Modelling unemployment rate in the Czech Republic

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1 Modelling nemploymen rae in he Czech Repblic ONDŘEJ ČÍŽEK Deparmen of Economeric Univeriy of Economic in Prage W. Chrchill Sq Prage CZECH REPUBLIC cizeko@ve.cz Abrac: Weak aggregae op demand and high nemploymen are boh baic feare of he economy in he Czech Repblic hee day. For hi reaon he model formlaed in hi paper i baed on he following raniion mechanim: High nemploymen lead o low conmpion demand. Prodcion i alo low a no one can afford o by he good which ain high nemploymen. The paper conribe o he exiing lierare by incorporaing hi Keyneian principle of weak aggregae demand ino he baic Diamond- Morenen-Piaride (DMP) model in a imple and novel way. Depie i impliciy he propoed model capre he eence of he crren economic crii. The parameer of he model are economerically eimaed. The eimaed model rn o o have mliple eqilibria which i inerpreed from an economic poin of view. Key-Word: nonlinear modelling nemploymen vacancie mliple eqilibria. Inrodcion The nemploymen rae in he Czech Repblic ha been wiching beween lower and a higher level in pa wo decade which i illraed in figre. Tradiional view i ha hee flcaion repreen cyclical movemen. In hi paper I explore a qeion wheher or no hi dynamic cold be modelled by an alernaive approach a raniion from a lower o a higher eqilibrim nemploymen rae nemploymen rae ime Fig. : Unemploymen rae in he Czech Repblic. To hi end a nonlinear model of labor marke in he Czech Repblic i formlaed in hi paper. Nonlineariy arie by making a probabiliy of finding a job endogeno. Thi probabiliy i modelled a a fncion decreaing in nemploymen. I will be hown ha hi feedback mechanim cae he mlipliciy of eqilibrim nemploymen rae. The iniion behind hi rel i ha here i low demand for labor in ime of high nemploymen. Therefore i i hard o find a job which ain nemploymen a high level. Thi formlaion principle i ppored by he Nobel Prize winner in economic Joeph Sigliz [] who ae ha Erope problem oday i a lack of aggregae demand. Thi aricle conribe o he exiing lierare by incorporaing he Keyneian principle of weak aggregae demand ino he baic Diamond-Morenen-Piaride (DMP) model of he labor marke. The DMP model i bil pon heoreical fondaion laid down by he Nobel Prize winner in economic Diamond [] Morenen [6] and Piaride [7]. The idea ha ineracion beween nemploymen and aggregae demand for op migh cae a mlipliciy of eqilibrim i no new in he lierare. The mo famo model wa formlaed by Diamond [] in which a mlipliciy of eqilibrim i indced by he ampion of increaing rern in maching rading parner. The rcre of hi model i qie differen from he rcre of he model formlaed in hi paper. Depie hi fac mliple eqilibrim poin exi in boh model de o he link beween nemploymen and aggregae op demand. For hi reaon Thi work i mmarized by Piaride [8]. E-ISSN: Volme 06

2 a comparion of hee wo model will be briefly decribed a well. In anoher example Kaplan Menzio [5] ed he DMP modelling framework o how ha he feedback beween employmen and prodc marke migh generae mliple eqilibria. The rcre of he paper i a follow. Fir of all he model i formlaed in chaper. In he nex chaper i i compared wih he very well known Diamond [] model. Economeric eimaion i decribed in chaper 4. Afer ha he eimaed model i analyed in chaper 5 epecially from a poin of view of mlipliciy of eqilibria. In paragraph 6 economic coneqence are diced and he final chaper 7 conclde.. Model. Unemploymen Dynamic Unemploymen i modelled in a conino ime. A daa are available only a dicree dae Shimer [] mehodology i ed o expre he dynamic in dicree ime ( + f ) ( + f ) ( ) U = + e L + e U () + f where U i nmber of nemployed L repreen he labor force i eparaion rae and f i jobfinding rae. The mearemen of raniion rae f i alo baed on Shimer [] mehodology. According o hi evidence here are banial flcaion in job finding probabiliy dring bine cycle freqencie while eparaion probabiliy i nearly acyclic. Thi gge ha in order o nderand flcaion in nemploymen one m nderand he flcaion in