Mathematical Model: The Long-Term Effects of Defense Expenditure on Economic Growth and the Criticism

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1 Journal of Physis: onferene Series PAPER OPEN AESS athematial odel: The ong-term Effets of Defense Expenditure on Eonomi Growth and the ritiism To ite this artile: Posma Sariguna Johnson ennedy et al 2018 J. Phys.: onf. Ser View the artile online for updates and enhanements. This ontent was downloaded from IP address on 30/01/2019 at 20:27

2 WA-athomteh 2018 athematial odel: The ong-term Effets of Defense Expenditure on Eonomi Growth and the ritiism Posma Sariguna Johnson ennedy 1*, Suzanna Josephine.Tobing 1, Rutman umbantoruan 1, Emma Tampubolon 1 and Adolf Bastian Heatubun 2 1 Faulty of Eonomi and Business, Universitas risten Indonesia, Jakarta, Indonesia 2 Universitas Pattimura, aluku, Indonesia * posmahutasoit@gmail.om Abstrat. This paper aims to form a mathematial model that an explain the influene of national defense budget on the eonomy through eonomi growth. The researh method is by literature review from the work of eonomists in making the prodution funtion model that an bring defense expenditure into the eonomi growth model. The model is two-setor eonomi model, established to look at the effets of defense spending and the eonomy. The model of Ram based on the neolassial prodution funtion approah. The externality effet of the military and non-military setors is different, so, they are inluded in the prodution funtion separately. 1. Introdution Aording to ornes & Sandler, the ativities of the government will affet the prodution apaity of the private setor though not refleted in pries of ompetitive markets. This externality, for example, an be formed from infrastruture ativities, training, eduation, nutrition improvement, and other ativities that an inrease the human resoures an. When ativities of one setor an inrease output from other setors, there is a positive externalities, as well as if the opposite ours. [1] To see the effet of national defense on the eonomy over in the long term, it is approahed through an analysis of the supply side or prodution side. The effet of defense spending on eonomi output are through the availability of its prodution fators, whether labor, apital and physial apital, as well as tehnologies that simultaneously affet potential eonomi output. Based on a formal model framework, a mathematial model would like to look at the effet of defense spending on eonomi growth. Although in reality the relationship is very omplex, but we make a mathematial simplifiation through eonomi growth model. In general, this study aims to form a mathematial model that an explain the influene of national defense budget on the eonomy through eonomi growth. The researh method is by literature review from the work of eonomists in making the prodution funtion model that an bring defense expenditure into the eonomi growth model. One approah that ommonly used in researh on the relationship between defense spending and eonomi growth is the neolassial prodution funtion approah, by reviewing the supply-side desription through aggregate output hanges [2]. It is also desribed by Ram [3], Biswas & Ram [4], ontent from this work may be used under the terms of the reative ommons Attribution 3.0 liene. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal itation and DOI. Published under liene by td 1

