Analysis of influential factors responsible for the effect of tax reduction on GDP

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1 Analyss of nflunal facors rsponsbl for h ffc of ax rducon on GDP Shgak Ogbayash, Kous Takashma and Yuhsuk Koyama 3, School of Socal Sysms Scnc, Chba Insu of Tchnology, Chba , Japan. shgak.ogbayash@-chba.ac.jp, akashma@og-lab.n 3 Collg of Sysms Engnrng and Scnc, Shbaura Insu of Tchnology 307 Fukasaku, Mnuma-ku, Saama-sh, Saama yuhsuk@shbaura-.ac.jp Absrac. Th facors rsponsbl for h ffc of a ax rducon on GDP ar analyzd usng boh agn-basd modlng (ABM), basd on h auhors prvous sudy, and a drvd s of quaons for ax rducon mulplrs, basd on Morshma s conomc lnkag abl. Th fndngs show ha, undr h balancd fnanc condon of govrnmn, h ax rducon mulplr s drmnd by h dffrnc bwn h ncras n dmand by consumrs or frms as a rsul of h ax rducon and h dcras n dmand by h govrnmn. To ncras h ffc of a ax rducon, s ncssary ha h ncrasd dsposabl ncom of consumrs or frms, as a rsul of h ax rducon, s mor lkly o b usd for consumpon and nvsmn. Kywords. Agn-basd modlng, Tax rducon, Mulplr, Publc xpndur, Balancd fnanc, Excuv compnsaon, Invsmn. Inroducon Agn-basd modlng (ABM) s wdly usd n socal smulaons o xplan or undrsand socal phnomna []. On mporan rsarch fld s h applcaon of ABM o macroconomc sysms, alhough hs sysms ar vry complx and nclud varous knds of agns and hr nracons. Whn usng ABM, s consdrd mporan ha h modl b as smpl as possbl, basd on KISS Prncpl, o undrsand h mos ssnal mchansms of h phnomna n quson []. Howvr, s also mporan o consdr all facors rqurd o rproduc h dsrd phnomna, bcaus h srucur of h arfcal sysm should b h sam as ha of h ral sysm o nabl h characrscs o mrg as hy do n h ral sysm. Esablshng h facors ssnal o rproducng h dsrd characrscs of h sysm can b don usng a srs of compur xprmns n whch only on consun facor of h modl s changd a a m, whl h ohr facors ar hld consan [, 3]. A numbr of ABM-basd rsarch suds hav focusd on varous macroconomc aspcs, such as busnss cycls, nnovaon, conomc growh, h rol of banks, monary polcs, ndusral dynamcs, and walh nqualy [4-7]. Mos of hs

2 suds rpord som nw fndng, bu h modl consuons wr dffrn n ach cas. Ths maks dffcul o dnfy h crucal assumpons of ach modl and o wha xn h assumpons ar mporan n rproducng h phnomna undr concrn. Rsarchrs hav also dvlopd rlavly mor praccal modls ha smula mulpl-mark conomc srucurs as laboraly as possbl [8, 9]. Howvr, gvn h naur of hs conomc phnomna, hs suds hav no fully clarfd h srucural facors of h modl ha ar mporan for hr rproducbly. Anohr ponal ara for applyng ABM n h ral world s govrnmn polcy formulaon, n aras such as ax rducon and publc xpndur. Accordng o Kyns mulplr hory [0], govrnmn publc xpndur and ax rducons ar ffcv polcs o promo a macro conomy. Howvr, h mulplrs of hs publc polcs ar rlavly small whn compard o h valus xpcd by h margnal propnsy o consum, h rason for whch s no wll undrsood. Movad by hs lack of undrsandng, h auhors consrucd a smpl, arfcal conomc modl conssng of consumrs, hr yps of producrs, a bank, and a govrnmn. Th condons rqurd for h modl o rproduc h posv nflunc of a ax rducon on GDP wr hn analyzd, wh h nnon of rvalng and xplanng h mchansm ha maks h publc polcy mulplr so low. Th fndngs show ha nffcncy n govrnmn xpndur, xcuv compnsaon, and nrnal funds for nvsmn ar all facors rsponsbl for h posv nflunc of a ax rducon on GDP. Hr, nffcncy of publc xpndur s dfnd as h rao of frm subsds o h sum of frm subsds and mark purchass [, ]. In h prsn sudy, addonal smulaons wr conducd o clarfy h mchansm xplanng why h abov facors n h modl ar rsponsbl for rproducng h posv nflunc of a ax rducon on GDP. In addon, w drvd a s of quaons for h ax rducon mulplr basd on our rvsd vrson of Morshma s conomc lnkag abl [3], and compard h nflunc of h abov-mnond facors agans h rsuls calculad usng ABM. In gnral, horcal approachs n macroconomcs ha assum compl qulbrum bwn dmand and supply and nglc h dvrsy of agns canno dscrb complx sysms wll. Howvr, hs approachs hav h advanag of bng abl o dscrb h mchansm bhnd h rlaonshps among h nflunal facors. In xplanng h nflunc of a ax rducon on GDP, mporan facor would no b h prc n qulbrum, bu h flow of funds among agns. In such cass, confrmng whhr h rsuls calculad usng ABM can b xpland by horcally drvd quaons could b an ffcv masur o valda h ABM sudy. Smulaon Modl. Ouln of modl Th agn-basd modl of h arfcal conomc sysm n h prsn sudy comprss consumrs, producrs, a bank, and a govrnmn as auonomous dcsonmakng agns. Consumrs and producrs ar ach dvdd no hr yps of agn.

