a (1 x k1) vector of ukow coefficiets (model parameters); v is a ( x 1) vector of idepedet idetically distributed (i.i.d) error terms. A importat potetial problem of the classical model (1) is omittig of sigificat explaatory variables. If a sigificat determiat of the depedet variable is t icluded ito the model, estimates of model parameters will be biased ad icosistet (well-kow omitted variables bias [10]). If objects i a study sample have a spatial structure ad a level of the spatial depedece betwee them is sigificat, the the omitted variable problem will arise. Spatial effects should be icluded ito the set of determiats to prevet this problem. Also estimatio of possible spatial effects ca be a subject of empirical researches. Spatial effects appear for objects located ear to each other. obler s law [11] says that everythig is related to everythig else, but ear thigs are more related tha distat thigs, so usually researchers expect that a level of the spatial relatioship is a fuctio of a distace betwee objects. his metric is called a spatial weight. here are some differet approaches to calculatio of spatial weights as well as differet defiitio of distace itself. A distace betwee two poit objects ca be estimated ot oly as a physical metric, but also as a travel time or cost, ad eve as a closeess of cotacts betwee objects (for example, import-export volumes or a umber of visitors betwee two cities). Objects with area (like coutries) require aother, border-based approach. here are some popular ways to calculate spatial weights for objects with area [6]. Distace-based eighbours approach defies two objects as related if the distace betwee them is less tha a predefied maximum distace. Whe list of eighbours is created, we ca assig spatial weights to each relatioship. he relatioship ca be biary (1 is preset, 0 if ot) or variable (for example, stadardised). Stadardizatio is used to create proportioal weights i cases objects have differet umbers of eighbours ad lays i divisio of each eighbour weight by the sum of all eighbour weights. A set of spatial weights for every two objects i a sample are usually compiled ito a cotiguity matrix W. he matrix W is a square x matrix, each elemet w ij represets a distace (geerally, a relatioship) betwee objects i ad j. Diagoal elemets of the matrix W are set to 0. here are two basic forms of spatial depedecy: 1. Spatial lags a value of the depedet variable for a give object is affected by variables (both explaatory ad depedet oes) i eighbour objects. his depedece directly follows from obler s law of geography.. Spatial errors there are some factors (ot icluded ito the model ad possibly uobserved) which have a ifluece o all object iside a area ad lead to commo directio of errors of predictio of the depedet variable. Both types of spatial depedecy lead to problems with the classical regressio model. Neglected spatial lags lead to the omitted variable problem ad icosistet estimates, ad eglected spatial errors make model estimate iefficiet. here are diagostic statistics developed to discover spatial relatioships. Mora s I is a test statistics for global spatial depedece [1]: e We MoraI = ~ N( 0,1), () e e 0

3 he 11 th Iteratioal Coferece RELIABILIY ad SAISICS i RANSPORAION ad COMMUNICAION -011 e = y Xβˆ, ˆ β are estimates of model parameters β. Mora s I coefficiet allows to discover spatial autocorrelatio of model residuals, but caot distiguish betwee spatial lags ad spatial errors. Lagrage Multiplier statistics [6] are used to test spatial lags (LM-lags statistic) ad spatial errors (LM-errors statistic) separately: 1 e Wy LM lags = J σ ε 1 e We LM errors = σ ε σ ε 1 = e e, ~ χ t = trace WW ~ χ () 1, (), 1 ( W W ), J = ( ˆ 1 WXβ ) I X ( X X ) X ( WX ˆ β ) If both statistics are sigificat, robust modificatios of these test statistics should be used. We do t require robust modificatios for empirical purposes of this research, so we skip formulas for them for space savig... he spatial autoregressive (SAR) model If diagostic statistics show presece of spatial depedece i the sample, it should be icluded ito the model for proper estimatio. he spatial autoregressive model icludes spatial effects ad ca be writte as: ( y) X, y = ρ spatial. lag β v (4) ( y). spatial. lag = Wy he feature of the model is the spatial lag compoet, reflectig a relatioship betwee the depedet variable i a give regio with the same variable i eighbour regios. Model parameter ρ ad its