An Equilibrium Model for an Open Economy. Romania s Case

Transcription

1 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 An Equlbu odel fo an Open Econoy. Roana s Case Caaln Angelo Ioan, Gna Ioan Absac: The odel pesened n hs acle s an adapaon of he IS-L odel fo an open econoy n whch boh he sac aspecs and dynac ones ae appoached. Also, based on he odel bul, s deened he level of poenal GDP and he naual uneployen ae. The deenaon of agnal an ndcaos of GDP and nees aes, allow o denfy pobles and he decons of acon o acheve econoc equlbu. Keywods: equlbu; GDP; nvesens; nees ae; consupon JEL Code: E7; E7. Inoducon The econoc equlbu poble, whose ogns and anfesaons ae los n he ss of e, s always new. Afe a nube of appoaches oe o less goous, ha have benchaks he lages econoc hnkes fo dffeen cuen and deologes (Fanços Quesnay, Léon Walas, Vlfedo Paeo, Alfed ashall) John aynad Keynes foulaed a fs econoc equlbu odel fo a closed econoy whou govenenal seco. The conoveses on econoc equlbu ge o he auaon and developen of fuhe eseaches, oday beng analyzed he flucuaons ha accopany hs pocess. Whn heoy of econoc equlbu, a synhec analyss s he IS- L odel conssng of sulaneous equlbu n wo akes, oney ake and he goods and sevces n an auakc econoy. Based on Keynesan acoeconoc equlbu, n 937, Roy Haod, Jaes eade and John Hcks ed o expess aheacal ajos elaons of Keynes' Assocae Pofesso, PhD, Danubus Unvesy of Gala, Faculy of Econoc Scences, Roana, Addess: 3 Gala Blvd, Gala, Roana, Tel.: , fax: , Coespondng auho: caaln_angelo_oan@unv-danubus.o. Asssan Pofesso, PhD n pogess, Danubus Unvesy of Gala, Faculy of Econoc Scences, Roana, Addess: 3 Gala Blvd, Gala, Roana, Tel.: , fax: , e- al: gna_oan@unv-danubus.o. AUDŒ, Vol 9, no, pp. -5

2 ŒCONOICA heoy, fnally o elucdae he neelaonshps beween heoy effecve deand and lqudy pefeence heoy. (Hahn, 977) John Hcks' IS-LL schee (Hcks, 937) s he pedecesso IS-L odel, he auho also yng o capue he eal opposon beween classcal and Keynesan heoy, uch cczed by J.. Keynes. Subsequen developens of Alvn Hansen (based on LL-IS schea) of 949 and 953 play an poan ole n syseazng known IS-L odel and, also, s populazaon. In hs book (Hansen, 959) n ode o ge he cuve IS, Hansen calls he nvesen deand funcon of Keynes and he neoclasscal paadg and fo he LL cuve s he cuve of pons whee supply and deand. (Beaud & Dosale, 996) The IS-L odel (Kng, 993; Lawn, 3a; Lawn, 3b; Roe, 996; Roe, ; Sh & Zoega, 9; Weeapana, 3) was he bass fo fuhe eseaches and we efe boh he heoecal and he epcal, he ajo a beng he heoecal econsucon and developen of he odel and paccal soluons o coplex pobles asng n he conex of globalzaon. (Gal, ) Thus, Sauleson and Solow nclude he ognal odel he Phllps cuve (96), Fleng undell and Fleng nclude balance of payens (96 and 96), odglan and Fedan use he consupon funcon (954 and 957), Tobn ncludes he deand fo oney (958). Unl he d 99 s, he os eseaches wee focused on odelng a closed econoy, hen econoc leaue appoached, wh sudes undeaken by auce Obsfeld and Kenneh Rogoff (995), sac and dynac equlbu n open econoes. Alhough econoc leaue ha exploes New Open Econoy acoeconocs (NOE odels) s no as ch as ha of he closed econoy odel, s a sgnfcan heoecal edfce fo he cuen acoeconoc odelng: Begn (4), Sch-Gohe and Ube () Jusnano and Peson (8 & ), aínez-gacía and Vlán (). The new appoach enables eseaches o explan he new changes ha have occued n he nenaonal acoeconoc envonen based on nospecon bu ahe on epcal causal obsevaons, and heoy s epcally valdaed n hese cases. In hs acle we popose, based on deologcal vson and sudes of he os poan eseaches n he feld o deene a odel fo an open econoy, wh applcaons on he Roanan case, wh epcal aguens, eanng fo each vaable used n he odel s specfed degee of nfluence. 3