job-finding probabiliy. The formlaion of he model preened in hi paper i baed pon hi rel. The emphai will herefore be given o he model of job-finding probabiliy.. Maching Fncion Sandard Cobb-Dogla maching fncion i ed o decribe he formaion of new relaionhip (mache) from he nmber of nemployed worker U and (nfilled) job vacancie V Kaplan Menzio [5] alo briefly dic lierare on mliple eqilibria in he DMP modelling framework and mmarize vario facor ha may lead o he exience of mliple eqilibria. α ( ) α M M V U = AU V () where 0 α 0. The ampion of conan rern o cale i in line wih mo empirical work (ee rvey performed by Piaride Perongolo [9]). Inerpreaion of hi ampion i ha he effecivene of he maching proce doe no depend on he ize of he labor marke. I will alo be amed ha all nemployed worker U have an eqal ampling probabiliy. The job-finding probabiliy F i hen given by M F = = A α () U V where denoe he marke ighne. U The correponding job finding rae i A > ( ) ( F ) f = ln. (4) The job-filling probabiliy i given by Q M α = A =. (5) V. Job creaion in he baic DMP model Concep decribed in previo wo bchaper. and. are freqenly ed in he andard DMP model. The DMP model i cloed by a free enry ampion. Under hi condiion vacancie are creaed a a flow co of C per period nil hey yield a zero profi. Thi can be decribed by he following condiion F C = Q J. (6) where J i he preen diconed vale of a filledjob in a repreenaive firm. The expreion Q J h repreen he expeced profi from poing a vacancy which i eqaed o he marginal co C of poing a vacancy. Aming Cobb-Dogla maching fncion he job filling probabiliy Q can be bied from (5) ino (6) which yield V A J α = U C. (7) Given he nmber of nemployed firm po more vacancie if he vale of a filled job J i E-ISSN: Volme 06

3 higher. However he iaion i complicaed a J alo depend on V and U. The vale of a job J i deermined by he aepricing eqaion. The baic idea i a follow: Once a repreenaive worker find a job hey prodce y of a ingle homogeno good each period for which hey are paid a wage w. The company profi in a given period i herefore y w. Prodcion i ppoed o la in fre period nil he job i deroyed which i modelled by a job dercion rae. Fre profi are diconed by inere rae r. The applicaion of he ae pricing heory in hi baic ep lead o J = y w. (8) + r Thi eqaion capre he baic idea for modelling job vacancie in he DMP framework. I claim ha he vale of a job i higher (and h firm po more vacancie) when he marginal prodc of labor i high relaive o he wage. The marginal prodc of labor nonehele depend on nemploymen U and he wage depend on nemploymen U a well a vacancie V. For laer comparion wih my own model I will briefly mmarize he effec of nemploymen on he nmber of vacancie poed by firm in he DMP model. The dependence of he wage and marginal prodc of labor on nemploymen U and on vacancie V will become apparen. Firly a high nemploymen U (compared o he nmber of vacancie V ) end o decreae wage w becae worker are in a weaker bargaining poiion. Lower wage mean higher profi and he increaed vale of a job J which encorage firm o creae more vacancie V. Secondly an increae in he nmber of nemployed worker i ppoed o lead o higher marginal labor prodciviy becae of he diminihing rern in prodcion. A a coneqence profi from employing addiional worker are increaed which lead o more vacancie poed by he firm. Finally an increae in nemploymen lead o he higher availabiliy of labor. For hi reaon firm have a higher probabiliy of filling a vacancy Q. Therefore here i alo a higher expeced profi For noaional impliciy he ime bcrip will be omied for a momen. from poing a vacancy Q J. The rel again i more vacancie V poed by he firm. For convenience hee ranmiion mechanim can be mmarized a follow: nemploymen (compared o vacancie) marke ighne wage firm' profi vale of a job vacancie (9) nemploymen marginal labor prodciviy (0) firm' profi vale of a job vacancie nemploymen availabiliy of labor probabiliy of filling a vacancy vacancie () Thee ranmiion mechanim decribe he opimal behavior of firm a well a worker which i derived from microeconomic