Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 COMMUNICATIONS IN SCIENCE AND TECHNOLOGY Homepage: cst.kipmi.or.id Applicatio of spatial error model usig GMM estimatio i impact of educatio o poverty alleviatio i Java, Idoesia Rya Willmada Jauardi *, Agug Priyo Utomo Departmet of Social Statistics, Sekolah Tiggi Ilmu Statistik Jl. Otto Iskadardiata 64C, East Jakarta, 13330. Idoesia Article history: Received: 4 Jue 2017 / Received i revised form: 23 November 2017 / Accepted: 27 November 2017 Abstract Java Islad is the ceter of developmet i Idoesia, ad yet poverty remais its major problem. The pockets of poverty i Java are ofte located i urba ad rural areas, domiated by productive age group populatio with low educatio. Takig ito accout spatial factors i determiig policy, policy efficiecy i poverty alleviatio ca be improved. This paper presets a Spatial Error Model (SEM) approach to determie the impact of educatio o poverty alleviatio i Java. It ot oly focuses o the specificatio of empirical models but also i the selectio of parameter estimatio methods. Most studies use Maximum Likelihood Estimator (MLE) as a parameter estimatio method, but i the presece of ormality disturbaces, MLE is geerally biased. The assumptio test o the poverty data of Java showed that the model error was ot ormally distributed ad there was spatial autocorrelatio o the error terms. I this study we used SEM usig Geeralized Methods of Momet (GMM) estimatio to overcome the biases associated with MLE. Our results idicate that GMM is as efficiet as MLE i determiig the impact of educatio o poverty alleviatio i Java ad robust to o-ormality. Educatio idicators that have sigificat impact o poverty alleviatio are literacy rate, average legth of school year, ad percetage of high schools ad uiversity graduates. Keywords: poverty ratio; educatio; spatial error model; robustess; MLE; GMM. 1. Itroductio Java Islad is the ceter of developmet i Idoesia, eve though poverty remais oe of its major problems. This ca be see from the cotributio of GDP of Java Islad from 2008 to 2013, which has bee cosistet i the 56 percet rate [1]. Still, i 2013 the majority of people who lived i poverty were cocetrated i Java. As show i Fig. 1, 54.45 percet of the total poor populatio i Idoesia live i Java [2]. So, eve though the Islad has a sigificat cotributio to the atioal ecoomy, it still caot get out of the poverty problem, with more tha half of Idoesia's poor populatio livig i the Islad. The pockets of poverty i Java are located i urba ad rural areas, domiated by productive age group populatio with low educatio ad productivity, which put this group at a disadvatage i the labor market. The icreasig poverty rate i both urba ad rural areas is due to the low quality of huma resources, of which educatio is a importat idicator [3], [4]. Additioally, poverty is also associated with iterregioal spatial iteractios associated with populatio mobility ad spatial impoverishmet [5]. Cradall ad Weber [6] explaied that poverty has a spatial iteractio. A regio with high poverty rate would affect ad be affected by other regios aroud it. * Correspodig author. Tel.: +62 852 40421858. Email: rw.jauardi@gmail.com 54.45% Sumatera Bali-Nusa Teggara Sulawesi 7.00% 3.43% 7.49% 5.96% 21.68% Java Kalimata Maluku-Papua Fig. 1. Percetage of people livig i poverty i Idoesia 2013 [2] Takig ito accout this spatial iteractio, a policy o poverty alleviatio ca beefit from ad made more efficiet by usig spatial aalysis. Numerous researches have icorporated spatial statistics whe examiig poverty. However, may of such research have focused o the specificatio of spatial statistical models rather tha the selectio of parameter estimatio methods. Although the use of parameter estimatio methods might ot make as sigificat differece as model specificatio, the existece of assumptio requiremets ad data coditios requires appropriate parameter estimatio methods [7]. To be best of our kowledge, existig spatial aalyses do ot take ito accout these assumptio requiremets explicitly perhaps iadvertetly. Spatial regressio parameters estimatio [8] ca 2017 KIPMI
54 Author ame / Commuicatios of Sciece ad Techology 0(0) (2017) 000 000 be obtaied through several estimatio methods such as Maximum Likelihood Estimatio (MLE) ad Geeralized Method of Momets (GMM). These two parameters estimatio methods are used for differet assumptio requiremets. We select GMM as a parameter estimatio method to overcome the bias associated with MLE. level, ot o the idividual or household poverty. Meawhile, the spatial data used i this study was derived from BPS mappig. 