Analyss of the Influence of Expendture olces of Government on Macroeconomc behavor of an Agent- Based Artfcal Economc System Shgeak Ogbayash 1 and Kouse Takashma 1 1 School of Socal Systems Scence Chba Insttute of Technology Chba 275-0016 Japan. ogbayash@sea.t-chba.ac.jp Abstract. An agent-based model of artfcal economc system ncludng government has been developed and the nfluences of publc polces on GD and related emergent behavor of macroeconomc phenomena have been analyzed. It was revealed that power law dstrbutons emerge durng smulaton n some factors such as assets of agents and GD ncreases wth an ncrease n the rato of effcent expendture polcy such as market purchasng Average prce ncreases or decreases when GD ncreases or decreases and the nfluence of tax rate on GD depends on the way of publc spendng. Most of these results are found to be qute consstent wth real data f t s assumed that publc spendng ncludes more than 10% of neffcent factors. Keywords: Agent-based modelng computatonal economcs government expendture polcy GD tax rate power law dstrbuton. 1 Introducton Agent-based modelng (ABM) s wdely used n socal smulaton because t s a class of modelng method used to explan or understand socal phenomena va a bottom-up approach [12]. Applcaton of ABM n macro-economc systems s one of the most mportant research felds because macro-economc systems are very complex and relate to many socal phenomena. ABM s expected to propose a new way to understand the mechansm of the behavor of complex macro economy. In prncple t mght even be possble to utlze ABM to understand or evaluate the effectveness of economc polces such as tax reducton and publc spendng as ponted out n the lterature [3]. The pror studes on ABM of macroeconomc systems are consdered to be dvded nto two types the research whch manly focuses on the emergence of macroeconomc phenomena and ts mechansms [45] and the research whch manly focuses on the development of the models of multple-market economy as a whole takng nto account the structure of real economy n as detal as possble[67]. Although there has been a lot of research whch focuses on varous aspects there has not been much research whch has focused on the role of government and the nfluence of publc polces on GD. In a prevous research[8] authors have
constructed a smple artfcal economc model composed of consumers three types of producers and a bank and revealed that ths smple model reproduces fundamental economc behavor such as loose equlbrum n prce busness cycle due to captal nvestment nfluence of money supply on GD etc. In ths study an agent based model of an artfcal economc system ncludng government has been developed based on the authors prevous model. Usng the model the nfluences of publc polces on GD and related emergent behavor of macro-economc phenomena has been analyzed. The obtaned results are compared wth those of a real system to check whether the model reproduces the real phenomena. 2 Smulaton Model The agent-based model of an artfcal economc system n the present study s composed of consumers producers a bank and government as autonomous decson makng agents as shown n equaton (1). It s assumed that producers are dvded nto 3 types of agents.e. retalers who produce fnal products for consumers wholesalers who produce and supply raw materals for retalers and an equpment maker who supples equpment for producton for other types of producers. Consumers are dvded nto prvate employees who work for a prvate company and publc employees who work for the government. Each agent has state varables and rules of actons. Market also has state varables although t does not have rules of actons. State varables of each agent related to cash and depost at the begnnng of each fscal perod are gven n equaton (2). Agent { C B G} { R W E} (1) C : Consumer : roducer B : Bank G : Government R : Retaler W : Wholesaler E : Equpment maker MC MC C C G 1 C MD MD 1 C MD MD 1 MC MC MD (1 r 1 C wthdraw {Sales r 1 wthdraw Expendtur e ) (1 b)x Interest 1 1 a Interest (Cost k {C} 1 1 1 porcy 1 G Tax revenue wagek Expendtur e k {C} 0 buy 1 1 bx 1 C 1 a wage 0 1 k )}(1 ctaxrate) Repayment 1 (2) where x wage (1 Taxrate) Consumptonbudget a bx Tax revenue : Fscal perod MC:Cash possessed by agent r wthdraw :Rato of k{c} Cost:Expendture of retaler to buy rawmaterals ctaxrate:corpratontax rate 0 MD r 1 (wage Taxrate) k k {} wthdraw {Sales wthdrawal moneyto total depost Interest Repayment:Decreaseagent n the balance of loaned money 1 1 1 wage Const wage Bonus Expendtur e (Cost 1 k{c} suffx:agent type MD:Depost of agent n the bank Interest:Blance of nterest pad bythebank Expendtur e porcy wage buy :Expendtureof Taxrate:Incometax rate. Market purchasng Frm subsdy 1 k )}ctaxrate consumer to buy retal product A set of actons of each agent composes a unt of perod and one perod s assumed to correspond to one month n the real system. Durng each perod some of the state varables of agents wll change n ts value due to the nteracton between agents. At