3 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3. The odel Equaons The fs equaon of he odel s he foula of he aggegae deand: () D=C+G+I+NX whee D he aggegae deand; C he acual fnal consupon of households; G he acual fnal consupon of he govenen; I he nvesens; NX he ne expo. A second equaon elaes he acual fnal consupon of households accodng o avalable ncoe V: () C=c V V+C, C, c (,) dc whee c V he agnal popensy o consue, c V = (,) and C s he dv nnsc acheved auonoous consupon of households. We wll assue below ha G and NX ae popoonal o he GDP, denoed by, gven ha n he absence of GDP can no engage any govenen spendng (excludng n hs analyss foegn loans) and also can no conduc foegn ade. (3) G=g, g (,) (4) NX=, (,) whee: g he agnal govenen consupon; he agnal ne expos Relave o nvesens, we wll consde a dec lnea dependence of he GDP level and nvese fo he nees ae: (5) I=n +, n (,),, I n he ae of nvesens, n (,); a faco of nfluence on he nvesen ae, ; The followng equaons expess he dependence of he ne ncoe GDP, he govenen ansfes (TR) and ax ae (TI): 4

4 (6) V=+TR-TI, TR (7) TR=, (,) (8) TI= +T, (,), T ŒCONOICA In equaon (7) we assued he lnea dependence of ansfes of GDP, assung n he case of he fees an affne dependence, T beng he ndependen axes fo he ncoe (popey axes and so on). Le noe ha: he agnal govenen ansfes and he ax ae, (,). The sac equlbu equaon s: (9) D= The followng se of equaons efes o oneay ssues. We assue so: () D= +,, whee: D he oney deand n he econoy; he ae of oney deand n he econoy; a faco of nfluencng he deand fo cuency fo he nees ae, ; he eal nees ae. The equlbu equaon beng: () D= whee epesens he oney supply. The dynac equaons of he odel ae: () (3) d =(D-), d d =(D-), d 3. The Sac Equlbu Fo ()-(8) we ge: (4) D=c V V+C +g +n + + =(c V +c V -c V +g +n + )-c V T +C + Nong: 5

5 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 (5) E= C cvt (6) = (7) = cv g n = cv g n le noe fs ha fo (), (6)-(8): V=(+ - )-T =-T, and: (8) C=c V (-T )+C =c V +E As n he absence of GDP (=) he consupon us be posve, follows ha E. Fo he fac ha (,), (,) we ge ha: = Wh he noaons (5)-(7), equaon (4) becoes: (9) D=(-)+ +E (,). The equlbu condon D= n (9) ples: (-)+ +E= heefoe: E () = The naual condon ha a he ncease of, us decease equed: so. Fo he fac ha c V,g,n,,, (,) we ge ha f and only f: () c V g n Slaly, fo equaons (),(): D= + = heefoe: () = The condon of equlbu on he wo akes (goods & sevces and oneay): (3) E Afe solvng he syse we have: 6

6 ŒCONOICA (4) E E The equaons (4) gve he sac equlbu odel. Nong now, fo splcy: (5) = (6) = E follows: E (7) E (8) E Fo foulas (4) we have heefoe: c (9) T V c,, cv, g n,, (3) T V cv,,,, g n,,, 7

7 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 cv (3) T c V, c (3) T, V c V,, g n,,,,, g n,,, To analyze he onoony of and of, s peave o sudy he sgns of T and. Nong: c (33) = V T T T we ge ha > f and only f T., = c VT On he ohe hand, snce E= C cvt.e. C cvt esuls: T -c V T = heefoe: c V T, -c V T =. T In concluson, we ge ha: c V T f T and c V T f T Afe hese consdeaons, hee ae hee an cases:. T > c V T 8

8 ŒCONOICA. T c V T 3. T c V T. On he ohe hand, he condon ha lead o C. Regadless of he above, we have: T lead o C, and s scly nceasng and scly convex wh espec o agnal govenen consupon g, wh espec o agnal ne expos, wh he ae of nvesens n and he agnal govenen ansfes. s scly deceasng and scly concave wh espec o he ax ae. s scly deceasng and scly convex n elaon o he ae of oney deand n he econoy. s scly nceasng and affne n elaon o he oney supply. s scly nceasng and scly convex wh espec o he agnal govenen consupon g, wh espec o he agnal ne expos, wh he ae of Invesens n and he agnal govenen ansfes. s scly deceasng and scly concave wh espec o he ax ae. s scly nceasng and scly concave n elaon o he ae of oney deand n he econoy. s scly deceasng and affne n elaon o he oney supply. We now have he followng cases: Case T and C (c V T, ) ples: T,. In hs case: s scly nceasng and scly convex n elaon o he agnal popensy o consue c V and he faco of nfluencng he deand fo cuency fo he nees ae. s scly deceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly nceasng and scly convex n elaon o he agnal popensy o consue c V. s scly deceasng and scly concave n elaon o he faco of nfluence on he nvesen ae and he faco of nfluencng he deand fo cuency fo he nees ae. Case T and C [, ] ples: T,. 9

