Influence of Inefficiency in Government Expenditure on the Multiplier of Public Investment

Transcription

1 Influence of Inefficiency in Governmen Expendiure on he Muliplier of Public Invesmen Shigeaki Ogibayashi, Kosei Takashima School of Social Science, Chiba Insiue of Technology, Chiba , Japan. Research Insiue, Chiba Insiue of Technology, Chiba , Japan. Absrac. Muliplier of public invesmen has been explained as he value of much more han 1 due o he indirec effec of public spending. However, i is repored ha acual mulipliers in real economy, someimes show he values less han 1, he reason of which has no been well explained in he lieraure. This paper analyzed he influence of inefficien public expendiure on GDP by boh agen-based model and heoreical derivaion of he equaion for he muliplier of public invesmen based on our revised version of Morishima s economic linkage able. Boh sudies indicae ha GDP decreases wih increasing he degree of inefficiency in public expendiure which is defined as he raio of he firm subsidy o he oal expendiure of he governmen and he muliplier of public invesmen becomes less han 1 when he degree of inefficiency is large enough as well as he raio of firm s invesmen spending o he oal amoun of subsidized fund is small enough. The reason for he occurrence of muliplier less han 1 is considered ha when he degree of inefficiency in public expendiure is large enough and firms are relucan o invesmen, much of he surplus amoun of subsidized funds could be deposied in he bank accoun, causing he decrease in he money sock in he marke. Keywords: Agen-Based Modeling, Inefficiency of Governmen Expendiure, Muliplier 1 Inroducion The economic effecs of fiscal policy have been sparked wide ineres especially since he grea recession from 007 o 009 [1]. For promoing economy while reducing governmen deficis, much aenion has been paid o undersanding how fiscal policy affecs he economy which is refleced in an ongoing debae over he size of he fiscal muliplier [1]. Muliplier of public invesmen has been explained as he inverse of marginal propensiy o save, according o he radiional economic heory []. I is also well known, however, ha acual muliplier of public invesmen is much less han he value expeced by he heory [3-8]. The muliplier of acual sysem is generally esi-

2 maed by hree mehods: macroeconomeric forecasing models, ime series models and dynamic sochasic general equilibrium (DSGE) models [1]. Alhough he esimaed values vary widely, i is widely recognized ha he muliplier could be less han one or negaive in some cases [1,3,4-8]. For example, Sugimoo [3] esimaes he muliplier of public invesmen in Japanese economy and repored ha he average muliplier ranges from 0.76 o 1.38 during he periods from 1955 o 001. Peroi [8] esimaed he muliplier of five advanced counries and repored ha he esimaed mulipliers of public invesmen range beween o 5.46, showing ha he muliplier could be no only less han one bu also negaive. A par of his discrepancy has been explained in he lieraure as he influence of oher facors such as he axaion and ransfer paymen o he households []. In addiion, Morishima [9] derived an equaion for he muliplier of public invesmen based on some reasonable assumpions under which he muliplier could be as low as 1.45, showing ha he muliplier is also affeced by he raio of impors and he firm s way of disribuion of he earnings surplus ec. However, hese facors only do no explain he reason why he muliplier shows less han one. Alhough here have been many argumens on his maer [1,5-8 ], he reason why he muliplier shows less han one is sill no conclusive. In his sense, here seems o be almos no previous papers ha quaniaively explained he reason why he acual mulipliers someimes show less han one or negaive. One ineresing sudy is he one presened by Peroi [8] who poined ou ha public invesmen migh be paricularly prone o poliical pressure and loaded wih porkbarrel projecs wih no economic raionale. In more exreme cases, i can foser downrigh corrupion and ren-seeking aciviies [8]. Alhough his explanaion seems o be reasonable, his idea was no evidenced by any quaniae analysis. On he oher hands, agen-based modeling (ABM) is considered o be one of good approaches o sudy he reason why he muliplier of public invesmen becomes less han one. The auhors have been working on agen-based modeling sudy on macroeconomic sysems, and poined ou wo hings in relaion o he muliplier under concern [10-13]. Firs, in ABM, here is one-o-one correspondence beween he macro phenomena and he model srucure ha is indispensable o reproduce he phenomena [10]. By sudying he model srucure ha is indispensable o reproducing he desired macro phenomena in erms of a series of compuer experimens, we can elucidae he underlined mechanism of he occurrence of he macro phenomena [10]. Second, in order o reproduce he posiive influence of ax cu, he model is required o include some degree of inefficiency in governmen expendiure, in which he inefficiency in governmen expendiure is defined as he raio of firm subsidy o he oal value of governmen expendiure [11, 1]. In he presen sudy, inroducing he idea of he inefficiency of governmen expendiure, which is defined as he raio of he firm subsidy o he oal expendiure of he governmen, we analyzed he influence of inefficien public expendiure on he muliplier of public invesmen as well as GDP by a series of compuer experimen based on he agen-based model of arificial economic sysems developed by auhors previous sudies [11-13]. In addiion, mahemaical equaions for he muliplier of public invesmen was derived based on our revised version of Morishima s economic linkage able, and he mechanism for he influence of he inefficiency of governmen