2. Theoretical Framework, Materials, ad Methods 2.1. Theoretical Framework Poverty is defied as a lack of meas ecessary to meet basic eeds such as food ad o-food as measured by expediture [2]. People who live i poverty are the oes with a average cosumptio per capita per moth below this established poverty lie. Poverty ca be measured i two dimesios: the moetary dimesio that covers isufficiet icome or cosumptio; ad o-moetary dimesios that covers isufficiet outcomes with respect to huma capital such as educatio, health, ad utritio [9]. Oe of the efforts to reduce ad cut the vicious cycle of poverty is to improve the educatio of the populatio [10]. The low educatio level of the poor will lead to a vicious cycle of poverty i the ext geeratio. People with low educatio will have low productivity; ad low productivity will lead to low icome, resultig i poverty. Poor households will fid it difficult to fiace their childre's schoolig so that it will produce the ext geeratio with similar low educatio thus creatig the ufortuate cycle of poverty. Throughout the world, it has bee foud that the probability of fidig employmet rises with higher levels of educatio, ad that earigs are higher for people with higher level of educatio [11]. This coectio betwee educatio ad poverty works through three mechaisms. Firstly, more educated people ear more. Secodly, more (ad especially better quality) educatio improves ecoomic growth ad thereby ecoomic opportuities ad icome. Thirdly, educatio brigs wider social beefits, such as ecoomic developmet, which will have a positive ripple effect o the poor regios. The theoretical framework compiled by Jajua ad Kamal [12] states that educatio has direct ad idirect effects i poverty alleviatio. From this theoretical framework, we cosider educatio ad skills of the idividual as the direct effects i poverty alleviatio. Fig. 2 depicts the impact of educatio o poverty alleviatio. 2.2. Materials The aalysis of this study icluded all regecies/cities i Java Islad. This study used secodary data from the 2013 Idoesia Cetral Bureau of Statistics (BPS) ad Idoesia Miistry of Educatio ad Culture for its 118 regecies/cities. Data used iclude: literacy rate (X 1), average legth of school year (X 2), percetage of high schools ad uiversity graduates (X 3), ratio of juior high school availability (X 4), ratio of seior high school availability (X 5), ad poverty ratio (Y). Poverty ratio is the proportio of the poor populatio with total populatio i a regio (regecy/city). It idicated the icidece of poverty i a regio, but igored the differeces i well-beig betwee differet poor households. The data used i this study was aggregate data i every regecy/city. This study was coducted at the spatial poverty 2.3. Methods Fig. 2. Impact of educatio o poverty alleviatio [12] The methods used i this research was Exploratory Spatial Data Aalysis (ESDA) ad iferece aalysis usig spatial regressio. The details of each aalysis are explaied below. 2.3.1. Exploratory Spatial Data Aalysis Exploratory Spatial Data Aalysis (ESDA) was used to describe spatial patters of poverty i Java Islad. ESDA [13] is a collectio of techiques to describe ad visualize spatial distributios; idetify spatial outliers; discover patters of spatial associatio, clusters or hot-spots; ad suggest spatial regimes or other forms of spatial heterogeeity. ESDA was applied based o Global Mora's I, Mora Scatterplot, ad LISA statistics. To idetify spatial patters, spatial clusterig associatio patters, ad outlier data, we used the followig statistical techiques for exploratory spatial data aalysis. 1. Costructig Spatial Weighted Matrices The basic form of spatial weighted matrices is a square symmetric weighted matrices (deoted W) (row stadardized) matrices that defie which areas are eighbors of a give area. Spatial weighted matrices is a weight deotig the stregth of the coectio betwee areas i ad j. I this study, we used cotiguity-based relatios based o modified quee cotiguity. Cotiguity-based relatios are mostly used i the presece of irregular polygos with varyig shape ad surface, sice cotiguity igores distace ad focuses istead o the locatio of a area. It was appropriate for areas i Java that had irregular polygos. Quee cotiguity defied a eighbor whe at least oe poit o the boudary of oe polygo is shared with at least oe poit of its eighbor (commo border or corer). Quee cotiguity weighted matrices (deoted W Q ) is deoted as follows: w 11 w 1j W Q = [ ] w ij = { 1, w i1 w 0. ij if i eighbor j otherwise I additio, the quee cotiguity weighted matrices used i this study was maually modified to maitai coectivity (1)
Jauardi et al. / Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 55 betwee areas. Thus, separate cross-islads areas like Bagkala ad Surabaya or Pulau Seribu ad Jakarta Utara still have access to iteract as eighborig areas. Coectivity betwee areas based o modified quee cotiguity weighted matrices was illustrated i Fig. 3. Fig. 3. Coectivity betwee areas based o modified quee cotiguity weighted matrices The obtaied quee cotiguity weighted matrices were trasformed ito the ormality matrices (row-stadardized), which is the spatial weighted value (deoted Wij) for each eighbor which forms the spatial weighted matrices W, accordig to followig equatio: W ij = w ij w j (2) W 11 W 1j W= [ ] (3) W i1 W ij 2. Aalyzig Global Idicators of Spatial Autocorrelatio by Usig Global Mora s I Statistics Mora's I [14] was used i this study to determie whether the value of eighborig areas were more similar tha would be expected uder the ull hypothesis. Mathematically, Global Mora's I statistics for observatio ad i-th observatio at the j-th locatio ca be formulated i followig equatio: I= W ij i=1 j=1 i j W ij (y i -y )(y j -y ) (y i -y ) 2 i E(1)=- 1-1, i j (4) (5) var R (I)= [( 2-3+3)S 1 -b[( 2 -)S 1-2S 2 +6S 0 2 ] (-1)(-2)(-3)S 0 2 - E(I) 2 (6) b= i=1 (y i -y )4 ( (y i -y ) 2 i=1 ) 2 (7) S 0 = W ij i=1 j=1 S 1 = 1 2 (W ij +W ji) 2 i=1 j=1 S 2 = (W i. +W.i ) 2 i=1 (8) (9) (10) W i. = W ij j=1 W.i = W ji j=1 (11) (12) Uder the radomizatio assumptio (deoted R), the rates were radom samples from a populatio whose distributio was ukow. Assumptio R is less restrictive sice their theoretical distributio is ofte ukow. The value of Global Mora's I rages betwee -1 ad 1. If I > E(I), the the spatial patter is clustered idicatig a positive spatial autocorrelatio. If I = E(I), the patter spread uevely (o spatial autocorrelatio), ad if I < E(I), the patter is diffused idicatig egative spatial autocorrelatio [15]. 