Mathematical and Quantitative Methods

Transcription

1 ŒCONOMICA Matheatcal and Quanttatve Methods A Matheatcal Model of an Open Econoy wth Applcatons n Roana Cataln Angelo Ioan 1, Gna Ioan Abstact: In ths pape, we fst study the statc equlbu of a a closed econoy odel n tes of dependence on natonal ncoe and nteest ate fo the an factos naely the agnal popensty to consue, tax ate, nvestent ate and the ate of cuency deand. In the second pat, we study the dynac equlbu solutons n tes of stablty. We thus obtan the vaaton functons of natonal ncoe and nteest ate vaaton and the lt values. Fnally, we popose two scenaos of econoc developent of Roana. Keywods: equlbu; deand; ncoe JEL Classfcaton: R1 1. Intoducton In a pevous pape, we poposed a odel of econoc equlbu n an open econoy. We wll esue n the fst pat, the odel equatons to te natually, the case study of theoetcal consdeatons. The odel pesented below s a genealzaton of a closed econoy odel wth govenent secto and oney aket (Stancu & Mhal, 9) whch the authos call M 3 - nae that we stll use when t efeences wll be equed. Unlke the classcal odel, we consde net expots as the dffeence between expots and pots. The essental dffeences copaed to the M 3, whch allow a oe ealstc analyss, ae the followng: 1. Govenent expendtues wee popotonal to the level of GDP (copaed to the M 3 whch ae consdeed constant). In pncple, we could consde a lnea 1 Assocate Pofesso, PhD, Danubus Unvesty of Galat, Faculty of Econoc Scences, Roana, Addess: 3 Galat Blvd, Galat, Roana, Tel.: , Fax: , Coespondng autho: cataln_angelo_oan@unv-danubus.o. Assstant Pofesso, PhD n pogess, Danubus Unvesty of Galat, Faculty of Econoc Scences, Roana, Addess: 3 Galat Blvd, Galat, Roana, Tel.: , Fax: , e- al: gna_oan@unv-danubus.o. AUDŒ, ol 9, no 5, pp

2 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, dependence of GDP, denoted by, but egesson analyss could not justfy the exstence of a nonzeo fee te of the egesson. It s clea fo the atheatcal calculus, that t ase natually fo the fact that, n the absence of potental GDP, govenent spendng cannot exst.. The nvestents dependence s lnea by GDP and nteest ate wthout fee te. Agan, the dffeence to the M 3 s the enuncaton of fee te (because of the falue to check the null hypothess), whch, n econoc tes, s that n the absence of output and onetay polcy, nvestents ae null. 3. Net expots wee consdeed to be popotonal to GDP, the absence of the constant te s due to nablty to pot o expot n the absence of the output. 4. Govenent tansfes wee assued to be popotonal to GDP (copaed to M 3 whee ae consdeed constant), agan wthout fee te because thee cannot be an output wthout the necessay tansfes. 5. The deand fo oney n the econoy was egaded as lnealy dependent on GDP and nteest ate, wth no fee te. Agan, the dffeence to the M 3 s the fee te wave, whch n econoc tes eans that n the absence of output and onetay polcy, oney deand n the econoy s null. The fst equaton of the odel s: (1) DCGINX whee: D aggegate deand; C actual fnal consupton of households; G collectve fnal consupton of geneal govenent; I nvestents; NX net expots The second equaton detenes the elatonshp between consupton of households and dsposable ncoe: () Cc C, C >, c (,1) whee: c agnal popensty to consupton, c d dc (,1) and C s autonoous consupton of households;

3 ŒCONOMICA dsposable ncoe (3) Gg, g (,1) whee: g agnal govenent consupton; output (4) In ; n (,1), < whee: n nvestent ate, n (,1); nfluence facto n the nvestents of the nteest ate, <; nteest ate (5) NXν ; ν (-1,1) whee: ν agnal net expots (6) TR-TI; TR> whee: TR govenent tansfes; TI taxes (7) TRθ ; θ (,1) whee: θ agnal ate of govenent tansfes (8) TI T, (,1); T R whee: tax ate, (,1); T ndependent of ncoe taxes (such as, fo exaple, popety taxes) (9) D the fst equaton of statc equlbu; 15

4 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 (1) MD, >, < whee: MD oney deand n the econoy; ate of oney deand n the econoy; nfluence facto of the deand fo oney n elaton to nteest ate, <; (11) MDM the second statc equlbu equaton whee: M oney supply. d (1) dt α(d-); α> the fst dynac equaton; d (13) dt β(md-m) β> the second dynac equaton whee: α - popotonalty constant of the speed of vaaton of output elatve to the gap between aggegate deand and GDP; β - popotonalty constant of the speed of vaaton n nteest ate n elaton to the gap between deand and supply of oney n the econoy.. Statc Equlbu Statc equlbu occus when aggegate deand equals output (equaton 9), and the supply and deand fo oney ae also equal (equaton 11). Fo equatons (1) (8) follow: (14) DCGINXc C g n ν c (TR- TI)C g n ν c (θ - -T )C g n ν c c θ -c -c T C g n ν (c c θ -c g n ν )-c T C [c (1θ - )g n ν ]C -c T 16

5 Notng: (15) E C ct (16) ω 1 θ 1 c 1 θ g n ν (17) χ ( ) 1 c ω g n ν esults, fst, fo (), (6), (7) and (8) and wth (15) and (16): ŒCONOMICA Cc C c (TR-TI)C c (θ - -T )C c [(1θ - )-T ]C c [ω-t ]C c ωc -c T c ωe so: (18) Cc ωe How, n the absence of the output () household consupton ust be postve, t follows that CE. Also, afte the assuptons that (,1), θ (,1) we obtan that: ω 1 θ (,) so t s stll postve. Wth the notatons (15) - (17), equaton (14) becoes: (19) D(1-χ) E The fst statc equlbu equaton D s now> (1-χ) E then: E-(1-χ)χ fo whee: E () χ χ The natual condton of deceasng the output to an nceasng of the nteest '() ate () etuns to χ < theefoe, togethe wth the hypothess fo (4) that s <, ples that χ>. Fo the fact that c,g,n,θ, (,1), ν (-1,1) follows that χ> o: 1 c 1 θ g n ν χ ( ) ( 1 θ ) 1 g n ν > c that: 1 g n ν c < 1 θ (1) > f and only f: and how 1 θ (,) esults, fnally, 17