the end of each fscal perod each agent settles the accounts wth double-entry bookkeepng method. By summng up the calculated data of all agents an nputoutput table of the artfcal system s defned and GD s obtaned at every fscal perod. The rules of actons of each type of agent are assumed as shown below. 2.1 Consumer Agent Consumer agents work at one of the producers or at the government n case of publc consumers get wages pay tax dependng on ther ncome and buy products suppled by retalers accordng to ther utlty functons wthn the lmt of cash at hand. Cash at hand s defned as the sum of Keynesan consumpton functon and the money wthdrawn from ther bank accounts accordng to the wthdrawal rato as shown n equaton (2). When there are goods of same class avalable n the market wth dfferent prces the consumer s assumed to select and purchase the cheapest one among them. The utltes for each class of products are gven randomly wth unform dstrbuton at the start of the smulaton. 2.2 roducer Agent roducers hre consumers as employees pay wages make producton plans produce products of several types supply and sell them n the market pay tax dependng on ther proft and depost and wthdraw money n the bank at every fscal perod. The wages are composed of a fxed salary whch s assgned to each consumer randomly between lower and upper lmts and a bonus whch s gven when the proft of the producer s postve. The amount of bonus s defned as the bonus rato tmes of the producer s surplus money and unformly assgned to each of the employees. 2.2.1 Retaler and Wholesaler The retalers and wholesalers decde both the amount and prce of each class of products where the prce s ncreased or decreased dependng on the amount of goods n stock at the end of the prevous perod. The amount of producton s decded so that the probablty of the occurrence of beng out of stock s less than 5% whch s estmated based on the total sales durng the most recent 10 perods. When the estmated prce s less than the runnng cost per product the mnmum prce s set to be the runnng cost. On the other hand when the estmated amount of producton s less than 70% of the producton capacty the mnmum amount of producton s set to be that amount. The producton capacty Y s defned by a Cobb-Douglas type functon as shown n equaton (3) where K s the number of equpments for producton L s the number of employees and α s 0.25. 1 Y AK L (3) Retalers and wholesalers have ntally one unt of equpment and ncrease the number one by one durng the smulaton by buyng equpment from equpment maker when the producton at maxmum capacty contnues for more than crtcal tmes. All of the necessary amount of money for nvestment s fnanced by the bank
and t s constantly pad back every perod for constant repayment perods. Addtonal nvestment durng the repayment perods s assumed to be not allowed. Retalers and wholesalers also have a bankruptcy rule. When the perod of no sales wth respect to a certan class of products contnues for more than crtcal tmes the producer quts producton of that class of product. The producer goes bankrupt when he quts the producton of all classes of products. In addton retalers requre one unt of raw materal for the producton of one unt of product and buy the necessary amount of materal n the market accordng to ther producton plans. When the amount of materal avalable n the market s less than the requred number the amount of products to be produced s lmted to that amount. Retalers also have a layoff rule. When the perod of defct contnues for more than a crtcal tme one of the employees s lad off and assgned to the producer whose amount of accumulated proft s the largest among producers. 2.2.2 Equpment Maker The equpment maker produces equpment accordng to the requrement from the retalers and wholesalers wthn the lmt of producton capacty. The prce of the equpment s assumed to be constant n the present study. 