3. Aalyzig Local Idicators of Spatial Autocorrelatio by Usig LISA Cluster Map I cotrast to the previously described Global Mora's I, which is a global idicators of spatial autocorrelatio, LISA idicated local autocorrelatio. I this case, LISA idetified the relatioship betwee a locatio of observatio to aother locatio of observatio. Furthermore, the clusterig of areas beloged to four types of spatial associatios ad visualized through the LISA cluster map [16]. The four possible scearios were as follows: a. Hot Spots, high-value locatio would be surrouded by high-value eighbors (high-high) b. Cold Spots, the low-value locatio would be surrouded by low-value eighbors (low-low) c. Outliers, high-value locatios would be surrouded by low-value eighbors (high-low) d. Outliers, low-value locatios would be surrouded by high-value eighbors (low-high) If the LISA cluster map showed ot sigificat results, it meat that the proximity of the area was ot closely related to the evets studied. 2.3.2. Spatial Regressio Spatial regressio is closely related to the autoregressive process, idicated by the depedece relatioship betwee a set of observatios or locatios. The relatios could also be expressed with the locatio value depedig o aother eighborig locatio value. Spatial regressio was used to aalyze the impact of educatio, with predictor variables as follows: literacy rate (X 1), average legth of school year (X 2), percetage of high schools ad uiversity graduates (X 3), ratio of juior high school availability (X 4), ad ratio of seior high school availability (X 5); ad poverty ratio i Java i 2013 as respose variable, takig ito accout spatial factors. There are two commo types of spatial regressio: 1. Spatial Lag Model (SLM) SLM [17] is a model that combies a classic regressio model with spatial lag i respose variables usig cross-
56 Author ame / Commuicatios of Sciece ad Techology 0(0) (2017) 000 000 sectioal data so ofte called spatial lag model. The SLM is formed whe ρ 0 ad λ = 0. This model assumed that the autoregressive process oly occurs i the respose variable. The spatial lag model that was possible to be formed i this research is as follows: Y i = ρ W ij Y j +β 0 -β 1 X1 i -β 2 X2 i -β 3 X3 i -β 4 X4 i -β 5 X5 i + ε i (13) j=1,i j with ρ is spatial lag coefficiet parameters o the respose variable. momet of coditio i the populatio by miimizig objective fuctio of the momet of sample coditio. Where g(β )= 1 z i=1 i(y i -X i β ) is the momet of sample coditio, z i is the istrumet variable, ad E(g(β))=0 is the momet of the populatio coditio. 2. Spatial Error Model (SEM) SEM [17] is a model i which the model-error has spatial correlatio. The SEM is formed whe ρ = 0 ad λ 0. This model assumed that the autoregressive process oly occurred i the model error. The spatial error model that was formed i this research was as follows: Y i = β 0 -β 1 X 1 -β 2 X 2 -β 3 X 3 -β 4 X 4 -β 5 X 5 +λ W ij u j +ε i (14) j=1,i j with λ as spatial error coefficiet parameters o error u, ad u as spatial error vector ( 1). To specify the appropriate model, we follow the steps illustrated i Fig. 4. I particular the focus was o detectig model specificatio due to spatial depedece (i the form of a omitted spatially lagged depedet variable ad spatial residual autocorrelatio). Four tests were performed to assess the spatial depedece of the model. The statistics were the simple LM diagostics for a missig spatially lagged depedet variable (Lagrage Multiplier (lag)), the simple LM diagostics for error depedece (Lagrage Multiplier (error)), variats of these robust to the presece of the other (Robust LM (lag) ad Robust LM (error) which diagoses for error depedece i the possible presece of a missig lagged depedet variable, Robust LM (lag) is the other way roud). All modellig process were calculated by R programmig usig spdep packages ad GeoDaSpace, two softwares for advaced spatial ecoometrics. 2.3.3. Parameter Estimatio Methods 1. Maximum Likelihood Estimator (MLE) The uderlyig assumptio of this estimator is the ormal distributio of model errors, i.e., N(0. σ 2 I). The log-likelihood fuctio ad estimator of SLM was: l L= l I-ρW - 2 l(2π) - 2 l(σ2 ) - (Y-ρWY-Xβ)'(Y-ρWY-Xβ) 2σ 2 (15) β =(X ' X) -1 X ' (I-ρW)Y (16) The log-likelihood fuctio ad estimator of SEM was: l L= l I-λW - 2 l(2π) - 2 l(σ2 ) - (Y-Xβ)'(I-λW)'(I-λW)(Y-Xβ) 2σ 2 (17) β =((X-λWX)'(X-λWX)) -1 (X-λWY)'(X-λWY) (18) 2. Geeralized Methods of Momet (GMM) The basic priciple of GMM is to estimate β so that the momet of coditio i the sample will be equal to the Fig. 4. Schematic process spatial regressio model specificatio Kelejia da Prucha (i Aseli) [8] argue that GMM is as efficiet as MLE. I additio, GMM is parameter estimator that did ot require the ormal distributio assumptio for model errors as required by MLE. This results i the GMM estimator for SEM. The GMM estimator ca be produced i three steps [18]: a. Build objective fuctio of the momet of sample coditio, that is the quadratic fuctio of momet of sample coditio based o specified spatial weightig matrices: Q(β )=g(β )'Wg(β ) (19) b. Obtai a cosistet but iefficiet estimate of β by miimizig the objective fuctio of the momet of sample coditio as follows: β [1] = arg mi β g(β )'Wg(β ) (20) c. Obtai a cosistet ad efficiet estimate of β by miimizig the objective fuctio of the momet of sample coditio with a optimized spatial weightig matrices based o β [1], as follows: β [2] = arg mi β g(β )'W opt g(β ) (21)