6 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Slaly, fo equatons (1) and (11): MD M s obtaned: M- fo whee: M () The equlbu condton n both akets (goods and sevces on the one hand and the oney of the othe) esultng fo equatons () and (): (3) 18 E χ χ M The soluton of the syste s: (4) M E χ Mχ E χ The equatons (4) chaacteze the statc equlbu condton of the odel. Fo equatons ()-(8), (1), (4) esult the values of an key ndcatos at the equlbu: (5) (6) (7) (8) (9) G g NX TR ν θ ( M E ) g χ ( M E ) ν χ ( M E ) θ χ ( M E ) TI T χ I n T ( M E ) n ( Mχ E ) ( n χ) M ( n ) χ MD χ ( M E ) ( Mχ E ) χ χ χ M E

7 (3) (3) TR C TI ( M E )( 1 θ ) ( M E )( 1θ ) χ T ŒCONOMICA ( M E )( 1θ ) c ( 1θ ) c M [( 1θ ) c χ] C c E ( 1θ ) c M [ ( 1 g n ν )] χ Notng now, fo splcty: χ 1 (33) Λ χ < (34) Γ ( M ) E Λ follows, also: (35) Mχ E < χ c c T C E Γχ EΛ MΛ Γ Λ Λ χ Substtutng (33), (34) and (35) nto foulas (4) follows: (36) Γ Λ Γχ EΛ MΛ Γ Λ Λ E Fo the foulas (4) o (36) wth notatons (33)-(35) esults, also, the patal devatves of fst and second odes of the equlbu values of the output and nteest ate espectvely, equed fo the analyss of statc equlbu at a change of odel paaetes. (37) c ( ωγ T Λ) ; g ν n Γ ; 19

8 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 θ c Γ ; MΛ Γ ; Γ ; M Λ MΛ Γ ; (38) c ( ωγ T Λ) ; g ν n Γ ; θ cγ ; MΛ Γ ; χγ ; MΛ χ Γ ; χλ M (39) 11 c ( ωγ T Λ) ω Λ ;

9 ŒCONOMICA 111 ΓΛ ν n g ; ΓΛ θ c ; ( ) Λ Γ Λ M ; ΓΛ ; M Γ Λ Λ χ ; M (4) ( ) Λ Λ ω ωγ T c ; ΓΛ ν n g ; ΓΛ θ c ; ( )Λ Γ Λ M ; χγλ ; M Γ Λ Λ χ ;

10 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 M 11 Fo the analyss of the nceasng o deceasng chaacte of o wth espect to each paaete of the odel (assung that eveyone else s constant), we can see that fo the foulas (37)-(39) the only dectly ndependent expessons fo the odel paaetes ae ωγ TΛ and MΛ Γ. Theefoe, t s necessay, fst of all, to study the sgn. The condton that wth: ω < ωγ TΛ ω M E Λ T Λ ω M E T χ Λ Λ ( ) Λ [ ( ) ( )] Γ T Λ > s equvalent to (fo the foulas 33 and 34) Λ ω M [ ωm ω ( C c T ) T ( χ) ] [ ωm ω C T ( χ c ω )] ω Λ C Notng: (41) Φ 1 follows that T T ( χ c ω ) ω ( χ c ω ) ω ω ( E) T ωm ωm Γ T Λ > f and only f: C <Φ 1. We see now that C Φ 1 f and only f: C ωc ωm T equvalently: χ cω. Theefoe: ωγ TΛ > C <Φ 1 C < T T Λ ( χ c ω ) ω ( χ c ω ) ω ωm ωm o,

11 ωc ωm T > χ c ω ωγ TΛ < C >Φ 1 C > ω C ωm T < χ c ω ωγ TΛ C Φ 1 C ωc ωm T χ c ω Slaly, the condton that MΛ < MΛ Λ M Λ Λ T T ( χ c ω ) ω ( χ c ω ) Γ MΛ ( ) M E Λ [ ( χ) ( M E) ] [ M( χ) ( M ( C c T ))] ω ωm ŒCONOMICA ωm Γ > s equvalent, successvely, wth: M Λ Λ ( M E) [ Mχ ( C ct )] Λ ( Mχ C ct ) Notng: Λ C c (4) Φ T c T Mχ follows that MΛ Mχ. Γ > f and only f: C >Φ. C We note now that C Φ f and only f: C Mχ T c. ct Mχ o, equvalently, 113

12 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Also: MΛ MΛ MΛ We have also the elatons: ct Mχ C > T Γ > C >Φ ct Mχ C < T Γ < C <Φ ct Mχ C T Γ C Φ ( χ c ω ) T ωm Mχ ct ω Φ 1 -Φ T T ( χ c ω ) ωm ω ( χ) Mω( χ) T ω ( χ) Mω( χ) ω ( χ)( T Mω) ω T Mω ωλ. C Mχ < c C Mχ > c C Mχ c Mω χ c ω T Mω T Note now that Φ 1 Φ f and only f. In ths stuaton, the condtons elatve to the poston of C elatve to Φ 1 Φ becoes: Mω T C <Φ 1 Φ Mω T C >Φ 1 Φ and C < and C > ( ω ) c χ M ( ω ) c χ M 114

13 Mω T C Φ 1 Φ and C ( ω ) c χ M ŒCONOMICA Because Λ<, <, >, ω> t follows that Φ 1 -Φ > f and only f T Mω > then: ωm T > Φ 1 >Φ ωm T < Φ >Φ 1 ωm T Φ Φ 1 Befoe consdeng the vaous cases geneated fo the level of taxes ndependent of ncoe (T ) and the autonoous consupton of households (C ) espectvely, eak that fo foulas (37)-(39) that: and ae stctly nceasng and stctly convex wth espect to the agnal govenent consupton g, that s an ncease n the shae of govenent consupton n GDP wll geneate a stonge gowth both GDP and nteest ate. As a esult of ths stuaton, an ncease n the budget dves to the ncease n GDP but wll affect also the gowth of the nteest ate, the last, wth consequences n nvestents. Natually the queston ases whethe the new level of nvestents wll lead to a decease o an ncease n GDP. The dffeental of nvestents n elaton to g s: di n d d n g n Γdg ( ) dg g dg n Γ dg - Γ dg The condton that ( n )Γ >, due to the fact that Γ<, s equvalent n > wth n < o:. Theefoe, an nvestent ate hghe than the theshold wll esult that the nvestent wll ncease, and fo a 115