sigificace represet a directio ad a power of this relatioship ad usually is a subject of researchers iterest. A detailed descriptio of the SAR model ca be foud at [6]. Note that it is supposed that Gauss-Markov coditios are satisfied for model s error compoet v..3. he stochastic frotier (SF) model he classical regressio approach (icludig the SAR model) is widely used to predict a average value of a depedet variable (for give values of determiats). Aother very practically importat issue is estimatio of uit s efficiecy level. Efficiecy is usually cosidered as a ratio of results (a depedet variable) ad resources used (determiats). here are some methodologies developed to estimate uit s efficiecy; may of them take a relative ature of the efficiecy idicator ito accout. Frotier-based methods cosist i costructig of a hypothetical set of 100% efficiet uits (a efficiecy frotier) ad estimatig of uit s efficiecy as a distace from this frotier. Stochastic frotier model utilises probabilistic approach to the efficiecy frotier ad ca be formalised as [5, 10]: y = f ( x, β ) ε, ε = v u, v ~ N(0, σ v ), u 0, ε is a ( x 1) vector of composite error terms, u is a ( x 1) vector of iefficiecy terms with o-egative values. e e t. (3) (5) 1

4 Sessio 1. Statistic Methods ad heir Applicatios he mai feature of the SF model is a composite error terms, which icludes ot oly i.i.d. radom errors v, but also a iefficiecy compoet u. he iefficiecy term u represets a distace from the efficiecy frotier ad is supposed to be o-egative. A distributio law of the iefficiecy term ca be selected by a researcher (subject to madatory o-egativity). Selectio betwee the classical ad the SF model is based o variaces of u ad v error terms. If the variace of u is sigificatly large relative to the total variace of the error term, the iefficiecy presets i data. A γ statistic is used to check this hypothesis: σ u γ =. (6) σ σ u v If γ is sigificatly differet from 0, the SF model is preferred. Detailed descriptio of stochastic frotier models is preseted i [5]..4. Formulatio of the spatial autoregressive stochastic frotier (SARSF) model I this research we try to combie the SF ad SAR models to costruct ad estimate a efficiecy frotier model i case of presece of spatial depedecies. We itroduce the spatial autoregressive stochastic frotier (SARSF) model as: y = ρwy Xβ ε, ε = v u, v ~ N(0, σ v ), u 0. he model is a compositio of the SF ad SAR models ad icludes features of both spatial lags i the fuctioal form ad the iefficiecy compoet i the radom errors. 3. Maximum Likelihood Estimatio of the SARSF Model A task of SARSF model parameter estimatio is very importat from applicatios, but icludes some difficulties. I this work we apply well-kow maximum likelihood estimator. he classical maximum likelihood approach requires a exact distributio law for the composite error term, iherited from the SF model. We assume ormal half-ormal specificatio of the error term: ε = v u, v v ~ N(0, σ ), u ~ N f u (0, σ ) A probability distributio fuctio for the composite error term ε i this case is preseted as [5]: σ ε ελ Φ σ σ ( ε ) = ϕ, σ u σ = σ u σ v, λ =, σ v φ ad Φ are stadard ormal probability desity ad distributio fuctios accordigly. Applyig a usual algorithm of likelihood fuctio costructio ad takig the edogeeity problem ito cosideratio [13] we receive the log-likelihood fuctio for the SARSF model: (7) (8) LogL ( ρ, β, σ, y, X, W ) = l l( σ ) π i= 1 i= 1 ε ε σ ελ l Φ σ l ( det( I ρw )) (9)

5 he 11 th Iteratioal Coferece RELIABILIY ad SAISICS i RANSPORAION ad COMMUNICAION -011 the compoet ελ l Φ i= 1 σ is iherited from the log-likelihood fuctio of the SF model ad the compoet i= 1 ( det( I W )) l ρ is iherited from the log-likelihood fuctio of spatial models. We skip a formal derivatio of the log-likelihood fuctio i this paper. Maximisatio of the log-likelihood fuctio with respect to its parameters is a separate computatioal problem (the fuctio ca have may local maximums, so selectio of iitial values becomes a highly importat task). Cosideratio of the computatioal problems lies outside of this research scope. 