International Parity Relations between Poland and Germany: A Cointegrated VAR Approach *

Transcription

1 Inernaonal Pary Relaons beween Poland and Germany: A Conegraed VAR Approach Agneszka SąŜka Ths verson: 5 February 008 Absrac Ths paper analyses emprcally he purchasng power pary, he uncovered neres pary and he real neres pary (Fsher pary) beween Poland and Germany. The nernaonal pary relaons are nvesgaed jonly whn he conegraed VAR framework. Our analyss fals o fnd evdence ha he pares, or any lnear combnaons of hem, hold for our daa se. We denfy wo long-run equlbrum relaons: one mposng a long-run homogeney resrcon on he domesc (.e. Polsh) and foregn (.e. German) nflaon and he domesc neres rae and one ha brngs ogeher he domesc real neres rae and he foregn nflaon. Anoher neresng resul s he weak exogeney of he devaon of he real exchange rae from he PPP and he srong exogeney of he German neres rae. Keywords: conegraed VAR, PPP, UIP, Fsher pary, Poland JEL: E3, E43, F3 The emprcal analyss n hs paper was carred ou whle I was parcpang n he Summer School n Economercs 006: Economerc Mehodology and Macroeconomc Applcaon, whch was organsed by he Deparmen of Economcs of he Unversy of Copenhagen. I owe a deb of graude o Kaarna Juselus and Heno Bohn Nelsen for her grea suppor, nvaluable advce and crcal commens. I would also lke o hank Søren Johansen and Anders Rahbek for nsprng lecures, Sebasan Gesen for fruful dscussons, Ian Babesk, Luboš Komárek, and anonymous referees for her helpful commens on earler versons of hs paper. Naonal Bank of Poland, Economc Insue, e-mal: agneszka.sazka@mal.nbp.pl

2 Inroducon Wh s accesson o he European Unon (EU) on May 004, Poland ook on a commmen o jon he Economc and Moneary Unon (EMU) upon fulfllng he convergence crera se n he Maasrch reay. The mng of he EMU accesson depends o a large exen on he counry s economc polcy decsons, whch affec he level and sably of prces, long-erm neres raes, he fscal poson and he nomnal exchange rae. However, he adopon of he euro s nevable, as none of he en counres ha became EU members n 004 has he formal rgh, as ha exercsed by Denmark and he Uned Kngdom, o op ou from EMU arrangemens. For a canddae counry wh a flexble nomnal exchange rae regme, as s he case wh Poland currenly, jonng he euro mples gvng up moneary polcy ndependence. The queson arses, hen, wheher he economy s rpe for he common moneary polcy. Ths problem has usually been analysed from he pon of vew of he opmum currency area heory (see Mundell 96; McKnnon 963; Kenen 969), whch weghs he benefs of he accesson o a moneary unon (ncreased mcroeconomc effcency) agans s coss (poenally more panful adjusmen o asymmerc shocks). A number of emprcal sudes n hs area concenrae on he symmery of shocks and shock ransmsson mechansms n a gven counry and s poenal parners n he moneary unon (see De Grauwe 003 for a survey). Ths paper asks a smlar queson o wha exen Poland has already acheved a suffcen degree of convergence wh he curren euro area members bu apples a dfferen perspecve, namely ha of nernaonal pary relaons: he purchasng power pary, he uncovered neres pary and he real neres pary. The basc logc behnd hs approach s ha he hree pares beween wo economes hold f goods and asse markes of hese economes are perfecly negraed,.e. when goods and capal are perfecly moble. If hs s he case, he economes n queson can form a common currency area whou fearng serous urbulence n case of asymmerc shocks; ndeed, he probably of such shocks s very low under such condons. There s vas emprcal leraure on he pary condons ha we are analysng bu usually each of hem s reaed separaely, whereas n our paper hey are modelled jonly whn he conegraed vecor auoregressve (VAR) framework. Ths jon modellng approach s orgnally due o Juselus and MacDonald (004a), who scrunsed he pary relaons beween Germany and he US. Essenally, he analyss n hs paper s an applcaon of her approach o he Polsh daa o he bes of our knowledge, he frs such one. Thus, we analyse emprcally o wha exen Poland s macroeconomc aggregaes of neres are nerrelaed wh hose of he curren EMU counres. The mos mporan emprcal quesons are he followng: do he nernaonal pary relaons posulaed by economc heory