3 Each agn s hrognous n s sa varabls and ohr paramrs ncludd n hr acon ruls. Tabl oulns h agns and hr acon ruls. Tabl. Ouln of agns and hr acon ruls.. Squnc of acons Th s of acons for ach agn comprs prod-basd uns, whr on prod s assumd o corrspond o on monh n h ral sysm. Durng ach prod, agns ac and nrac wh ach ohr accordng o a squnc of svn sps. A h nd of h squnc for ach prod, a GDP valu s calculad basd on an npu-oupu abl oband by summng ach agn s accoun daa. Th dals of h svn sps dscrbng h squnc of agns acons ar as follows:. Agns pay any unpad ax for h prvous prod. Afr payng ax, agns cra a budg plan for consumpon, payng wags, or publc spndng.. Raw maral makrs dcd on h amoun and prc of producs o b producd, produc svral yps of raw marals, and supply hs o h maral goods mark. 3. Ralrs dcd on h amoun and prc of producs o b producd, purchas raw marals n h maral goods mark, produc svral yps of consumpon goods, and supply hs producs o h consumpon goods mark. 4. Consumrs, ralrs, raw maral makrs, and h govrnmn purchas producs n h consumpon goods mark. 5. Ralrs and raw maral makrs judg h ncssy of nvsmn basd on oal sals n prvous prods and, f ncssary, nvs n qupmn. 6. Each frm pays wags o mploys and xcuv compnsaon o h xcuv, and h govrnmn pays wags o publc workrs. 7. Each agn sls s accouns usng h doubl-nry bookkpng mhod. Thy calcula hr ncom and prof for h currn rm, and hn drmn h amoun of ax o b pad basd on hs fgurs. If ncssary, a ralr may dsmss a workr, dpndng on h profs of h currn and prvous prods, or may dcd o sop producng a cran yp of produc aloghr, dpndng on s oal sals.

4 .3 Ouln of agn s dcson-makng ruls.3. Consumr agn bhavor ruls Consumrs cra a budg for consumpon, E b. Ths budg s dfnd as h sum of h rms basd on afr-ax ncom I (-r _ax )(rprsnd by h Kynsan consumpon funcon [0]), and a whdrawal rao of r wd ms hr bank dpos, D, a ach fscal prod,. Th formula for h budg s shown n Equaon (). Hr, r _ax s h ncom ax ra, a s h consumr s basc consumpon, and b s h margnal propnsy o consum as pr h Kynsan consumpon funcon. Th whdrawal rao, r wd, s slcd randomly for ach agn durng ach prod. E = a + bi ) + b ( r _ ax rwd D () Whn purchasng producs n h consumpon mark, consumrs slc and purchas producs whn h lm of hr consumpon budg accordng o h uly funcon for ach class of producs gvn by Equaon (). Hr, w s h wgh of h uly for ach yp of class,, whch s randomly assgnd o ach agn, x s h numbr of producs purchasd, p s h prc of a produc, andα s an xponn of x rangng bwn 0 and. Whn hr ar goods of h sam class avalabl n h mark a dffrn prcs, consumrs slc and purchas h chaps avalabl. α max u = w x s.. p x E () b.3. Producr agn bhavor ruls Th ralrs and raw maral makrs boh dcd on h amoun and prc of h producs hy wll produc. Th prc of a produc n a produc class ncrass or dcrass, dpndng on how much of h produc s n sock a h nd of prvous prod. Producon lvls ar dcdd n such a way ha h probably of bng ou of sock s lss han 5%. Ths s smad basd on h oal sals ovr h mos rcn n prods. If h smad producon s lss han 70% of producon capacy, h mnmum amoun of producon s s a h 70% lvl. Th producon capacy, Y, s dfnd by h Cobb-Douglas producon funcon [0], as shown n Equaon (3), whr K s h numbr of uns of qupmn usd n producon, L s h numbr of mploys, and α s assumd o b 0.5. In addon, A s a proporonaly consan assgnd randomly o ach producr bwn a lowr and uppr lm. I s assumd ha hs valu s pcular o ach producr, and rprsns ha producr s chncal capably. Y α α ( K, L) = A K L (3) Ralrs and raw maral makrs nally hav on un of qupmn and a spcfd numbr of mploys. Thy wll nvs o ncras hr producon capacy whn producon a maxmum capacy connus byond a crcal prod, basd on h xpcd prof. Thy dcd o nvs whn h xpcd fnancal bnf gvn

5 by Equaon (4) s posv. Hr, p s prc of a produc of class, c s h varabl cos pr un produc, r 0 s h borrowng nrs ra, F s h amoun borrowd o buy on un of qupmn, N s h rpaymn prod, and w s h fxd wag pr mploy. I s assumd ha h dprcaon prod of h qupmn s h sam as h rpaymn prod. { Y ( K +, L) Y ( K, L) } ( r / N) ] π = max[( p c ) 0 F (4) K + Whn hy dcd o nvs, half of h ncssary funds ar fnancd by h bank and h rs s fnancd by h frm s nrnal funds. Th funds for nvsmn fnancd from h bank ar rpad as a fxd amoun n ach prod and for a consan numbr of conscuv rpaymn prods. Durng h rpaymn prods, addonal nvsmn s no longr allowd whn h oal numbr of nvsmns xcds a cran uppr lm. Th qupmn makr producs qupmn n accordanc wh h rqurmns of h ralrs and raw-maral-makrs whn s producon capacy lm. In h prsn sudy, h prc of h qupmn s assumd o b consan. On xcuv and svral workrs ar assgnd o ach of h producr agns. Th producrs pay a wag o workrs and h wag plus xcuv compnsaon o h xcuv n ach prod. Th xcuv compnsaon n h ral world comprss a pad salary, a bonus, and long-rm ncnvs. In h prsn modl, h pad salary s assumd o b h sam as h wags pad o workrs, h long-rm ncnvs ar gnord, and only h bonus s dfnd as h xcuv compnsaon whch s pad from afr-ax profs. Wags comprs a fxd salary, randomly assgnd o ach mploy bwn a lowr and an uppr lm, and a bonus gvn whn h producr s prof s posv. Th oal spn on wags for ach producr, E w, s gvn n Equaon (5), whr W f s h oal fxd salary, W b s oal amoun pad n bonuss, EC s h amoun pad as xcuv compnsaon, π s h prof bfor ax, and AC s accumulad arnngs. In addon, W b s dfnd as r b π, whr r b s h bonus rao, and EC s h xcuv compnsaon rao mulpld by h afr ax prof, and dfnd as π (-r b )(-r c_ax )r, whr r c_ax s h corporaon ax ra and r s h xcuv compnsaon rao. W f Ew = W f + Wb W f + Wb + EC f f f π < 0 (5) π > 0 and AC < 0 π > 0 and AC > 0 Ralrs also hav a dsmssal rul and bankrupcy rul, dals of whch ar prsnd n h ODD proocol gvn n h Appndx..3.3 Bank agn bhavor ruls Th bank rans h surplus mony of ohr agns n hr rspcv bank accouns, arns nrs on long-rm and shor-rm loans, and pays wags o s mploys and axs o h govrnmn n ln wh s nrs ncom. Th bank lnds mony as long-rm loans o producrs n ln wh hr dmands for nvsmn, chargng a 3%