3 expendiure on he muliplier of public invesmen as well as he reason why he muliplier someimes shows less han one is discussed. Simulaion Model.1 Ouline of model The agen-based model of an arificial economic sysem in he presen sudy comprises consumers, producers, a bank, and a governmen as auonomous decisionmaking agens. I is assumed ha consumers and producers are divided ino hree ypes of agen, respecively. Each agen is heerogeneous in is sae variables and oher parameers included in heir acion rules. The ouline of agens and heir acion rules is given in Table 1. Table 1. Ouline of agens and heir acion rules.. Sequence of acions The se of acions of each agen comprises period-based unis, where one period is assumed o correspond o one monh in he real sysem. During each period, agens ac and inerac each oher according o a sequence of seven seps. In addiion, each agen records he ransacion daa according o double-enry bookkeeping mehod. A he end of he sequence for each period, each agens seles he accoun and a GDP value is calculaed based on an inpu-oupu able obained by summing up he accoun daa of each agen. The deails in he sequence of agens acion in each of he seven seps are described below. 1. Agens pay unpaid ax for previous period. Afer paying ax, agens make a budge plan for consumpion or public spending, wages o be paid for workers.. Raw-maerial-makers decide he amoun and price of producs o be produced, produce producs of several ypes of raw maerials and supply hem o he maerial goods marke.

4 3. Reailers decide he amoun and price of producs o be produced, purchase raw maerials in he maerial goods marke, produce producs of several ypes of consumpion goods and supply hose producs o he consumpion goods marke. Here, he price and amoun of producion are influenced by he resul of purchasing raw maerials in he maerial goods marke before producion. 4. Each of he consumers, reailers, raw-maerial-makers and he governmen purchases producs in he consumpion goods marke according o heir consumpion preferences. 5. Each firm pays wages for employees and execuive compensaion for he execuive and he governmen pays wages for public worker. 6. Reailers and raw-maerial-makers judge he necessiy of invesmen on he basis of oal sales in he previous periods and, if necessary, inves in equipmen by purchasing a se of equipmen from equipmen maker. 7. Each agen seles is accouns hrough a double-enry bookkeeping mehod, where he income or profis for he curren erm is calculaed, based on which he amoun of ax o be paid is deermined. If necessary each reailer dismisses a worker on he basis of profis for he curren and previous periods or decides o sop producion of a cerain ype of producs on he basis of is oal sales..3 Ouline of agen s decision-making rules.3.1 Behavioral rules of consumers Consumers make budge for consumpion E b which is defined as he sum of par of income I defined by Keynesian consumpion funcion and wihdrawal raio r wd imes of he bank deposi D a each fiscal period as shown in Equaion (1), where r i_ax is income ax rae, a is basic consumpion and b is he marginal propensiy o consume of Keynesian consumpion funcion. The wihdrawal raio r wd is given a random for each agen. E = a + bi ) + r b ( 1 ri _ ax wd D (1) When purchasing producs in consumpion goods marke, consumers selec and purchase producs wihin he limi of budge for consumpion. The class and number of he producs o purchase are decided so as o maximize he uiliy according o he uiliy funcion given by Equaion (), where w i is he weigh of uiliy for each ype of class i which is randomly assigned for each agen, x i is he number of producs o purchase, p i is he price of produc andα is an exponen of x i ranging beween 0 and 1. When here are goods of he same class available in he marke a differen prices, he consumers selec and purchase he cheapes one among hem. α max u = w x s.. p x E i i i i i i b () Each of he consumers makes wo ypes of decision making a each period, deciding he class of producs o purchase and he amoun o purchase

5 Wih respec o deciding he class of producs, each of he consumers has is own uiliy for each of he class of producs which is also a funcion of he number of producs o be bough, and decides o purchase he combinaion of he class and number of consumpion goods so as o maximize his uiliy funcion..3. Behavioral rules of producers The reailers and raw maerial makers boh decide on he amoun and price of he producs hey will produce. The price of a produc in a produc class increases or decreases, depending on how much of he produc is in sock a he end of previous period. Producion levels are decided in such a way ha he probabiliy of being ou of sock is less han 5%. This is esimaed based on he oal sales over he mos recen en periods. If he esimaed producion is less han 70% of producion capaciy, he minimum amoun of producion is se a he 70% level. The producion capaciy, Y, is defined by he Cobb-Douglas producion funcion [3], as shown in Equaion (3), where K is he number of unis of equipmen used in producion, L is he number of employees, and α is assumed o be 0.5. In addiion, A is a proporionaliy consan assigned randomly o each producer beween a lower and upper limi. I is assumed ha his value is peculiar o each producer, and represens ha producer s echnical capabiliy. Y α 1 α i ( K, L) = Ai K L (3) Reailers and raw maerial makers iniially have one uni of equipmen and a specified number of employees. They will inves o increase heir producion capaciy when producion a maximum capaciy coninues beyond a criical period, based on he expeced profi. They decide o inves when he expeced financial benefi given by Equaion (4) is posiive. Here, p i is price of a produc of class i, c is he variable cos per uni produc, r 0 is he borrowing ineres rae, F is he amoun borrowed o buy one uni of equipmen, N is he repaymen period, and w is he fixed wage per employee. I is assumed ha he depreciaion period of he equipmen is he same as he repaymen period. { Y ( K + 1, L) Y ( K, L) } ( r 1/ N) ] p = max[( p c ) 0 F (4) K i i i i + i When hey decide o inves, half of he necessary funds are financed by he bank and he res is financed by he firm s inernal funds. The funds for invesmen financed from he bank are repaid as a fixed amoun in each period and for a consan number of consecuive repaymen periods. During he repaymen periods, addiional invesmen is no longer allowed when he oal number of invesmens exceeds a cerain upper limi. The equipmen maker produces equipmen in accordance wih he requiremens of he reailers and raw-maerial-makers wihin is producion capaciy limi. In he presen sudy, he price of he equipmen is assumed o be consan. One execuive and several workers are assigned o each of he producer agens. The producers pay a wage o workers and he wage plus execuive compensaion o