opimizaion in he DMP framework. In a diagrammaic analyi hi opimal behavior i raced by he vacancy pply (VS) crve. In an nemploymen-vacancie plane hi crve lope pward becae he rie in nemploymen lead o more vacancie. VS crve i an analogy o he radiional labor demand crve..4 Job creaion in he preened model The baic DMP framework mmarized in he previo bchaper will be modified in hi paper by inrodcing he Keyneian principle of weak op demand. The vale of a job J i no evalaed on he bai of he crren and expeced fre prodcion y a in relaion (8). The crren and expeced firm fre profi will inead be deermined by he crren and expeced fre ale. Thi modelling prempion i baed on he fac ha in realiy firm ypically do no have problem prodcing op. The problem i o find comer who will by he prodc which applie pariclarly in ime of economic crii. The prodcion of a firm i conrained by demand and for hi reaon he relaion (8) i modified a follow: E-ISSN: Volme 06

4 J = (... ) p Y d Y d Y d y w r. () where p ( ) ( 0) repreen a probabiliy ha an op prodced will be old d Y i he (real) d aggregae demand in he period Y + i he k aggregae demand for he period + k which i expeced in he crren period. For impliciy I ame ha y w and r from he eqaion () are conan over ime. The ampion of a conan y reflec he Keyneian view ha he pply-ide of an economy doe no play a crcial role in explaining he crren economic crii. Similarly he eparaion rae doe no play an imporan role in explaining he rie in nemploymen in he Czech Repblic dring he crren economic crii (Shimer [8]). The inere rae r ha been low and able ince he beginning of he crii. For hee reaon he eparaion rae and he inere rae are boh regarded a conan. There are wo baic modelling ie in he DMP framework. The fir i how worker and firm come ogeher and he econd i how hey deermine wage. I hold be reed here ha he ie of deermining a wage will no be modelled in hi paper. I make an ampion of conan wage which i definiely an imporan implificaion. Nonehele i can be jified from an empirical a well a heoreical poin of view. There i a good deal of empirical lierare dealing wih icky wage which canno be rveyed here. Bewley [] book ackle he ie of wage rigidiy from a novel mehodological perpecive and evidence i fond o ppor vario wage-ickine heorie. Wihin he DMP modelling framework a nmber of ahor (e.g. Shimer [0] Hall [4]) emphaized ha he baic DMP model ha difficly acconing for he volaile behavior of labor marke aciviy hrogh he bine cycle a lea for andard calibraion of parameer. Shimer [0] howed ha replacing he Nah bargaining olion wih a fixed wage dramaically increae he variabiliy of nemploymen and vacancie. The probabiliy p( Y d Y d Y d ) i he only variable ha i no conidered conan over ime in he relaion (). Thi probabiliy cold be viewed a a fncion which i increaing in aggregae demand. For hi reaon he vale of a job i viewed a an increaing fncion of oal op demand ( d d d ) J = J Y Y Y. () The crren and fre expeced domeic d d d demand Y Y + Y + i deermined by crren a well a pa level of oal income. Since oal aggregae income i negaively correlaed wih he crren a well a pa nemploymen U U... here hold be a negaive relaionhip U d d beween Y Y + Y d + and he crren a well a lagged vale of nemploymen U U U... The vale of a job can be viewed a a decreaing fncion of nemploymen (...) J = J U U U. (4) For impliciy i will be amed ha only crren nemploymen U i relevan regreor J J = J( U) < 0. (5) U Crren income play an imporan role in conmpion deciion of hoehold. Thi Keyneian argmen wa empirically confirmed by Campbell Mankiw []. Nonehele hi implificaion doe no play a crcial role in he preened model. Vario verion of life-cycle hypohee cold h be incorporaed ino he modelling framework ed in hi paper. The ranmiion mechanim from nemploymen U o he vale of a job J can be mmarized a follow: nemploymen oal income domeic demand for prodc firm' profi vale of a job. (6) I i imporan o re ha he relaion (5) i in riking conra o he model of vacancie in he DMP model. Recalling he mechanim (9)-() i i apparen ha a rie in nemploymen ha exacly he oppoie effec on he vale of a job in he DMP model. The effec of nemploymen on vacancie i decribed by he fncion V( U ) which i obained by biing fncion (5) ino he eqaion (7) v ( ) V U A J( U ) α = U C. (7) E-ISSN: Volme 06