6 nrs ra. Th bank also lnds mony as shor-rm loans o producrs o m hr rqurmns whn hr workng capal o pay fxd wags and/or purchas raw maral bcoms suffcnly small. In h prsn sudy, h nal funds avalabl o h bank s s o b vry larg so ha hr s no lmaon on lndng o producrs, xcp n h cas whn long-rm loans ar no fulflld durng h rpaymn prods..3.4 Govrnmn agn bhavor ruls Th govrnmn collcs corporaon ax and ncom ax, pays wags o publc mploys, and uss h rsulan mony for publc xpndur, accordng o hr xpndur polcy. Corporaon ax s only collcd whn h prof of h producr s posv, and h ax ra s assumd o b consan. Incom ax s also assumd o b consan and s collcd accordng o h consumr s ncom. Th wags of publc mploys ar drmnd a ach fscal prod so ha hy ar qual o h avrag valu of a prva mploy s combnd fxd wag and bonus. Wh rgards o xpndur polcs, mark purchasng, frm subsdy, and combnaons of h wo ar sd. Mark purchasng s an xrm cas of ffcn publc xpndur n whch h govrnmn drcly purchass goods a h mark prc. Ths polcy corrsponds o h cas whr h govrnmn placs job ordrs wh frms n a complly compv suaon a h mark prc. Frm subsdy s an xrm cas of nffcn publc xpndur n whch h govrnmn dsrbus funds o producrs vnly, whou any lmaons on hr us. Ths polcy corrsponds o h cas n whch h govrnmn placs job ordrs a a much hghr prc han xpcd n h mark or pays mony for jobs ha hav no conomc valu. 3 Smulaon Condon A smulaon program was consrucd usng C++ wh an objc-ornd mhod. Th smulaon condons ar gvn n h hr sub-abls of Tabl. Tabl (a) shows h fxd paramrs wh valus ha rman consan durng h smulaon. Tabl (b) shows h nal condons. Hr, h valus ar nally gvn by a unform random numbr, bu may chang durng ach smulaon run. Tabl (c) shows h smulaon paramrs as xprmnal lvls. Ths ar consan, bu chang n ach smulaon run o clarfy hr nflunc on macroconomc bhavor n h arfcal conomc sysm. In addon, h paramrs dsplayd as a rang of wo valus n Tabl ar assgnd a unform random numbr whn hs rang whn h smulaon sars, or durng h smulaon. Th smulaon condons as xprmnal lvls ar dvdd no wo cagors: an analyss of h ncom ax ra and an analyss of h corporaon ax ra. In h formr cagory, h whdrawal rao of dposs was changd durng h xprmn o chang h margnal propnsy o consum. In h lar cagory, h xcuv compnsaon rao was changd o chang h lvl of h us of nrnal funds. In addon, n h cas of lar cagory, h numbr of nvsmns durng h ovrall smulaon prod wr also analyzd as a funcon of h corpora ax ra.

7 Tabl. Smulaon condon 4 Smulaon Rsuls Th nflunc of xcuv compnsaon and h fnancng rul usng nrnal funds on h rlaonshp bwn GDP and h corporaon ax ra s shown n Fg. as a ypcal rsul oband n h auhors prvous sudy. I was also found ha nffcncy of publc xpndur s anohr nflunal facor []. To undrsand h mchansm of how hs facors affc h rlaonshp bwn GDP and ax ra, addonal smulaons wr conducd n h prsn sudy. Th mark purchasng rao rprsns h ffcncy of publc xpndur and h consumrs whdrawal rao s an ndcaor of hr margnal propnsy o consum. Fg. shows h dpndncy of h rao of an ncras n GDP du o an ncom ax rducon on h mark purchasng rao and h consumrs whdrawal rao. Hr, h rao of h GDP ncras was dfnd as h rao of an ncrmnal ncras n h orgnal valu whn h ncom ax ra was rducd from 30% o 0%. In Fg., ach plo rprsnd by a squar shows h nrval bwn h frs and hrd quarls of h rao of GDP ncras, whch was oband by changng h nalzaon of h psudo-random numbr gnraor n C++ n n parns. I s nod ha, n Fg., h rao of GDP ncras du o an ncom ax rducon bcoms largr as h whdrawal rao ncrass and h mark purchasng rao dcrass. Fg.. Influnc of xcuv compnsaon on h rlaonshp bwn GDP and corporaon ax ra: (a) whou h fnancng rul usng nrnal funds; and (b) wh h fnancng rul usng nrnal funds [].