3 hold for Poland relave o he euro area? Wha are he common sochasc rends drvng nflaon, neres raes and he real exchange rae agans he EMU? Do he developmens n Poland sgnfcanly affec hose n he common currency area, or can he laer be reaed as exogenously gven when analysng he Polsh economy? The EMU s represened by Germany, he larges of s members and a neghbour of Poland, whch makes he mos naural reference economy for sudyng Poland s nernaonal rade and paymens relaons wh he euro area. The remander of hs paper s srucured as follows. The nex secon presens he hree nernaonal pary relaons, brefly revews he relevan leraure, and derves hypoheses ha can be esed whn he conegraed VAR framework. Secon 3 vsually nspecs he daa used n he VAR model, whch s presened n Secon 4. Secon 5 repors he oucome of he conegraon analyss. Secon 6 summarses he man fndngs and concludes. Inernaonal pary condons The purchasng power pary (PPP) s one of he mos exensvely suded relaonshps n he nernaonal economcs. In s srong form can be wren as follows: ppp = p + p s () where ppp s he devaon from PPP (alernavely, he real exchange rae mulpled by -), p and p are, respecvely, domesc and he foregn prce levels, and s s he spo exchange rae (n prce noaon,.e. he prce of foregn currency n uns of domesc currency). All lowercase varables n hs paper, excep for he bond yelds or neres raes, are n logs so ha her frs dfferences can be nerpreed as he raes of change n he underlyng varable. Emprcally, he PPP condon s verfed f E ppp s a saonary process. The second mporan relaonshp s he uncovered neres pary (UIP): m m ( s ) = + () m where E denoes he expeced value gven he nformaon se avalable a me, s he dfference operaor and m and m are, respecvely, he domesc and he foregn bond yelds wh maury m. 3 Thus, he UIP posulaes ha he expeced rae of denomnaon of he domesc currency should be equal o he home vs. foregn neres spread (he erms neres raes, bond Admedly, neres raes and exchange raes have been heavly nfluenced by fnancal flows, where he German mark was no always he domnan currency. Neverheless, of all EMU counres Germany seems o be he bes sngle reference counry due o s economc sze and geographc proxmy o Poland. For smlar reasons, Germany was reaed as a naural anchor counry n vrually every arcle wren n he 990s on he opmaly (or smply vably) of he fuure moneary unon n EC/EU counres (see, e.g. Bayoum, Echengreen 99a; 99b and he vas leraure ha was poneered by hese papers). The begnnng of hs secon draws heavly on Juselus, MacDonald (004a), Secon. 3 Noe ha UIP may apply o shor or o long bond yelds; see Juselus, MacDonald (004a) for a dscusson.