5 Noe ha he effec of increaed ambigo. On he one hand he fir erm U i U increae. On he oher hand he econd erm A J U / C α i lowered. Nonehele marke ( ( ) ) / ighne i no brdened wih hi ambigiy ( U ) V( U) A J( U) α = U where / < 0. U C. (8) The fncion J ( ) hold be non-negaive. Specifically I ame he following parly linear fncional form where ( ) max ( ) J U = a b J. (9) a b c J 0. Sbiing (9) ino (8) yield ( U ) [ max ( a b ) ] / =. (0) The relaion (0) decribe he proce of creaing job and i given in erm of marke ighne.. Comparion wih he Diamond cocon model The baic idea of he famo Diamond [] model will be briefly decribed here in order o compare i wih my own model. Aggregae pply i deermined by he arrival of prodcion opporniie which i modelled a a Poion proce wih arrival rae a. Each opporniy bring y ni of op and co c. I i amed ha y i he ame for all projec b ha c varie wih diribion G. Each opporniy i randomly drawn from G wih co known before he deciion on nderaking he projec. I i amed ha only prodcion opporniie wih co below c are nderaken. The limiing vale c i he only conrol variable in he model ha i o be deermined by opimizaion. Each projec i nderaken inanly. I i frher amed ha individal canno conme he prodc of heir own invemen b rade heir own op for ha prodced by oher. Moreover individal canno nderake a prodcion projec if hey have nold prodced op on hand. Th individal have 0 or y ni for ale. The former α are looking for prodcion opporniie and are referred o a nemployed. The laer are rying o ell heir op and are referred o a employed. Only he employed have prchaing power and repreen an effecive demand. Aggregae demand i deermined by he arrival of poenial rading parner which i modelled for each individal a a Poion proce wih arrival rae b( e ) b ' > 0 where e i he fracion of he poplaion employed in rading. The ampion b ' > 0 repreen increaing rern o cale in maching rading parner. The employmen rae fall from each compleed ranacion a a previoly employed peron become eligible o nderake a prodcion opporniy and rie whenever a prodcion opporniy i nderaken. The dynamic of employmen i given by ( ) ( ) ( ) e = a e G c e b e () Seing e = 0 in () i i eay o ee ha eadyae employmen rae rie wih de dc e = 0 c > 0 () which how ha aggregae demand (meared a he nmber of rader e eeking o prchae) rie when he aggregae pply (meared by c ) i increaed. Diamond [] alo howed he oppoie relaion dc 0 de > () which ae ha he aggregae pply (meared by c ) rie when he aggregae demand (meared by e ) i increaed. The iniion behind hi rel can be decribed by he following mechanim ( ) employme rae e rading opporniie a he prodc marke profi from nderaking a job opporniy c. (4) Mechanim (4) i imilar o ha decribed in my own model by (6). The rel () i in fac an analogy o he relaion (5) in my model according o which he vale of a job i a decreaing fncion E-ISSN: Volme 06

6 of he nmber of nemployed ( J / U < 0). Uing he ymbol e o denoe he nmber of employed worker a in he Diamond model he condiion J / U < 0 cold be eqivalenly expreed a dj 0 de > (5) from which he analogy o () become more apparen. A Diamond [] explained he rel () migh cae he exience of mliple eqilibrim nemploymen rae. My model i imilar in hi repec a he backward caaliy decribed by (0) i he reaon for he exience of mliple eqilibrim a well. Thi opic will be diced in deail laer in he chaper Economeric Eimaion Economeric eimaion wa performed ing monhly daa from he Czech Repblic. All hee daa were colleced from he official webie of he Miniry of Labor and Social Affair of he Czech Repblic: hp://poral.mpv.cz/z/a/nz/me. Job-finding probabiliy F i meared by he Shimer [] mehod. To apply hi mehodology he erie for he hor-erm nemployed peron 4 wa ed. Marke ighne wa calclaed a = V / U where ime erie for V and U wa direcly obained from he above menioned webie. Firly he ochaic verion of he regreion () wa eimaed F = A e (6) α ε where ε i i.i.d. random error. The eimaion wa performed by ordinary lea qare (OLS) afer log-linearizaion for he daa ranging from 997 M o 05 M8. The rel are a follow: 5 ( ˆ ln F ) =.69 + ( 0.78) ln ( ) R = 0.59.