2.3 Bank Agent The bank keeps surplus money of other agents n ther bank accounts and lends money as a long term loan to producers accordng to ther demands for nvestment wth the nterest rate of 3%. The bank also pays wages to the employees and pays tax to the government accordng to the nterest ncome. The bank also lends money as a short term loan to the producers accordng to ther requrement when ther workng captal becomes short. In the present study the ntal amount of funds n the bank s set to be very large so that there s no lmtaton on lendng money to meet the demand of producers except that addtonal requrement of long term loans s not fulflled durng the repayment stage. 2.4 Government Agent The government collects tax from the producers and consumers n the form of corporaton tax and ncome tax respectvely pays wages to the publc employees and spends the resultant money for publc spendng accordng to the expendture polcy n every fscal perod. Corporaton tax s only collected when the proft of the producer s postve and tax rate s assumed to be constant. Income tax s collected accordng to the consumer s ncome and tax rate s also assumed to be a constant value. The wage of publc employees s determned at each fscal perod so that t equals the average value of prvate employees wage as the sum of fxed wage and bonus. As the expendture polces market purchasng frm subsdy and the combnaton of them are tested assumng the extreme cases of effectveness n publc spendng. The market purchasng s an expendture polcy where the government drectly purchases goods n the market wth the market prce. When there are goods of the
same class avalable n the market wth dfferent prces the government selects and purchases the cheapest one among them. Ths polcy corresponds to the extreme case of effcent government spendng where the government orders jobs to the frms n a completely compettve stuaton wth the same prce level expected n the market The frm subsdy s an expendture polcy where the government evenly dstrbutes funds to producers wthout any lmtaton of ther use. Ths polcy corresponds to the extreme case of neffcent spendng where the government orders jobs to the frms wth a much hgher prce level than expected n the market or pays money for the jobs whch have no publc meanng n the socety. 3 Smulaton Condtons A smulaton program has been constructed usng Mcrosoft Vsual C++ wth object orented programmng where agents are represented as objects programmed as nstances of classes. The numbers of agents are 100 20 3 1 1 1 for consumer retaler wholesaler equpment maker bank and government respectvely. The nfluences of expendture polces by the government tax rate and consumpton functon of consumers on the macroeconomc behavor of the system such as GD average prce etc are analyzed and compared wth that of the condton wthout a government. The dstrbutons of varous factors ncludng consumer s assets producer s assets as well as total sales maxmum dfference n the prce of products at each fscal perod and the dfference n GD durng each perod are also analyzed to confrm the emergent behavors of macroeconomc phenomena. Table 1. Smulaton condtons. Smulaton condtons are gven n the Table 1 whch are dvded nto three tables fxed parameters whose values are constant ntal condtons whose values may change durng each run of smulaton and smulaton parameters whch are constant but changed for each run of smulaton to clarfy ther nfluence on macroeconomc behavor n the present artfcal economc system. As shown n Table 1(a) each run
of smulaton ncludes 360 perods and repayment perod of producers s assumed to be 120. Expendture polces of government and tax rate are changed as expermental condtons as shown n Table 1(c) and ther nfluence on GD or other economc factors are nvestgated. Among these values number of agents bonus rate and ntal captal of agents are determned so that they are almost mnmal under the condton of the occurrence of stable fund crculaton. 4 Smulaton Results 4.1 Emergent ropertes n the resent Artfcal Economc Systems Before analyzng the nfluence of publc expendture and tax rate on GD emergent behavor of macro-economc phenomena n the model such as the dstrbutons of varous factors are analyzed. Fgure 1 shows the chronologcal change n GD and Gn coeffcent of consumers under the non-government condton. It s noted that GD shows cyclc up-and-down movements n tme representng busness cycles. The cycle of ths long term busness cycles s almost concdent wth the repayment perod 120. The prmary cause of these busness cycles s dscussed n the authors prevous work [8] and consdered as a result of fnance and repayment of funds by producers for captal nvestment. The captal nvestment occurs as a result of emergent behavor due to the nteracton among agents va market. Although ntal assets of consumers denoted by consumer s depost n Table 1 s gven by a unform random number between 30000 and 50000 nequalty of consumer s assets emerges and Gn coeffcent vares between 0.2 and 0.6 durng the smulaton as shown n Fgure1. It s also noted that the Gn coeffcent shows peak values when GD becomes local maxmum although ther behavors are not so smlar. Fg. 1. Cyclc change on GD(upper) and Gn coeffcent (lower) under the condton wthout government. Fgure 2(a) shows the relatonshp between consumer s assets and the populaton who have that amount of assets namely the consumer s assets dstrbuton. It s