8 Fg.. Influnc of consumrs' margnal propnsy o consum on h ra of chang of GDP by ncom ax rducon. Fg. 3 shows h dpndncy of h rao of a GDP ncras du o a corporaon ax rducon on h ffcncy of publc xpndur for varous xcuv compnsaon raos. As shown n Fg. 3, h rao of h GDP ncras du o a corporaon ax rducon ncrass as h xcuv compnsaon rao ncrass and as h mark purchasng rao dcrass (.., lss ffcn publc xpndur). To undrsand why h nrnal funds rul affcs GDP, h numbr of nvsmns was nvsgad as a funcon of h corporaon ax ra for varous lvls of mark purchasng raos, as shown n Fg. 3. In Fg. 3(b), h ax rducon promos nvsmns. Th rason for hs ndncy s ha h ncras n nrnal funds du o h ax rducon ncrass nvsmn, bcaus h dcson o nvs dpnds on h amoun of nrnal funds n cas of nrnal funds rul. Fg. 3. (a) Th nflunc of producrs' margnal propnsy o consum on h ra of chang of GDP causd by a corporaon ax rducon; (b) Th nflunc of h ax ra and h rao of mark purchasng on h numbr of nvsmns whn xcuv compnsaon s Dscusson As xpland n h nroducon, h auhors prvous work showd ha nffcncy n govrnmn xpndur, xcuv compnsaon, and nrnal funds for nvsmn ar all rsponsbl for h posv nflunc of a ax rducon on GDP. Ths was confrmd by h addonal analyss n h prsn sudy dscrbd abov. To undrsand why hs facors affc h ax rducon mulplr, hs scon drvs a s of quaons for h mulplr basd on our rvsd vrson of Morshma s conomc lnkag abl [3].

9 Tabl 3. Rvsd abl of conomc lnkags In Morshma s abl of conomc lnkags, h ndvduals ar dvdd no workrs, nrprnurs, and rnrs, and frms and ohr scors ar dvdd no an nvsmn scor, forgn rad, govrnmn, bank, and h rs. In addon, ndusral oupus ar assumd o b consumpon goods and capal goods, h prcs of whch ar assumd o b consan. Som corrcons nd o b mad for h purpos of analyss. To analyz h nflunc of a ax rducon on GDP, w dvd h group of nrprnurs n Morshma s abl no xcuvs, who pay ncom ax, and managmn scors, who pay corporaon ax. In addon, o consdr h nffcncy of publc xpndur, w dvd govrnmn xpndur pg, n Morshma s abl no (-η)pg for buyng goods and ηpg for a subsdy, whch s addd o prof of frms, whr η s h nffcncy of publc xpndur. Tabl 3 shows h rvsd abl of conomc lnkags, 5. Mulplr of ncom ax rducon An ncom ax rducon ncrass h dsposabl ncom of workrs and xcuvs, hrby ncrasng h dmand for consumpon goods as a drc rsul. Ths ncrass h oal sals of h consumpon goods ndusry, whch n urn ncrass h dsposabl ncoms of workrs and xcuvs. Thus, h ovrall dmand for consumpon goods s gvn by Equaon (6), f w gnor h dmand of ohr scors such as rnrs, whr c w s avrag margnal propnsy o consum, ΔG s oal valu of h ax rducon, and ηs h nffcncy of publc xpndur. p X = b p X + ( c b )( G) whr, b = c ( ) wa 3 w w w 3 3 b = c ( )( c ) αη + ( η) = { c ( W ) + c ( ( w G = ( W ) + ( ( w w w m p + c ( )( m m ) απ) m ) α mc ) απ)}/ G p (6) Th GDP s gvn by Equaon (7). Subsung Equaon (6) no Equaon (7), w can oban h mulplr of h ncom ax rducon, as gvn n Equaon (8).

10 Y = p X + p X µ p X µ p X = ( µ ) p X + ( µ ) p X whr, µ = r( p * Y = µ ) ( c G b ' µ = r( p * ( w b3 5 5 ) p ) a p ) a 5 : Rao 5 : Rao of mpor goods n h prc of consumabl goods of mpor goods n h prc of durabl goods (7) (8) In Equaon (8), b 3 shows h govrnmn s margnal propnsy o consum, bcaus ndcas h rao of h govrnmn s consumpon. Thrfor, Equaon (8) ndcas ha h mulplr of ncom ax rducon s drmnd by h dffrnc bwn h avrag margnal propnsy o consum of consumrs and ha of h govrnmn. Assumng c w = c and ha subsung ypcal valus n our smulaon, as prsnd n h prvous scon, as w = = 0., wa 3 /p = wa 3 /p = 0.6, m = 0.5, c /p = c /p = 0.8, = = 0 no Equaon (8), h mulplr of h ncom ax rducon s rprsnd as a funcon of h ffcncy of publc xpndur and of h margnal propnsy o consum, as shown n Fg. 4. I s nod ha hs ndncy concds wh h rlaonshp shown n Fg., oband from h smulaon. Fg. 4. Th nflunc of ffcncy of publc xpndur and margnal propnsy o consum on h mulplr of ncom ax rducon. 5. Mulplr of corporaon ax rducon Th mulplr of h corporaon ax rducon would b vry small, f h nrnal funds ncrasd as a rsul of h ax rducon s assumd no o b usd for nvsmn. Hr, w drv h quaon for h mulplr basd on Tabl 3, assumng ha β ms h amoun of h ax rducon s usd for nvsmn. Ths nvsmn ncrass h dmand for capal goods, whch ncrass h oal sals of frms. Ths ncrass h dsposabl ncom of workrs and xcuvs, and hrfor, ncrass h dmand for consumpon goods. On h ohr hand, h govrnmn dcrass publc xpndur o compnsa for h dcras n ax rvnu undr h balancd budg condon. Th ovrall dmand for consumpon goods and capal goods ar rprsnd by Equaons (9) and (0), rspcvly. Subsung Equaons (9) and (0) no Equaon (8), w oban Equaon (), whch rprsns h mulplr for h corporaon ax rducon.