3 WA-athomteh 2018 Atesoglu and ueller [5], intz & Huang [6][7], and Ward & Davis [8] and Heo [2]. This theory is widely used beause it is onstruted from a onsistent theory struture.[9] This theory assumes that real output per apita and apital stok growth will remain in a onstant level over a period of time despite short-term flutuations. It is also assumed that an inrease in labor and apital input at the steady level will also inrease the aggregate output at a steady level. [10] Then the hange from the aggregate output will be explained through hanges in apital and labor. In neolassial growth theory, explains that is no hannel of government spending that affets longterm eonomi growth.[11] The simplest model in shaping the eonomi model is to form the assumption of a losed eonomy and a prodution setor, where output is a homogeneous good that an be onsumed at one invested. Investment produes new physial apital, and the apital depreiates at a onstant rate. Households and firms are onsidered joint units (whih have input and manage tehnologies that transform inputs to output), the market is negleted. The urrent output produed at time t (Y) is affeted by the prodution funtion of apital () and labor () depending on the time (t) to reflet the effets of tehnologial development, desribed as follows Y (t) = F [ (t), (t), t]. [12] However, many assumptions are developed in modeling to inlude government expenditures with the approah of the neolassial prodution funtion. Government defense expenditure and its overall impat on growth an be analyzed in the ontext of dividing the eonomy into several setors, not just one setor. These setors form externalities that affet other setors. The assumptions that divide maroeonomi into two setors, government and non-government (private) are preeded by Ram [3], Biswas and Ram [4], based on the idea of non-export-export model by Feder [13]. 2. ethod One ommon approah used to look at the effet of defense spending and eonomi growth is the neolassial prodution funtion approah. That is by reviewing the supply-side desription through the aggregate output hanges.[2][14] Antonakis argues that, it is important to build models by dividing the eonomy into setors aimed at apturing the impat of military spending on growth, although not reviewing the influene of other maro variables. Thus the overall influene of military spending on growth is analyzed in the ontext of dividing the eonomy into several setors, in whih setors form externalities that affet other setors.[15] The two-setor eonomi model established to look at the effets of defense spending and the eonomy is a model of Ram based on the neolassial prodution funtion approah built by Feder and Deninsons. [3] Feder writes that aggregate growth is related to hanges in apital and labor through a ertain or underlying prodution funtion.[13] He built a two-setor prodution funtion model, onsisting of export and non-export setors. Deninson's soure-of-growth model uses a supply-side desription of aggregate output hange, whih explains aggregate growth in its hanges to apital and labor.[16] Based on their views Feder, Deninson, and Ram built a model of two setors also by omprising the government setor and the private setor. In the development of defense eonomis, the Feder-Ram model is widely used in explaining the relationship between military budget and eonomi growth from the supply side. The two-setor model built by Ram is the military output setor (, government) and ivil output setor (, private setor). Both setors use labor () and apital (), while the prodution funtion of the military will exert external effets on prodution from the private setor. [3] The aggregate prodution funtion of the output of the eonomi setors is given by the following funtions: ( (, m, m ) ) (, ) (,, ) (1) 2

4 WA-athomteh 2018 imitations of endowment fators are as follows: is i is S m, i (2) And the national inome is: Y (3) The sum of these "butter" and "guns" an only be understood if their value is in monetary output ompared to the quantity output. It would be better to be formed in the normalization of pries, as follows: Y P. r.(, ) Pm. r.( m, m) (4) where Pm and P are onstant unitary units of money pries assoiated with the output quantity of r. and r. From this model an be formed marginal produts of both labor (, ) and apital (, ) whih an be made proportionally between setors, is a derivative of the prodution funtion of inputs, namely: 1 (5) The notations in equation (5), show the external effets of military output to the private setor, and denote the relative fator produtivity differene between the two setors. If 0 and/or 0, an inrease in military output will ause a large growth rate of total Y output, from the sum of and, using the given prodution funtion and. Equation (5) is equivalent to: Pm. r Pm. r 1 P. r P. r (6) Equation (6) shows the omparison between the produtivity of marginal fators between different prodution depending on the pries used on setoral outputs. Differentiation of (3), (1), and (2) forms the eonometri speeh of the growth equation, as follows: I Y.. Y Y 1 Y (7) where the dot notation indiates the rate of hange in proportion or growth rate. I/Y and /Y are notations of the ratio of investment and military spending to total output. While I = d whih is a net investment. Using equation (1) and the onstant elastiity of to equation (5) an be hanged in the form of: I Y ( ) Y 1 Y. (8) Where : dy Y Y, d, d,,,. Y Y (9) The differene in (7) with (8) is that in equation (7) hypothesis testing is possible only if the variables and are zero. However this would ause the oeffiient of (/Y) to be zero thus reduing the estimate of the standard growth equation. Using equation (8), we an be estimated 3