4. Data ad Model Specificatio he empirical part of this research is devoted to aalysis of broadbad adoptio i Europea coutries ad estimatio of this process efficiecy. For the model specificatio we require iformatio about the depedet variable (broadbad adoptio), a set of explaatory variables (which determies the depedet variable) ad geographical iformatio. hree mai data sources are used for this research: 1. he Eurostat (the Statistical Office of the Europea Commuities) database [14] is a source of geeral iformatio about EU member states. he iformatio about each coutry icludes: a. Broadbad peetratio rate, a umber of broadbad services subscribers per 100 ihabitats (i 009). his is the depedet variable of our research. b. Populatio desity, persos per square kilometre (010). c. Gii coefficiet, a measuremet of icome distributio iequality (009). d. Phoes, a umber of fixed phoe lies per 100 ihabitats (010). e. Mobiles, a umber of active mobile phoe umbers per 100 ihabitats (009).. Measurig the Iformatio Society 010 executive summary [15] from Iteratioal elecommuicatio Uio (IU) used for iformatio about prices of broadbad services: a. Price GNI, a fixed broadbad sub-basket as a % of gross atioal icome per capita (009). 3. hematicmappig web site [16] is used for iformatio about borders of Europea coutries i form of shape files. Descriptive statistics of characteristics above are preseted i the able 1. able 1. Data descriptive statistics Parameter Mea Stadard Mi Max deviatio Broadbad, subscribers per 100 ihabitats PopulatioDesity, persos/km Gii PriceGNI, fixed broadbad sub-basket as a % of GNI per capita Phoes, lies per 100 ihabitats Mobiles, lies per 100 ihabitats Regardig the depedet variable, the broadbad peetratio rate is the most frequetly used metric for broadbad adoptio. here are some other idicators proposed (for example, traffic volume), but they are quite specific ad used relatively rare. 3

6 Sessio 1. Statistic Methods ad heir Applicatios We expect a positive relatioship betwee the populatio desity ad broadbad adoptio. his expectatio is supported by a higher level of broadbad adoptio i urba areas. Also providig of broadbad coectio is techically easier ad cheaper i desely populated areas. Icome distributio iequality is supposed to be egatively related to the broadbad peetratio rate. At this momet broadbad Iteret coectio still ca be classified as a superior product, so we expect that a higher level of icome iequality should lead to lower percet of broadbad subscribers. A average price of broadbad services is supposed to have a egative impact o broadbad adoptio (although we do t claim that the estimated relatioship is a demad curve due to possible complexity of the latter). his metric is costructed as a share of broadbad cost i gross persoal icome ad is comparable betwee coutries. his property is ecessary for our purposes ad implicitly excludes a ifluece of coutry-specific price ad ecoomic developmet levels. Phoes (both fixed ad mobile) adoptio levels are frequetly used [4] as a metric of techical preparedess of a coutry ad a level of potetial demad. Geerally, broadbad services ca be cosidered as competitor for fixed phoe lies, due to widely used VoIP software, so from our poit of view it should t be used as a resource at least for the efficiecy frotier model. But we iclude these variables out of regards to other researchers to check the differece. Usig the SARSF model specificatio (7) ad the Cobb-Douglas fuctioal form, we costructed the empirical ecoometric model: ( l Broadbad ) l Broadbad = β0 ρ sp. lag β1 lgii β l PriceGNI β3 l PopulatioDesity β4 l Phoes β5 l Mobiles v u We uderstad that uder selected specificatio the depedet variable is limited (0 Broadbad Peetratio Rate 1*umber of homes/offices/other places to have broadbad coectio), ad the liear model is ot quite appropriate i this case ([10]). Due to the lower boud (the upper boud is ot a real restrictio i practice), a limited depedet variable modificatio of the model should be theoretically used. We leave this shortcomig of our model for simplicity; it did t lead to problems of iterpretatio ad to a sigificat bias of the estimates. 5. Empirical Results We composed a study data set of iformatio for all 7 EU member states i 009 or 010 ( data available) years; we do t cosider a pael data set i this research). he empirical research icludes the ext steps: 1. Estimatio of the classical regressio model (1) parameters ad aalysis of its residuals for possible spatial depedecy.. Estimatio of the stochastic frotier model s parameters with differet sets of explaatory variables. 3. Aalysis of the SF model s efficiecy estimates. 