4 yelds, and Treasury bll raes are used nerchangeably n hs paper). Assumng raonal expecaons, we have: ( s+ m ) m ε (3) s + m = E + + where ε s a whe nose error erm. Combnng () and (3) leads o: m m ( ) ε m s + m = + Under he assumpon of raonal expecaons, esng he UIP amouns o esng wheher ε n (4) s saonary. The hrd pary relaon ha we are neresed n s he real neres pary (RIP): r = r (5) m m or raher s esable verson: r m r = ν (6) where m m r and m r are he domesc and he foregn real bond yelds wh maury m, respecvely. If he RIP holds, hen ν n (6), whch s he emprcally observed real neres dfferenal beween home and foregn counry, should be a saonary process. Now, a useful relaon s he Fsher decomposon sang ha he nomnal bond yeld s he sum of he real yeld and he expeced nflaon rae over a gven perod ( o + m): ( p ) m m r + E + m = (7) Usng he Fsher decomposon, equaon (6) can be rewren n he followng way: ( p+ m p m ) + ν m m = E + Agan assumng raonal expecaons, we have: m m ( ) ( p+ m p+ m ) = ν.e. he RIP holds emprcally f he dfference beween he neres spread and he nflaon dfferenal s saonary. The economc raonale behnd he hree pares s gven by arbrage on goods and asse markes. Specfcally, f goods are perfecly moble across counres, hen arbrage ensures ha her prces afer accounng for expeced changes n he value of he varous currences are ulmaely equalsed, whch s refleced n he PPP condon. Furher, f capal s perfecly moble across counres, hen arbrage ensures ha yelds on asses of hese counres agan afer accounng for expeced changes n he value of her respecve currences are also equalsed, whch s refleced n he UIP. I can be shown ha he PPP and he UIP, aken ogeher, mply he RIP (see Lambele, Mhalov 005); n oher words, arbrage on goods and asse markes ulmaely leads o an equalsaon of real reurns on asses. An mplcaon ha he hree pares hold s, hus, ha he goods and asse markes of wo economes are o a large exen negraed. Ths, n urn, means ha hese economes can share a currency and a common moneary polcy 3 (4) (8) (9)

5 whou fearng serous urbulence when large asymmerc shocks occur. Indeed, he probably of such shocks s very low, because economes whose markes are negraed also share a common busness cycle and usually have smlar oupu srucures (see Mongell 005). The hree pares have been analysed very exensvely usng varous mehods; heorecal and emprcal sudes n hs feld are dscussed a lengh n he mea-sudes of MacDonald (998) and Sarno, Taylor (00). 4 The general upsho of hs leraure s ha he pares, aken alone, seldom hold emprcally n ypcal daa samples. Only for very long me seres, spannng a cenury or so, or for panel daa of large dmensons can he pares be emprcally verfed. As menoned n Secon, he emprcal mehodology n hs paper follows he approach pu forward by Juselus and MacDonald (004a), who scrunse he nernaonal pary relaons (he hree dscussed above and he erm srucure of neres raes) beween Germany and he USA. The analyss srongly rejecs he saonary of sngle pares, bu by allowng he laer o be nerrelaed recovers her saonary. The auhors also argue ha he apparen nonsaonary of he smple pares s due o very slow adjusmen o susanable exchange raes. The approach of Juselus and MacDonald s based on earler work by Juselus (990; 99; 995), Johansen and Juselus (99), and MacDonald and Marsh (997), and was also appled o Japan vs. he USA by Juselus and MacDonald (004b). Anoher mporan excepon o he rule ha emprcal research n hs area concenraes on only one of he pares s a recen paper by Lambele and Mhalov (005), who also model he hree pares jonly usng varous sngle equaon and sysem equaon esmaon mehods. The auhors refer o he pares as he rplepary law, sressng ha hey are closely nerrelaed. Robus evdence s found ha he pares hold n he long run, on average, and ex pos. The jon modellng of he varous pares whn he conegraed VAR framework can help undersand he forces drvng he enre sysem of varables of neres. We beleve ha he VAR mehodology self s superor o srucural smulaneous equaon models, because all relevan varables enerng he pares are jonly deermned so ha none of hem can from he ouse be reaed as exogenously gven, and because he drecon of causaly s unceran. The conegraon approach, moreover, allows one o deermne no only he shor-run dynamcs of he sysem, as n he case of (srucural) VAR models, bu also he long-run equlbrum relaons beween he varables. Specfcally, our am s o fnd conegraon relaons ha reflec he hree pary relaons. If he smple pares do no hold,.e. f he lnear combnaons of varables ha defne he pares are non-saonary, we can sll es wheher saonary lnear combnaons of hese non-saonary relaons exs. 4 For recen emprcal analyses of he pares for he case of emergng economes and n parcular of he Cenral and Eas European counres see e.g. Bekı, Boršč (007); Sders (006); Gannells, Papadopoulos (006); Sngh, Banerjee (006). 4