Jauardi et al. / Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 57 3. Results Java had a wide spread poverty amog its regios. Through ESDA, we could describe the spatial distributio patter which icluded patters of spatial associatio ad idetificatio of outlier data from poverty ratio. ESDA was applied based o: (1) Global Mora's I statistics score which described the effects of global spatial autocorrelatio, ad (2) LISA cluster map which described the effects of local spatial autocorrelatio through spatial weighted matrices based o modified quee cotiguity. Table 1. Global Mora's I statistics calculatio Variable I E(I) pseudo p-value Y 0.5354-0.0085 0.001 The calculatio results i Table 1 showed that there were statistically spatial autocorrelatio effects i poverty amog regios i Java i 2013. This was idicated by pseudo p-value less tha 5%. The table also idicated that that I > E(I), which meat that the spatial patter of poverty amog regios i Java Islad was clustered. To determie which regio has a sigificat effect o spatial associatio i geeral, we used LISA cluster map. As show i Fig. 5, there were three sigificat spatial distributio patters of poverty based o the LISA calculatio results. of multicolliearity i certai predictor variables would cause greater of stadard error ad thus iterfere the results of the aalysis. If the VIF value is less tha 10 the it ca be cocluded that there is o multicolliearity. If a multicoliearity is foud i the model, oe solutio is to remove oe of the variables from the model. The goal is to extract iformatio that is already represeted by the other predictor variables. The results of the multicolliearity diagostics are displayed o Table 3. Variable Table 3. Multicolliearity diagostics results VIF value Step 1 Step 2 X 1 2,477 1,465 X 2 10.987 Removed X 3 7,447 1,895 X 4 1,965 1,96 X 5 3,023 2,986 From the above table, appropriate predictor variables that could be used i this study were obtaied. The average legth of school year variable was removed because it had VIF > 10. There was a possibility that average legth of school year (X 2) correlated with percetage of high schools ad uiversity graduates variable (X 3). After all the predictor variables were free from multicolliearity, we built the spatial regressio model. Before determiig the appropriate model, we did model specificatio betwee SLM ad SEM. The results of model specificatio are displayed o Table 4. Model specificatio by LM ad Robust LM diagostics showed that Spatial Error Model (SEM) was better suited for this study. Additioally, the Robust LM (lag) value was smaller tha Robust LM (error) value, ad the Robust LM (error) was more sigificat tha Robust LM (lag). Table 4. LM ad Robust LM diagostics results for spatial regressio model specificatio Fig. 5. Poverty cluster i Java Islad based o LISA cluster map Table 2. Sigificat spatial distributio patters of poverty based o LISA cluster map Patters High-High Low-Low Low-High Regios Bayumas Regecy, Purbaligga Regecy, Bajaregara Regecy, Kebume Regecy, Purworejo Regecy, Woosobo Regecy, Blora Regecy, Tuba Regecy, Sampag Regecy, ad Pamekasa Regecy Lebak Regecy, Serag Regecy, Tagerag Regecy, Tagerag City, Tagerag Selata City, Jakarta Barat City, Jakarta Selata City, Jakarta Utara City, Jakarta Pusat City, Jakarta Timur City, Bekasi Regecy, Bogor Regecy, Bekasi City, ad Depok City Tegal Regecy, Slema Regecy, ad Proboliggo City To see the spatial effects o poverty i Java Islad, we used spatial regressio model. Before determiig the appropriate model, multicolliearity diagostics usig Variace Iflatio Factor (VIF) was coducted to see if there were correlatios amog the predictor variables. The presece Diagostics Value p-value Lagrage Multiplier (lag) 18.156 0.0000* Robust LM (lag) 0.4512 0.5018 Lagrage Multiplier (error) 25.463 0.0000* Robust LM (error) 7.7582 0.0053* Sigif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Meawhile, based o ormality test results, data error i this study was ot ormally distributed. The result of ormality test by Jarque-Bera test is displayed o Table 5. The p-value of Jarque-Bera is 0.0013 (i.e. reject ull hypothesis where ull hypothesis is error ormally distributed). Table 5. Normality test result Test Value p-value Jarque-Bera 13.246 0.0013* Sigif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Spatial regressio modellig by SEM was estimated usig Geeralized Method of Momets (GMM) estimator. The GMM was used because the ormal distributio assumptio for model errors was ot met. The followig table is a summary of the model.
