A Spatial Econometric Model of the Korean Economy

Transcription

1 A Spatial Ecoometric Model of the Korea Ecoom Doleswar Bhadari Ph.D. Uiversit of New Mexico Brea of Bsiess ad Ecoomic Research 303 Girard Blvd STE 6 Uiversit of New Mexico Albqerqe New Mexico 873 Tel Fax bhadar@m.ed Tom Johso Ph.D. 5 Middlebsh Hall Commit Polic Aalsis Ceter Uiversit of Missori-Colmbia Colmbia MO JohsoTG@missori.ed Deis P. Robiso Ph.D. 5 Middlebsh Hall Commit Polic Aalsis Ceter Uiversit of Missori-Colmbia Colmbia MO Robisode@missori.ed

2 A SPATIAL ECONOMETRIC MODEL OF THE KOREAN ECONOMY ABSTRACT Usig Korea regioal data a spatial simltaeos eqatio model was developed ad estimated sig a geeralized spatial three-stage least sqares procedre. This model cotais 0 eqatios for local fiace the labor maret ad the hosig maret -local revee local expeditres hosig its poplatio ecoomicall active poplatio mber of stdets iad ot-commtig mber of firms ad emplomet i o-basic sectors. Emplomet ad ecoomic developmet expeditres are the mai drivers of the model. A sigificat crosscot ad cross-eqatio spillover effect is estimated. Redced form estimates were derived from strctral eqatios ad it is fod that additioal emplomet opportities geerated i a certai cot will have a positive impact o all sectors of the ecoom icldig local fiace the hosig maret demograph ad the labor maret. The spatial spillover effect is estimated o eighborig coties reslted from the emplomet opportities created i a residece cot. It appears that the estimated parameters ted to be sesitive to the specificatio of weight matrices. The model was validated based o forecastig accrac of i-sample data sig mea absolte percetage error.

3 . Itrodctio The developmet of ecoometric models for ecoomic impact aalsis ad ecoomic forecastig has bee of cotios iterest to regioal ecoomists. I this paper sch a model is applied to the Korea regioal ecoom. Regios withi a cotr are ope ecoomies experiecig extesive iter-area spillovers. For example emplomet chage i oe regio ma affect the poplatio commtig patter ad demad for pblic services i earb area. To accot for the iterregioal spillovers a complete versio of spatial model was developed for the Korea ecoom sig geeralized spatial three-stage least sqares GS3SLS procedre. This model is somewhat similar to other fiscal impact models developed i the Uited States based o cot-level its of aalsis the most commo of which are the Show Me Model Johso ad Scott 006 the Virgiia Impact Proectio Model Johso 99 the Iowa Ecoomic/Fiscal Impact Modelig Sstem Sweso ad Otto 998 the Idaho model Cooe ad Fox 994 a Itegrated Ecoomic Impact ad Simlatio Model for iscosi Coties Shields 998 ad the Small Area Fiscal Estimatio Simlator for Texas Evas ad Stallma 006. Oe of the e elemets i these models is emplomet as a egie of ecoomic growth ad chage at the local level. Usig Korea data for 005 a model is estimated sig a GS3SLS procedre developed b Keleia ad Prcha 004. The model cotais eqatios of local revees local expeditres total hosig its poplatio total stdets i- ad ot-commig mber of firms ad o-basic emplomet. A simltaeos sstem of spatiall iterrelated cross-sectio eqatios cotaiig spatial lags i both the depedet variables ad their error terms is cosidered. Feedbac effects de to both the simltaeos relatioships betwee eqatios ad the spatial liages are also ivestigated. To validate the model a o-spatial model NS3SLS

4 simltaeos spatial lag model SL3SLS spatial error model SE3SLS ad spatial lag ad spatial error model SLE3SLS are estimated. Usig a measre of forecastig accrac mea absolte percetage error [MAPE] the performace of the models is ivestigated. The rest of the paper is orgaized as follows. Sectio otlies the obectives of this research; Sectio 3 discsses the data ad data sorces; ad Sectio 4 otlies the spatial model estimatio procedre. Sectios 5 ad 6 discss the model specificatio ad reslts respectivel ad Sectio 7 smmarizes ad cocldes.. Research Obectives The primar obective of this std is to bild a rigoros ecoometric model for the Soth Korea ecoom that ca be applied to alterative polic scearios. The specific obectives are:. to develop ad estimate a GS3SLS model for local regios i Korea. to estimate the iterregioal spillover effect of the labor maret ad the local pblic fiace ad hosig maret ad 3. to perform polic aalsis based o the redced form estimates. 3. Data This empirical wor focses o the relatioships ad spatial iteractios amog labor maret the local pblic fiace maret ad the hosig maret. Althogh Korea regios are comparativel cetralized etities it is assmed that these etities are idepedet decisiomaig bodies. Admiistrative divisios of Soth Korea are divided ito Special Cit tebeolsi 6 Metropolita Cities gwageosi ad 9 Provices do. Based o poplatio these are frther sbdivided ito a variet of smaller etities icldig cities si coties g wards g tows ep districts meo eighborhoods dog ad villages ri. The data