(7) (0.0) (0.0) The eimae ˆ α = 0.78 i in line wih he rel of oher empirical die which are mmarized by Piaride Perongolo [9] and according o which hi parameer range from 0. o The nmber of worker whoe nemploymen ha no exceeded one monh. 5 Sandard error of he eimaed coefficien are indicaed in parenhee below he parameer. Secondly he regreion (0) wa eimaed in he following form 0.78 a b = + η (8) where η i i.i.d. random error and 0.78 i he vale of he eimaed coefficien ˆα. The parameer i no eimaed economerically. The lowe vale of marke ighne wa aained wa approximaely eqal o 0.06 which can be een from figre. We definiively conclde ha However i i impoible o ay anyhing more concerning he vale of he parameer on he bai of he hiorical daa. For hi reaon he vale of he parameer i no obained ing economeric echniqe. Inead vario plaible vale of hi parameer will be aken ino accon and coneqence o he model properie will be analyed marke ighne year Fig. : Marke ighne in he Czech Repblic. The regreion (8) wa eimaed by andard OLS for daa ranging from 997 M o 05 M8 a follow: ˆ = R = (9) (0.0) (0.6) 5. Eqilibrim nemploymen rae Under he ampion of conan labor force L = L and eparaion rae = he eqaion () i lighly modified a follow: ( f) ( f) = ( e ) e f + + where = U / L i nemploymen rae. Thi eqaion implie ha a aionary nemploymen rae = aifie E-ISSN: Volme 06

7 0 = + f ( ) ( + f ( ) ) ( e ) (0) where = i he eparaion rae in 05 M8 f indicae ha (he la dae in he daae) and ( ) a aionary vale of f i a fncion of a aionary nemploymen rae. In order o decribe he fncion f ( ) in more deail le ar wih he eqilibrim vale of marke ighne which i obained from (9) ( ) ( ) / 0.78 =. () From now on I will rern o he pecificaion (0) which yield a aionary vale of marke ighne in he following form ( ) max{ } / 0.78 =. () Differen vale of he lower bond 0 will be diced laer in hi ecion. The probabiliy of finding a job in a aionary ae i obained from (7).69 ( ) ( ) 0.78 F = e () and he correponding job-finding rae i ( ) ln ( F( ) ) f (4) which define he fncion f ( ) in eqaion (0). Eqaion (0) i nonlinear hence mliple olion may exi. The expreion on he righ hand ide of (0) i a fncion of he variable which will be denoed g( ) g( ) e + f ( ) ( + f ( ) ) ( ). (5) The fncion g( ) calclaed for vario vale of he lower bondary of marke ighne i depiced a he following figre g() g() g() g() lower bond: 0.0 o (a) lower bond: 0.06 o o (b) lower bond: 0.0 o o o (c) lower bond: 0.0 o o o (d) Fig. : Eqilibrim nemploymen rae for differen vale of he lower bondary of marke ighne. E-ISSN: Volme 06

8 In he graph (a) we can ee ha here i only one olion o he eqaion g( ) = 0. Thi mean ha he eqilibrim nemploymen rae i niqe in hi cae and eqal approximaely o = Thi eqilibrim i able which follow immediaely from he fac ha he vale g( ) can be inerpreed a. + Nonehele he lower bond on marke ighne = 0.0 i no realiic. We already know from figre ha marke ighne can aain a vale a low a When he lower bond i decreaed o = 0.06 here i alo anoher eqilibrim = 0.. Thi eqilibrim i emiable a nemploymen rae converge o i when > b converge o when <. If he lower bond i frher decreaed o = 0.0 here are hree olion o he eqaion g( ) = 0. Therefore hree eqilibrim nemploymen rae = 0.07 = 0. and = 0. exi in hi cae. The eqilibrim and are able while he eqilibrim i now nable. Decreaing he lower bond o = 0.0 doe no change he eqilibria = 0.07 = 0.. B he eqilibrim wold now be = 0.4. If he lower bond i decreaed even frher o he vale of zero hen he eqilibria = 0.07 = 0.ill wold no change b he eqilibrim wold now be =. 