14 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 lowe nvestent ate than the ncease n the shae of govenent consupton n GDP wll lead to a decease n nvestent. How, n foulas (1) and (9): C G I NX wll esult, fnally, an nceasng espectvely deceasng GDP. and ae stctly nceasng and stctly convex wth espect to ν, that s an ncease n the shae of net expots to GDP wll geneate a stonge ncease both of GDP and nteest ate. The dffeental of nvestents n elaton to ν s: di n d d n ν dν ν dν n Γ dν - Γ dν ( n ) Γdν. The condton that ( n )Γ >, due to the fact n > that Γ<, s equvalent wth n < o othe:. Theefoe, fo an nvestent ate hghe than the theshold wll esult that the nvestent wll ncease, and fo a lowe nvestent ate than the ncease n the shae of the agnal net expots n GDP wll lead to a decease n nvestent. Slaly to the above, would esult n the end, an ncease o, espectvely, decease n the GDP. 116 and ae stctly nceasng and stctly convex wth espect to n the nvestent ate, that s an ncease n the shae of nvestent n GDP wll geneate a stonge ncease both of GDP and nteest ate. Ths late aspect s noal, because the acceleaton of nvestents eque addtonal fundng souces leadng to geate nteest ate. and ae stctly nceasng and stctly convex wth espect to the agnal ate of govenent tansfes θ, that s an ncease n the shae of tansfes n GDP wll geneate a stonge ncease both of GDP and the nteest ate. The dffeental of the nvestents n elaton to θ s: di n d d n θ dθ θ dθ n c Γ dθ - c Γ dθ ( n ) cγdθ. The condton that ( n )Γ >, due to the fact

15 ŒCONOMICA n > that Γ<, c >, s equvalent wth n < o othe:. Theefoe, fo an nvestent ate hghe than the theshold wll esult that the nvestent wll ncease, and fo a lowe nvestent ate than the ncease n the agnal ate of tansfes n GDP wll lead to a decease n nvestent. Slaly to the above, would esult n the end, an ncease o, espectvely, decease n the GDP. and ae stctly deceasng and stctly concave wth espect to tax ate, that s, an ncease n the shae of taxes n GDP wll lead to a decease becong geate of GDP and nteest ate. Fo foula (8) we have: dti d d - c Γ d < theefoe an ncease n the tax ate wll lead to a loss of tax evenue. Also, fo the equatons () and (6), we have C c C and TR -TI fo whee: C c ( TR - TI )C c c TR -c TI C. Dffeentatng, assung that tansfes TR ae constant, we obtan that dc c d -c dti c d -c d ( 1 ) cγd < so the actual fnal consupton of households wll decease. s stctly deceasng and stctly convex wth espect to the ate of oney deand n the econoy, that s an ncease n deand fo cuency elatve to GDP level wll geneate a decease becong oe subdued of GDP. Also, s stctly deceasng and stctly concave wth espect to oney deand ate, that s an ncease n deand fo cuency elatve to GDP level wll geneate a decease becong oe ponounced of the nteest ate. The dffeental of nvestents wth espect to s: di n d d n d d -n Γ d - χγ d ( χ n ) Γd <. Theefoe, nceases n the deand fo oney elatve to GDP wll (assung constancy of othe paaetes) to a decease n nvestent, GDP plctly. Followng ths analyss, the dynacs of oney deand wll be lowe to the GDP s gowth. 117

16 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 s s stctly nceasng and lnea, and s stctly deceasng and lnea wth espect to the oney supply M,.e. an ncease n the oney supply wll dm se by vtue d M ΛdM >, the gowth of GDP, and snce d dm M χλdm < a decease of the nteest ate. Fo the eanng dependences, we have now 13 cases wth an appeaance, at fst sght, foal, but postonng n the followng analyss, on concete data, tends n both GDP and nteest ate. ωm T < Case 1:, C <Φ 1 <Φ. In ths stuaton: fo whee: ω Γ T Λ > and MΛ Γ < and ae stctly deceasng and stctly concave n elaton to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T < Case :, C Φ 1 <Φ. In ths case: C T ( χ cω ) ωm ω C ωm T ω o, equvalent: χ cω, and ωγ TΛ and MΛ Γ < fo whee: and ae constants wth espect to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) 118

17 ŒCONOMICA s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T < Case 3:, Φ 1 <C <Φ. In ths case: fo whee: ω Γ T Λ < and MΛ Γ < and ae stctly nceasng and stctly convex wth espect to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly deceasng and stctly concave n elaton to the factos that nfluence the deand fo oney n elaton to nteest ate ( ) ωm ct Mχ T < C Case 4:, Φ 1 <Φ C. In ths case:, C Mχ T c, ωγ TΛ < and MΛ Γ fo whee: and ae stctly nceasng and stctly convex wth espect to the agnal popensty to consupton (c ) and ae constants wth espect to factos that nfluence nteest ates n nvestents ( ) s constant n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s constant n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T < Case 5:, Φ 1 <Φ <C. In ths case: fo whee: ω Γ T Λ < and MΛ Γ > and ae stctly nceasng and stctly convex wth espect to the agnal popensty to consupton (c ) and ae stctly nceasng and stctly convex wth espect to the facto of nfluence n the nvestent ate ( ) 119

18 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T Case 6:, C <Φ 1 Φ. In ths case: C < MΛ Γ < fo whee: 1 ( ω ) c χ M, ω Γ T Λ > and and ae stctly deceasng and stctly concave wth espect to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T Case 7:, C Φ 1 Φ. In ths case: C MΛ Γ fo whee: ( ω ) c χ M, ω Γ T Λ and and ae constants wth espect to the agnal popensty to consupton (c ) and ae constants wth espect to factos that nfluence nteest ates n nvestents ( ) and ae constants wth espect to factos that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T Case 8:, Φ 1 Φ <C. In ths case: C > MΛ Γ < fo whee: ( ω ) c χ M, ω Γ T Λ < and and ae stctly nceasng and stctly convex wth espect to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( )