11 p X = b p X + b ' p X + ( b b ) G whr, b = c ( ) a w p + c ( )( ) α mc p w b ' = c ( ) a w p + c ( )( ) α mc p w b = c ( ) α, 4 w w α : Rao of xcuv compnsaon m m (9) p X = p I = β G (0) whr, β : Rao of consumpon for nvsmn o h amoun of ax rducon Y = ( µ )( b ' β + b4 b3 ) ( b ) + ( µ ) β G = Aβ + ( b b )( µ ) ( b ) 4 3 whr, A : Mulplr of frm' s nvsmn () In Equaon (), h rms β and b 4 rprsn h rao of consumpon for nvsmn and xcuvs margnal propnsy o consum, rspcvly, and hr sum rprsns h rao of consumpon o h oal amoun of h ax rducon. Thrfor, Equaon () ndcas ha h mulplr of h corporaon ax rducon s drmnd by h dffrnc bwn h subsanal margnal propnsy o consum of frms and ha of h govrnmn. Assumng c w = c = 0.9, w = = 0., wa 3 /p = wa 3 /p = 0.6, m = 0.5, c /p = c /p = 0.8, = = 0, and subsung hs valus no Equaon (9) as ypcal valus n h smulaon, h mulplr of h corporaon ax rducon s rprsnd n Fg. 5. I s nod ha h mulplr ncrass as h rao of xcuv compnsaon ncrass, and as h ffcncy of publc xpndur dcrass. Ths ndncy agrs wh ha shown n Fg. 3(a). I s also nod ha h mulplr ncrass as h valu of β ncrass. Ths ndncy agrs wh h rlaon shown n Fg. 3(b). Th rason why h ulzaon of nrnal funds for nvsmn s an ndspnsabl condon for rproducng a posv nflunc of a ax rducon on GDP n our smulaon [] s ha frms mus us par of hr ncrasd nrnal funds, as a rsul of h corporaon ax rducon, for nvsmn. Fg. 5. Th nflunc of h ffcncy of publc xpndur, α and β, on h mulplr of h corporaon ax rducon. (α:xcuv compnsaon rao, β:consumpon rao for nvsmn) 6 Concluson Th facors rsponsbl for h ffc of a ax rducon on GDP wr analyzd usng boh ABM, basd on h auhors prvous sudy, and a horcal drvaon of a s of quaons for h ax rducon mulplrs, basd on our rvsd vrson of Morshma s conomc lnkag abl. As a rsul, h followng fndngs wr oband.

12 ) In h ABM analyss, h rao of h GDP ncras du o h ax rducon ncrass as h ffcncy of publc xpndur dcrass n h cas of boh ncom ax and corporaon ax rducons. Th rao of h GDP ncras also dpnds on h margnal propnsy o consum, n h cas of h ncom ax rducon, and on h xcuv compnsaon rao and h frquncy of nvsmns n h cas of h corporaon ax rducon. ) Th quaons for h ax rducon mulplr, whch wr drvd n h prsn sudy, showd ha h mulplrs hav h sam dpndncy on h nflunal facors obsrvd n ABM analyss. I was found ha h mos mporan facor n h cas of h corporaon ax rducon s h rao of h ncrasd consumpon for nvsmn o h oal amoun of h ax rducon. 3) Th drvd quaons suggs ha, undr h balancd fnanc condon, h ax rducon mulplr s drmnd by h dffrnc bwn h ncrasd consumpon of goods and h amoun of nvsmn by consumrs or frms, and h dcrasd dmand by h govrnmn. Th crcal amoun of consumpon for a posv mulplr bcoms largr f publc xpndur bcoms mor ffcn. Rfrncs. Trano, T. (008). Byond h KISS prncpl for agn-basd socal smulaon. Journal of Soco-Informacs, (), 75.. Farmr, J. D., & Foly, D. (009). Th conomy nds agn-basd modllng. Naur, 460(756), Croson, R., & Gächr, S. (00). Th scnc of xprmnal conomcs. Journal of Economc Bhavor & Organzaon, 73(), Ashraf, Q., Grshman, B., & How, P. (0). Banks, mark organzaon, and macroconomc prformanc: an agn-basd compuaonal analyss (No. w70). Naonal Burau of Economc Rsarch. 5. Russo, A., Caalano, M., Gaffo, E., Gallga, M., & Napolano, M. (007). Indusral dynamcs, fscal polcy and R&D: Evdnc from a compuaonal xprmn. Journal of Economc Bhavor & Organzaon, 64(3), Dos, G., Fagolo, G., & Rovnn, A. (00). Schumpr mng Kyns: A polcyfrndly modl of ndognous growh and busnss cycls. Journal of Economc Dynamcs and Conrol, 34(9), Bruun, C. (000). Growh and nqualy n agn-basd modls-ffc of nroducng a walh ax. 8. Rabro, M., Tglo, A., & Cnco, S. (0). Db dlvragng and busnss cycls: An agn-basd prspcv. Economcs Dscusson Papr, (0-3). 9. Sprgg, J. A., and Ehln, M. A. (004). Full mploymn and compon n h aspn conomc modl: Implcaons for modlng acs of rrorsm. US Dparmn of Enrgy. 0. Krugman, P., and Wlls, R. (009). Economcs. nd Edon. Worh Publshrs.. Ogbayash, S., and Takashma, K. (03). Influnc of Govrnmn Expndur Polcs and Tax Ra on GDP n an Agn-Basd Arfcal Economc Sysm. In Agn-Basd Approachs n Economc and Socal Complx Sysms VII (pp. 47-6). Sprngr Japan.. Ogbayash, S., and Takashma, K. (0). Influnc of Corporaon Tax Ra on GDP n an Agn-Basd Arfcal Economc Sysm. 4h World Congrss on Socal Smulaon, Spmbr 4-7, Morshma, M. (984). Th Economcs of Indusral Socy. Cambrdg Unvrsy Prss.