5 sed i this std come from 7 local govermet its that cosist of 7 metropolita cities 77 cities ad 88 coties. Amog the 7 regios 40 are rral with a poplatio of less tha ad 3 are rba with a poplatio of more tha Ths the aalsis icldes all 7 regios i Korea with poplatio over All the data sed to codct this std are secodar data collected b the Korea Natioal Statistical Office. Data related to area emplomet hosig its stdet poplatio ad mber of firms were obtaied from Korea s Si or G s Statistical Year Boo 005. Emplomet data is divided ito basic ad o-basic sectors. Basic sectors i Korea ecoom area farmig ad mafactrig; ad o-basic sector is service sector. Emplomet i basic sectors allows s to estimate the mltiplier effects i the Korea ecoom. Local revee ad expeditre data were obtaied from Korea Local Fiacial Year Boo 005. Local revees cosist of local tax receipts other receipts local share tax atoomos district cotrol grats ad sbsidies Local fiace MOGAHA. Geerall cities tax shares are higher abot 50% tha coties abot 0%. The revee strctre of local govermets is preseted i Table. Poplatio ad i-commters ad ot-commters data were obtaied from Korea Cess of Poplatio data. I this aalsis the cross-sectioal data of 7 coties ad cities was sed for 005. A list of variables ad their smmar of statistics sch as mber of observatios meas stadard deviatios ad miimm ad maximm vales for each variable are preseted i Table. 4. The Spatial Model Estimatio Procedre To begi with a sigle eqatio spatial ecoometric model is itrodced. This is a commol sed model i ecoomics ad other fields. The the featres of a simltaeos sstem of eqatios are added. The geeral specificatio of the sigle eqatio is Y λ Y Xβ ε

6 where ε ε Aseli 988. Y is a colm vector of observatios o a depedet variable; X is a vector of explaator variables that are assmed to be correlated with error terms; is a cotigit weight matrix; λ ad are spatial lag ad spatial error parameters to be estimated; β is the colm vector parameters of explaator variables; ad is a idepedet ad ideticall distribted error term. ε is a spatial error term that ca be solved as ε I. Spatial depedece has two sorces: both error terms ad depedet variables ma be correlated across space. However this sigle eqatio model does ot serve the prpose becase a simltaeos sstem of eqatio is eeded. Followig Keleia ad Prcha 004 a GS3SLS model is specified as follows: _ Y Y B X C Y A... m U Y X x... x U... Y... _ m m... m i wir r. r where is the vector of cross-sectioal observatios o the depedet variable x is the vector of cross-sectioal observatios o the lth exogeos variable is the spatial lag of is the distrbace vector of i the th eqatio is a weight matrix ad B C A are parameter matrices of mxm xm ad mxm correspodig variables respectivel. The athors also allow for the spatial atocorrelatio i the error term as follows: U U R E m with E ε... ε R diag m U m m where ε deotes the colm vector of idepedet ad ideticall distribted error terms ad deotes the spatial atoregressive parameters. is the spatial lag of.

7 4. GS3SLS Estimatio Procedre The estimatio procedre cosists of a iitial two-stage least sqares SLS estimatio followed b estimatio of the spatial atoregressive parameter a geeralized spatial SLS estimatio ad fll iformatio estimatio GS3SLS. The first three steps complete the geeralized spatial two-stage least sqares GSSLS ad the fial steps tae care of the crosseqatio error correlatio Keleia ad Prcha 004. GS3SLS procedre accots for two factors. First it taes care of the simltaeit bias which arises whe a depedet variable is correlated with aother eqatio s error term. Secod it allows correlated errors betwee eqatios which improved the efficiec of the parameter estimates. 4. Iitial SLS Estimatio The first step i the estimatio process cosists of the estimatio of the model parameter vector β i a sigle-eqatio spatial ecoometric model b SLS sig all exogeos variables their spatial lag vales ad the twice spatiall lagged exogeos variables i.e. X X X. The residal of this step is compted as follows: Z δ 3 where Z icldes all the edogeos ad exogeos variables iclded i the SLS regressio. 4.3 Estimatio of Spatial Atoregressive Parameter Eqatio implies that ε 4 ad premltiplicatio of this term b the weights matrix gives ε The followig three eqatio sstem is obtaied from the relatioships betwee eqatios 4 ad 5: ε ε 5

8 ε ε ε ε 6 If the expectatios are tae across 6 the the resltig sstem wold be as follows: E ε ε ε ε ε ε 7 E tr tr E 0 σ 8 0 E E tr E E E E E σ 9

9 0 E E tr E E E E E σ 0 The right-had side of eqatio 0 ca be writte i the followig form: 0 Tr σ This sstem of eqatio ca be writte as γ α α γ Γ Γ where Γ 0 Tr The parameter vector σ wold be determied i terms of the relatio i eqatio. The miimize the followig eqatio: Γ Γ g g σ σ Γ 0 Tr g 3 here ad.

10 4.4 Estimatio of GSSLS I this stage a Cochrae-Orctt tpe trasformatio is applied to depedet edogeos ad exogeos variables of the sigle-eqatio spatial ecoometric model b sig estimated spatial atoregressive parameters to accot for the spatial correlatio. Let ad. The the eqatio becomes: Z Z Z δ [ Z Z ] Z Z δ ε ˆ ˆ ˆ ˆ 4 ˆ H where Z P Z with P H H H H H assmig is ow. This ˆ δ becomes the GSSLS estimator. The feasible GSSLS estimator for sa defied b sbstittig the geeralized momets estimator [ ˆ ˆ ] ˆ Z Z Z ˆ F δ F ˆ is ow for i eqatio 4 that is Fll Iformatio Estimatio GS3SLS Up to this poit or model accots for the potetial spatial correlatio bt it does ot tae ito accot the potetial cross-eqatio correlatio i the iovatio vector ε. To accot for this it is helpfl to stac the eqatios i 4 as δ ε Z 6 where Z... m m m diag Z ;... ad δ δ... δ m m It is assmed that Eε 0 ad Eε ε Σ I. If ad Σ are ow a atral sstem of istrmetal variables estimator of δ wold be