19 ŒCONOMICA s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T > Case 9:, C <Φ <Φ 1. In ths case: fo whee: ω Γ T Λ > and MΛ Γ < and ae stctly deceasng and stctly concave wth espect to the agnal popensty to consupton (c ) and ae stctly deceasng and stctly concave n elaton to the facto of nfluence n the nvestent ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm ct Mχ T > C Case 1:, C Φ <Φ 1. In ths case: o, C Mχ T c equvalent:, ωγ TΛ > and MΛ Γ fo whee: and ae stctly deceasng and stctly concave wth espect to the agnal popensty to consupton (c ) and ae constants wth espect to the facto that nfluence nteest ates of nvestents ( ) and ae constants wth espect to factos that nfluence the deand fo oney n elaton to nteest ate ( ) T Case 11: fo whee: ωm >, Φ <C <Φ 1. In ths case: ω Γ T Λ > and MΛ Γ > and ae stctly deceasng and stctly concave wth espect to the agnal popensty to consupton (c ) and ae stctly nceasng and stctly convex wth espect to the facto of nfluence n the nvestent ate ( ) 11

20 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) ωm T > Case 1:, Φ <Φ 1 C. In ths case: C T ( χ cω ) ωm ω o, equvalent: ωc ωm T χ cω, ωγ TΛ and MΛ Γ > fo whee: and ae constants wth espect to the agnal popensty to consupton (c ) and ae stctly nceasng and stctly convex wth espect to the facto of nfluence n the nvestent ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly nceasng and stctly convex wth espect to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) T Case 13: fo whee: ωm >, Φ <Φ 1 <C. In ths case: ω Γ T Λ < and MΛ Γ > and ae stctly nceasng and stctly convex wth espect to the agnal popensty to consupton (c ) and ae stctly nceasng and stctly convex wth espect to the facto of nfluence n the nvestent ate ( ) s stctly deceasng and stctly concave n elaton to the facto that nfluence the deand fo oney n elaton to nteest ate ( ) s stctly nceasng and stctly convex wth espect to factos that nfluence the deand fo oney n elaton to nteest ate ( ) 1

21 3. The Detenaton of the Potental GDP. Okun's Law ŒCONOMICA The classcal defnton of potental GDP s one oe o less foal n the sense that t s that level of GDP n the condtons of an optal opeaton wthout balances n the econoy. Followng the odel pesented above, we defne the equlbu state as potental GDP. Theefoe, we defne the potental GDP ( ) by the foula: (43) M E χ Once detened the level of potental GDP, we natually put the poble of calculatng the natual ate of uneployent. The well-known expesson of Okun's law s: (44) whee: c cuent GDP; ( u u ) potental GDP; u the uneployent ate; u the natual ate of uneployent; c facto of popotonalty Due to the dffcultes of Okun's law (n the sense that the detenaton of the constant c eques both knowledge of potental GDP - defned by foula (43) and the natual ate of uneployent - whch s exactly the appoach the font) s used n pactce, a odfed fo of t (wth the assupton that the econoy s tunng to potental GDP and the natual ate of uneployent knows no sgnfcant vaatons n shot ntevals): (45) a c u The detenaton of the constants a and c s ade wth elatve ease, usng lnea egesson, gven that the statstcs ae known as the level of GDP () and obvous the vaatons ( ) and the uneployent ate. Substtutng the value of c as detened by the foulas (43) and (44) we obtan the natual ate of uneployent: 13

22 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 (46) u u c 1 χ u c c( M E ) Fo equaton (46) t s obseved that the natual ate of uneployent nceases χ c M E >. n elaton to the facto ( ) 4. The Dynac Equlbu Equatons (1) and (13) ae dynac equlbu laws. It s obseved that fo the d d values of and n the statc equlbu, follows: dt dt so the dynac pocess becoes statonay. Consde then the syste of dffeental equatons of fst ode fo the foulas (1) and (13): (47) d α(d ) dt d β(md M) dt, α,β> Fo (1) and (19) we can ewte (47) as: d αχ α αe dt d β β βm (48) dt l (t) ~ l (t) ~ Fo (48) follows: t, t, ~, ~ R f and only f: 1. (αχβ ) 4αβ : 14

23 ŒCONOMICA 15 (49) ( ) χ χ α αχ β αχ β αχ β β α α αχ β αχ β χ αβ χ αχ β αβ αχ β αχ β β α α αχ β αχβ αχβ αχβ αχβ t t t t E M te ) E( M e E M 4 E M e ) ( M E 4 te ) E( M and: χ χ χ E M ~ M E ~. (αχβ ) 4αβ > and λ 1 λ ae eal oots of the equaton: λ (αχβ )λ-αβ(χ ): (5) χ χ α αχ λ α αχ λ χ λ λ λ λ t t 1 1 t t 1 M E e k e k M E e k e k 1 1 whee: ( ) ( ) ( ) ( ) M E M E k M E M E k λ λ χ αχ λ αχ λ χ χ α α λ λ χ χ α α χ αχ λ αχ λ and: χ χ χ E M ~ M E ~

24 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, (αχβ ) 4αβ < and λ 1 µν, λ µ-ν, ν ae agnay oots of the equaton: λ (αχ-β )λ-αβ(χ ): (51) χ χ ν χ β χ αχ β αχ β β ν ν χ χ χ ν χ χ α αχ β αχ β α ν ν χ µ µ µ µ t t t t E M t sn e ) ( M) ( E E) M )( ( 1 t cos e E M E M t sn e ) ( E) M ( E) M )( ( 1 t cos e M E and: χ χ χ E M ~ M E ~ It s obseved n the thee cases above that the lt ~ of the output s just and those of nteest ate ~ s. 5. The Analyss of the Roanan Econoy In ths secton we wll apply the theoetcal odel outlned above fo the Roanan econoy. The data taken nto account shall elate to the peod 1-1 fo the sple eason that to the yea, the econoy went though a stng foeve estuctung and eodelng. In ode to coelate the eal data collected fo Roanan offcal souces (Roanan Statstcal eabook, Monthly Statstcal Bulletns of NSI and NBR) o ntenatonal (Wold Bank), we fst detene the cuulatve deflato and nflaton facto elatve to a efeence peod, such as.

25 ŒCONOMICA Consdeng the GDP s deflato coespondng to the yea n : GDP deflato,n GDP no n aln GDP ealn, we wll copute the cuulatve deflato elatve to, by the foula: GDP GDP GDP cuulatve deflato,n whee GDP deflato, 1. cuulatvedeflato,n-1 deflato, n k 1 n GDP deflato, k 1 The obtaned date s shown n Table 1. Table 1. The Detenaton of Cuulatve Deflato of GDP ea (n) Deflato GDP (GDP deflato,n ) Cuulatve deflato (GDP deflato cuulatve,n ) Souce: Wold Bank Consdeng, also, the consue pce ndex: CPI fo the yea n : CPI n, π n CPI n-1-1 nflaton, we wll copute the cuulatve consue pce ndex CPI cuulatve, elatve to the efeence peod by the foula: CPI cuulatve,n CPI cuulatve,n-1 CPI whee CPI 1 we obtan: n n 1 CPI k k 1 17

26 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Table. The Detenaton of Cuulatve Inflaton ea (n) The Consue Pce Index (CPI n 1π n ) Inflaton facto (π n ) The cuulatve Consue Pce Index (CPI cuulatve,n ) Souce: INSSE 5.1The Detenaton of the Lnea Regesson Cc C Dung 1-1, the fnal ndvdual consupton of households (C) and the dsposable ncoe () had the followng values: Table 3. The Actual Fnal Consupton of Households and the Dsposable Incoe n the Peod 1-1 ea Actual fnal consupton of households (l. cuent) C Actual fnal consupton of households (l. le-) C Natonal dsposable ncoe (l. cuent) Natonal dsposable ncoe (l. le-)

27 ŒCONOMICA Souce: INSSE The coespondng egesson analyss of data n Table 3 (n llon-) povdes the followng esults: The epcal coelaton coeffcent s ρ The ctcal value of the coelaton coeffcent c fo 1 values of exogenous vaable s.576 fo a sgnfcance level of oe than.95, so how ρ>c a lnea dependence between vaables ay exst. The R Squae.8831 eans that 88.31% of the total vaaton of consupton vaable s explaned by the vaaton of the natonal dsposable ncoe, the eanng 11.69% beng due to othe factos. The Fshe-Snedeco statstcs F allows the analyss of the null hypothess H whch states that all egesson coeffcents ae equal to. Coputng F α,k,n-(k1) whee α.5, k1 (the nube of degees of feedo coespondng egesson (explanatoy facto), N-(k1)1 (the nube of degees of feedo coespondng to esdual facto (unegsteed factos), f F F α,k,n-(k1) then the null hypothess H wth pobablty 1-α wll be ejected, that s at least one of the coeffcents can be nonzeo. If F>F α, k, N-(k1) then the null hypothess H states that all coeffcents ae null, the egesson beng not vald. In ths case, F and F.5; 1; Theefoe, the null hypothess H s ejected wth pobablty

28 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Sgnfcance F value epesents the pobablty that the egesson equaton cannot explan the evoluton of the endogenous vaable (lnks concdental phenoenon). If Sgnfcance F<α then the null hypothess H s ejected wth pobablty 1-α, so t s possble that at least one coeffcent be dffeent fo. In the pesent odel we have Sgnfcance F <.5 so the null hypothess H s ejected wth pobablty.95. Relatve to the values P-value, f one value s less than α then the vaable sgnfcantly nfluences the pocess. In ths case: P-value(C ) and P- value(c ) so both autonoous consupton of households and natonal dsposable ncoe affects household fnal consupton. The ntevals [Lowe 71%, Uppe 71%] ae the confdence ntevals n whch belong the coeffcents. If belongs to the ange then do not eject the null hypothess elatve to the coeffcent, so the vaable s futhe eoved fo the odel. In the case of ou egesson, C [3.4576; ] and c [.69769,.9357] so, besdes the ejected of null hypothess, t can be stated that the values of C and c wth a hghe pobablty of.71 belong n the espectve ntevals. Theefoe, afte the egesson analyss, we obtan that the aveage of the household fnal consupton dependence of natonal dsposable ncoe s: (5) C whee: (53) c.863 (54) C

29 ŒCONOMICA 15 y.86x R² C Fgue 1. The dependence of household fnal consupton by the natonal dsposable ncoe dung 1-1 Fo equaton (5) we obtan that at an ncease of 1 llon le- of the dsposable ncoe, the fnal consupton of households wll ncease, on aveage, wth 8.63 llon- (n tes of autonoous consupton household constant). 5.. The Detenaton of the Lnea Regesson Gg Dung the peod 1-1, the collectve fnal consupton of geneal govenent (G) ecods the followng values: 131

30 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Table 4. The Collectve Fnal Consupton of Geneal Govenent dung ea The collectve fnal consupton of geneal govenent (l. cuent) G Souce: INSSE The collectve fnal consupton of geneal govenent (l. le-) G Also n the sae peod, the Goss Doestc Poduct (denoted n the odel wth ) has the followng values: ea GDP (l. cuent) Table 5. Goss Doestc Poduct dung 1-1 GDP (l. le-) Souce: INSSE

31 ŒCONOMICA The coespondng egesson analyss of data fo tables 4 and 5 (n llon-) povdes the followng esults: The epcal coelaton coeffcent s ρ >.576 fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst. The R Squae.4836 eans that 48.36% of the total vaance of the vaable collectve fnal consupton of govenent s explaned by the vaaton n GDP, the eanng 51.64% beng due to othe factos. The Fshe-Snedeco statstcs F and F.5;1; , so how F> F.5;1;11 then the null hypothess H wll be ejected wth pobablty.95, so the coeffcent g can be nonzeo. Sgnfcance F <.5 theefoe t s possble that the value g be dffeent fo. P-value(g ) so the GDP affects the collectve fnal consupton of govenent. Studyng the nteval [Lowe95%,Uppe95%] we have that g [ , ] wth a pobablty geate than.95. Afte the egesson analyss, we obtan that, on aveage, the collectve fnal consupton of govenent dependence fo GDP s: (55) G whee: (56) g G y.76x R² Fgue. The dependence of the collectve fnal consupton of govenent fo GDP (l. le-) 133

32 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Fo equaton (55) we obtan that at an ncease of 1 llon le- of GDP, the geneal govenent fnal consupton wll ncease by an aveage of 76. llon The Detenaton of the Lnea Regesson In Gven the exstence of sgnfcant nflaton, we fst calculate the eal nteest ate d n π n ( n ) though the foula n 1 π n whee d n s the nonal nteest ate. Table 6. The Nonal and Real Inteest Rates ea (n) The nonal nteest ate (d n ) The eal nteest ate ( n ) Souce: INSSE Dung 1-1, nvestents (I) have the followng values: 134

33 ea Investents (l. cuent) I ŒCONOMICA Table 7. Investents dung 1-1 Investents (l. le-) I Souce: INSSE The coespondng egesson analyss of data fo tables 5, 6 and 7 (n llon- ) povdes the followng esults: The epcal coelaton coeffcent s ρ >.576 fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst. The Fshe-Snedeco statstcs F and F.5;; , so how F> F.5;;1 then the null hypothess H wll be ejected wth pobablty.95, so at least one coeffcent can be nonzeo. Sgnfcance F <.5 theefoe t s possble that the values n and be dffeent fo. P-value(n ) and P-value( ) eans that the level of GDP and the eal nteest ate nfluences the level of nvestent wth a degee of confdence ove 86 %. Studyng the nteval [Lowe86%, Uppe86%] we have that n [ , ] and [ ,-19.54] wth a pobablty geate than.86. Afte the egesson analyss, we obtan that, on aveage, the nvestent dependence fo GDP and the eal nteest ate s: 135

34 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 (57) I whee: (58) n (59) Fo equaton (57) we obtan that an ncease of 1 llon le- of GDP, gven n the condtons of a constant eal nteest ate, nvestents wll gow, on aveage, by 78.4 llon le-. Also, n tes of GDP constant, an ncease n the eal nteest ate by.1 wll geneate a decease n nvestents of llon le The Detenaton of the Lnea Regesson NXν Dung 1-1, Net Expots (NX) have ecod the followng values: ea 136 Net Expots (l. cuent) NX Table 8. Net Expots of Roana dung 1-1 Net Expots (l. le-) NX Souce: INSSE The coespondng egesson analyss of data fo tables 5 and 8 (n llon-) povdes the followng esults: The epcal coelaton coeffcent s ρ >.576 fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst.

35 ŒCONOMICA The R Squae.34 eans that only.34% of the total vaance of the vaable Net Expots s explaned by the vaaton n GDP, the eanng 79.66% beng due to othe factos. The Fshe-Snedeco statstcs F and F.5;1; , so how F> F.5;1;11 then the null hypothess H wll be ejected wth pobablty.95, so the coeffcent ν can be nonzeo. Sgnfcance F <.5 theefoe t s possble that the value ν be dffeent fo. P-value(ν ) so GDP affects Net Expots. Studyng the nteval [Lowe95%, Uppe95%] we have that ν [ , ] wth a pobablty geate than.95. Afte the egesson analyss, we obtan that, on aveage, the Net Expots dependence fo GDP s: (6) NX whee: (61) ν y -.858x R² NX Fgue 3. Net Expots dependence fo GDP (l. le-) 137

36 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Fo equaton (6) we obtan that at an ncease of 1 llon le- of GDP, Net Expots wll decease by an aveage of 85.8 llon The Detenaton of the Lnea Regesson TRθ Dung 1-1, govenent tansfes (TR) have ecoded the followng values: ea 138 Govenent tansfes (l. cuent) TR Table 9. Govenent Tansfes of Roana dung Souce: INSSE Govenent tansfes (l. le-) TR Because afte a peod of negatve tansfes (1-7) follows a evesal of decton caused by the enty of Roana nto the Euopean Unon and labo gaton to oe econocally developed countes, we pefo egesson analyss only on the peod 8-1, govenent tansfes agnal ate thus beng detened uch close to the cuent tend. The egesson analyss fo the peod 8-1 (tables 5 and 9) povdes the followng esults: The epcal coelaton coeffcent s ρ >.878 (coespondng to a total of 5 values of exogenous vaable) fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst. The R Squae value.1137 eans that only 11.37% of the total vaance of the govenent tansfes s explaned by the vaaton n GDP, the eanng 88.63% beng due to othe factos.

37 ŒCONOMICA The Fshe-Snedeco statstcs F and F.5;1;4.4453, so how F> F.5;1;4 then the null hypothess H wll be ejected wth pobablty.95, so the coeffcent θ can be nonzeo. Sgnfcance F.7473<.5 theefoe t s possble that the value θ be dffeent fo. P-value(θ ) so GDP affects govenent tansfes. Studyng the nteval [Lowe95%, Uppe95%] we have that θ [ , ] wth a pobablty geate than.95. Theefoe afte the egesson analyss, we obtan that, on aveage, the dependence of govenent tansfes on GDP s: (6) TR whee: (63) θ y.1x R² TR Fgue 4. Govenent tansfes dependence fo GDP (l. le-) Fo equaton (6) we obtan that at an ncease of 1 llon le- of GDP, the govenent tansfes wll ncease, on aveage, by 1. llon le-. 139

38 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, The Detenaton of the Lnea Regesson TI T Dung 1-1, the level of taxes (TI) has the followng values: ea 14 Taxes (l. cuent) TI Table 1. Taxes dung 1-1 Taxes (l. le-) Souce: INSSE The coespondng egesson analyss of data fo tables 5 and 1 (n llon- ) povdes the followng esults: The epcal coelaton coeffcent s ρ >.576 fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst. The R Squae value.988 eans that 9.88% of the total vaance of the taxes s explaned by the vaaton n GDP, the eanng 7.1% beng due to othe factos. The Fshe-Snedeco statstcs F and F.5;1;1.4134, so how F> F.5;1;1 then the null hypothess H wll be ejected wth pobablty.95, so at least one of the coeffcents can be nonzeo. Sgnfcance F <.5 theefoe t s possble that at least one coeffcent to be dffeent fo wth a pobablty geate than.95. TI

39 P-value(θ ) so GDP affects govenent tansfes. ŒCONOMICA Studyng the nteval [Lowe95%, Uppe95%] we have that θ [ , ] wth a pobablty geate than.95. P-value(T ) and P-value( ) , so both ndependent of ncoe taxes and GDP nfluence (wth a hghe pobablty than.95) the collecton of taxes. Intevals [Lowe95%, Uppe95%] ae: T [ , ], [.398,.7617]. Followng egesson analyss, we obtan that, on aveage, the GDP dependence of taxes s: (64) TI whee: (65).385 (66) T The dependence of Taxes fo GDP (l. le-) y.383x R².988 TI Fgue 5. Fo equaton (64) we obtan that at an ncease of 1 llon le- of GDP, taxes wll ncease, on aveage, wth 38.5 llon- (n the hypothess of ndependent of ncoe taxes constancy). 141

40 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, The Detenaton of the Lnea Regesson MD Dung 1-1, the deand fo cuency n the Roanan econoy (MD) had the followng values: ea The oney deand (l. cuent) MD Table 11. The Money Deand n the Peod 1-1 The oney deand (l. le-) MD Souce: INSSE The coespondng egesson analyss of data fo Tables 5, 6 and 11 (n llon- ) povdes the followng esults: The epcal coelaton coeffcent s ρ >.576 fo a sgnfcance level of oe than.95, so that the lnea dependence between vaables ay exst. The Fshe-Snedeco statstcs F and F.5;; , so how F> F.5;;1 then the null hypothess H wll be ejected wth pobablty.95, so at least one coeffcent can be nonzeo. Sgnfcance F, <.5 theefoe t s possble that the values and be dffeent fo. 14

41 ŒCONOMICA P-value( ) and P-value( ) eans that the level of GDP and the eal nteest ate nfluences the level of oney deand wth a degee of confdence ove 95%. Studyng the nteval [Lowe95%, Uppe95%] we have that [ , ], [ , ] wth a pobablty geate than.95. Afte the egesson analyss, we obtan that, on aveage, the oney deand fo GDP and the eal nteest ate s: (67) MD whee: (68) (69) Fo equaton (67) we obtan that at an ncease of 1 llon le- of GDP, gven a constant eal nteest ate, the deand fo oney wll ncease, on aveage, wth llon-. Also, n tes of GDP constant, an ncease n the eal nteest ate by.1 wll geneate a decease n deand fo cuency by llon le The Detenaton of Statc Equlbu dung 1-1 In pevous sectons, we saw that odel paaetes wee detened n the lnea egessons wth one o two vaables based on the dynacs of the an econoc ndcatos n the peod 1-1. Due to hgh levels of coelaton coeffcents, we can consde constant paaete values so detened. Howeve n the analyzed peod, oney has whee gone consdeable fluctuatons fo yea to yea (wth extees -1.97% - 9 and % - 5) wth an annual aveage of 19.59%. As a esult of ths stuaton, we wll detene the statc equlbu values of the output, the eal nteest ate and othe econoc ndcatos, copang the wth the actual values ecoded, all calculatons beng pefoed fo copaablty n the cuency of. 143

42 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 The evoluton of GDP (effectve and potental) dung 1-1 (l. le-) Fgue 6. 1.% The evoluton of the eal nteest ate (effectve and potental) dung % 6.% 4.%.%.% 1 -.% Fgue

43 ŒCONOMICA The evoluton of govenent tansfes (effectve and potental) dung 1-1 (l. le-) TR TR Fgue 8. The evoluton of taxes (effectve and potental) dung 1-1 (l. le-) TI TI Fgue

44 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, The evoluton of the dsposable ncoe (effectve and potental) dung 1-1 (l. le-) Fgue 1. The evoluton of actual fnal consupton of households (effectve and potental) dung 1-1 (l. le-) C C Fgue

45 ŒCONOMICA The evoluton of collectve fnal consupton of geneal govenent (effectve and potental) dung 1-1 (l. le-) G G Fgue The evoluton of nvestents (effectve and potental) dung 1-1 (l. le-) I I Fgue

46 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, The evoluton of Net Expots (effectve and potental) dung 1-1 (l. le-) NX NX 18.% 16.% 14.% 1.% 1.% % 6.% Fgue 14. The evoluton of the uneployent ate (eal and natual) dung % u u Fgue 15. We wll dvde the length of ths peod n thee equal ntevals, coespondng to enhance econoc stages, expanson and the css. Concdentally o not, these peods concde wth electon cycles that have dstnct developental stateges, unfotunately less n lne wth the equeents of econoc theoy.

47 ŒCONOMICA 1. Peod 1-4 ea/ Indcato Table 1. Man Econoc Indcatos of Roana n effectve potental effectve/ potental effectve potental effectve/ potental % % 3.% 7.77% 41.16% 4.87% 7.56% 64.49% TR % % TI % % % % C % % G % % I % % NX % % u 8.6% 18.3% 47.19% 8.1% 15.95% 5.78% M ea/ Indcato 3 4 effectve potental effectve/ potental effectve potental effectve/ potental % % 3.7% 7.33% 41.89% 7.48% 6.95% 17.65% TR % % TI % % % % C % % G % % I % % NX % % u 7.% 13.9% 54.98% 6.% 8.18% 75.83% M The fst eak, afte the analyss of the Table 1, s that n the peod of econoc consoldaton, the effectve GDP was appoach contnuously to the potental, fo 83.64% n 1 to 96.64% n

48 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 In the peod 1-3, the eal nteest ate was uch below potental, wth dffeences of 3-4%, confng the pocyclcal polces epoted n the pevous chapte when the acoeconoc analyss was based on offcal statstcs. The negatve gap between eal nteest ate and that potental, led to the begnnng of the Roanan econoy oveheatng that boosted the next peod (5-8). Lnked to ths negatve phenoenon, the fnal consupton of households nceased uch exaggeated, eachng a potental elatonshp to 83.1% n 1 and to 96.% n 4. Tax evenue (taxes) s not close to the potental theshold, equally evolved GDP. Thus, f n 1 the ato GDP effectve /GDP potental was 83.64%, the ato TI effectve /TI potental was only 71.43%, whle the end of the peod n whch GDP effectve /GDP potental 96.64% the ato TI effectve /TI potental was 8.87%, the gap between the two atos nceasng. These dffeences can be explaned ethe by neffcent collecton syste at natonal level o on account of tax evason gowng. Relatve to govenent spendng stands, at fst sght, a paadoxcal fact. If n the fst two yeas they wee placed at odds of 79.58% and 76.45% of the potental, n the last two yeas they have exceeded the axu level stood at % and 1.3% of the econoc balance dctates. The explanaton s sple but, as we shall see n the next peod, the phenoenon s chaactestc of electoal tetables. The ato of effectve nvestents to potental eveals a faly close coelaton elatve to GDP gowth (the effectveness eanng questonable). The effectve uneployent ate n 1-3 was uch below the natual (as defned above, elatve to the potental level of GDP) stood at about half the foecast odel. In 4, the dffeence between the two ates has deceased notceably (6.% - effectve ate to 8.18% - the natual ate). On the othe hand, dung ths peod, the analyss based on the Natonal Insttute of Statstcs and the Mnsty of Labo eveals a dscepancy between the elatve dynacs of the uneployed and the eployed n the econoy. 15

49 ŒCONOMICA 8.% The evoluton of uneployed and the eployees dung % 4.%.%.% % -4.% uneployed eployees Fgue 16. Souce: INSSE, Labo Mnsty In the analyzed peod, the aveage of the elatve dynacs of the nube of uneployed was % (epesentng thus a decease n the nube of uneployed), whle the aveage gowth n the nube of eployees was only -.34% (the nube of jobs educng theefoe wth an aveage.34% evey yea). The queston s the absopton of the uneployed nto the labo aket, n the peod whee evew has been a vey bg gap. On the one hand, the gdty and nflexblty ecoded at all levels of the labo aket and the hgh level of taxes led to a educed eployablty n ths peod. On the othe hand, a egesson analyss between dynac collecton of taxes and the evoluton of uneployent shows a vey nteestng stuaton. Regesson equaton: TI PS TI -.47 PS.3916 whee: TI collected taxes, and PS nube of uneployed pesons show an nvese dependence between tax collecton and nceased uneployent. At fst glance, t sees a noal phenoenon, because the ncoe fo uneployent benefts beng geatly educed copaed to the peod of eployent, the ates wll decease. Fo the egesson equaton, we note that at an ncease n the nube of uneployed, collectng taxes deceased by 4.7%. On the othe hand, the level of taxaton, n 1-4, showed an aveage of 1.54%. The dffeence 151

50 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 between these two values can have two causes: ethe the aplfcaton of the phenoenon of egaton (and theefoe a segent of the populaton goes out of the syste) o aplfcaton of black wok, justfyng also the eployablty gap epoted above. The dependence of elatve dynac collecton of taxes and the elatve dynacs of uneployent dung % -4.% -.%.%.% 4.% 6.% 8.% 1.%.% Relatve dynac collecton of taxes 15.% 1.% 5.%.% -5.% -1.% -15.% Relatve dynacs of uneployent y -.47x.39 R².5348 Fgue % 15

51 ŒCONOMICA. Peod 5-8 ea/ Indcato Table 13. Man Econoc Indcatos of Roana n effectve potental effectve/ potental effectve potental effectve/ potental % %.54% 4.8% 11.8% 1.8% 3.54% 51.45% TR % % TI % % % % C % % G % % I % % NX % % u 5.9% 9.99% 59.9% 5.% 7.55% 68.87% M ea/ Indcato 7 8 effectve potental effectve/ potental effectve potental effectve/ potental % %.5% 1.5% % 1.49% -.87% TR % % % TI % % % % C % % G % % I % % NX % % u 4.1% 6.85% 59.86% 4.4% 4.87% 9.3% M The analyss of Table 13 shows that n the peod of econoc expanson began n 4, the actual GDP was close to the potental fo 93.5% n 5 to 99.% n

52 ACTA UNIERSITATIS DANUBIUS ol 9, no 5, 13 Contay to econoc theoy and pactce, povdng that n peods of econoc expanson the actual GDP ust exceed the potental and the actual uneployent ate beng below the natual ate n Roana was a paadoxcal stuaton. If actual uneployent ate eaned below the natual (5.9% vesus 9.99% - 5, 5.% to 7.55% - 6, 4.1% to 6.85% - 7, 4.4% to 4.87% n 8), the actual GDP has eaned below the potental. On the othe hand, elatve to the evoluton of the nube of eployees n elaton to owneshp, one can speak of two dstnct peods. In the fst of these (5-6) the nube of eployees n the publc secto fell consdeably fo yea to yea (8.3% % - 6), whle the pvate secto has nceased staff 7.89% n 5 and 5.3% n 6. In the second peod (7-8) the budget unt nceased by 1.67%, whle n 8 and to decease.68%. Meanwhle, gowth n pvate unts staff antaned the tend fallng to 6.1% n 7 and 5% n 8. On the whole eployed populaton s obseved, howeve, a contnung declne n the publc shae of 3.79% n 5 to 8.81% n 8. In absolute values, t s obseved that the nube of eployees ade edundant n the publc secto ove ths peod fa below of the new eployees n the pvate secto. Thus, n 5, 134 thousand people cae out of the publc syste coesponded to 4 new pvate secto jobs, n 6: 55 exts fo the publc to the pvate face to 163 entes, n 7 thee was excess job eployent n both sectos, as n 8 to egste 1 depatues fo the publc and 171 pvate avals. Because the actual uneployent ate eaned below the natual ate, and the actual GDP was below the potental, we consde that nputs wee ethe pooly allocated o nsuffcently. In suppot of ths testony s the dynac evoluton of the ost potant secto of the econoy, naely ndusty, whee the nube of eployees deceased contnuously n the peod, whch eans that staffng wee ade n sectos wth low added value. Relatve to the eal nteest ate can be obseved agan two peods. The fst of these (5-6) t was fa below the potental ate (.54% vesus 4.8% n 5 and 1.8% to 3.54% n 6) whch led to the easng lendng, as eflected n the evoluton of household consupton fo a ato of 95,9% of potental n 5, eached alost axu n % (beng uncoelated wth the actual GDP shae n the potental of only 96%). The explanaton s vey sple, followng the evoluton of net expots. Fo a tade defct of 1817 llon le- ecoded n 5, n 6 t nceased to llon le-, thus encouagng lendng was ade not to stulate doestc poducton, but n the puchase of poted poducts. The second peod (7-8) can be descbed as a blendng of oppostes. On the one hand, the estctve polcy of the Natonal Bank whch used benchak 154