13

14 Appndx: Ovrvw, Dsgn concps, Dals Proocol Ths appndx dscrbs h modl n rms of h Ovrvw, Dsgn concps, and Dals(ODD) proocol by Grm, al.(006). Grm, al. (006)). Purpos Th purpos of hs modl s o xprmnally lucda h undrln mchansm of h complx macroconomc phnomna. Th modl also am o clarfy h condons undr whch h modl srucurs rproduc hs phnomna n an agn-basd arfcal conomc sysm whr macroconomc ndcaors mrg as a rsul of agns' acons and nracons. In h prsn sudy, h purpos of hs modl focuss on lucdang h modl srucur o rproduc h posv nflunc of corpora ax rducon on GDP and o oban a clarr undrsandng of h mchansm bhnd hs ffc.. Ens, sa varabls, and scals Th ns ncludd n hs modl ar agns, goods, and marks, whch ar h mnmum rqurmns of a macro conomy of a naon. Agns nclud h followng: consumrs, comprsng workrs and xcuvs of prva scor frms and publc workrs; producrs, comprsng ralrs, raw maral makrs, and an qupmn makr; a bank; and a govrnmn. Goods nclud consumpon goods for any agns, raw maral goods for ralrs, and qupmn as capal goods for ralrs and raw maral makrs. Th mark s dvdd no a consumpon goods mark and a raw maral goods mark. W assum ha capal goods ransacons ak plac drcly bwn qupmn makrs and buyrs. Fg. shows h rlaonshp bwn hs ns, ncludng h flows of goods, labor, and funds among h agns. Fg. Ouln of h ns and hr rlaonshps Th ns ncludd n hs modl and hr characrscs ar dscrbd n Tabl.

15 Tabl. Ens ncludd n h modl and hr characrscs Sa varabls ar dvdd no hos for agns and hos for ohr ns. Each agn blongs o a dffrn cagory, accordng o s bhavor, such as agns n gnral, buyrs, nrprss, and producrs. Sa varabls for agns ar dvdd no hos for an agn s bhavoral cagory and hos pcular o ach yp of agn. Sa varabls for ach bhavoral cagory ar dscrbd n Tabl, and h sa varabls pcular o ach yp of agn ar dscrbd n Tabl 3. Th sa varabls of ohr yps of ns ar dscrbd n Tabl 4. Tabls, 3, and 4 prsn h characrscs of h sa varabls: h nal sngs, dffrncs among agns, and how valus chang wh a chang n m sp. Th nal sngs ar h valus assgnd o h sa varabls of h objcs whn h objcs ar crad. Th dffrnc among agns shows whhr h valus ar h sam or dffrn among h agns. Th chang n m sp ndcas whhr h valus ar m dpndn. Tabl. Sa varabls for agns bhavoral cagory

16 3 Tabl.3 Sa varabls pcular o ach yp of agn Tabl.4 Sa varabls of ohr yps of ns 3. Procss ovrvw and schdulng Th prsn modl consss of hr submodls: a funds crculaon submodl, a prc qulbrum submodl, and an nvsmn submodl. Th funds crculaon submodl consus h fundamnal srucur of h modl n whch h lar wo submodls ar mplmnd. Th modl consss of hr procsss: nalzaon, whr h objcs of h ns ar crad and nalzd; h squnc of svn acons prformd by agns durng ach m sp; and h calculaon of h avrag GDP and ohr sascal daa of macroconomc ndcaors. Th svn sps comprs h acons a h bgnnng of vry m sp, h producon of raw marals, h producon of consumpon goods, purchasng of consumpon goods, paymn of wags, acons for nvsmn, and h acons a h nd of vry m sp. Th psudocod ha dscrbs hs procss s gvn n Fg, and h squnal vns conducd by ach yp of ny durng ach m sp ar dscrbd n Fg. 3.

17 4 Fg. Psudocod of h modl Fg.3 Th squnal vns n ach m sp for ach yp of ny

18 5 4. Dsgn concps Basc prncpls: Th gnral concp undrlyng h modl dsgn of ABM s ha h bhavor of an arfcal conomc sysm can mmc h ral-world bhavor f h modl srucur and h srucur of h ral sysms hav a homomorphc rlaonshp. Ths rlaonshp s consdrd o b fulflld whn h srucural facors of h modld sysm ar ssnally h sam as hos of h ral sysm wh rspc o h rlvan macroscopc conomc phnomnon. Thrfor, ABM can b usful n dscrbng h mchansm of a macroconomc phnomnon by prformng conrolld xprmns n whch only on facor of nrs vars a a m, whl holdng ohr facors consan. In hs way, ABM clarfs h srucural condons ncssary for h modl o rproduc h macroconomc phnomnon bng sudd. Emrgnc: Th modld arfcal sysms should nclud hrognous and auonomous agns. Thr bhavoral ruls mgh b smlar, bu h valus of hr sa varabls should b dffrn. Thrfor, h hrognous agns bhav dffrnly and nrac wh ach ohr. Macroscopc phnomna mrg from hs acons and nracons, whch affcs h mcroscopc bhavor of h agns, rsulng n a mcro-macro lnk n h dynamcs of h sysms. In hs way, arfcal conomc sysms can bhav as complx sysms. Adapaon: Ralrs and raw maral makrs adjus h prc and numbr of producs hy supply o h mark by gaugng h dmand n h mark. To do so, hy obsrv h numbr of sock ms ha rman unsold a h nd of ach m sp. Ths producrs also us h mark dmand o adjus hr producon capacy and numbr of mploys. In hs way, h arfcal conomc sysms n hs sudy possss an nrnal adapaon mchansm. Objcvs: Consumrs and producrs hold hr own objcv funcons, such as maxmzng uly or profs. Prdcon: Ralrs and raw maral makrs prdc h oal sals of hr goods basd on h sals fgurs from h n mos rcn prods. Basd on hs prdcon, hy dcd on h amoun of producon n h nx m sp so ha h probably of goods bng ou of sock s lss han 5%. Whn hy dcd o nvs n qupmn, hy frs prdc h fnancal bnf of h nvsmn by smang h ncras n prof gand from a on-un ncras of qupmn and h subsqun ncras n producon capacy. Snsng. Ralrs and raw maral makrs gaug h mark dmand by obsrvng h amoun of goods sll n sock a h nd of ach m sp. Thy also calcula h opmal numbr of mploys basd on h prof of h currn rm, as wll as h ponal fnancal bnf of ncrasng or dcrasng h numbr of mploys and, hrfor, hr producon capacy. Inracon. Th prc qulbrum s loosly aand by h nracon bwn agns purchasng acons and producrs acons whn adjusng hr producon lvls and produc prcs. In addon, h crculaon of funds and h mrgnc of varous macroconomc ndcaors,