58 Author ame / Commuicatios of Sciece ad Techology 0(0) (2017) 000 000 Table 6. Model parameter estimates, estimates of stadard error of the parameters, ad pseudo R-Squared of SEM by MLE ad GMM SEM MLE SEM GMM Parameter Estimates Estimates Std. Std. Error (p-value) (p-value) Error (Itercept) 52.7044 54.0939 7.5309 7.3672 β 1-0.3705-0.3853 0.0314 0.0312 β 3-0.1298-0.1282 0.0858 0.0841 β 4-0.0260-0.0452 0.0565 (0.3122) (0.2148) 0.0572 β 5-0.0430-0.0296 0.0531 (0.2234) (0.2901) 0.0535 λ 0.5579 0.5114 0.0866 0.0837 Sigif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Pseudo R-Squared 0.5987 0.6002 Table 7. Variace of estimators i SEM by MLE ad GMM Parameter SEM MLE SEM GMM β 1 0.0107 0.0106 β 3 0.0800 0.0768 β 4 0.0347 0.0355 β 5 0.0306 0.0311 λ 0.0815 0.0761 I terms of the estimates of stadard errors of parameters, MLE produced slightly larger stadard errors for the sigificat parameter estimates ad slightly smaller stadard errors for the o-sigificat parameter estimates tha GMM. The MLE ad GMM also produced slightly differet results i the parameter estimates (i.e. λ, β 1, β 3, β 4, β 5 ). GMM, which was free of distributioal assumptio for the model errors, had pseudo R-squared comparable to that of MLE. The pseudo R- squared of SEM GMM was 0.6002. The results idicated that GMM was better tha MLE i terms of pseudo R-squared. Pseudo R-Squared is used to describe how close the data to the fitted regressio lie. I this study, these results meat that the SEM GMM with variables of literacy rate (X 1), percetage of high schools ad uiversity graduates (X 3), ratio of juior high school availability (X 4), ad ratio of seior high school availability (X 5) could explai 60.02% the variability of the poverty ratio i Java. The variace of each parameter estimator for the parameter β 1, β 3, β 4, β 5, ad λ was also computed for MLE ad SEM GMM (Table 7). Theoretically, MLE is most efficiet (producig lowest variace) if the ormality assumptio is met. But i this study, MLE produced much larger variace tha GMM for the sigificat parameter. Uder the o-ormality, GMM was better i terms of the variace tha MLE. This results idicated that GMM was as efficiet as MLE ad robust to o-ormality. Based o the results obtaied i Table 6, the SEM equatio formed is as follows: Ŷ i =54,0939-0.3853X 1-0.1282X 3-0.0452X 4-0.0296X 5 + u i (22) u i =0.5114 W ij u j (23) j=1,i j Sigificace test of model parameter estimates i Table 6 showed that the variable of literacy rate (X 1), percetage of high schools ad uiversity graduates (X 3), ad spatial error (λ) had sigificat effect to poverty ratio i Java i 2013. The sigificat coefficiet λ idicated that autoregressive process o model error sigificatly iflueced the regios poverty ratio i Java i 2013. If the variable of literacy rate (X 1), percetage of high schools ad uiversity graduates (X 3), ratio of juior high school availability (X 4), ad ratio of seior high school availability (X 5) was igored or equal to zero, the poverty ratio i Java was estimated at 54.09%. Assumig the coditio of other variables is costat, the icrease i literacy rate i a regio by 1% ca reduce the poverty ratio of a regio by 0.3853%. Similarly, if the percetage of high schools ad uiversity graduates rose 1% i a regio the the poverty ratio i the regio will reduce by 0.1282%. The variables of ratio of juior high school availability (X 4) ad ratio of seior high school availability (X 5) also had a egative relatioship with poverty ratio. That is, the higher the ratio of school availability to both juior ad seior high school, the lower the poverty ratio. However, the variable of ratio of juior high school availability ad ratio of high school availability had o sigificat effect o poverty ratio. 4. Discussio Based o the results i Table 2, regios with high poverty teded to be surrouded by regios with high poverty as well, ad vice versa, regios with low poverty teded to be surrouded by similar low poverty. This pheomeo has bee described by Cradall ad Weber [6] i which they argued that poverty has a spatial iteractio. However, we also foud the outliers i this pheomeo. There were three regios which beloged to low-high clusters, low poverty regios surrouded by high poverty eighbors. The regios were: Tegal Regecy (10,75%) as low-poverty regio surrouded by Brebes Regecy (21,12%), Bayumas Regecy (19,44%), Purbaligga Regecy (21,19%), ad Pemalag Regecy (19,27%) as high-poverty eighbors; Slema Regecy (10,44%) as low-poverty regio surrouded by Kulo Progo Regecy (23,31%) ad Guug Kidul Regecy (22,71%) as high-poverty eighbors; ad Proboliggo City (10,92%) as low-poverty regio surrouded by Proboliggo Regecy (22,22%) as highpoverty eighbors. This coditio might lead to two possible scearios: the lowpoverty regio affects or be affected by the high-poverty eighbors. Which of these two scearios will likely to happe depeds o may factors. Oe of the cotributig factors is literacy rate. Accordig to this model, a sigificat icrease i literacy rate could reduce poverty ratio. As Murray ad Shilligto [19] describe, a perso with low literacy skill teds to be usuitable for a job compared to those with higher literacy skill. Regios with higher literacy rate have a populatio with a higher chace of eterig the labor market ad earig icome so as to avoid poverty. I aggregate, it ca reduce the poverty ratio i a regio. I additio, a icrease i the percetage of high schools ad uiversity graduates also has a sigificat impact