4. Estimatio of the SARSF model s parameters ad aalysis of relatioships discovered. I terms of this research the most iterestig part of the first step was aalysis of spatial depedecies. able icludes observed values for Mora s I (), LM-lags, ad LM-errors test statistics (3), p-values for them (a ull hypothesis for all tests is a absece of spatial depedecies i residuals) ad resultig coclusios. able. Results of the tests for spatial depedece of classical regressio s OLS residuals est statistic Observed p-value Coclusio value Global Mora's I Sigificat spatial depedece Lagrage multiplier statistic for spatial lags Sigificat spatial lags Lagrage multiplier statistic for spatial errors Weakly sigificat spatial errors Spatial depedecy testig results with differet test statistics are ot cotradictory all statistics show a presece of spatial depedecies. he sigificat value of Mora s I idicates the presece of global spatial depedecy, ad LM-lags ad LM-errors tests allow us to idetify its type. he value of (10) 4

7 he 11 th Iteratioal Coferece RELIABILIY ad SAISICS i RANSPORAION ad COMMUNICAION -011 the LM-lags test statistic is sigificat (at the 5% level), ad the value of the LM-errors test statistic is ot, so followig Aseli s [6] recommedatio we choose the spatial lag type of depedecy for our further research. Separately we estimated the SF model (5) to discover possible iefficiecies i broadbad adoptio. We ivestigated two differet sets of explaatory variables with Phoes ad Mobiles idicators icluded ad without them; estimatio results for both models are preseted i the able 3. able 3. Compariso of stochastic frotier model with ad without Phoes i explaatory variables Estimates for the SF model with Phoes i explaatory variables Estimates for the SF model without Phoes i explaatory variables Parameter Coefficiet p-value Coefficiet p-value Itercept L(Gii) L(PriceGNI) L(PopulatioDesity) L(Phoes) L(Mobiles) γ he most iterestig result of model compariso is related with the presece of iefficiecies i data. he γ statistic (6) idicates that there are o iefficiecies i the SF model with Phoes ad Mobiles, ad there are highly sigificat iefficiecies i the SF model without these idicators. echically it meas that Phoes are correlated with iefficiecies of the model without them, but there are two differet ways to iterpret this result. he first oe is to deote the Phoes idicators are a sigificat resource for the broadbad peetratio rate, which should be used for its predictio ad maagig. he secod oe is to coclude that coutries, iefficiet with respect to broadbad adoptio, are also less developed with respect to phoe lies. We ca t make a coclusio about the correct iterpretatio o the base of our model, so their compariso is a matter of a separate work. I this research we preferred the secod way of iterpretatio ad coclude that both Broadbad ad Phoes are metrics of a geeral level of coutry s telecommuicatio developmet. he stochastic frotier approach allows estimatig iefficiecy values for each coutry i the data set. We preset the estimated values i form of the map (Figure ). Figure. Efficiecy of broadbad adoptio i EU member states A average value of the estimated efficiecy levels is 81.73% with miimum 57.78% (Romaia) ad maximum 94.79% (Estoia). he overall distributio of efficiecy levels has obvious traces of spatial depedecies areas with relatively high ad relative low efficiecy levels are clustered. 5

8 Sessio 1. Statistic Methods ad heir Applicatios he SARSF model embodies both spatial depedecies ad efficiecy levels. o estimate the parameters of the SARSF model (10) we utilised maximum likelihood estimatio techique (9). Estimates, calculated usig our ow module for CRAN R software, are preseted i the equatio (we put correspodig p-values i brackets udereath the model parameters estimates): l Broadbad = sp. lag (0.047) 0.61lGii (0.046) ( l Broadbad ) 0.31l PriceGNI (0.01) 0.015l PopulatioDesity (0.65) (0.004) v u he model is formulated i the Cobb-Douglass fuctioal form, so estimated values are elasticities of explaatory factors. Sigs of estimated coefficiets completely match our expectatios. Gii coefficiet has a sigificat egative ifluece o broadbad adoptio (a higher level of icome iequality leads to worse broadbad adoptio i a coutry). Prices of broadbad services also have a expected egative elasticity. Populatio desity is detected as a isigificat factor for broadbad adoptio (perhaps due to its average ature a metric of populatio distributio should be tested for a strog coclusio). A sigificat positive value is revealed for the spatial lag of the broadbad peetratio rate, so a high value of broadbad peetratio rate i eighbour coutries eforces broadbad adoptio i a give coutry. he presece of spatial depedecy ca be justified i differet ways techical possibilities, istallatio ad maiteace costs. Additioal ivestigatios are required to provide a strog explaatio of the positive spatial lag discovered. 