9 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 s scly nceasng and scly convex n elaon o he agnal popensy o consue c V and n elaon o he faco of nfluence on he nvesen ae. s scly deceasng and scly convex n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. s scly nceasng and scly convex n elaon o he agnal popensy o consue c V and he faco of nfluence on he nvesen ae. s scly deceasng and scly concave n elaon o he faco of Influencng he deand fo cuency fo he nees ae. Case 3 T and C (,) ples: T,. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly deceasng and scly convex n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. s scly nceasng and scly convex n elaon o he faco of Influence on he nvesen ae. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly nceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly nceasng and scly concave n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. Case 4. T and C (c V T, ) ples: T, s scly nceasng and scly convex n elaon o he agnal popensy o consue c V and he faco of nfluencng he deand fo cuency fo he nees ae. s scly deceasng and scly concave n elaon o he faco of Influence on he nvesen ae. s scly nceasng and scly convex n elaon o he agnal popensy o consue c V. s scly deceasng and scly concave n elaon o he faco of nfluence on he nvesen ae and he faco of nfluencng he deand fo cuency fo he nees ae. Case 5. T and C [, ] ples: T,

10 ŒCONOICA s scly deceasng and scly concave n elaon o he agnal popensy o consue c V and he faco of nfluence on he nvesen ae. s scly nceasng and scly convex wh espec o. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V, he faco of nfluence on he nvesen ae and he faco of nfluencng he deand fo cuency fo he nees ae. Case 6. T and C (,) ples: T, s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly nceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly deceasng and scly convex n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly nceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly nceasng and scly concave n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. Case 7. T and C (c V T, ) ples: T, s scly deceasng and scly concave n elaon o he agnal popensy o consue c V and he faco of Influence on he nvesen ae. s scly nceasng and scly convex n elaon o he faco of Influencng he deand fo cuency fo he nees ae. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V, wh he faco of nfluence on he nvesen ae and he faco of nfluencng he deand fo cuency fo he nees ae. Case 8 T and C [,) ples: T,. s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly nceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly deceasng and scly convex n elaon o he faco of nfluencng he deand fo cuency fo he nees ae.

11 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 s scly deceasng and scly concave n elaon o he agnal popensy o consue c V. s scly nceasng and scly convex n elaon o he faco of nfluence on he nvesen ae. s scly nceasng and scly concave n elaon o he faco of nfluencng he deand fo cuency fo he nees ae. 4. The Deenaon of he Poenal GDP. Okun's Law Consdeng he oney supply consan n e, we can consde as poenal GDP value, he sac equlbu value: (34) * = E Once deened he poenal level of GDP, we naually pu he poble of deenng he naual ae of uneployen. The known expesson of Okun's law s: * * (35) cu u whee: * he acual GDP; * he poenal GDP; u he uneployen ae; u * he naual ae of uneployen; c a faco of popoonaly. Due o he dffcules n he applance of Okun's law (conssng n he possbly o deene he poenal GDP - ade n condons of full eployen of labo) and also he naual ae of uneployen, s used n pacce, a odfed fo of, as follows: (36) a cu The advanage of hs s o elnae he explc expessons of he poenal GDP and he naual uneployen. On he ohe hand, n ou analyss, we wll deene he value of he consan c usng he elaon (36) and hen nseng no (35) whch allows he deenaon of he naual ae of uneployen a a gven e.