6 he execuive in each period. The execuive compensaion in he real world comprises a paid salary, a bonus, and long-erm incenives. In he presen model, he paid salary is assumed o be he same as he wages paid o workers, he long-erm incenives are ignored, and only he bonus is defined as he execuive compensaion which is paid from afer-ax profis. Wages comprise a fixed salary, randomly assigned o each employee beween a lower and an upper limi, and a bonus given when he producer s profi is posiive. The oal spen on wages for each producer, E w, is given in Equaion (5), where W f is he oal fixed salary, W b is oal amoun paid in bonuses, EC is he amoun paid as execuive compensaion, π is he profi before ax, and AC is accumulaed earnings. In addiion, W b is defined as r b π, where r b is he bonus raio, and EC is he execuive compensaion raio muliplied by he afer ax profi, and defined as π (1-r b )(1-r c_ax )r e, where r c_ax is he corporaion ax rae and r e is he execuive compensaion raio. W f Ew = W f + Wb W f + Wb + EC if if if π < 0 (5) π > 0 and AC < 0 π > 0 and AC > Bank agen behavior rules The bank lends money in he form of long-erm loans o producers (in line wih heir demands for invesmen), charging a 3% ineres rae. The bank also lends money o producers in he form of shor-erm loans so ha hey may mee heir requiremens when heir working capial o pay fixed wages and/or purchase raw maerials becomes sufficienly depleed. In he presen sudy, he bank is iniially given a very large quaniy of funds so ha here is no limiaion on lending o producers, excep in he case where long-erm loan paymens are no fulfilled during he repaymen period..3.4 Governmen agen behavior rules The governmen collecs corporae ax and income axe, pays wages o public employees, and uses he resulan money for public expendiure according o he expendiure policy. The wages of public employees are deermined a each fiscal period so ha hey are equal o he average income of privae employees. As for expendiure policies, marke purchasing, firm subsidy, and combinaions of hese are esed. Marke purchasing is an exremely case of efficien public expendiure in which he governmen direcly purchases goods in he marke a he marke price. This policy corresponds o he public expendiure where he governmen places job orders wih firms in a compleely compeiive siuaion a he marke price. Firm subsidy is an exremely case of inefficien public expendiure in which he governmen evenly disribues funds o producers wihou any resricions on heir use. Much of he funds disribued could be ransferred o he bank accoun wihou being used in he marke. This policy corresponds o he public expendiure where he governmen places job orders a a much higher price level han expeced in he marke or pays money for jobs ha have no economic value.

7 For esimaing he muliplier of public invesmen, he governmen spends addiional expendiure ΔG during he specified periods in he simulaion which is assumed o be financed by he issuance of governmen bonds. For simplificaion, however, addiional expendiure for public invesmen ΔG is simply added o he oal budge obained from he ax revenue, wihou aking ino accoun he bond marke and relevan ransacions. 3 Simulaion Condiions For he analysis of he influence of inefficiency in governmen expendiure on he muliplier of public invesmen, a series of compuer experimens are sysemaically conduced, changing he specific condiions one by one wih oher condiions being kep consan. Simulaion condiions as experimenal levels are shown in Table. As given in Table, five facors are employed as experimenal levels, which are 1 he upper limi on he number of loans which is an index for he credi resricion, hreshold on he decision making on invesmen which means he criical number of periods during which firms ake ino accoun he oal sales for he decision making on invesmen (i.e. if he producion a maximum capaciy wih he sae being sold ou coninues beyond his criical periods, he firm is assumed o decide o inves), 3 he iming of public invesmen in business cycles, 4 oal amoun of he funds for public invesmen, and 5 he degree of he inefficiency in governmen expendiure. Table. Simulaion condiions as experimenal levels These experimenal facors and levels are described in more deail as follows. The upper limi on he number of loans is he maximum number of loans ha he firms can have in he same period, which are assumed o be or 3, he former corresponds o severer credi resricion. The hreshold on he decision making on invesmen is he number of periods wih no socks. If he sae being ou of sock coninued under he producion wih maximum capaciy he firms decide o inves. This number corresponds o he firms willingness for invesmen, which is assumed o be 10, or 0, he former corresponds o he firms being posiive in invesmen. The iming of public invesmen in business cycles is he period for he governmen o sar invesmen, which is assumed o be jus before he boom in a cyclic variaion in GDP (i.e. business cycle), jus afer he boom, during he middle of growing sage, during he middle of declining sage, or near he peak. Here, he oal amoun of he funds for invesmen is divided ino 1 pars, and each incremen of he public in-