19 6 such as GDP, ar h rsul of h acons of agns and hr nracons. Th nvsmn bhavor s also a rsul of h nracon bwn buyrs and producrs. Sochascy: Varous sa varabls ar randomly dfnd a h sar of h smulaon or durng h smulaon. Typcal xampls ar agns nal funds, sa varabls ha dsngush agns (.g., produc classs), producon capacs, uly wghs, and a consumr s workplac. Ths ar dfnd usng random numbrs wh a unform dsrbuon. Th ordr of agns acons for h sam yp of agn s also dfnd by shufflng h s of agn d numbrs usng a unform random numbr a vry m sp.. Obsrvaon: A h nd of ach m sp, ach agn sls s accoun usng h doubl-nry bookkpng mhod. An npu-oupu abl for h arfcal sysm s dfnd by summng h calculad daa for all agns. Th macroconomc ndcaors, such as GDP, ax rvnu, oal funds for ach yp of agn, oal salars pad by producrs, and h oal numbr of nvsmns, ar calculad basd on h npu-oupu abl and ohr accoun daa of h agns. In addon, sascal daa, such as h oal numbr of goods producd or bough durng ach m sp, h avrag prc of producs, and h amoun of funds crculad bwn h bank and ohr yps of agns, ar also calculad a h nd of ach m sp. Th avrag valus of hs daa for h ovrall smulaon can also b oband and usd for varous yps of analyss. 5. Inalzaon All sa varabls of h agns ar nalzd whn h agn objcs ar crad. Ths nal valus ar dscrbd n Tabl 5 and Tabl 6. An Agn d s squnally assgnd for ach agn, bu hs numbr s only usd o dsngush agns. Each agn objc s nally assgnd randomly o on of h yps of agns. Tabl.5 Inalzaon of sa varabls for agn's bhavoral cagory Tabl.6 Inalzaon of sa varabls pcular o ach yp of agns

20 7 6. Inpu daa No daa from h ral sysm s usd as npu daa for h smulaon. 7. Submodls 7. Funds crculaon submodl Ths submodl consus h fundamnal srucur of h modl, h ouln of whch s dscrbd n h psudocod prsnd n Fg.. Th basc prncpls of h crculaon of funds and addonal bhavoral ruls ar prsnd blow. () Basc prncpls of funds crculaon. Consumrs work for on of h ohr agns, rcv wags, buy consumpon goods producd by ralrs, and pay ncom ax o h govrnmn. Ralrs produc consumpon goods usng raw maral goods suppld by raw maral makrs, whr mnmum uns of supply chan procsss ar mplmnd n h modl. Th bhavoral ruls for h srags of consumr purchasng and producrs producon ar dscrbd n h prcqulbrum submodl. Ralrs and raw maral makrs nvs n qupmn whn dong so wll ncras hr prof. Th nvsmn srags ar dscrbd n nvsmn submodl. Th govrnmn lvs ncom ax and corporaon ax, pays wags o publc mploys and conducs publc xpndur, comprsng mark purchasng as an xrm cas of ffcn publc spndng and frm subsds as an xrm cas of nffcn publc spndng. In hs way, funds crcula among agns n h arfcal conomc sysms as a rsul of agns acons and nracons. () Rlad bhavoral ruls. ()- Agns bhavoral ruls for drmnng hr consumpon budg. Evry agn, ohr han h bank, drmns a consumpon budg a h bgnnng of ach m sp. Th dfnons of h budg ar dffrn ach yp of agn. For h consumr agn: E b = a + bi + r wd D

21 8 whr, E b : Consumr s consumpon budg a: Basc consumpon; b: Margnal propnsy o consum; I : afr-ax ncom; r wd : Whdrawal rao; D : Bank dpos For h producr agn: Purchasng rao mulpld by h amoun of nrnal funds For h govrnmn agn: E E wag b = all _ b whr, G E b : Toal publc xpndur budg E _ : Toal amoun of ax rvnu all b wag G : Toal salars pad o publc mploys Th budgs for mark purchasng and for frm subsds ar dfnd as h rao of h rspcv amoun of publc xpndur o h oal budg. ()- Paymn of salars. Salars pad by nrprss. Each nrprs agn pays a fxd salary, a bonus, and xcuv compnsaon. Th oal amoun pad as salars dpnds on boh h bfor-ax prof and accumulad prof, as gvn blow: W f f π < 0 Ew = W f + Wb f π > 0 and AC < 0 W + W + EC f π > 0 and AC > 0 f b whr, E w: Toal salary amoun W f : Fxd salary W b : Bonus EC: Excuv compnsaon AC: Accumulad profs Th oal amoun of salars pad o workrs or o xcuvs s gvn blow. W = W + W / n for workrs W C C = W f f b + W b / n + EC for xcuvs whr, W c: Toal salars pad o workrs or o xcuvs n: Th numbr of mploys Salars pad by h govrnmn Th govrnmn pays fxd salars o publc workrs basd on h prvously drmnd budg for wags. ()-3 Agns bhavoral ruls for slng accouns a h nd of ach m sp Th ruls for consumrs Consumrs dfn h amoun of ncom ax o b pad basd on hr ncom and rmmbr hs as h amoun of unpad ax: Tax = WC r _ ax whr, Tax : Th amoun of ncom ax r _ax : Th ncom ax ra A par of consumrs ncom, ncludng unpad ax, s kp on hand as cash and dposd n h bank, as gvn blow: dpos = b)( W ( r )) a ( C _ ax