clearly shown that consumer s assets dstrbuton s represented by a power law dstrbuton. It s noteworthy as shown n Fgure 2(b) that the dstrbuton of maxmum dfference n the prce of same product class purchased n the market n each fscal perod s also represented by a power law dstrbuton. Note that n the present model the prces of the product of same product class n the market are n prncple dfferent dependng on the producers. Smlarly t s confrmed that the total sales and total assets of retalers also shows power law dstrbuton. As the power law dstrbuton s one of the features of complex system [9] t s consdered that these nequalty behavors of varous factors such as consumer s assets etc. are the propertes emerged as a result of nteractons among consumers and producers. In addton the absolute values of the change n GD durng each fscal perod also shows power law dstrbuton as shown n Fgure 3. Namely although the long term busness cycles are due to the fnance and repayment of producers for captal nvestment the fact that small short term varatons shown n Fgure 3 are represented by power low dstrbuton suggests that the GD n the present calculaton s also an emergent property of artfcal economc system as a result of nteractons among agents. Fg. 2. (a) Consumers asset dstrbuton (left) and (b) dstrbuton of the maxmum dfference n the market prce of same product class (rght). Fg. 3. Dstrbuton of absolute value of the change n GD durng every fscal perod
4.2 Influence of Expendture olces of the Government on the Behavor of Macro-economy of the Artfcal Economc System Under the condton wth constant tax rate the nfluences of two types of expendture polces of government on GD are analyzed and calculated GD level s compared wth the GD wthout government. Two types of expendture polces are market purchasng and frm subsdy whch are defned as the extreme cases of effcent and neffcent way of publc spendng respectvely. Fgure 4 shows chronologcal change n GD and average prce of products n the market where these factors under the expendture polcy of market purchasng and frm subsdy are compared wth those n the case wthout government. It s noted n Fgure 4 that durng the whole perods the level of GD s larger n the case of market purchasng and smaller n the case of frm subsdy than that n the case wthout government. The average prce of products shows smlar behavor wth that of GD. It s also noted n Fgure 4 that there s a tendency for the prce to ncrease or decrease as the GD s ncreasng or decreasng. Thus nflaton or deflaton proceeds when GD s ncreasng or decreasng accordng to the present model. Fg. 4. Influence of expendture polces of the government on GD (upper) and average prce of retaler products (lower). 4.3 Influence of Tax Rate on GD Influence of tax rate s dependent on publc spendng. Therefore the rato of market purchasng has been changed and the nfluence of ncome tax rate and corporaton tax rate on GD s analyzed for varous ratos of market purchasng. Here the rato of market purchasng s defned by the amount of expendture for market purchasng dvded by the sum of the amount of expendture for market purchasng and frm subsdy. Margnal propensty to consume s assumed to be 0.7 and GD averaged for 360 perods s employed as the value of GD. The nfluence of tax rate on GD s shown n Fgure 5 for varous ratos of market purchasng. In case of 100% of the rato of market purchasng GD ncreases wth ncreasng ncome tax rate as shown n Fgure 5(a). Ths tendency s consdered to