11 δ [ Zˆ Σ I Zˆ ] Zˆ Σ I 7 here ˆ m Z diag Zˆ ad ˆ Z P Z H To estimate eqatio 6 the estimators for ad Σ are eeded to be fod. Let... m where deotes the geeralized momets estimator for. The cosistet estimator of Σ is is ˆ σ l l Σˆ where Σˆ is estimated as a m m matrix whose l th elemet F ε ε ad ε Z ˆ δ. 8 Replacig the vale cosistet estimator i eqatio 7 a feasible GS3SLS estimator is obtaied as δ F [ Zˆ Σˆ I Zˆ ] Zˆ Σˆ I 9 5. Model Specificatio The model developed specified ad estimated below is a combiatio of labor marets hosig marets demograph ad local pblic fiace variables; however the labor marets pla the cetral role i this modelig framewor. The model is bilt o the assmptio that ecoomic growth is largel cased b a exogeos icrease i emplomet. Emploers create local obs while the residetial choices of emploees create local labor forces. Each emploer faces a short-r labor sppl withi commtig distace from the plat ow as the commtig shed. Other emploers withi the commtig shed share the same worforce. Similarl each member of the local labor force faces a demad for labor that cosists of the sm of all obs withi his or her commtig shed. Also other worers withi the commtig shed share the same labor demad forces bt ma be sbect to labor demads form otside the commtig shed of the first worer.

12 Idividal worers mae residetial decisios based o ob availabilit relative costs of livig local ameities qalit of pblic services ad other items that affect their qalit of life. The worers also choose amog available obs based o sill reqiremets wage rates ob secrit ad commtig costs. As the same time emploers locate their plats based o cost of doig bsiess maretig cosideratios ad the availabilit of worers ad other resorces. The labor maret allocates obs amog the crretl emploed i-commters ot-commters ad i-migrats. Some ew obs are also tae b crretl emploed worers who chage positios. As Tiebot 956 poits ot the worers also choose a residece commit that offers a mix of local pblic goods ad services best sited to their tastes. B choosig to relocate or votig with their feet cosmers reveal their prefereces for local pblic goods. Together with the labor maret ad pblic goods maret eqilibrim the poplatio of local areas is determied. Or model has 0 strctral eqatios each of which has the followig geeral form that is similar to the stadard Cliff ad Ord 973 tpe model with a spatial depedet variable lag ad a spatial atoregressive error term: Y ε J N a 0 λ Y ε β Z ε 0 For the th eqatio Y is a colm vector of observatios o the depedet variable Y Y is a colm vector of observatios o the spatiall weighted averages of the N depedet variable Z is a matrix of observatios o the edogeos ad exogeos variables for the th depedet variable is a matrix of spatial weights that relate all locatios i or cross-sectio sample to their eighborig locatios. The parameters a λ β ad are the GS3SLS estimates ε is a spatiall related regressio error term ad is a

13 regressio error term with the sal idepedet ad ideticall distribted statistical properties. Frthermore the spatiall related error term ε ca be solved i terms of ad : I ε. The spatial lag variables for a cot are defied as the weighted average vales for the set of eighborig coties i.e. if the are located with 30 m of radial distace. These eighbors average vales for all geographic its are compted b post-mltiplig a rowormalized spatial weights matrix b a colm vector of cross-sectioal observatios of a variable. A spatial weights matrix is a sqare matrix that relates each cross-sectioal it to its iqe set of eighbor areas. A row-ormalized spatial weights matrix is oe whose row sms are all eqal to oe. Three tpes of row-ormalized spatial weights matrices are ivestigated i this paper. First a simple gravit weighted iverse distace row-ormalized spatial weights matrix is sed whose tpical vales are X Di G [ wi ] N X J D J if is a eighbor of i otherwise w 0. i ij Secod a more tpical gravit row-ormalized weighted iverse distace sqared spatial weights matrix was sed whose commo elemets are X Di G [ wi ] N X J D J if is a eighbor of i otherwise w 0. i ij

14 The weight variable i the gravit calclatio X is sed to accot for isses related to size or mass. Larger ad heavier obects are more attractive tha are smaller ad lighter obects ad places closer together have greater attractio. To measre this size or mass emplomet total is sed. D i is the distace i miles betwee locatios i ad. Distace is calclated from oe poplatio cetroid to aother. Third a row-ormalized spatial weights matrix with iform vales was sed whose tpical vales are [ w ] U i if locatio is withi 30 m from locatio i or w 0 N i if ot N is the mber of locatio i s eighbors. i i As Keleia ad Robiso 995 poit ot two of the estimated parameters i eqatio 0 eed special metio: λ ad the spatial lag ad spatial atoregressive parameters respectivel. The parameter spaces for these estimated coefficiets have a restricted rage: ψ < < where eg λ ψ pos ψ eg is the largest egative eigevale of the spatial weights matrix ad ψ pos is the smallest positive eigevale of the spatial weights matrix. This rage will alwas provide a clear parameter space that icldes the vale zero. If the spatial weights matrix is row-ormalized i.e. the row elemets of sm to or i other words form a proportio distribtio the the smallest positive eigevale will alwas eqal ψ. However except for a few theoretical tpes of spatial weights matrices the largest pos egative eigevale is greater tha < ψ 0. This meas that the parameter space for eg < the spatial lag ad spatial atoregressive parameters will be i geeral betwee some vale less tha ad whe the spatial weights matrix is row-ormalized. The expaded versio of eqatio 0 is as follows. The expected sigs are preseted i the parethesis st below each explaator variable.