6. Coclusios Recetly sigificat iterest has bee give to impact of broadbad services adoptio o sustaiable atioal ecoomic growth. Efficiecy of broadbad adoptio becomes oe of importat logterm competitive advatages of coutries. At the same time, broadbad adoptio i a give coutry has sigificat spatial effects ad ehaces developmet of broadbad ad other services i eighbour coutries. I this article we combie the stochastic frotier model, frequetly used for efficiecy estimatio, with spatial ecoometric models. he proposed spatial autoregressive stochastic frotier model is used for estimatio of broadbad adoptio efficiecy i EU coutries. A maximum likelihood estimator for the spatial autoregressive stochastic frotier model was proposed ad implemeted as a module for R software. We use the data sample for years to aalyse factors, ifluecig o broadbad adoptio i EU member states. A sigificat egative relatioship betwee broadbad peetratio rate ad average prices for broadbad service is cofirmed. A higher level of populatio icome iequality (i form of the Gii coefficiet) is also discovered as a sigificatly egative factor of broadbad adoptio. We have discovered sigificat spatial lags of broadbad peetratio rates, which make the proposed spatial autoregressive stochastic frotier model a preferred oe i this case. he estimated sig of the spatial lag is positive as expected, so higher broadbad peetratio rates i eighbour coutries have a positive impact o broadbad adoptio i a give coutry. Aother cosiderable output of this research is estimates of broadbad adoptio efficiecy i EU member states. From our poit of view, these estimates, calculated o the base of the proposed model, perform better tha the covetioal oes, because it icludes both ifluece of coutry-specific resources ad spatial effects. Ackowledgemet he author is grateful to Ermao Affuso, researcher at the Departmet of Agricultural Ecoomics ad Rural Sociology of Aubur Uiversity, for providig very useful commets about maximum likelihood estimatio of the spatial autoregressive stochastic frotier model. 6

9 he 11 th Iteratioal Coferece RELIABILIY ad SAISICS i RANSPORAION ad COMMUNICAION -011 Refereces 1. Forefeld, M., Delauay, G., Elixma, D. he Impact of Broadbad o Growth ad Productivity. A study o behalf of the Europea Commissio. 008, 14 p. Available at Alle Cosultig Group rue Broadbad: Explorig the Ecoomic Impacts. 003, 56 p. Available at Broadbadproductivity_1.pdf 3. Gillet, S. E., Lehr, W. H., Sirbu, M. Measurig Broadbad s Ecoomic Impact. Fial Report. Natioal echical Assistace, raiig, Research, ad Evaluatio Project # p. Available at /v1/mitcmubbimpactreport.pdf 4. Ford, G. S., Koutsky,. M., Spiwak, L. J. he Broadbad Efficiecy Idex: What Really Drives Broadbad Adoptio across the OECD? Phoeix Ceter Policy Paper Series, p. 5. Kumbhakar, S. C., Lovell, C. A. K. Stochastic Frotier Aalysis. Cambridge: Cambridge Uiversity Press, p. 6. Aseli, L. Spatial Ecoometrics: Methods ad Models. Dordrecht: Kluwer Academic Publishers, p. 7. Schmidt, A. M., Moreira, A. R. B., Helfad, S. M., Foseca,. C. O. Spatial stochastic frotier models: accoutig for uobserved local determiats of iefficiecy, Joural of Productivity Aalysis, Vol. 31 (), 009, pp Barrios, E. B., Lavado, R. F. Spatial Stochastic Frotier Models, PIDS Discussio Paper Series, No , p. 9. Affuso, E. Spatial autoregressive stochastic frotier aalysis: A applicatio to a impact evaluatio study: Aubur Uiversity Workig Papers, 010, 19 p. Available at Greee, W. Ecoometric Aalysis. Pretice Hall, th Ed. 13 p. 11. obler, W. A computer movie simulatig urba growth i the Detroit regio, Ecoomic Geography, Vol. 46, Issue, 1970, pp Mora, P. A. P. Notes o Cotiuous Stochastic Pheomea, Biometrika, Vol. 37, pp Arbia, G. Spatial ecoometrics: statistical foudatios ad applicatios to regioal covergece. Spriger, p. 14. Statistical Office of the Europea Commuities (Eurostat), Statistics Database, 011. Available at [Accessed: Jul. 06, 011]. 15. Iteratioal elecommuicatio Uio, Measurig the Iformatio Society 010, Executive Summary, 010, 1 p. Available at Sadvik, B. World Borders Dataset, 010. Available at 7