8 vesmen is coninuously added o he budge during 1 periods for purchasing capial goods or subsidizing o he firms, depending on he degree of he inefficiency in governmen expendiure. Here, exac period of he peak or boom in business cycle varies for differen experimenal levels on he upper limi on he number of loans ( or 3; wo levels) and he hreshold on he decision making on invesmen(10 or 0; wo levels). Therefore, exac periods for he sar of he invesmen were se differenly depending on he 4 experimenal levels, which were analyzed by prior experimen in he condiion wihou public invesmen. Toal amoun of he funds for public invesmen were also changed o be small, middle or large as experimenal levels which are se 1.5, 1.5 and.,0 imes respecively, of he sandard value calculaed based on he average ax revenue during 360 periods. The sandard value on he average value of he ax revenue was priory calculaed for each of he 4 experimenal levels saed above under he condiion wihou public invesmen, assuming he degree of he inefficiency in governmen expendiure is zero. The inefficiency in governmen expendiure was changed for 0% o 100% wih an inerval of 10% for each of he above menioned 60 condiions( levels for each of 1,, 5 levels for 3, 3levels for 4) The muliplier due o he public invesmen is calculaed based on equaion (6), in which he incremen of he increase in GDP due o he public invesmen is assumed o be he average of he difference beween he GDP afer he invesmen and ha before he invesmen. DGDP = sar + 1 ( = sar GDP GDP 1DG sar ) (6) The simulaion condiions wih respec o he base condiion oher han experimenal facors are given in Table 3.

9 Table 3. Simulaion condiion of non-experimenal level 4 Simulaion Resul Fig.1 shows he variaion of GDP during he whole simulaion periods, showing business cycle caused by he repeiion of bank financing for he firm s invesmen and he subsequen repaymen. GDP a each period as well as he average GDP during he whole periods of simulaion, becomes smaller as he inefficiency in governmen expendiure becomes larger, as shown in Fig.1 and Fig.. This endency is caused because a par of he money ransferred o he firms in he form of firm subsidy as a resul of he inefficien governmen expendiure is saved in he bank accoun wihou being consumed in he marke, resuling in he decrease in he money sock in he marke, as revealed in our previous sudy [9]. Fig. 1. Influence of inefficiency of governmen expendiure on GDP circulaion

10 Fig.. Influence of inefficiency of governmen expendiure on he GDP average of 360 periods The inefficiency in governmen expendiure also affecs he muliplier of public invesmen. An example of his endency is shown Fig.3, in which public invesmen sared jus before he boom of a business cycle, which is near he 140 periods in Fig 1. I is noed in Fig.3 ha he muliplier decreases wih an increase in he degree of inefficiency in governmen expendiure; i becomes less han one when he inefficiency exceeds 50% when he amoun of he funds for public invesmen is large. When ha amoun is small, he muliplier becomes negaive when he inefficiency is large enough, bu his is only because he amoun of funds for invesmen is no enough compared wih he ampliude of he cyclic variaion in GDP. Hereafer, herefore, only he calculaed resul in he case wih large amoun of funds for invesmen will be presened. In order o undersand he reason why he muliplier decreases wih an increase in he inefficiency in governmen expendiure, oal amoun of firms deposi and he firms balance of loan were analyzed. As shown in Fig.4, wih an increase in he inefficiency in he governmen expendiure, he balance of he loan decreases and he firms deposi in he bank increases. This resul suggess ha a leas a par of he funds ransferred o he firms as a resul of he inefficien governmen expendiure, will be used by firms for increasing he bank deposi as well as for decreasing he balance of loan by he repaymen, causing a decrease in money sock in he marke, hus decreasing he muliplier. The muliplier decreases wih an increase in he inefficiency in public expendiure, because his endency becomes larger when he inefficiency in governmen expendiure is larger. Fig. 3. The muliplier of public invesmen as a funcion of he inefficiency in governmen expendiure, calculaed under he condiion where he public invesmen is conduced before he boom sage, he loan limi is and he invesmen hreshold is 0.