15 4 3 3 ε α α α α α COMIN EMPNBAS POPTOT REVLOC REVLOC ± ε β β β β β EMPNBAS COMIN POPTOT EXPLOC EXPLOC 4 3 ± ε δ δ δ δ COMIN POPTOT HOUSTOT HOUSTOT 3 ± ε γ γ γ POPEAP POPTOT POPTOT 4 3 ± ε λ λ λ λ EMPNBAS POPTOT POPEAP POPEAP 3 ± ε μ μ μ POPTOT STDTTOT STDTTOT ± ± ε ν ν ν ν ν ν ν ν EXPED CEMP AEMP AREA EMPTOT POPEAP COMOUT COMOUT ± ± ε π π π π π π π AEMP AREA CEMP EMPTOT POPEAP COMIN COMIN ± ± ε AEMP AREA POPTOT FIRMTOT FIRMTOT ± ± ε σ σ σ σ σ σ σ CEXPED AEXPED EXPED AREA EMPTOT EMPNBAS EMPNBAS Variables ames ad descriptios are preseted i Table. 6. Model Estimatio Reslts ad Discssio As metioed i the previos sectio a GS3SLS procedres is applied to estimate the parameter vale of or model which cosists of 0 spatiall iterrelated simltaeos eqatios.

16 Before estimatig the model sig GS3SLS the differet models were estimated sig ordiar least sqares OLS ad GSSLS ad evalated idividall based o several criteria adsted R correct sigs statistical sigificace. Table 3 presets the parameters estimates ad their sigificace b OLS GSSLS ad GS3SLS procedres. Overall the sigs of the parameter estimates appeared to be robst; however the magitdes of these estimates var across differet estimatio procedre sed. I some cases ot ol the magitde of the coefficiet chage bt also the sig of the coefficiets flip as the estimatio procedre is chaged. For example the variable i-commters appears to be sigificat ad positive i explaiig local revee i OLS model however it is egative ad sigificat i GS3SLS model. The same variable appears to be o-sigificat i local expeditre eqatio sig OLS procedre however it is highl sigificat ad egative i GS3SLS. Liewise spatial lag of local revee is egative ad sigificat i local revee eqatio whe sed OLS procedre however it is positive ad sigificat whe sed GS3SLS procedre. This shows that whe spatial iteractio ad crosseqatio iteractio are tae ito accot the biased parameter estimates ma be estimated. Compared to GSSLS it is fod that the magitde of the GS3SLS coefficiets of ma explaator variables appear to have chaged sigificatl. Most estimated parameter vales are sigificat at the % level ad a few at the 5% ad 0% levels. The fact that all eqatios have a R vale higher tha 0.90 idicates that or model possesses reasoabl high explaator power. Most of the estimated parameter vales have sigs that wold be expected or ca be explaied. The reslts are based o a gravit-based row-ormalized weight matrix weight divided b distace; however differet weight matrices have bee tried. A separate sectio is devoted to a detailed sesitivit aalsis of weight matrices. The followig reslts ad their iterpretatios are based o simltaeos spatial lag model SL3SLS.

17 The maorit of spatial lags of depedet variables appear to be sigificat at the 5% level. This shows evidece of sigificat spatial spillover i Korea regios. Based o the magitde of the estimated coefficiets the positive spatial patter appears to be strogest for poplatio stdets mbers ot-commters ad i-commters. The egative spatial patter appears to be strogest for local expeditres ad mber of firms. The egative sig of the spatial lag of local expeditre spports previos stdies i which local pblic expeditres e.g. trasport edcatio pars ad recreatio have spillover effects i the eighborhood Case Hies ad Rese 993; Mrdoch Rahmatia ad Thaer 993. The spatial lag of local revee is isigificat. This ma be partl de to overdepedece of local regios o cetral govermet for revee geeratio; less flexibilit o the part of local govermet for polic maig; ad 3 formla-drive revee collectio. The coefficiets of spatial lag of poplatio ad the mber of stdets are ot sigificat. As expected spatial depedece for i-commtig ad ot-commtig is positive ad sigificat. As expected local revee is positivel ad sigificatl impacted b poplatio ad o-basic emplomet whereas it is egativel impacted b i-commtig. Local expeditre is fod to be depedet o ad ifleced b poplatio ad emplomet i o-basic sectors sigificatl ad positivel. Uexpectedl it is egativel impacted b i-commtig. It is hpothesized that i-commtig will exert a positive iflece o local expeditre becase it represets the datime poplatio of the area ad higher demad for services b emploer which frther pshes the demad for local services. This ma be de to lac of a icome variable i the local expeditre eqatio. De to the lac of a icome variable it is ot