5 WA-athomteh 2018 separately to identify separately from the "externality effet" and the "marginal fator produtivity differential effet". 3. Result and Disussions uh debate has emerged against the defense-growth model that begins with the Feder-Ram model. Some experts provide support, suh as Deger and Sen that haraterize the externality model of Feder- Biswas-Ram as "a splendid empirial workhorse to investigate the impat of military expenditure on growth."[17] intz and Stevenson (1995) seen using formal justifiation to inlude military expenditure as explanatory variables in growth regression analysis with single-equation growth analysis, based on neolassial growth theory as its foundation.[18] Or, Biswas and Ram state, at least stands out well on the framework of neolassial prodution funtions.[4] His famous approah is the emergene of a diret link from the theoretial model to the eonometri speifiation. However, many ritis say that Ram's study does not inlude other independent variables that also affet eonomi growth. From the eynesians see that neolassial approah is not able to answer the problem in the short term, espeially if there are shoks enountered. Full eonomi onditions are only limited to long-term models that are diffiult to implement in reality. But Dunne, Smith, and Willenbokel said formation of the model faed many inauraies. Feder- Ram model that notation of differenes in fator of marginal produtivity between setors, as in the following: 1 (10) atually gives some wrong interpretations. In empirial literature, non-zero is generally interpreted to reflet a situation in whih one setor is more effiient or less produtive in its fator users than others.[19] For example, Ward et al estimates a negative sign for Taiwan whih an be inferred "that in omparison to the ivil setor, the military setor is realized more ineffiiently".[20] Antonakis[15] and Atesoglu and ueller[5] write something similar: "Without a strong ompetitive pressure that leads to... effiieny in the management and use of resoures, it an be argued that marginal produtivity fators are muh lower in the defense setor". Suh interpretations do not onform to a reognized model of theory. Another argument that the approah to apture some of the behavior of off-the-prodution funtions is not appropriate. The derivation of the empirial growth equation: I Y.. Y Y 1 Y (11) is speifi to a ertain level whih is not different for intra-setoral organizations. The model was built inapable to alulate the intra-oriental organizational ineffiieny. The next question is whether the migration of a resoure that raises real GDP is what the soial really wants an not be answered without knowing where the relative P prie is used in an adequate Y alulation that reflets the soial marginal rate of substitution, the exhange of for. If that is the ase, the non-zero reflets the situation of the produt mix in a large eonomy and the alloation of inter-setoral fators in eeonomy as a whole is ineffiient. There is not muh we an do to onvert inputs into outputs in individual setors. In theoretially, there are many eonometri problems in estimating the Feder-Ram model. In the Feder-Ram equation where eonometrially it an be derived as: I Y Y Y (12) 4

6 WA-athomteh 2018 It an not be indiated whih is a variable and whih serves as a parameter. This equation treats apital (as a form of influene) is asymmetri, and it is lear that. /Y hills as a onstant 1,. I/Y ompilation is divided as a parameter and a variable,.i/y. It is not lear from where error origin and 2 why it is treated as white noise. We see the example, Wijeweera & Webb [21] examined the eonomi growth for Sri anka using the Feder-Ram usage model [22], Atesoglu odel [23] and Haliioglu [24]. In the Feder-Ram model the results showed t-statistis for eah major oeffiient ( and ) were positive, but not statistially signifiant in the experiments inluded for military-ontrolled operations (). Sine wages are insignifiant it an not be ensored whether or not pngelpangin positively affets eonomi growth in Sri anka. Not only are the oeffiients sttistially insignifiant, but R 2 is also very low whih means that the model is not strong enough to get out of the eonomy. All this leaves doubt on the Feder-Ram model to see the relationship between spae and eonomi growth in the ase of Sri anka.[21] 4. onlusion The Feder-Ram model of eonomi growth is very broad by people where its limitations are tried to be overome by various irles of eonomist. Dunne, Smith, and Willenbokel ritiize by stating that there is no solid basis and eonometri reason for using this Feder-Ram model. As for the various simultaneous problems by reating a growth rate of the same dimensions, when the ombination of the military is onstant, the net output will determine the movement of the military. The multiolinearity between the two final forms yields a large standard error and the estimated inauray (not appropriate foreast) of the parameters of the externalities. The model is stati, there is no lagged regressors or dependent variables, whih pose a major problem in time-series in ross-setion.[19] The next model of Feder-Ram was developed by intz & Huang with some modifiations. intz & Huang, argued that the externality effet of the military and non-military setors is different. Therefore, the effets of externalities of the military publi setor, the non-military publi setor, and the private setor are inluded in the prodution funtion separately.[25] Aknowledgments This researh was onduted, thanks to simlibtamas researh grant given by inistry of Researh, Tehnology and Higher Eduation of Indonesia, oordination of Private Higher Eduation Region III (opertis III) in Fisal Year 2018, Researh Institutions and ommunity Servie of Universitas risten Indonesia (PP UI) and Faulty of Eonomis and Business of Universitas risten Indonesia. Referenes [1] ornes, Rihard & Todd Sandler. (1986). The Theory of Externalities, Publi Goods, and lub Goods. ambridge : ambridge University Press. [2] Heo, Uk. (1998) odeling The Defense-Growth Relationship Around The Globe. Journal of onflit Resolution, Vol. 42 : [3] Ram, Rati. (1986) Government Size and Eonomi Growth: A New Framework and some Evidene from ross-setion and Time-Series Data, Amerian Eonomi Review, Vol.76 (1) : [4] Biswas, B. & Ram, R. (1986). ilitary Expenditures and Eonomi Growth in ess Developed ountries: An Augmented odel and Further Evidene, Eonomi Development and ultural hange, Vol. 34. [5] Atesoglu, H. Sonmez & ueller, J. ihael. (1990). Defene Spending and Eonomi Growth, Defene Eonomis, Vol. 2(1) :