12 ŒCONOICA Beng so deened he consan c, we have fo (34), (35): * (37) u u = u * c * c c E Fo equaon (37) s obseved ha. c E * u nceases wh wh he faco 5. The Dynac Equlbu The equaons () and (3) s consued as laws of dynac equlbu. Le so he syse of fs ode dffeenal equaons: (38) d (D ) d,, d (D ) d Fo (),(9) we can we (38) as: (39) d E d d d Usng he lea fo appendx A., follows ha: l () ~, l () ~, ~, ~ R + f and only f:. =(+ ) +4 = hen: (4) E( ) e E E 4 e ( ) E 4 e E( ) e E 3

13 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 4 and: E ~ E ~. =(+ ) +4 and ae oos of he equaon: +(- )- ( + )= hen: (4) E e k e k E e k e k whee: E E k E E k and: E ~ E ~ 3. =(+ ) +4 and =+, =-, ae oos of he equaon: +(- )-( + )= hen:

14 ŒCONOICA 5 (4) E sn e ) ( ) ( E E) )( ( cos e E E sn e ) ( E) ( E) )( ( cos e E and: E ~ E ~ We wll call ~ - he l of he oupu and ~ - he nees ae l. 6. The Analyss of he Roanan Econoy Usng he daa able A. and he esuls of analyzes fo he appendx A. hee ae obaned he coespondng egesson equaons fo Roana dung -. Table The egesson equaon The egesson s coeffcens C=.5956V c V =.5956 C = G=.773 g =.773 I= n =.877 = NX= = TR=.977 =.977 TI= =.695 T = D= =.885 =

15 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 Subsung n elaons (4) we oban he values of sac equlbu ae, fo (expessed n -naonal cuency) and =63.5: = and =-.53=-.53%. Consdeng he nflaon ae fo as =5.79% we oban usng he foula: n= whee n s he nonal nees ae: n=5.73%. On he ohe hand, he poenal level of GDP calculaed by foula (3) n he peod was: Table I can heefoe be seen ha n, he Roanan econoy was close o he poenal oupu level, he only dsubng faco beng he ae aveaged 6.5% hghe han hose of equlbu. Relave o Okun's law, he daa n able A., gves us a value fo c=.77. Fo foula (35) follows, fo Roana: (43) Anul * - * * % % % % % % % % % % % * u = u Consdeng he oneay base fo he efeence peod, we ge: * 6

16 ea The eal uneployen ae (u) The naual uneployen ae (u * ) ŒCONOICA Dffeence u-u * 8.6% 6.59%.% 8.% 8.6%.4% 3 7.% 9.4% -.% 4 6.%.% -4.9% 5 5.9% 8.77% -.87% 6 5.% 6.34% -.4% 7 4.% 3.45%.65% 8 4.4% 4.76% -.36% 9 7.8% 5.45%.35% 6.87% 5.35%.5% 5.% 4.36%.76% Table 3 The coespondng daa fo he ables and 3 show ha n 3-6 and n 8 he Roanan econoy was oveheaed, Roana's GDP beng n excess n copason o he poenal level. Thus, n 4, he elave dffeence was 8.44% beng explaned and jusfed by an ll-founded elave ncease n he oneay base of 5.67% fo he pevous peod when he ncease was angng beween.98% and 3.47%. Snce 9 he suaon has changed adcally, s level beng 4.4% less han he poenal, he dffeence becong salle ove e. Relave o he uneployen ae, he phenoenon has evolved alos dencal. If n 3-6 and n 8 was an ove-hng (wh a axu dffeence of - 4.9% n he sae yea 4), snce 9, he econoc css se, he appopae values ove % (wh a peak n 9 of.35% above he naual level). Relave o he ae evoluon, we have: ea The nonal nees ae (n) The equlbu nonal nees ae () Table % 4.87% -4.7% 8.47% 9.97% -.5% %.% -3.37% n- 7

17 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 4.7% 7.95%.3% % 3.74% -4.5% % 9.38% -.94% % 5.89%.57% % 7.3%.33% % 5.77% 3.56% 6.67% 6.44%.3% 6.5% 5.73%.5% I s noed ha n he peods -3 and 5-6, he NBR s (he Naonal Bank of Roana) nees ae was below he equlbu level. Dung he css, snce 9, has ovewheled he equlbu (even wh 3.56% n 9) whch led o he deepenng css by dscouagng nvesens. Consdeng now he dynac evoluon of GDP and he oney deand ae obaned aveage values = and = whee. The gaphs of pogesson o equlbu values ae: Fgue. The evoluon of GDP fo < ( naonal cuency) Consdeng now peubed values =3 and =7, fo whch =, we oban gaphs of evoluon owads equlbu values: 8