18 possible to test the hpothesis that more afflet commities demad higher qalit services ad are more willig to pa for them. The total hosig its eqatio is estimated as a fctio of spatial lag of itself poplatio ad i-commtig. As expected total poplatio is fod to be the most importat determiat of hosig its. It is estimated that i-commtig is sigificatl ad egativel associated with total hosig its; which is expected. A poplatio eqatio is estimated as a fctio of spatial lag of itself ad ecoomicall active poplatio. Becase labor force data is ot available the ecoomicall active poplatio is sed as a prox of labor force. As expected ecoomicall active poplatio is fod to be sigificat to explai the poplatio. As a prox of labor force ecoomicall active poplatio eqatio is estimated as a fctio of spatial lag of itself poplatio ad emplomet i o-basic sectors. As expected ecoomicall active poplatio is positivel impacted b poplatio ad emplomet i obasic sectors. Stdet mbers is estimated as a fctio of spatial lag of itself ad poplatio. As expected stdet mber is positivel ad sigificatl impacted b poplatio. Ot-commtig eqatio is estimated as a fctio of spatial lag of itself ecoomicall active poplatio emplomet area area emplomet exteral emplomet ad ecoomic developmet expeditres. The variable area emplomet is also called as expasio variable which captres the strctral chages that are cased b the differet sizes of coties. All variables are sigificat. The sigs of all variables are as expected. It appears that exteral emplomet drives the ot-commtig p whereas ecoomic developmet expeditres drive it dow. The estimated parameter of the expasio variable area emplomet is sigificat ad egative. This implies that for larger coties the area variable decreases the margial effect of

19 emplomet o ot-commtig eve thogh the area variable aloe ma ot be sigificat. I this case the area variable is also sigificat ad positive. As expected the positive sig of the coefficiet for the area variable shows that as the cot area icreases ot-commtig also icreases. I-commtig is estimated as a fctio of the spatial lag of itself ecoomicall active poplatio emplomet exteral emplomet area area emplomet. The sigs of all variables are as expected except for exteral emplomet. A icrease i ecoomicall active poplatio teds to decrease the i-commtig; which is logical. As expected the emplomet variable is fod to be sigificat ad positive. This implies that icreased emplomet opportities i residece coties create icreased i-commtig. Srprisigl the exteral emplomet is positive ad sigificat. Area variable has a expected positive sig bt it ot sigificat. The expasio variables area emplomet have a sigificat ad egative coefficiet. It appears that for larger coties the area variable decreases the margial effect of emplomet o i-commtig. The mber of firms is modeled as a fctio of spatial lag of itself poplatio area ad area emplomet. All variables have expected sigs ad are sigificat. It appears that mber of firms icreases as the area poplatio area emplomet icrease. As expected the mber of firm variable is strogl ad egativel impacted b spatial lag of itself. This implies that there is competitio amog firms located i residece coties ad eighborig coties. Emplomet i o-basic sectors is estimated as a fctio of the spatial lag of itself emplomet total area ecoomic developmet expeditres exteral ecoomic developmet expeditres ad expasio variable area ecoomic developmet expeditres. All explaator variables are fod to be sigificat except spatial lag of depedet variable ad

20 exteral ecoomic developmet expeditres. The egative sig of the spatial lag variable idicates that icreased o-basic emplomet i eighborig regios egativel impacts the residece cot. As expected emplomet total variable sigificatl ad positivel impacts o-basic emplomet. The ecoomic developmet expeditres appear to impact sigificatl ad positivel. The coefficiet of area ecoomic developmet expeditres appear to be egative ad sigificat. This implies that for larger coties the area variable decreases the margial effect of ecoomic developmet expeditre o o-basic emplomet. 6. Sesitivit of Choice of Spatial Liages The ma alterative methods of specificatio of spatial liages creates difficlties ad cotroversies i spatial data aalsis. Sesitivit aalsis is sed to determie how sesitive a model is to chages i the weight matrices represetig differet spatial liages. It is possible to bild the cofidece i the model b stdig certaities that are associated with differet weight matrices. As metioed earlier three spatial weight matrices are sed based o distace weight ad iverse distace ad weight ad iverse distace sqared. The latter two are also called gravit based matrices. The total emplomet is sed as a weight variable. Usig differet matrices the model Table 4 is estimated sig GS3SLS procedre. Overall reslts appear to be robst across differet spatial liages. However the magitde ad sigificace of coefficiets of some variables are fod to be sesitive to the choice of spatial matrices. For example spatial lag of local expeditre is sigificat ad egative i the model that sed the gravit based weight matrices whereas it is ot sigificat i the model that sed iform weight matrix. The spatial lag of ecoomicall active poplatio is egative ad sigificat whe sed with iform weight matrices however it is ot sigificat whe gravit based weight matrices were sed. However the sig remais the same. Liewise spatial lag of emplomet i o-basic sectors is

21 sigificat ad egative i a model that sed iform spatial weight matrix whereas the same variable is ot sigificat i both the models that sed gravit based weight matrices. I some cases it appears that the magitde of the variables are also chaged which shows that aaltical reslts ma be sesitive to the specificatio of spatial weight matrix. 6. Model Validatio The fact is that i geeral model validatio ad model bildig processes move together. Before decidig o a ideal model MAPE was sed as a measre of the forecast accrac to evalate these models Table 7. Based o MAPE criterio sed i i-sample data it appears that ot all eqatios cosistetl perform well see Table 8. Predictive accrac of local revee local expeditres poplatio ot-commters mber of firms ad emplomet i o-basic sectors are fod to be better i the SLE3SLS model whereas hosig its ecoomicall active poplatio total stdets are better forecasted b the SL3SLS model. Noe of the eqatios i a SE3SLS model ad NS3SLS model have better forecastig accrac tha the SLE3SLS model ad SL3SLS model except i-commtig variable. This implies that there exists a sigificat spatial spillover effect i Korea local ecoomies. Althogh both SL3SLS ad SLE3SLS models appeared to be similar i terms of overall MAPE statistic SL3SLS model have a advatage of beig parsimoios. Aother advatage of SL3SLS over SLE3SLS is that the redced form soltios are eas to hadle ad mae ititive sese. Therefore redced form estimates is estimated sig strctral eqatio obtaied from SL3SLS model. 6. Redced Form Estimates The redced form eqatios are obtaied b solvig strctral eqatios derived from SL3SLS model. I this case all edogeos variables are fctios of exogeos variables. Solvig spatial strctral eqatios to obtai a redced form eqatio is a datig tas.