Jauardi et al. / Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 59 o poverty alleviatio. Silva [20] documets that poverty declies with icreasig years of educatio. Icreasig oe year of educatio will icrease the huma capital. The icreased huma capital will cotribute egatively to the possibility of beig i poverty. The variables of ratio of juior high school availability ad ratio of seior high school availability also had a egative relatioship with poverty ratio, but they had o sigificat effect o poverty ratio. This might be due to the differece i calculatio approach of poverty ratio ad the ratio of school availability i both juior ad seior high schools. The poverty ratio calculatio used a household approach, while the school availability ratio of both juior ad seior high schools used a idividual approach of school age (ages 13 to 15 years for juior high school ad 16 to 18 years old for high school). Icreasig the ratio of school availability to both juior ad seior high schools would oly affect the icreased chace of a certai school-age populatio to have a certai educatio. Whe there is a decrease i oe poor household i a regio, the its poverty ratio will also decrease. Meawhile, whe a household i a regio i which a household member has the opportuity to go to school ad receive a certai educatio due to a icrease i the umber of schools, the poverty level i the regio does ot ecessarily decrease, but the school availability ratio will. Based o the resultig spatial error equatio i Equatio 23, the poverty of a regio would icrease by a multiple of 0.5114% of the spatial weightig of each regio, if the average error of the eighborig regio rises by 1%. For example, Sampag Regecy had a spatial weightig with its eighborig area of 0.50 (provided i Appedix A) ad the spatial error equatio of Sampag was: u Sampag =0.5114 0.50 3 j=1,i j u Sampag =0.2557u Bagkala +0.2557u Pamekasa Sampag Regecy had two eighborig regios: Bagkala Regecy ad Pamekasa Regecy. If oe or all of regios variable of error (u j) was icreased so that the average of all eighborig regios were icreased by 1%, the Sampag Regecy would get the effect of icreased poverty rate of 0.2557%. These results meat that there were iflueces of the predictor variables other tha the oes used i this study from the eighborig areas. These results were cosistet with those preseted by Heiger ad Sel [21], i which they argued that spatial variatios i poverty level are ofte caused by factors with spatial dimesio of the surroudig areas. I this study, Sampag regecy was the regio with the highest poverty rate ad lowest literacy rate ad percetage of high schools ad uiversity graduates. Furthermore, Sampag regecy was also surrouded by high-poverty regios. Meawhile Tagerag Selata city was the regio with the lowest poverty rate ad high literacy rate ad percetage of high schools ad uiversity graduates, so as Yogyakarta city ad Cimahi city. They were also surrouded by low-poverty regios. Based o these results, the govermet ca improve the efficiecy ad effectiveess educatio ad poverty alleviatio u j policy by payig more attetio to the cluster of high poverty ad low educatio regio. 5. Coclusio We compare MLE ad GMM parameter estimatio methods for spatial error model. Our results idicate that SEM usig GMM estimatio sigificatly better tha MLE, i terms of pseudo R-squared ad variace uder the oormality. However, i terms of model specificatio, the results do ot make a sigificat differece betwee GMM ad MLE. The estimates of parameters ad its stadard error have a slight differece. These results idicate that GMM is as efficiet as MLE ad robust to o-ormality. Therefore, the selectio of the parameter estimatio methods may deped o the distributio of data ad variables, as well as the purpose of the specific research. Based o these results, educatio idicators that have sigificace impact to poverty alleviatio i Java are literacy rate, average legth of school year, ad percetage of high schools ad uiversity graduates. By ESDA, there were positive spatial autocorrelatio effects i poverty amog regios i Java i 2013 so as to form the clusters of poverty regios. This study showcases oe alterative to spatial statistics ad parameter estimatio methods besides the commoly used MLE, ad compare it with other methods like GMM. Future studies ca also test other alteratives such as Quasi Maximum Likelihood. Refereces 1. Bada Pusat Statistik. Peghituga da Aalisis Makro Kemiskia Idoesia 2014. Jakarta, Idoesia: BPS, 2014. 2. Bada Pusat Statistik. Data da Iformasi Kemiskia Kabupate/Kota 2013. Jakarta, Idoesia: BPS, 2013. 3. H. Widodo. Potret Pedidika di Idoesia da Kesiapaya Dalam Meghadapi Masyarakat Ekoomi Asia (MEA). Jural Cedekia. 2 (13) (2015) 209 307. 4. C. Neilso, D. Cotreras, R. Cooper, ad J. Herma. The Dyamic Poverty i Chile. Joural of America Lati Studies. 40 (2008) 251-273. 5. M. D. Partridge ad D. S. Rickma. The Geography of America Poverty: Is There a Need for Place-Based Policies?. Oklahoma, USA: Oklahoma State Uiversity, 2006. 6. Cradall, S. M. & Bruce A. W. Local Social ad Ecoomic Coditios, Spatial Cocetratios of Poverty, ad Poverty Dyamics. USA: Orego State Uiversity, 2004. 7. J. Lu ad L. Zhag. Evaluatio of Parameter Estimatio Methods for Fittig Spatial Regressio Models. Forest Sciece. 56 (5) (2010) 505-515. 8. L. Aseli. Spatial Ecoometrics. A Compaio of Theoretical Ecoometrics. 14 (2003) 313 330. 9. A. Couduel, S. H. Jesko, ad T. W. Queti. Poverty Measuremet ad Aalysis. Washigto DC, USA: World Bak, 2001. 10. C. M. Eirea. Poverty ad Educatioal Disadvatage: Breakig the Cycle. Dubli, Irelad: INTO Publicatio, 1994. 11. S. va der Berg. Poverty ad Educatio. Paris, Frace: Iteratioal Istitute for Educatioal Plaig ad Iteratioal Academy of Educatio, 2008. 12. P. Z. Jajua & U. A. Kamal. The Role of Educatio ad Icome i Poverty Alleviatio: Cross Coutry Aalysis. The Lahore Joural of Ecoomics. 16 (1) (2011) 143 172. 13. L. Aseli. Exploratory Spatial Data Aalysis i a Geocomputatioal Eviromet. New York, USA: Wiley ad Sos, 1998.
60 Author ame / Commuicatios of Sciece ad Techology 0(0) (2017) 000 000 14. P. A. P. Mora. Notes o Cotiuous Stochastic Pheomea. Biometrika. 37 (1950) 17 23. 15. J. Lee & D. W. S. Wog. Statistical Aalysis with Arcview GIS. New York, USA: Joh Wiley & Sos, 2001. 16. L. Aseli. Local idicators of spatial associatio LISA. Geographical Aalysis. 27 (1995) 93 115. 17. L. Aseli. Spatial Ecoometrics: Methods ad Models. Netherlads: Kluwer Academic Publishers, 1988. 18. H. B. Nielse. Geeralized Method of Momets (GMM) Estimatio [Olie]. Available: http://www.eco.ku.dk/metrics. [Accessed: 22-Ja-2017] 19. S. Murray & R. Shilligto. From Poverty to Prosperity: Literacy s Impact o Caada s Ecoomic Success. Ottawa, Caada: Caadia Literacy ad Learig Network, 2011. 20. I. de Silva. Micro-Level Determiats of Poverty i Sri Laka: a Multivariate Approach. Iteratioal Joural of Social Ecoomics. 35(3) (2008) 140-158. 21. N. Heiger ad M. Sel. Where are the Poor? Experieces with the Developmet ad Use of Poverty Maps. Washigto DC, USA: World Resource Istitute, 2002
Jauardi et al. / Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 61 Appedix A Neighborhood ad spatial weightig value of regios i Java Islad i 2013 Regio Regio Number of Neighbor Regios Neighbor Spatial Weightig Value 1 Kab. Kepulaua Seribu 1 6 1.00 2 Kota Jakarta Selata 6 3, 4, 5, 29, 118, 115 0.17 3 Kota Jakarta Timur 6 2, 4, 6, 22, 28, 29 0.17 4 Kota Jakarta Pusat 4 2, 3, 5, 6 0.25 5 Kota Jakarta Barat 5 2, 4, 6, 113, 115 0.20 6 Kota Jakarta Utara 6 1, 3, 4, 5, 22, 113 0.17 7 Kab. Bogor 11 8, 9, 20, 21, 22, 24, 28, 29, 112, 113, 118 8 Kab. Sukabumi 4 7, 9, 25, 112 0.25 9 Kab. Ciajur 6 7, 8, 10, 11, 20. 23 0.17 10 Kab. Badug 7 9, 11, 17, 19, 23, 26, 30 0.14 11 Kab. Garut 4 9, 10, 12, 17 0.25 12 Kab. Tasikmalaya 5 11, 13, 16, 17, 31 0.20 13 Kab. Ciamis 6 12, 14, 16, 31, 32, 33 0.17 14 Kab. Kuiga 5 13, 15, 16, 33, 61 0.20 15 Kab. Cirebo 5 14, 16, 18, 27, 61 0.20 16 Kab. Majalegka 6 12, 13, 14, 15, 17, 18 0.17 17 Kab. Sumedag 6 10, 11, 12, 16, 18, 19 0.17 18 Kab. Idramayu 4 15, 16, 17, 19 0.25 19 Kab. Subag 6 10, 17, 18, 20, 21, 23 0.17 20 Kab. Purwakarta 5 7, 9, 19, 21, 23 0.20 21 Kab. Karawag 4 7, 19, 20, 22 0.25 22 Kab. Bekasi 5 3, 6, 7, 21, 28 0.20 23 Kab. Badug Barat 6 9, 10, 19, 20. 26, 30 0.17 24 Kota Bogor 1 7 1,00 25 Kota Sukabumi 1 8 1,00 26 Kota Badug 3 10, 23, 30 0.33 27 Kota Cirebo 1 15 1,00 28 Kota Bekasi 4 3, 7, 22, 29 0.25 29 Kota Depok 5 2, 3, 7, 28, 118 0.20 30 Kota Cimahi 3 10, 23, 26 0.33 31 Kota Tasikmalaya 2 12, 33 0.50 32 Kota Bajar 2 13, 33 0.50 33 Kab. Cilacap 6 13, 4, 32, 34, 37, 61 0.17 34 Kab. Bayumas 7 33, 35, 36, 37, 59, 60, 61 0.14 35 Kab. Purbaligga 4 34, 36, 58, 59 0.25 36 Kab. Bajaregara 6 34, 35, 37, 39, 57, 58 0.17 37 Kab. Kebume 5 33, 34, 36, 38, 39 0.20 38 Kab. Purworejo 4 37, 39, 40, 68 0.25 39 Kab. Woosobo 7 36, 37, 38, 40, 55, 56, 57 0.14 40 Kab. Magelag 8 38, 39, 41, 54, 55, 62, 68, 71 0.13 41 Kab. Boyolali 9 40, 42, 43, 45, 46, 47, 54, 63, 71 42 Kab. Klate 4 41, 43, 70, 71 0.25 0.09 0.11
62 Author ame / Commuicatios of Sciece ad Techology 0(0) (2017) 000 000 Regio Regio Number of Neighbor Regios Neighbor Spatial Weightig Value 43 Kab. Sukoharjo 6 41, 42, 44, 45, 63, 70 0.17 44 Kab. Woogiri 6 43, 45, 70, 73, 74, 92 0.17 45 Kab. Karagayar 7 41, 43, 44, 46, 63, 92, 93 0.14 46 Kab. Srage 4 41, 45, 47, 93 0.25 47 Kab. Groboga 8 41, 46, 48, 50, 51, 53, 54, 93 0.13 48 Kab. Blora 6 47, 49, 50, 93, 94, 95 0.17 49 Kab. Rembag 3 48, 50, 95 0.33 50 Kab. Pati 5 47, 48, 49, 51, 52 0.20 51 Kab. Kudus 4 47, 50, 52, 53 0.25 52 Kab. Jepara 3 50, 51, 53 0.33 53 Kab. Demak 5 47, 51, 52, 54, 65 0.20 54 Kab. Semarag 8 40, 41, 47, 53, 55, 56, 64, 65 0.13 55 Kab. Temaggug 4 39, 40, 54, 56 0.25 56 Kab. Kedal 5 39, 54, 55, 57, 65 0.20 57 Kab. Batag 5 36, 39, 56, 58, 66 0.20 58 Kab. Pekaloga 5 35, 36, 57, 59, 66 0.20 59 Kab. Pemalag 4 34, 35, 58, 60 0.25 60 Kab. Tegal 4 34, 59, 61, 67 0.25 61 Kab. Brebes 6 14, 15, 33, 34, 60, 67 0.17 62 Kota Magelag 1 40 1,00 63 Kota Surakarta 3 41, 43, 45 0.33 64 Kota Salatiga 1 54 1,00 65 Kota Semarag 3 53, 54, 56 0.33 66 Kota Pekaloga 2 57, 58 0.50 67 Kota Tegal 2 60, 61 0.50 68 Kab. Kulo Progo 4 38, 40, 69, 71 0.25 69 Kab. Batul 4 68, 70, 71, 72 0.25 70 Kab. Guug Kidul 5 42, 43, 44, 69, 71 0.20 71 Kab. Slema 7 40. 41, 42, 68, 69, 70, 72 0.14 73 Kab. Pacita 3 44, 74, 75 0.33 74 Kab. Poorogo 7 44, 73, 75, 76, 90, 92 0.14 75 Kab. Treggalek 3 73, 74, 76 0.33 76 Kab. Tulugagug 5 74, 75, 77, 78, 90 0.20 77 Kab. Blitar 4 76, 78, 79, 103 0.25 78 Kab. Kediri 6 76, 77, 79, 89, 90. 102 0.17 79 Kab. Malag 9 77, 78, 80, 85, 86, 88, 89, 104, 110 80 Kab. Lumajag 3 79, 81, 85 0.33 81 Kab. Jember 4 80, 82, 83, 85 0.25 82 Kab. Bayuwagi 3 81, 83, 84 0.33 83 Kab. Bodowoso 4 81, 82, 84, 85 0.25 84 Kab. Situbodo 3 82, 83, 85 0.33 85 Kab. Proboliggo 7 79, 80, 81, 83, 84, 86, 105 0.14 86 Kab. Pasurua 6 79, 85, 87, 88, 106, 110 0.17 87 Kab. Sidoarjo 4 86, 88, 97, 109 0.25 88 Kab. Mojokerto 8 79, 86, 87, 89, 96, 97, 107, 110 0.11 0.13
Jauardi et al. / Commuicatios i Sciece ad Techology 2(2) (2017) 53-63 63 Regio Regio Number of Neighbor Regios Neighbor Spatial Weightig Value 89 Kab. Jombag 6 78, 79, 88, 90, 94, 96 0.17 90 Kab. Ngajuk 6 74, 76, 78, 89, 91, 94 0.17 91 Kab. Madiu 6 74, 90, 92, 93, 94, 108 0.17 92 Kab. Mageta 6 44, 45, 74, 91, 93, 108 0.17 93 Kab. Ngawi 7 45, 46, 47, 48, 91, 92, 94 0.14 94 Kab. Bojoegoro 7 48, 89, 90, 91, 93, 95, 96 0.14 95 Kab. Tuba 4 48, 49, 94, 96 0.25 96 Kab. Lamoga 5 88, 89, 94, 95, 97 0.20 97 Kab. Gresik 4 87, 88, 96, 109 0.25 98 Kab. Bagkala 2 99, 109 0.50 99 Kab. Sampag 2 98, 100 0.50 100 Kab. Pamekasa 2 99, 101 0.50 101 Kab. Sumeep 1 100 1,00 102 Kota Kediri 1 78 1,00 103 Kota Blitar 1 77 1,00 104 Kota Malag 1 79 1,00 105 Kota Proboliggo 1 85 1,00 106 Kota Pasurua 1 86 1,00 107 Kota Mojokerto 1 88 1,00 108 Kota Madiu 2 91, 92 0.50 109 Kota Surabaya 3 87, 97, 98 0.33 110 Kota Batu 3 79, 86, 88 0.33 111 Kab. Padeglag 2 112, 114 0.50 112 Kab. Lebak 5 7, 8, 111, 113, 114 0.20 113 Kab. Tagerag 7 5, 6, 7, 112, 114, 115, 118 0.14 114 Kab. Serag 5 111, 112, 113, 116, 117 0.20 115 Kota Tagerag 4 2, 5, 113, 118 0.25 116 Kota Cilego 1 114 1.00 117 Kota Serag 1 114 1.00 118 Kota Tagerag Selata 5 2, 7, 29, 113, 115 0.20