result because the money whch s to be transferred to the consumer s bank account n the form of depost s collected by the government and consumed for buyng products n the market thus ncreasng the demand n the market. In case of 0% of market purchasng that means 100% of frm subsdy GD remarkably decreases wth an ncrease n ncome tax rate. Ths tendency s consdered to result because government funds obtaned by collectng tax are transferred to the frm s bank account almost wthout ncreasng consumer s ncome and money supply n the market. It s noteworthy that ths negatve correlaton of GD wth ncome tax rate s observed n Fgure 5(a) when the rato of market purchasng s less than 90%. Ths result suggests that f a negatve correlaton of GD wth ncome tax rate s observed n the real system t possbly means that the government expendture ncludes more than 10% of neffcent way of publc spendng. The comparson of the present result wth real data wll be dscussed n the next secton. The multplers of the reducton of ncome tax rate on GD are also calculated and t was revealed that the calculated multpler vares between 0 and 1.3 correspondng to the rato of market purchasng between 90% and 0%. The nfluence of corporaton tax s shown n Fgure 5(b) for varous ratos of market purchasng. In contrast to the nfluence of ncome tax rate GD ncreases wth an ncrease n corporaton tax rate regardless of the rato of market purchasng. Ths tendency s consdered to result because under the condton of present study where overseas market and labor market are neglected the money whch s to be transferred to the frm s bank account s collected by the government and more or less consumed n the market thus ncreasng the demand n the market. Even n case of 100% of frm subsdy tendency s the same because the redstrbuted funds to the frms are partly transferred to the consumer resultng the ncrease n the demand n the market. Fg. 5. (a) Influence of ncome tax rate (left) and (b) nfluence of corporaton tax rate (rght) on GD averaged for 360 perods 4.4 Influence of Margnal ropensty to Consume on GD The nfluence of margnal propensty to consume on GD s analyzed for varous ratos of market purchasng where ncome tax rate and corporaton tax rate are both fxed to be 20%. It was confrmed as shown n Fgure 6 that GD ncreases wth an ncrease n the rato of market purchasng and decreases wth a decrease n the margnal propensty to consume regardless of the rato of market purchasng. GD
level exceeds that of non-government condton when the rato of market purchasng s more than 70% or 80% dependng on the margnal propensty to consume. It was also revealed that the multplers of the reducton of ncome tax rate on GD decreases wth a decrease n margnal propensty to consume. Fg. 6. Influence of margnal propensty to consume on GD averaged for 360 perods. 5 Dscussons As shown n Fgure 4 there s a tendency for the prce to ncrease or decrease as the GD ncreases or decreases. Ths tendency s compared wth real data. The chronologcal data of GD and consumer prces n G7 countres for more than 10 years are avalable n the IMF world economc outlook database [10]. Fgure 7 shows the relatonshp between annual growth rates of GD and ncreasng rates of consumer s prces n Japan durng 1980 to 2010. As shown n Fgure 7 that postve correlaton between growth rate of GD and ncreasng rate of consumer s prces s observed. It s noted that nflaton or deflaton s observed n most of the 23 years of postve GD growth rate or n most of the 7 years of negatve GD growth rate. Ths result s qualtatvely concdent wth the calculated result of present study. Influence of ncome tax rate and corporaton tax rate on GD calculated n the present study has been compared wth the observed tendency n the real economc system where estmated results usng Short-Run Macroeconometrc Model for Japanese economy reported n the lterature [1112] are assumed to be the real data. Table 2 shows the estmated multplers on GD when ncome tax or corporaton tax s reduced for 3 years by the amount correspondng to 1% of nomnal GD [12]. As shown n Table 2 reducton of the ncome tax rate wll result n the ncrease of GD n the real economy n Japan. The multplers of tax reducton on GD range between 0.2 and 1.2 whch are close to the calculated value f government expendture n the real system s assumed to nclude more than 10% of neffcent way of publc spendng. From ths pont of vew the present results on the nfluence of ncome tax rate on GD s n good agreement n ts tendency wth the real data f t s assumed that the way of publc spendng by the government s not perfectly effcent but ncludes some amount of neffcent factors. Ths mght be reasonable to occur because when