22 However b followig Keleia ad Prcha 004 we obtaied a redced form estimate of spatial simltaeos lag model which is as follows. U A Y C X B Y Y _... m Y... x x X... m U... m Y m... r r ir i w. where is regios m edogeos variables ad exogeos variable. The dimesio of coefficiet as follows: m m m m m A C B m Y vec M M x x X vec x M M If A ad A are coformable matrices the vec A A A vec I A Berc et al 993. Followig this rle redced form soltio of eqatio wold be as follows. [ ] x I C A I B 3 { } m x I C A I B I I ] [ 4 The dimesio of coefficiet matrices are as follows: m m m m m m B β β β β β K M O M M O M M KK m m A m λ λ λ K K M O M L whe ol the depedet variable has spatial lag. Redced form estimate is ver hge to preset i a table however the reslts of impact estimates are preseted i the ext sectio. Dr. Deis Robiso with the help of Keleia ad Prcha 004 developed the eqatio 4.

23 6.3 Impact Estimatio The iqeess of the soltio is that cross-cot spatial spillover effect ca be estimated throgh this model. Oce the redced form eqatio is obtaied it ca be sed for impact aalsis prpose. Althogh there are seve exogeos variables i the model emplomet is oe of the mai drivig forces for all sectors of the ecoom. Chages i emplomet lead to icreases i poplatio ad wage levels which ltimatel alter demads for pblic services ad the revees available to fd these services. To demostrate how the model wors ad to determie a reasoable estimate of the impact a 000 obs icrease is hpothesized i Gag cot of Psa Provice. As a test commit Giag Cot is a fairl small cot with a poplatio of approximatel Usig the redced form coefficiets of or model the impacts of a emplomet chage was estimated o the Giag Cot ecoom. Chage i emplomet also chages the exteral emplomet for other coties. It also affects the expasio variable area emplomet. After accotig for these chages the impact of 000 ew obs was estimated sig a redced form eqatio of spatial lag simltaeos eqatio model. The creatio of additioal obs cased a icrease i local revee of 3.6 billio wo ad a icrease i expeditres of 3. billio wo. The ew obs also cased the followig icreases: - total hosig its b 48; - ecoomicall active poplatio b 660; - mber of stdets b 356; - i-commters b 39; - ot-commters b 67; - mber of firms b 9;

24 - o-basic emplomet b 83. Also estimated was the spatial spillover effect of additioal 000 obs to eighborig regios. It is fod that 0 eighborig coties impacted b this chage i emplomet; however ol for coties appeared to have sizable impact Table 6. Oce the spatial impact spillover to coties other tha Giag is removed the impacts estimated from spatial ad ospatial model ca be compared. The reslts show that the itra-cot impact estimates of the o-spatial model are 0% to 9% lower tha the impacts estimated b the spatial model for for depedet variables local revee local expeditre hosig its ad mber of firms Table 6b. This implies that if the spatial spillover effect is igored we ma be derestimatig the impact o these variables. I i-ad ot-commtig o-spatial model overestimate the impact- 9% ad 4% respectivel. Poplatio related variables sch as total poplatio total stdets ad ecoomicall active poplatio both model predictios fod to be comparable. This implies that there is little spatial spillover effect i these variables. This shows that accotig for spatial iteractios is imperative to improve model performace. 7. Smmar ad Coclsio As stated previosl i the research obective the primar goal of this std was to develop ad estimate a model that accots for the cross-cot ad cross-eqatio spillover effects i local regios i Korea. The differet versios of a spatial model is estimated that accots for the iterregioal spillover effect. The model-bildig process bega with the estimatio ad evalatio of each eqatio sig criteria sch as R ad t-statistics. The all eqatios were collapsed ito oe sstem ad estimated model sig GS3SLS. Before fializig the model was validated based o predictive accrac as measred b MAPE statistic. A SL3SLS model is fod to be the best model for Korea regios. The model cotais eqatios

25 for local revee local expeditres total hosig its poplatio total ecoomicall active poplatio mber of stdets l i- ad ot-commtig total firms ad o-basic emplomet ad assmes that emplomet is the mai driver of the Korea regioal ecoom. Other exogeos variables iclded i this model were ecoomic developmet expeditres area ad expasio variables. It is fod that a sigificat cross-cot ad cross-eqatio spillover effects exist i Korea regios. The reslts i some cases appear to be sesitive to the choice of spatial liages as defied b weight matrices.