7 WA-athomteh 2018 [6] intz, Alex & Huang, hi. (1990) Defene Expenditures, Eonomi Growth and the Peae Dividend, Amerian Politial Siene Review, Vol. 84 (4) : [7] intz, Alex & Huang, hi. (1991) Guns versus Butter : The Indiret ink. Amerian Journal of Politial Siene, Vol. 35 (3) : [8] Ward,.D; Davis, D.R (1992) Sizing up the Peae Dividend: Eonomi growth and military spending in the US, , Amerian Politial Siene Review, Vol. 86 (3). [9] Sandler, Todd. & Hertley, eith The Eonomis of Defene. ambridge surveys of Eonomi iterature, U : ambridge University Press. [10] Solow, Robert. (1970) Growth Theory : An Exposition. New York: Oxford University Press. [11] Solow, Robert. (1957) A Tehnial hange and the Aggregate Prodution Funtion, Review of Eonomis and Statistis, Vol.39 (3), pp [12] Barro, R. J. & Sala-I-artin, X. (1995). Eonomi Growth. New York : Graw-Hill. [13] Feder, Gershon. (1983) On Exports and Eonomi Growth, Journal of Development Eonomis, Vol. 12 : [14] Heo, Uk. & arl DeRouen Jr. (1998) ilitary Expenditures, Tehnologial hange, and Eonomi Growth in The East Asian NIs, Journal of Politis, Vol. 60 : [15] Antonakis, Niholas. (1999) Guns versus Butter: A ulti-setoral Approah to ilitary Expenditures and Growth with Evidene from Greee, , Journal of onflit Resolution, Vol. 43 (4) : [16] Denison, Edward F Trends in Amerian Eonomi Growth, Washington, D : Brookings Institution. [17] Deger, Saadet & Sen, S. (1983) ilitary expenditures, Spin-off and Eonomi Development, Journal of Eonomi Development, Vol. 13. [18] intz, Alex & Stevenson, R. (1995) Defene Expenditures, Eonomi Growth and the Peae Dividend : A ongitudinal Analysis of 103 ountries, The Journal of onflit Resolution, Vol.39 (2) : [19] Dunne, J.; Smith, Ron; Wellenbokel, Dirk. (2005) odels of military expenditure and Growth: A ritial Review, Defene and Peae Eonomis, Vol.16 (6). [20] Ward,.D.; Davis, D.R. & ofdahl,.. (1995) A entury of Tradeoffs : Defense and Growth in Japan and the United States, International Study Quarterly, Vol. 39, No.1, pp [21] Wijeweera, Albert; Webb, atthew J. (2009). Using the Feder-Ram and ilitary eynesian odels to Examine the ink between Defense Spending and Eonomi Growth in Sri anka, Defene and Peae Eonomi. [22] Wilkins, Nigel. (2004). Defene Expenditure and Eonomi Growth : Evidene from a Panel of 85 ountries, Shool of Finane Eonomis Sydney. [23] Atesoglu, H. Sonmez. (2002) Defense Spending Promotes Aggregate Output in the United States : Evidene from ointegration Analysis, Defense and Peae Eonomis, Vol. 13 (1) : [24] Haliioglu, Ferda. (2004). Defense Spending and Eonomi Growth in Turkey : An Empirial Appliation of New aroeonomi Theory, Review of iddle East Eonomis and Finane, Vol. 2 (3). [25] Huang,. & intz, A. (1991) Defene Expenditures and Eonomi Growth: The Externality Effet, Defene Eonomis, Vol. 3 (11). 6