22 9 Th ruls for producrs Producrs dfn hr prof basd on oal sals and oal xpnss: Prp = S (W f + co + n + dp ) whr, Pr p : Th prof bfor bonus S: Toal sals Σco: Toal xpnss for raw marals n: Inrs o b pad dp: Dprcaon xpnss Producrs dfn h amoun o b pad as bonuss o mploys basd on h prof bfor bonuss, as gvn blow. Thy rmmbr hs as h amoun of unpad bonuss: W = Pr r b p bonus whr, r bonus : Th rao of bonus Basd on hs valu, hy dfn hr bfor-ax prof as gvn blow: Pr = Pr ( r ) a_ax p bonus whr, Pr a_ax : Th bfor-ax prof Thn, hy calcula h amoun of corporaon ax o b pad and rmmbr hs as h amoun of unpad ax: Taxc = Prp( rbonus )rc_ax whr, Tax c : Th amoun of corporaon ax r c_ax : Th ra of corporaon ax Basd on hs valu, hy dfn hr afr-ax prof and xcuv compnsaon, and rmmbr hs as unpad xcuv compnsaon: EC = Pr ( r )( r )r p bonus c_ax xc whr, r cx : Th rao of xcuv compnsaon Exracng h xcuv compnsaon from hr afr-ax prof nabls producrs o dfn hr accumulad prof, as gvn blow: Ac = Ac + Pr ( r )( r )( r ) p bonus c _ ax Th ruls for h govrnmn Th govrnmn dfns h oal amoun of ax rvnu and xpnss, and passs h rsulan mony on o h nx prod. ()-4 Ohrs Th ruls for dsmssal A h nd of ach m sp, h ralr frs on of s mploys f s dsmssal flag rachs a crcal valu. Th mploy o b frd s slcd a random and s assgnd o h producr wh h largs accumulad prof. Th ruls for soppng producon and for bankrupcy A h nd of ach m sp, h producr sops producon of a cran class of produc f s flag rachs a crcal valu. Whn a producr sops all s produc classs, hn gos bankrup and a nw producr objc s crad wh nw nal varabls. 7.. Prc qulbrum submodl Th prsn modl mmcs h prc qulbrum n h mark accordng o h followng wo prncpls. () Lows-prc-ornd purchasng sragy by buyrs. cx

23 0 All buyrs purchas consumpon goods whn h lms of hr consumpon budg. If hr ar producs whn sam produc class, bu wh dffrn prcs, hy wll slc h chaps of hm. Th consumpon goods bough ar ndxd by buyr's d and ar rmovd from h mark and movd o h buyr. In addon, consumrs purchas producs o maxmz hr uly whn h lm of hr consumpon budg. α maxu = w x s.. p x E whr, w : Th wgh of uly for ach produc of class x : Th numbr of producs o purchas p : Th prc of a produc α: An xponn of x () Sock-conrol-ornd producon sragy by sllrs. ()- Th bhavoral ruls usd by producrs o drmn h prc of hr producs. Th prc of a produc s dfnd accordng o h numbr of producs n sock and h amoun bough n h mark. ( + γ ) p f s = 0 p = ( γ d ) p f s > 0 and p < pav whr, γ : Th rao of a prc ncrasng γ d : Th rao of a prc dcrasng s - : Th amoun of goods n sock a h nd of prvous prod p - av: Th avrag prc of goods bough n h mark n h prvous prod ()- Th sragy for amoun o b producd (h producon plan) --Th numbr of producs o b producd n a gvn prod s dfnd so ha h probably of goods bng ou of sock s 5%: qs = qµ +. 65qσ whr, q s : Targ numbr of goods n sock q μ : Avrag sals durng h pas n prods q σ : Sgma of oal sals durng h pas n prods --Producrs dcd on h numbr of producs o produc accordng o h numbr of producs n sock, adjusng hr arg as shown blow. q ( ) f s 0 s + ε = q = qs ( ε ) s f s > 0 If q > Y ( K, L) q = Y ( K, L) whr, q : Th amoun of producon ε: Th rao of changng amoun of producon Y (K, L) = A K α L -α : Producon capacy K: Th numbr of uns of qupmn for producon L: Th numbr of mploys A: A proporonaly consan b 7.3. Invsmn submodl

24 () Producrs bhavoral ruls for nvsmn dcsons Th ralr or raw maral makr dcds o nvs whn h hr condons lsd blow ar fulflld. Onc h agn dcds o nvs, bcoms a candda for nvsmn and s ncludd n h ls of canddas ownd by an qupmn makr. Condons for nvsmn: ) Th nvsmn flag numbr xcds a crcal valu for nvsmn. ) Th fnancal bnf from an ncras n on un of qupmn s posv, as gvn blow. π = max[( p c ) Y ( K +, L) Y ( K, L) ( r0 + / N) F] > K { } 0 whr, p : Th prc of goods of produc of class c: Th varabl cos pr un produc r 0 : Th borrowng nrs ra F: Th borrowd mony rqurd o buy on un of qupmn N: Th rpaymn prod. 3) Th accumulad prof a h nd of currn rm s grar han half h ncssary funds for nvsmn. () Th bhavoral ruls for qupmn makrs. Equpmn makrs randomly slc on of h canddas for nvsmn and sll ha agn a un of qupmn. If hr s mor han on candda, h qupmn makr connus unl h numbr of uns rachs h qupmn makr's producon capacy. (3) Producrs bhavoral ruls for fnancng and buyng qupmn. Th slcd ralr or raw maral makr purchass on un of qupmn. Bfor purchasng, h agn fnancs half h ncssary funds usng nrnal funds from accumulad profs and h ohr half from h bank. Afr purchasng, h ralr or raw maral makr rnws s producon capacy by ncrasng h numbr of uns of qupmn by on n h Cobb-Douglas-yp quaon.