26 Table. Revee Strctre of Local Govermet i Korea Year Sorces of Revee % Local tax No-tax revee Trasfer revee from cetral govermet Local bod Sorces: Fiacial Yearboo of Local Govermet

27 Table. Variables Variable Descriptios ad Descriptive Statistics a Variable Label Mea SD Miimm Maximm AREA Area i sqare ilometers POP_TOT Poplatio sqared millio EMP_TOT Total emploed people A_EMP Area emplomet EXP_ED Ecoomic developmet expeditres C_EMP Exteral emplomet A_EXPED Area ecoomic developmet expeditres REV_LOC Local Aal Revee EXP_LOC Local aal expeditres HOUS_TOT Total hosig its POP_TOT Total poplatio POP_EAP Ecoomicall active poplatio STDT_TOT No. of total stdets COM_OUT Ot-commters COM_IN I-commters FIRM_TOT Total mber of firms EMP_NBAS No basic emplomet other tha farm ad mafactrig emplomet _REV_LOC Spatial lag of local revee _EXP_LOC Spatial lag of local expeditres _HOUS_TOT Spatial lag of total hosig its _POP_TOT Spatial lag of total poplatio _POP_EAP Spatial lag of ecoomicall active poplatio _STDT_TOT Spatial lag of total stdets _COM_OUT Spatial lag of ot-commters _COM_IN Spatial lag of i-commters _FIRM_TOT Spatial lag of firm total _EMP_NBAS Spatial lag of emplomet i o-basic sectors a N 7

28 Table 3. Regressio Reslts: Ordiar Least Sqares ad Geeralized Spatial Two-Stage ad Three-Stage Least Sqares GSSLS GS3SLS Model Variables OLS Estimates p-vale Estimates p-vale Estimates p-vale Itercept < < <.000 Local Revee _REV_LOC a POP_TOT.358 < < <.000 EMP_NBAS.0657 < <.000 COM_IN a <.000 Local Expeditre Total Hosig Uits Poplatio Ecoomicall Active Poplatio Total stdets Ad R Itercept < < <.000 _EXP_LOC < POP_TOT < < <.000 COM_IN a <.000 EMP_NBAS < < <.000 Ad R Itercept < < <.000 _HOUS_TOT POP_TOT < < <.000 COM_IN < < <.000 Ad R Itercept < < <.000 _POP_TOT POP_EAP < < <.000 Ad R Itercept < < <.000 _POP_EAP POP_TOT < < <.000 EMP_NBAS < < <.000 Ad R Itercept _STDT_TOT POP_TOT 0.6 < < <.000 Ad R

29 Table 3 Cotied Variables OLS Estimates p-vale GSSLS Estimates Model Ot-commters p-vale GS3SLS Estimates p-vale Itercept _COM_OUT POP_EAP < < <.000 EMP_TOT < AREA A_EMP < <.000 C_EMP a EXP_ED < <.000 I-commters Ad R Itercept -748 < < <.000 _COM_IN <.000 POP_EAP < < <.000 EMP_TOT < < <.000 C_EMP < <.000 AREA A_EMP < <.000 Nmber of Firms Emplomet i o-basic sectors Ad R Itercept < <.000 _FIRM_TOT < < <.000 POP_TOT < < <.000 AREA A_EMP < <.000 Ad R Itercept < < <.000 _EMP_NBAS EMP_TOT < < <.000 AREA EXP_ED <.000 A_EXPED < < <.000 C_EXPED Ad R a Idicates that the sigificace of the coefficiet chage as we chage estimatio procedres.

30 Table 4. Geeralized Spatial Three-Stage Least Sqares Reslts sig Differet eight Matrices eight ad distace Uiform eight ad distace sqared Model Variables estimates p-vale estimates p-vale estimates p-vale Itercept < < <.000 _REV_LOC POP_TOT < < <.000 EMP_NBAS < < <.000 COM_IN < < <.000 Itercept < < <.000 _EXP_LOC a POP_TOT < < <.000 COM_IN < < <.000 Local Revee Local Expeditre Total Hosig Uits Poplatio Ecoomicall Active Poplatio Stdets Total Ot-commters I-commters EMP_NBAS < < <.000 Itercept < < <.000 _HOUS_TOT a POP_TOT < < <.000 COM_IN < < <.000 Itercept < < <.000 _POP_TOT POP_EAP < < <.000 Itercept < < <.000 _POP_EAP a POP_TOT < < <.000 EMP_NBAS 0.3 < < <.000 Itercept _STDT_TOT POP_TOT < < <.000 Itercept _COM_OUT < POP_EAP < < <.000 EMP_TOT AREA A_EMP < < <.000 C_EMP EXP_ED < <.000 Itercept < < <.000 _COM_IN < < <.000 POP_EAP < < <.000 EMP_TOT < < <.000 C_EMP < <.000 AREA A_EMP < < <.000

31 Table 4. Cotied Uiform eight ad distace eight ad distace sqared Model Variables estimates p-vale estimates p-vale estimates p-vale Itercept < < <.000 _FIRM_TOT < < <.000 POP_TOT < < <.000 AREA Firms Total Emplomet i obasic sectors A_EMP < < <.000 Itercept < < <.000 _EMP_NBAS a < EMP_TOT < < <.000 AREA EXP_ED < < <.000 A_EXPED < < <.000 C_EXPED a a Idicates that the sigificace of the coefficiet chage as we chage weight matrices. Table 6. Ecoomic Impact Estimated From Spatial Lag Model a. Provice G or Si REV_LOC EXP_LOCHOUS_TOTPOP_TOTPOP_EAPSTDT_TOTCOM_OUT COM_IN FIRM_TOTEMP_NBAS Psa Ylsa Gg-B Gg-B Gg-Nam Gg-Nam Gg-Nam Gg-Nam Psa Ylsa Gg-Nam Giag-G Yl-G Pohag-Si Gg-Si Chagwo-Si Gimhae-Si Milag-Si Yagsa-Si Psa Ylsa Jihae-Si Total Impact a Effects of 000 ew obs created i Giag Cot of Psa Provice Korea

32 Table 6b. Ecoomic Impact Compariso of a Spatial ad No-Spatial Model a Variable Impact from spatial model Impact from o-spatial model Percetage differece Local revee millio wo % Local expeditres millio wo % Hosig its % Poplatio % Ecoomicall active poplatio % Nmber of stdets % Ot-commters % I-commters % Nmber of firms 9 7-0% Emplomet i o-basic sector % a Effects of 000 ew obs created i Giag Cot of Psa Provice Korea.