6. Economic Dicion Marke ighne in he Czech Repblic wa 0.5 a he beginning of he economic crii in 008. There wa a ignifican decreae in beqen period and wa a low a 0.06 in 00. From hee fac i eem o me ha he marke ighne cold qie eaily fall even o a zero vale. A mliple eqilibrim model of he labor marke i h more iable han a radiional model wih niqe eqilibrim. The exience of mliple eqilibrim nemploymen rae in my model can be explained by a le effecive labor marke dring ime of high nemploymen. Firm open only a few vacancie dring a receion (crii) becae demand for heir op i low. For hi reaon i i hard for nemployed worker o find job which mainain nemploymen a high level. Comparing figre wih figre reveal ha oberved nemploymen rae doe no wich beween eqilibria. The reaon i ha he eqilibrim m be higher han = 0.. B from figre we can ee ha he oberved nemploymen rae ha no exceeded he level of 0.0. Therefore he dynamic of he oberved nemploymen rae cold be eqally well decribed by a radiional model wih only one eqilibrim. Nonehele he formlaed model warn ha mliple eqilibria exi and ha he oberved nemploymen rae migh begin o converge o he eqilibrim whenever > = 0.. Noe from figre ha he nemploymen rae in he Czech Repblic wa approximaely eqal o 0.0 in 0 which wa very near o he nable eqilibrim. The dynamic of he nemploymen rae in 04 and 05 were h nclear lae in 0. I i probably he cae ha a mall negaive hock cold have caed he convergence o he eqilibrim. On he oher hand a poiive hock migh have led o convergence a he poin which i wha eem o have happened. 7. Conclion The imporan conclion i he mlipliciy of eqilibrim nemploymen rae for he economerically eimaed model. Specifically here are wo able eqilibrim poin provided ha he nmber of nfilled vacancie (marke ighne) i fficienly low in ime of high nemploymen. The lower able eqilibrim nemploymen rae aain a vale of The higher able eqilibrim emerge when marke ighne i allowed o fall below a vale of The lower i i allowed o fall he higher he econd able eqilibrim. If he lower bondary for marke ighne i 0.0 hen a higher eqilibrim wold aain a vale 0.. There i alo an nable eqilibrim nemploymen rae which eqal 0.. The imporance of hi lie in he fac ha he nemploymen rae in he Czech Repblic wa 0.0 in 0. The labor marke in he Czech Repblic wa h very cloe o nable eqilibrim. In ch a iaion only a iny negaive hock cold have caed he convergence o a higher ineffecive able eqilibrim. Similarly only a mall poiive hock migh have led o he convergence o he E-ISSN: Volme 06

9 lower eqilibrim poin which i wha eem o have happened. Depie he exience of mliple eqilibria he hypohei ha he oberved nemploymen rae ha been wiching beween wo eqilibria in he la wo decade rned o no o be correc. The reaon i ha he le effecive eqilibrim nemploymen rae hold be well above he vale of 0.0 while he oberved nemploymen rae ha no exceeded hi vale. Acknowledgemen Financial ppor of VŠE IGA IG4004 and VŠE IP i graeflly acknowledged by he ahor. Reference: [] Bewley T. F. Why wage don fall dring a receion. Harvard Univeriy Pre 999. [] Campbell J. Y. Mankiw G. N. The repone of conmpion o income: A croconry inveigaion. Eropean Economic Review Vol pp [] Diamond P. A. Aggregae demand managemen in earch eqilibrim. Jornal of Poliical Economy Vol. 90 No. 5 pp [4] Hall R. E. Employmen flcaion wih eqilibrim wage ickine. American Economic Review Vol. 95 No. pp [5] Kaplan G. Menzio G. Shopping Exernaliie and Self-Flfilling Unemploymen Flcaion. Jornal of Poliical Economy (forhcoming) 05. [6] Morenen D. T. Propery righ and efficiency in maing racing and relaed game. American Economic Review Vol. 7 No pp [7] Piaride C. A. Shor-rn eqilibrim dynamic of nemploymen vacancie and real wage. American Economic Review Vol. 75 No pp [8] Piaride C. A. Eqilibrim nemploymen heory nd ed. MIT Pre 000. [9] Piaride C. A. Perongolo B. Looking ino he Black Box: A Srvey of he Maching Fncion. Jornal of Economic Lierare Vol pp [0] Shimer R. The cyclical behavior of eqilibrim nemploymen vacancie and wage: Evidence and heory. American Economic Review Vol. 95 No. 005 pp [] Shimer R. Reaeing he In and O of Unemploymen. Review of Economic Dynamic Vol. 5 No. 0 pp [] Sigliz J. E. Crii: Principle and Policie: Wih an Applicaion o he Erozone Crii. In: Proceeding of he Inernaional Economic Aociaion 0 Beno Aire rond-able 0. E-ISSN: Volme 06