11 Fig. 4. The influence of he inefficiency in governmen expendiure on he amoun of firms deposi and loan, calculaed under he condiion where he public invesmen, he amoun of which is large, is conduced before he boom sage, he loan limi is and he invesmen hreshold is 0. The decreasing endency of he muliplier wih an increase in he degree of inefficiency in governmen cexpendiure is consisenly observed when he iming of public invesmen is changed in five experimenal levels as shown in Fig.5. When he muliplier in he case of differen iming of public invesmen, he muliplier in he case of he iming of invesmen in growing sage or in he sage jus afer he boom shows larger muliplier compared wih oher condiions. The reason for his endency is ha, invesmen is more frequenly occur in hese cases of he iming of public invesmen han in oher cases, hus making he public invesmen increase GDP more effecively. Fig. 5. The muliplier as a funcion of he inefficiency in governmen expendiure for various imings of governmen expendiure in business cycles, calculaed under he condiion where he amoun of he public invesmen is large, he loan limi is and he invesmen hreshold is 0. The willingness of firms o inves also affecs he muliplier. The index for he willingness of invesmen in he presen simulaion is inroduced in erms of he number of loans and he hreshold on he decision making on invesmen as given in Table 3. As shown in Fig.6, he muliplier becomes larger when he hreshold on he decision making on invesmen is large. Alhough, he influence of he number of loans is no significan his resul suggess ha he muliplier becomes larger when he firms mind for invesmen is larger.

12 Fig. 6. Influence of hreshold on decision making on invesmen on he relaionship beween he muliplier of public invesmen and he inefficiency in governmen expendiure calculaed under he condiion where he amoun of he public invesmen is large and he public invesmen is conduced before he boom sage. 5 Analysis of he muliplier of public invesmen based on economic linkage able In he auhors previous sudy [11], i has been revealed ha he posiive muliplier of he reducion in income ax is only reproduced in ABM when some degree of he inefficiency in governmen expendiure is assumed, and he muliplier decreases wih an increase in he inefficiency in governmen expendiure. The reason for he dependency of he muliplier on he inefficiency in governmen expendiure is ha he muliplier of ax reducion become posiive only when he marginal propensiy o consume of he governmen is smaller han ha of he privae secor which decreases wih an increase in he inefficiency in governmen expendiure because a par of he subsidized funds is likely o be deposied in he firms bank accouns wihou being consumed in he marke [1]. In addiion, in he auhors previous sudy on he effec of he reducion in corporae ax on GDP, i has been revealed ha in order o reproduce posiive muliplier in corporae ax reducion, he model srucure is required o include no only he inefficiency in governmen expendiure bu also include he execuive compensaion and he uilizaion of inernal funds for invesmen. Based on hese previous sudies, he presen sudy analyzed he influence of he inefficiency in governmen expendiure by ABM approach and elucidaed as shown in he previous secion of his paper ha he muliplier of public invesmen is grealy influenced by he inefficiency in governmen expendiure and he muliplier could be less han one when he inefficiency in governmen expendiure is large enough. On he oher hand, a mahemaical model in which economical equilibrium is assumed is anoher approach o analyze he muliplier of public invesmen and has an advanage in obaining he insigh of underlined mechanism. Morishima derived a se of equaions for he muliplier of public invesmen based on an economic linkage able, assuming an indusrial sociey where no primary secor of indusry exiss and all of he raw maerials are impored from ouside of he sociey. Morishima s model, however, has some poins o be revised. In Morishima s able of economic linkages, a managemen secor of a firm who pays corporae ax does no exis, and herefore, an

13 enrepreneur has a role of boh an execuive and a managemen secor of a firm. In addiion, he inefficiency in governmen expendiure is also no aken ino accoun. In his case, he governmen expendiure for public invesmen is assumed o be direcly consumed in he marke a he marke price. In he presen sudy, herefore, we divide he enrepreneurs in Morishima s sudy ino execuives who receive execuive compensaion as well as paying income ax, and a managemen secor who pay corporae ax. In addiion, o consider he inefficiency of public expendiure, we divide governmen expendiure pg, in Morishima s able ino (1-η)pG for buying goods and ηpg for a subsidy, which is added o he profi of firms, where η is he inefficiency in governmen expendiure. Table 4 shows he revised able of economic linkages. Using he Table 4, le us derive a se of equaions for he muliplier of public invesmen based on he Morishima s assumpions and procedure for he derivaion of he eauaions. According o Morishima, we can se he following assumpions. Columns 1 and in Table 4 represen price-deermining equaions in producion secors and he sum of each column is zero. Oher columns show he budge equaions for each economic agens and he sum of each column can be se zero if he funds circulaion can be assumed in equilibrium. In addiion, he sum of each row can be se zero, if we can assume ha 1 prices of consumpion goods and capial goods are consan respecively because he producion is flexibly adjused and any excess amoun in demand as well as supply does no occur in boh indusries. moneary marke is in equilibrium, 3 sock marke is no aken ino accoun, demand and supply in bond marke as well as foreign exchange marke are in equilibrium and exchange rae is consan, and so on. In he presen sudy, i is also assumed ha reniers and bond marke in Table 4 do no exis. Under hese assumpions, an aggregae increase in he producion of capial goods due o he invesmen in public or privae secor may resul in an increase in he income and consumpion of each economic agen, hus induces an aggregae increase in he producion of consumpion goods. This resuls in an increase in GDP which is calculaed as he sum of he increased demand in boh consumpion and capial goods minus oal paymen for impored maerials. Table 4. Economic linkage able usded in he presen analysis which is a revised version of Morishima s able. [See ref. 9]