33 Table 7. Estimated Coefficiets ad Probabilit Vale of No-spatial Spatial Error Spatial Lag ad Spatial Lag ad Error Models Model Local Revees Local Expeditres Hosig Uits Poplatio Ecoomicall Active Poplatio Stdets Total Ot-commters I-commters Variables No-spatial 3SLS Spatial error 3SLS Spatial lag 3SLS Spatial lag ad spatial error 3SLS p- p- p- p- estimates vale estimates vale estimates vale estimates vale Itercept < < < <.000 _REV_LOC POP_TOT < < < <.000 EMP_NBAS < < < <.000 COM_IN < < < <.000 Itercept < < < <.000 _EXP_LOC POP_TOT < < <.000 COM_IN < < < <.000 EMP_NBAS < < < <.000 Itercept < < < <.000 _HOUS_TOT POP_TOT < < < <.000 COM_IN < < < <.000 Itercept < < < <.000 _POP_TOT POP_EAP < < < <.000 Itercept < < <.000 _POP_EAP a POP_TOT < < < <.000 EMP_NBAS < < < <.000 Itercept < < _STDT_TOT POP_TOT < < < <.000 Itercept _COM_OUT POP_EAP < < <.000 EMP_TOT < AREA a A_EMP < < <.000 C_EMP a < EXP_ED a < < Itercept < _COM_IN < POP_EAP < < < <.000 EMP_TOT < < < <.000 C_EMP < < < AREA A_EMP < < < <.000

34 Table 7 Cotied Model Firms Total Emplomet i Nobasic Sectors Variables No-spatial 3SLS Spatial error 3SLS Spatial lag 3SLS Spatial lag ad spatial error 3SLS p- p- p- p- estimates vale estimates vale estimates vale estimates vale Itercept < < <.000 _FIRM_TOT < <.000 POP_TOT < < < <.000 AREA A_EMP < < < <.000 Itercept < < < <.000 _EMP_NBAS a EMP_TOT < < < <.000 AREA a EXP_ED < < < <.000 A_EXPED < < < <.000 C_EXPED a < a Idicates that the sigificace of the coefficiet chage as we chage estimatio procedres. Table 8. Mea Absolte Percetage Error as a Measre of Forecastig Accrac i Differet Models Eqatios Spatial lag ad spatial error model Spatial error model Spatial lag model No-spatial model REV_LOC EXP_LOC HOUS_TOT POP_TOT POP_EAP STDT_TOT COM_OUT COM_IN FIRM_TOT EMP_NBAS Average Coefficiet of variatio

35 REFERENCES Aseli L Spatial Ecoometrics: Methods ad Models. Dordrecht: Klwer Academic Pblishers. Berc P. ad K. Sdsaeter Ecoomist s Mathematical Maal d Editio. Berli: Spriger-Verlag. Case A.C. J.R. Hies ad H.S. Rose Bdget spillovers ad fiscal polic iterdepedece: Evidece from the states. Joral of Pblic Ecoomics 5: Cliff A.D. ad J.K. Ord Spatial Atocorrelatio. Lodo: Pio. Cooe S. ad L. Fox. Usig the Idaho Fiscal Impact Model for Local Fiscal Impact Assessmet. Agricltral Ecoomics Research Series 94-8 Dept. Agricltral Ecoomics ad Rral Sociolog Uiversit of Idaho Moscow Idaho October 994. Evas G.K. ad J.I. Stallma SAFESIM: The Small Area Fiscal Estimatio Simlator. I T.G. Johso D.M. Otto ad S.C. Deller eds. Commit Polic Aalsis Modelig. Ames IA: Blacwell Pblishig. Johso T.G. 99. A descriptio of the VIP model. Upblished mascript Departmet of Agricltral Ecoomics Virgiia Poltechic Istitte ad State Uiversit Blacsbrg. Johso T.G. ad J.K. Scott The Show Me Commit Polic Aalsis Model. I T.G. Johso D.M. Otto ad S.C. Deller eds. Commit Polic Aalsis Modelig pp.9-9. Ames IA: Blacwell Pblishig. Keleia H.H. ad I.R. Prcha Estimatio of simltaeos sstems of spatiall iterrelated cross sectioal eqatios. Joral of Ecoometrics 8: Keleia H. H. ad D. Robiso Spatial correlatio: A sggested alterative to the atoregressive model. I New Directios i Spatial Ecoometrics. New Yor: Spriger- Verlag. Mrdoch J.C. M. Rahmatia ad M.A. Thaer A spatiall atoregressive media voter model of recreatio expeditres. Pblic Fiace Qarterl : Shields M A itegrated ecoomic impact ad simlatio model for iscosi coties. Upblished Doctoral Dissertatio Uiversit of iscosi Madiso. Sweso D. ad D. Otto The Iowa Ecoomic/Fiscal Impact Modelig Sstem. Joral of Regioal Aalsis ad Polic 8: Tiebot C.M A pre theor of local expeditres. The Joral of Political Ecoom 645: