SPATIAL ANALISIS OF EFFECT OF GOVERNMENT EXPENDITURES ON ECONOMIC GROWTH

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1 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp SPATIAL ANALISIS OF EFFECT OF GOVERNMENT EXPENDITURES ON ECONOMIC GROWTH Zba KARJOO MA student of economcs, Department of Economcs, Azad Islamc Unversty, khorasgan Branch Department of Economcs, Islamc Azad Unversty, khorasgan Branch, Isfahan, Iran (correspondng author) Abstract Majd SAMETI Assocated professor of economcs, Department of Economcs, Unversty of Isfahan Department of Economcs, Unversty of Isfahan, Isfahan, Iran Among the many factors whch affect the economc growth of a country, governments are consdered to be the most nfluental stmulants. Due to the mportance of studyng government expendture on economc growth, many technques have been suggested n ths regard.. In ths artcle we apply a new technque, namely the Spatal Econometrcs Method. Ths method examnes "neghborhood" and "locaton" factors, whch are nfluental n debltaton and renforcement. Usng Ram s growth model (1986) and applyng the geographc aspect to global regresson models, we attempt to dscover the effect of U.S state government expendtures on the economc growth of ts states. It was revealed that the growth of each state s nfluenced by that of ts neghborng states and that state government expendtures have no effect on economc growth. In addton, the growth of the labor force s ntroduced as an nfluental element affectng state economc growth. Keywords: Government expendtures, spatal econometrcs, geographc weghted regresson JEL classfcaton: C31, E62, H72, R12 1. Introducton Economc growth and ts underlyng foundatons are mportant factors dscussed wdely n recent years. Government expendture s a major factor that nfluences economc growth through ts allocaton to educaton, nfrastructure, publc goods and servces and law enforcement. Varous methods have been used to nvestgate the effect of government expendture on economc growth wth dfferent results. Based on a cross-country study for 96 countres, Landau 1983 [1], found a negatve relatonshp between government expendture and economc growth. Atrayee [2] reached the same results for the Unted States over the years between by developng a mult-equaton model. However, Kormend and Megure 1985 [3] found a non-sgnfcant relatonshp whle Summer and Heston 1984, Ram 1986 [4] found postve and sgnfcant effect. Moreover; Haggns et al (2006 [5], based on data from 1970 to 1998, examne ths relatonshp on three.e. the federal, state and local levels. Usng the 3SLS-IV approach they clarfed that the federal, state and local governments are ether negatvely correlated, or, uncorrelated wth economc growth. Most of the studes mentoned above consdered the economc growth of one or several places as dependent varable and place-specfc factors as ndependent varables. But one of the nfluental factors whch was most often gnored was locaton and, as a result, the contguousness of physcal place. Therefore, because of the spatal dependency that exsts between varous regons the classcal assumptons for estmaton usng the OLS approach would not be satsfed [6]. By addng geographc aspects to econometrc analyss, a new method was ntroduced called spatal econometrcs. Consequently the methods of estmaton changed. Today many economc studes use ths method as a useful technque to complete prevous models and ncrease the power of prospectve predcton [7],[8],[9].

2 48 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp In ths study, we present a bref ntroducton to spatal econometrcs. We then compare the global regresson and geographc weghted regresson models and prove that the latter s the more approprate choce. Fnally we apply spatal analyss to examne the effect of government expendture on economc growth and to detect models of spatal dependency. 2. Methodology 2.1. Geographc weghted regresson Ths method was ntroduced for the frst tme by L.Anseln [10]. Many specalsts n economy, geography and other regonal scences use the technque as a major part of plannng for urban development. In ths knd of regresson, the global form of regresson such as Y = a0 + a k k x k + ε (1) changes to: k (2) y (, ) (, ) = a0 u v + ak u v x k + ε ( u ) where, v a ( u, v ) s the co-ordnate of the th pont n space and k k (, ) of the contnuous functon a u v shown as: T ( ) = ( ) s a realzaton at pont. Consequently the estmator of the varables s 1 T ( ) ( ) aˆ u, v X w u, v X X w u, v Y W denotes an n n weghted matrx smlar to the weghted regresson matrx, the elements of whch are 1 f the two regons are contguous and 0 f otherwse. For easer computaton the matrx has to be normalzed so that ts elements are dvded by the number of neghbors [11]. One of the ways to form ths matrx s by usng the lattude and longtude of the regons as used n certan software such as GWR Spatal heterogenety Spatal heterogenety s varaton n relatonshp over space such that every pont n space may have dfferent relatonshps. Thus the lnear relatonshp s shown as: y (3) = x β + ε (4) Where represents ponts n space and s a vector of ndependent varables assocated wth ts parameter β. ε denotes a stochastc dsturbance Spatal dependency Spatal dependency may occur n many models whch mean that the amount of Y n locaton mght be assocated wth Y n neghborng locaton j. In other words [12]: ( j) y = f y = 1,2,..., n( j ) (5) There are two major models that contan spatal dependency: The frst s the spatal autoregressve model (SAR) shown as: y = ρwy + xβ+ε (6) ε N ( 0, 2 σ I ) n where y s an n 1 vector of dependent varables, x contans the n k vector of ndependent varables and w s a spatal weghted matrx always of frst-order contguty. If, the

3 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp coeffcent on the spatal lagged dependent varable, s sgnfcant the model wll be proved to be SAR. In other words the level of Y (the dependent varable) depends on the level of Y n neghborng regons. Fgure.1 llustrates ths concept. Fgure 1. Spatal autoregressve model (SAR) Source: www. s4.brown.edu The second model s the Spatal Error Model (SEM). Ths model ncludes the unmeasured errors and ndependent varables of contguous ponts whch, beng unmeasurable, are consdered wthn the error doman. Ths model s shown as: y = x β + u u ε = λw u + ε N ( 0, 2 σ I ) n Y s an n 1 vector of dependent varables, x s an n k matrx of ndependent varables and w s a spatal weghted matrx. Statstcally sgnfcant, a coeffcent on the spatally correlated errors, s the sgn of the exstence of an SEM model shown n Fgure 2. Fgure 2. Spatal error model (SEM) (7) 2.4. Economc model and data sources Source: www. s4.brown.edu To analyze the spatal aspect, and nvestgate the effect of government expendtures on economc growth the Rat Ram 1984 growth model was used. Based on ths model, whch s adapted from reasonng developed by Greshon Feder[13], economy conssts of two sectors: government and non-government. The output of these sectors s the result of ther labor and captal. In addton, non-government outputs are derved from government outputs. The fnal

4 50 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp model s shown wth Y representng the total output of the two sectors, I the total nvestment, L ɺ the growth of the labor force, and fnally G ɺ representng government expendtures: I δ G Y = α + β L+ θ G + θ G Y 1+ δ Y Moreover α s the margnal product of captal n the non-government sectors, β and θ are respectvely the elastcty of non-government output wth respect to L and the elastcty of nongovernment output wth respect to G. ndcates dfferences n nput factors n the two sectors. For example postve shows hgher nput productvty n the government sector. 3. Data Data was collected from the US Census Bureau, Federal Reserve and State Government Fnances. Spatal analyss s carred out for 2006 and 2009 (before and after the 2008 Unted States fnancal crss) wth the data of all ffty states. GWR, Geoda and GIS were used as the necessary software. 4. Result 4.1. Global regresson versus geographc weghted regresson The frst step n provng the dfference between global regresson and Geographc Weghted Regresson (GWR), s estmatng the parameters of the global model usng the OLS approach over a perod of two years. Accordng to the t-statstc, the growth of the labor force s the only sgnfcant varable whereas the growth of government expendtures, besde other varables, s nsgnfcant. Table 1. Parameter estmaton of global model by OLS approach YEAR Intercept I/GDP L ɺ G ɺ (G/Y) G ɺ *** (3.1) ** (-0.54) * (2.55) (0.75) (-0.33) (-1.27) (-0.36) (-0.62) (-1.1) (1.06) (8) *** Estmated values ** t-statstc values * Rejecton of H 0 at 5% level of sgnfcance To compare these two models, an ANOVA test has been used to test the null hypothess that the GWR model represents no mprovement over a global model. As the F-statstcs results show, GWR s the approprate model for predcton. Table 2. An ANOVA test for comparson of two models Year F- statstcs By swtchng the model from global to GWR, the values of R 2 and R 2 Adj change; accordng to Table 3 these values ncrease. Ths can be descrbed as ncrease n the power of the model as a result of consderng locaton factors collectvely as a new ndependent varable. Table 3. Coeffcent of determnaton and adjusted coeffcent of determnaton n two models Global Regresson Geographc Weghted Regresson R 2 Adj R 2 R 2 Adj R 2

5 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp A fve-number summary of the local parameters estmates s shown n Table 5. The mnmum effectveness of the only sgnfcant varable.e. the growth of the labor force on economc growth s 0.36 and belongs to the state of Vermont and ts maxmum, 1.19, to the state of Alaska. Table 4. A fve-number summary of the local parameters estmaton Year Mn Lower Medan Upper Max Quartle Quartle Intercept (I /Y) L G G Y G To llustrate the ntensty of ths effect, a GIS map was desgned (Fgure3). The dark and brght colors respectvely represent the strong and weak nfluence of labor force growth on economc growth. As s shown, the hghest effect of labor growth on the economc growth of the states s seen n the northern and north western states (Alaska beng one) and ts least effect belongs to the eastern and north eastern states (such as Vermont). Fgure 3. Intensty of labor growth effects on economc growth 4.2. Detectng spatal dependency The Moran-I statstcs and scatterplot are two ndces used to examne the presence and extent of spatal dependency n economc growth. The results below show a spatal dependency n the economc growth of the states n the 2009 model (Fgure 4). The Moran-I scatterplot also demonstrates ths. Ths plot presents economc growth on the horzontal and

6 52 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp spatal lag on the vertcal axs. Based on ths scatterplot, the states dsperson n the frst and thrd quadrants n Fgure.4 declares that the states wth postve economc growth are located near other states whch lkewse have postve growth and states wth negatve growth are neghbors to ther lkewse peers. Fgure 4. Spatal dependency among economc growth of states (2009) Table 5 shows the exstence of spatal dependency as SAR and SEM models. The sgnfcant P-values admt the exstence of these two models. These two knds of spatal dependences have been confrmed only n the 2009 model. Table 5. Models of spatal dependency MI/DF VALUE PROB Test Moran's I (error) Lagrange Multpler (lag) Lagrange Multpler (error) Lagrange Multpler (SARMA) After detectng these dependences, the estmaton of varables s provded. The coeffcent estmaton of the SAR and SEM 2009 models are presented n Table 6 as: Table 6. Estmaton of, SAR and SEM model (2009) Varables\models SAR SEM Intercept (-1.11) * (-1.72) I/GDP

7 Karjoo Z., Samet M., Regonal Scence Inqury, Vol. VII, (1), 2015, pp (-0.054) (0.19) L (-0.63) (-0.63) G G Y (-1.4) (-1.24) G (1.3) (1.16) ρ (1.9) - λ (2.25) R * t-statstc t-statstc of Table 6 shows the parameters are not sgnfcant but λ (t =2.25) and ρ (t=1.9) are sgnfcant. So the presence of neghborhood effects s proved. Also the other mportant results whch can be concluded from ths table are: 1. Sgnfcant ρ shows that economc growth of states s affected by economc growth of contguous states. 2. sgnfcant λ and consequently presence of SEM model confrm that there are some unknown factors of contguous states that have nfluence on economc growth whch s consder as an error term of the model. 5. Concluson Government expendture and ts effects on economc growth have been subjected to varous economc studes n the past few decades. Among the possble methods, spatal analyss wth ts consderaton of the contguty factor s one of the new and competent ways to nvestgate ths cause and effect. By applyng ths method to the Rat Ram 1986 growth model for the 2006 and 2009 data, the results presented n ths study ndcated that geographc weghted regresson was more approprate than global models. Moreover, state government expendture has no effect on economc growth but the growth of the labor force has a sgnfcant and postve effect on the economc growth of the states. As spatal analyss results showed, two models of spatal dependency, SAR and SEM, have been absorbed n the 2009 model.

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