the government orders some job to the frms frms may have a strong ncentve to make contract wth hgher prces whle publc employee has generally speakng comparatvely weak ncentve to decrease the prces. As for the nfluence of corporaton tax rate on GD on the other hand there s a bg dfference between calculated and observed results. Namely the reducton of corporaton tax rate wll also result n the ncrease n GD n the real economy as shown n Table 2. Ths result s completely opposte n tendency wth the calculated result as shown n Fgure 5(b) where GD decreases wth decreasng corporaton tax rate. Ths s consdered because present model assumed to neglect labor market nternatonal tradng and advance nto oversees market. Fg. 7. Relatonshp between ncreasng rate of average prce and GD growth rate. Table 2. Estmated multplers on GD when tax rate s reduced 6 Concluson An agent based model of an artfcal economc system ncludng government has been developed based on the authors prevous model. Usng the model the nfluences of publc polces on GD and related emergent behavor of macroeconomc phenomena have been analyzed and the followng results have been obtaned. 1) Although the assets of agents are ntally assgned by unform random numbers nequalty of assets emerges durng the smulaton and the dstrbutons of varous factors such as consumers assets maxmum dfference n market prce n each fscal perod total sales of retalers and the change n GD durng every perod are represented by power law dstrbuton. Ths suggests that varous macro factors emerges due to the nteracton between agents n the present model 2) As a result of analyzng the nfluence of expendture polces on GD employng market purchasng and frm subsdy as the extreme cases of effcency n publc spendng t s revealed that market purchasng has a postve nfluence on the
GD and frm subsdy has a negatve nfluence. GD ncreases wth an ncrease n the rato of market purchasng and GD level exceeds that of non-government condton when the rato of market purchasng s more than 70% or 80% dependng on the margnal propensty to consume. 3) It s also found that GD ncreases wth a decrease n ncome tax when the rato of market purchasng s less than 90% whle GD ncreases wth an ncrease n corporaton tax rates and the average prce ncreases or decreases when GD ncreases or decreases. These results have been compared wth the real data n Japan and t s revealed that the obtaned results of present study reproduce the feature of real economy observed n Japan except for the nfluence of corporaton tax f t s assumed that publc spendng ncludes more than 10% of neffcent factors. The calculated nfluence of corporaton tax on GD s not consstent wth the real data the reason of whch s consdered that present model neglects the labor market and nternatonal transactons. References 1. TeranoT.: "Beyond the KISS rncple for Agent-Based Socal Smulaton" "Journal of Soco-Informatcs" Vol.1 No.1(2008) 175-187. 2. TesfatonL. JuddK.L.:"Handbook of computatonal economcs Volume 2: Agent-based computatonal economcs" North-Holland (2006). 3. FarmerJ.D. FoleyD.:"The economy needs agent-based modellng" "Nature" Vol. 460 August 6 (2009) 685-686 4. BruunC. :"The economcs of Keynes n an almost stock-flow consstent agent-based settng" n "Computable constructve and behavoural economc dynamcs - Essays n honour of Kumaraswamy (Vela) Veluplla" ed. by Stefano Zambell Routledge Fronters of oltcal Economy 2010. 5. DosG. FagoloG. and RoventnA. :"Schumpeter Meetng Keynes: A olcy-frendly Model of Endogenous Growth and Busness Cycles" Workng aper Laboratory of Economcs and Management (LEM) (2008) 6. TegloA. RabertoM. CncottS.: "Endogenous Credt Dynamcs as Source of Busness Cycles n the EURACE Model" "rogress n Artfcal Economcs" Sprnger(2010) 203-214. 7. SprggJ.A. EhlenM.A. :"Full Employment and Competton n the Aspen Economc Model: Implcatons for Modelng Acts of Terrorsm." Sanda Natonal Laboratores SAND2004-5500 Nov(2004) 8. OgbayashS. TakashmaK.: "Mult-Agent Smulaton of Fund Crculaton n an Artfcal Economc System Involvng Self-Adjustng Mechansm of rce roducton and Investment" "ICIC Express Letters" Vol.4 No.3(2010)877-884.7. 9. Bak.: how nature works: "the scence of self-organzed crtcalty" Coperncus Books (1999). 10. IMF : "World Economc and Fnancal Surveys World Economc Outlook Database" October 2010 http://www.mf.org/external/pubs/ft/weo/2010/02/weodata/ndex.aspx 11. Cabnet Offce Government of Japan Offce for Econometrc Analyss : "Economc and Fscal Model (ver.2010)" Economc and Socal Research Insttute Cabnet Offce (2010) 12. SakumaT et. al. : "The ESRI Short-Run Macroeconometrc Model of the Japanese Economy: Basc Structure Multplers and Economc olcy Analyses (2011 verson)"economc and Socal Research Insttute Cabnet Offce Tokyo Japan ESRI Dscusson aper Seres No.259 January.(2011) p.p41-44