18 ŒCONOICA Fgue. The evoluon of GDP fo = ( naonal cuency) Fnally, consdeng now new peubed values =3 and = -6 fo whch, we oban gaphs of evoluon owads equlbu values: Fgue 3. The evoluon of GDP fo ( naonal cuency) Fo he gaphs above, appeas ha he os favoable suaon o acheve poenal oupu n es of a nu nees s he coespondng value of n whch appoxaely seven yeas o oban opu. Ohewse hee s a vey weak decease of he eal nees ae whch s kep a hgh enough levels, accopaned by a educon n GDP ove a peod of abou hee yeas, whch s unaccepable. Theefoe he condon ha (+ ) +4 s he os convenen. 9

19 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 Consdeng: we fnd ha: Copung he paal devaves of fo he exsng oneay bass n, we ge o a. vaaon of paaees: c V,, 547, 553,, 393,, g,, n,, In elaon o he above ndcaos, s noed ha n he case of IS vaables, he lages GDP's gowh s due o he ae of nvesens, ne expos and agnal govenen consupon. A sla ncease can be acheved also by an nceasng n he agnal popensy o consue. 7. Conclusons The odel pesened above shows a oe flexbly n acoeconoc odelng, because eoves he coon assupons of consancy of vaables. Thus, ne expos, govenen consupon and ansfes ae appoached by he econoec dependence of GDP. Afe he analyss of sac equlbu hee ae obaned he value of poenal GDP and he nees ae. The dynac analyss evealed hee cases of econoc developen n whch boh GDP and nees aes convege o l values, clealy dencal wh hose n he sac equlbu. The hee cases whch ae dependen on sascal paaees, push fase o slowe he econoy o he equlbu. Fo pedced equlbu values, we have defned he poenal GDP, based on whch we deened (wh Okun's law) he naual ae of uneployen. Roana's suaon, pesened n he case sudy, eveals a conadcoy econoc polcy. Thus, alhough econoec ndcaos leadng o opal convegence () of GDP o he poenal, hs s due o copensaon daa peod. In fac, n 3-6 and 8, he Roanan econoy was oveheaed, wh an oveeployen of labo and a posve oupu gap. In he peod of econoc css, he uneployen has euned o a elavely noal suaon, n un he nees ae has nceased unjusfed (8,9) led o dscouagng nvesens. Recen yeas (, ) appoached he nees ae fo equlbu, whch was efleced n an dynac nceased of nvesens. Fo Roana, he analyss of agnal ndcaos poposes as decons fo gowh, he ncease of nvesens, ne expos, govenen consupon agnal, bu also he agnal popensy o consue (condoned by he ecovey of he ade balance whch ecod a defc and o sulae he doesc poducon).

20 8. Refeences ŒCONOICA Beaud, chel & Dosale, Glles (996). La pensée éconoque depus Keynes/The Econoc hough snce Keynes. Pas: Édon du Seul. Begn, Paul R. (4). How well can he new open econoy acoeconocs explan he exchange ae and cuen accoun? NBER Wokng Pape, No Gal, Jod (). The eun of he Phllps cuve and ohe ecen developens n busness cycle heoy. Spansh Econoc Revew. Spnge-Velag. Hahn, Fank Hoace (977). Keynesan Econocs and Geneal Equlbu Theoy: Reflecons on Soe Cuen Debaes. coeconoc Foundaons of acoeconocs eded by Hacou, London, pp Hansen, A.H. (959). A Gude o Keynes. UK: c Gaw-Hll. Hcks, J.R. (937).. Keynes and he Classcs ; A Suggesed Inepeaon. Econoeca, Vol. 5, No., pp Jusnano, Alejando & Peson, Buce (8). Can Sucual Sall Open Econoy odels Accoun fo he Influence of Foegn Dsubances? NBER, Wokng Pape, No. 4547, Decebe. Jusnano, Alejando & Peson, Buce (). oneay polcy and unceany n an epcal sall open-econoy odel. Jounal of Appled Econoecs, Volue 5, Issue, Januay, pp Kng, Robe G. (993). Wll he New Keynesan acoeconocs Resuec he IS-L odel? Jounal of Econoc Pespecves, Vol. 7, No, Wne, pp Lawn, Phlp A. (3a). Envonenal acoeconocs: Exendng he IS-L odel o Include an 'Envonenal Equlbu' Cuve. Ausalan Econoc Papes, Vol. 4, ssue, pp Lawn, Phlp A. (3b). On Heyes IS L EE poposal o esablsh an envonenal acoeconocs. Envonen and Developen Econocs, Vol. 8, pp. 3 56, Cabdge Unvesy Pess. aínez-gacía, Enque & Vlán, Dego (). Bayesan Esaon of NOE odels: Idenfcaon and Infeence n Sall Saples. Fedeal Reseve Bank of Dallas, Globalzaon and oneay Polcy Insue, Wokng Pape, No. 5, ach. Roe, Davd (996). Advanced acoeconocs. UK: cgaw-hll. Roe, Davd (). Keynesan acoeconocs whou he L Cuve. Jounal of Econoc Pespecves, Vol. 4, No (Spng), pp Sch-Gohe, Sephane & Ube, an (). Closng sall open econoy odels. Jounal of Inenaonal Econocs 6, ach, pp Sh, R.P. & Zoega, G. (9). Keynes, nvesen, uneployen and expecaons. Inenaonal Revew of Appled Econocs, 3(4), pp Weeapana, Akla (3). Ineedae acoeconocs whou he IS-L odel. Jounal of Econoc Educaon, 34, 3, Sue, pp. 4-6.