14 5.1 Derivaion of he equaion for he muliplier of public invesmen Muliplier of public invesmen for capial goods where required funds are all financed by he governmen deb. Le s us derive a se of equaions for he muliplier of public invesmen, assuming ha he public invesmen is conduced in he capial goods marke, he inefficiency in governmen expendiure is aken ino accoun and he budge for public invesmen does no affec he public spending based on he ax revenue. Under his assumpion, if he amoun of public invesmen and he inefficiency in governmen expendiure are denoed by G, and η,respecively, governmen s consumpion for direcly purchasing capial goods is represened by ( 1 η ) G,and η G represens governmen s ransfer paymen in he form of firm subsidy which migh be added o he firm s earnings surplus. In addiion, i is assumed ha βimes of η G is used for he invesmen by firms. Under hese assumpions, he increased incremens of he oal demand for capial goods and consumpion goods are given in equaions (7) and (8) respecively, where w p1d D1 is he increased incremen of he oal demand for consumpion goods by e he workers and is ha by he execuives. p1dd1 p βη (7) ( η G X = G + 1 ) w e p1 X1 = p1dd1 + p1dd1 D (8) The increased demands by workers and execuives are represened as given in equaion (9) where W and Π are he increased income of workers and execuives respecively which are given in equaion (10) because he sum in row 3 or row 7 is zero. w e 1 1 = cw( 1 w) W, p1 1 = ce(1 e)(1 m p (9) ) α Π W = wa η (10) 31 X1 + wa3 X, Π = mc1 X 1 + mc X + G Subsiuing equaions (9) and (10) ino equaion (8), he increased demand of consumpion goods is represened as given in equaion (11). p b ' 1 X1 = p X (11) 1 b1 where, β 1 = c β ' = c (1 ) w (1 ) w w w w p 1 w p α α c (1 )(1 e + c (1 )(1 e e e m c1 ) αm p m 1 c ) α m p η + 1 (1 β ) η

15 Equaion (11) represens he increased demand in consumpion goods indusry which is induced by he increase in demand in capial goods indusry resuled by he public invesmen. The increase in GDP by public invesmen is calculaed as he sum of he increased demands in boh consumpion and capial goods indusries minus oal paymen for impored maerials as given in equaion (1), where u 1, u represens he raio of impored maerials in he price of consumpion goods and capial goods respecively. b ' Y = ( 1 µ 1 ) + (1 µ ) p X (1) 1 b1 p * p were µ = r a µ = r 5 5, 1 51, a5 p1 p Subsiuing equaion (7) ino equaion (1), muliplier of public invesmen is given in equaion (13). * Y G β ' = ( 1 µ 1) + (1 µ ) ) 1 β1 { 1 (1 β η} (13) 5. Muliplier of public invesmen for capial goods under balanced budge condiion. When a par of he required funds for public invesmen γ G, where = 0~1,is financed by he ax revenue, governmen consumpion oher han he invesmen is decreased by γ G, resuling in he decrease in he muliplier of public invesmen. Le he governmen consumpion based on he ax revenue is efficienly conduced in he consumpion goods marke. Then equaions (8) and (13) are revised as equaion (14) and equaion (15), respecively. w e 1 X1 = p1dd1 + p1dd1 DG p D γ (14) γ Y G β " = ( 1 µ 1) + (1 µ ) ) 1 β1 { 1 (1 β η} (15) where, " ' γ β = β {1 (1 β ) η 5.3 The approximae numerical values of he muliplier of public invesmen Assuming ypical values for he parameers included in equaion (9), he numerical values of he muliplier of public invesmen are esimaed for various influenial fac-

16 ors such as he inefficiency in governmen expendiure, raio of he profis disribued o he execuives, ec. Le he workers marginal propensiy o consume c w be 0.9 and ha of he execuives c e, 0.4. The income ax raes for he workers and he execuives are assumed o be boh 0%. The indirec-ax rae on consumpion goods and ha on capial goods are boh 5% (ha is, 1 = =0.05), while he rae of mark-up m is 30%. Supposing ha he capial goods indusry is more labor-inensive han he consumpion goods indusry, le us assume ha he wages per uni of oupu in he capial goods indusry amouns o 50% of he price of he produc, while he same figure is only 40% in he consumpion goods indusry (ha is wa 31 /p 1 =0.4, wa 3 /p =0.5). Given hese numerical values, we can calculae boh c 1 /p 1 and c/p a In addiion, le he marginal propensiy o impor of each indusry wih respec o is oupu is 10% (i.e. μ 1 = μ =0.1). Given hese numerical values, we can calculae he muliplier of public invesmen for various values of is influenial facors. Fig. 7 shows he muliplier of public invesmen as a funcion of he degree of inefficiency in governmen expendiure for various values of he raio of profis o be disribued o execuives α, assuming haβ equals zero. Fig. 7. Influence of he inefficiency in governmen expendiure and he raio of he execuive compensaion, where β=0. As shown in Fig. 7, muliplier of public invesmen is grealy influenced by he degree of inefficiency in governmen expendiure. The muliplier can be less han one if he degree of inefficiency in governmen expendiure is 30% or more. The raio of profis o be disribued o execuives α also affecs he muliplier, bu he degree of is influence is no so large. The reason why he muliplier increases wih increasing α is ha a par of he earnings surplus of a firm disribued o he execuives increases he oal demand for consumpion goods by he execuives. I is noed in Fig. 7 ha he muliplier is around 1.4 when he inefficiency in governmen expendiure is zero, which is almos similar value o ha of Morishima s analysis and is much smaller compared wih he inverse of marginal propensiy o save. This is because he ne effec of invesmen in GDP is decreased due o he paymen of axes, accumulaion of earnings surplus of firms and he paymen of impored maerials. However, hese facors only canno accoun for he muliplier ha is less han one. I is also noed ha in he case of Morishima s analysis where he inef-

17 ficiency in public invesmen is no aken ino accoun, he muliplier of public invesmen in he capial goods indusry is he same value wih he muliplier of invesmen conduced by he firms as far as he invesmen in capial goods indusry is concerned. In oher words, here is no difference beween he invesmen in capial goods indusry by he governmen and ha by privae firms. However, i is considered reasonable o consider ha here mus be big difference beween he invesmen by he governmen and ha by privae firms, which will be discussed in he nex secion. In he case where β imes of he funds disribued o he firms by public invesmen in he form of firm subsidy is used for he firms invesmen, he muliplier becomes larger wih an increase in he value of β as illusraed in Fig.8, and ifβ=1, he influence of he inefficiency in governmen expendiure disappears. This is because whenβ=1, all of he funds supplied by public invesmen, including he one disribued o he firms, are used for he invesmen for capial goods indusry. Fig. 8. Influence of he inefficiency in governmen expendiure on he muliplier of public invesmen and he influence of β in equaion (3), where α=0.5. When he funds required for public invesmen are in some exen, financed by he ax revenue, muliplier is grealy decreased as shown in Fig.9.This resul suggess ha he main reason for he occurrence of negaive muliplier is ha he funds for public invesmen are no financed 100% deb, bu financed by he ax revenue in some exen. Fig. 9. Muliplier as a funcion of he inefficiency in governmen expendiure for various degree of balanced budge condiions (i.e. γ=1:100% balanced budge,γ=0:100% deb-financing, where α=0.5,β=0).

18 6 Discussions --- Wha is he reason why muliplier becomes so small and wha is he source of he inefficiency in governmen expendiure in he acual sysems ---. The resuls of he agen-based modeling approach (see Fig. 3-Fig. 6) and mahemaical model approach (see Fig. 7-Fig. 9) in he presen sudy consisenly elucidae ha he muliplier of public invesmen is grealy influenced by he inefficiency in governmen expendiure. Therefore, he direc answer o he quesion why muliplier becomes as small as less han one is ha he effec of public invesmen on he economy is grealy deerioraed by he inefficien governmen expendiure. Then he nex quesion is he reason why governmen expendiure is likely o be inefficien. As menioned in he previous secion, here mus be big difference beween he invesmen by he governmen and ha by privae firms. One of he big differences beween hem is considered ha he governmen has less incenive in minimizing he cos han privae firms. The amoun of paymen for purchasing goods or services by he governmen is likely o be larger han heir economic value. The difference beween hem is somehing like a ransfer paymen o he firms or firm subsidy wihou any resricion on i use. The money hus disribued o he firms is likely o be saved in he bank as earnings surplus wihou being used in he economic aciviies, causing he decrease in he muliplier wih an increase in he degree of inefficiency in governmen expendiure as indicaed in Fig. 7. As explained in he beginning of his secion, he inefficiency in public expendiure is defined in he presen sudy as he raio of he governmen expendiure for firm subsidy o he oal amoun of public spending. In he acual economy, he ransfer paymen o he firms such as firm subsidy is included in various manners. Examples are as follows; direc ransfer paymen o he firms for heir specific economic aciviies in he case of he privaizaion of governmen s specific funcion, governmen s selling public asses o he firms wih lower price compared wih he marke price, he difference of which corresponds o he firm subsidy in he presen sudy, a preferenial reamen by he governmen o a specific firm (i.e. so called ren-seeking), public paymen of wages or rewards for aciviies or businesses ha have no or less economic value including he firms indirec paymen o individuals or oher firms from he subsidized funds, ec. These kinds of ransfer paymen are no likely o be criicized because hey are ofen conduced nominally as policies for promoing economy or welfare. In any case, however, if he amoun of funds paid by he governmen o he firms or organizaions is larger han he marke value of heir economic aciviies, hen he difference corresponds o he firm subsidy in he presen sudy which causes inefficiency in governmen expendiure. The inefficiency in governmen expendiure defined in he presen sudy is hardly verified in he acual economy based on he accouning daa of he governmen, because i would be difficul o compare he governmen paymen wih marke value. I is well known, however, ha he public invesmen ofen resuls in he very small economic effec. In addiion, i would be rue according o he lieraure ha he muliplier of public invesmen in he acual economy ofen becomes very small value and

19 someimes show he value less han one. The presen sudy indicaes ha hese facs can be well undersood by inroducing he idea of inefficiency in governmen expendiure, which is considered o be he main reason why mulipliers are ofen so small compared wih he value expeced by he marginal propensiy o consume. On he bases of above-menioned discussion, i is considered ha he influence of he inefficiency in governmen expendiure on he muliplier of public invesmen shown in he presen sudy gives us an imporan implicaion abou he reasons why he repeiion of public invesmen in Japan since he collapse of bubble economy in 1989 had lile effec in simulaing he economy while increasing he balance of governmen bonds, and why he small governmen policies in he U.S. and UK in 1980 s was effecive. I is considered ha he reason why public invesmen is less effecive han he governmen s consumpion as poined ou by Peroi [8] is ha governmen has less incenive in minimizing he cos han firms in invesmen and public invesmen migh be likely o be subjeced o poliical pressure. 7 Conclusion The presen sudy analyzed he influence of he inefficiency in governmen expendiure on he muliplier of public invesmen by boh agen-based model and he mahemaical derivaion of he equaion for he muliplier of public invesmen based on an economic linkage able. Boh approaches indicae ha he muliplier of public invesmen is grealy influenced by he inefficiency in governmen expendiure, which is defined as he raio of he firm subsidy o he oal expendiure of he governmen. In addiion, he muliplier of public invesmen becomes less han 1 when he inefficiency is large enough and firms are relucan o invesmen. In he case of balanced budge condiion where funds for public invesmen are financed by he fiscal ax revenue in some exen, he muliplier could be negaive when he governmen expendiure is inefficienly conduced. I is considered ha he source of he inefficiency in governmen expendiure comes from he endency ha governmen has less incenive in minimizing he cos and in some cases public invesmen is likely o be subjeced o poliical pressure which migh resul in irraional public spending. If he governmen spending is more effecively conduced, while minimizing he cos as well as sanding agains poliical pressure in some cases, he muliplier of public invesmen could be expeced much larger, and i would be possible ha he public invesmen works well in promoing he economy, while he governmen deb being kep in a low level. References 1. Whalen, Charles J., and Felix Reichling.: The Fiscal Muliplier and Economic Policy Analysis in he Unied Saes. Conemporary Economic Policy,(015).. Krugman, P., and Wells, R. : Economics. nd Ediion. Worh Publishers,(009)

20 3. Sugimoo, A.: Reconsideraion of Mulipler Theory and Fiscal Policy, Managemen Informaion Research, Sesunan Universiy, vol. 16,No, pp.11-8 (008) 4. Muraa,K.,Saio,T.,Tanabe,K.,Iwamoo,K.: The ESRI Shor-Run macroeconomeric Model of Japanese Economy(005 version) Basic Srucure, Mulipliers, and Economic Policy Analyses-, ESRI Discussion Paper series No15, Economic and Social Research Insiue, Cabine Office, Japan (005) 5. Bruckner,M,Tuladhar,A: Public Invesmen as a Fiscal Simulus: Evidence from Japan s Regional Spending During he 1990s, IMF Working Paper, WP/10/110,(010) 6. The Effeciveness and Scope of Fiscal Simulus. OECD Economic Oulook, Inerim Repor March 009.pp Baum, A., Poplawski-Ribeiro,M., and Weber,A. :Fiscal Mulipliers and he Sae of he Economy." IMF Working Paper. Inernaional Moneary Fund.WP/1/86,(01) 8. Perroi,R.: Public Invesmen: Anoher(Differen) Look, Working Paper n.77,universia Bacconi, Via Salasco pp.1-47,(004) 9. Morishima, M. : The Economics of Indusrial Sociey. Cambridge Universiy Press.(1984) 10. Takashma,K.,Ogibayashi,S.:Model Srucure of Agen-Based Arificial Economic Sysem Responsible for Reproducing Fundamenal Economic Behavior of Goods Marke, The 5h World Congress on Social Simulaion, Nov.(014) 11. Ogibayashi,S.,and Takashima,K.: Influence of Governmen Expendiure Policies and Tax Rae on GDP in an Agen-Based Arificial Economic Sysem. In Agen-Based Ap-proaches in Economic and Social Complex Sysems VII (pp ). Springer Japan,(013). 1. Ogibayashi,S.,Takashima,K. : Influence of Corporaion Tax Rae on GDP in an Agen- Based Arificial Economic Sysem, Advances in compuaional Social Science, Springer japan, pp ,(014) 13. Ogibayashi, S., & Takashima, K. : Muli-Agen Simulaion of Fund Circulaion in an Arificial Economic Sysem Involving Self-Adjused Mechanism of Price, Producion and Invesmen. In Innovaive Compuing, Informaion and Conrol (ICICIC), 009 Fourh Inernaional Conference on, pp IEEE.(009)