21 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 Appendx A. A esul on he sably of soluons of a syse of dffeenal equaons of fs ode, lnea, wh consan coeffcens sasfyng soe condons Lea Le he syse of dffeenal equaons: dx a d d c d Then l X() X ~, l () ~ bx e, a,b,c,d,e,fr, a,b,d, c,e,f, X()=X, ()=. d f. =(a-d) +4bc= wh he soluon:, X ~, ~ R f and only f: ad ad a d bf e(a d) de bf bf de X X b e X 4 e 4 a d (a d) (a d) ad ad af ce a d bf e(a d) a d ce af 4 e X b e 4 a d a d b (a d). =(a-d) +4bc and ae oos of he equaon: -(a+d)+(ad-bc)=: e,fr wh he soluon: k k de bf X ke k e ad bc a a ke k e b b ax a whee: ax a ce af ad bc de bf ce af b b ad bc ad bc de bf ce af b b ad bc ad bc 3. =(a-d) +4bc and =+, =-, ae he oos of he equaon: - (a+d)+(ad-bc)=: e,fr wh he soluon:

22 ŒCONOICA X X de bf e ad bc af ce e ad bc d a (d a)(bf de) b(af ce) bf de cos b X e sn (ad bc) ad bc d a (d a)(af ce) c(de bf ) ec af cos cx e sn (ad bc) ad bc Appendx A. The lnea egessons Regesson C=c V V+C G=g I=n + NX= ulple R R Squae Sgnfcance F.355E-5 5.3E-.35E E-5 Inecep Sa (Inecep) P-value (Inecep) Lowe 95% (Inecep) Uppe 95% (Inecep) X Vaable Sa (X Vaable ) P-value (X Vaable.355E-5 9.E-.438E E-6 ) Lowe 95% (X Vaable ) * Uppe 95% (X Vaable ) * X Vaable Sa (X Vaable ) P-value (X Vaable ) Lowe 95% (X Vaable ) * Uppe 95% (X Vaable ) * - * Lowe 86.%, Uppe 86.% Regesson TR= TI= +T D= + ulple R R Squae Sgnfcance F 4.7E E-7 Inecep Sa (Inecep) P-value (Inecep) Lowe 95%

23 ACTA UNIVERSITATIS DANUBIUS Vol 9, no. /3 ea Acual fnal consu pon of househo lds (l. le ) - C - (Inecep) Uppe 95% (Inecep) X Vaable Sa (X Vaable ) P-value (X Vaable.33E E-7 ) Lowe 95% (X Vaable ) Uppe 95% (X Vaable ) X Vaable Sa (X Vaable ) P-value (X Vaable ) Lowe 95% (X Vaable ) Uppe 95% (X Vaable ) Avalabl e ncoe (l. le ) - V - Acual fnal consupo n of he govenen (l. le ) - G - GDP (l. le ) - - Inves ens (l. le ) - I - Real nees ae (whou nflaon ) - - Ne expo (l. le ) - NX - Goven en ansfes (l. le ) - TR - Table A. Tax aes (l. le ) - TI - oney deand daly aveage (l. le ) - D Souce: The Sascal eabook of Roana 4

24 ŒCONOICA Table A.. The elave vaaon of GDP and he absolue vaaon of he uneployen ae dung - Relave vaaon of GDP () Absolue vaaon of he uneployen ae (u) Souce: The Sascal eabook of Roana Table A.3. The uneployen ae dung - Uneployen ae (u) 8.6% 8.% 3 7.% 4 6.% 5 5.9% 6 5.% 7 4.% 8 4.4% 9 7.8% 6.87% 5.% Souce: The Sascal eabook of Roana 5