6 Before we proceed o he emprcal analyss, an mporan cavea s n order. The above equaons defne he hree pares n her srong form, whch does no allow for perssen deparures of he real exchange rae, he nomnal neres spread and he real neres rae from he levels mpled by he respecve pary condon. The weaker form of hese equaons, n conras, allows for permanen (or a leas perssen) deparures from hese levels. Such deparures can resul from nsuonal or srucural characerscs of economes n queson. Emprcal ess of he pares n her weaker form conss n esng wheher he equaons (4) and (6) each nclude a non-zero consan erm or a deermnsc me rend, wh he erm ε n equaon (4) and ν n equaon (6) beng whe nose (zero mean) error erms. Smlar remarks apply o equaon (), where he erm ppp need no be saonary bu can also be rend-saonary. Ths s he sraegy ha we follow n our emprcal analyss. Afer all, only seems naural ha he RIP beween Poland, a former cenrally planned ranson economy, and Germany, a sable marke economy, canno hold n s srong form hroughou any reasonable sample perod, whch mus cover years of cachng up and hus of fallng real neres dfferenal. The same apples o he remanng wo condons. 3 A vsual nspecon of he pares Before analysng he nernaonal pares presened n Secon whn he conegraed VAR framework, we frs nspec hem graphcally. An ocular analyss of varous lnear combnaons of he relevan me seres can sugges a frs enave answer o he queson wheher he pares hold emprcally. The underlyng me seres n Fgures o 4 are defned n Secon 5 and her levels and dfferences are depced n Fgure A. n he Appendx. From he cross plo of he nomnal exchange rae and he prce dfferenal beween Poland and Germany (see he upper panel of Fgure ) s dffcul o ell wheher and o wha exen he former has mrrored he laer. The reason for hs s ha he prces seem o be negraed of order, I(); hs was confrmed by formal ess whch wll be dscussed n Secon 5. The mddle panel of Fgure depcs he devaon from PPP (he real exchange rae mulpled by -) 5 and he nflaon dfferenal. If he PPP held, hen he real exchange rae and he prce dfferenal would move ogeher and he devaon from PPP would be saonary. As can be seen from he fgure, here s hardly any evdence of PPP holdng. However, he pcure mgh be blurred by he fac ha he sample perod has been he me of nensve ranson from a cenrally planned o a marke economy and hgh producvy growh n Poland relave o Germany. As a consequence, boh he real exchange rae and he prce 5 The devaon from PPP n Fgure and he rae of deprecaon n Fgure were scaled by he facor 0 o ease nerpreaon of he cross plos. 5

7 dfferenal have exhbed pronounced rends: he former a posve 6, he laer a negave one, whch mgh make dffcul o ell wheher he exchange rae s a leas rend-saonary or no. The boom panel of Fgure, whch depcs he derended seres, shows ha he devaon from PPP s no even rend-saonary. Fgure : The behavour of prces and exchange raes Prce dfferenal Spo exchange rae Inflaon dfferenal Devaon from PPP Inflaon dfferenal, derended Devaon from PPP, derended Source: IMF Inernaonal Fnancal Sascs, Naonal Bank of Poland, own calculaons Furher we look a he deprecaon rae and he home vs. foregn neres dfferenal (Fgure ). If he UIP held, he wo seres would move ogeher and he dfference beween he wo would be saonary (see equaon (4)). The upper panel of he fgure s agan dffcul o nerpre because he neres rae spread s rendng (whch s agan a by-produc of he economc ranson), whereas he deprecaon rae s no. The boom panel shows he derended seres 7, whch reveal a smlar pcure: here s hardly any evdence supporng he UIP. 6 Noe ha ppp s he real exchange rae mulpled by - so ha a posve rend n ppp means a real apprecaon rend, alhough a rse n s means nomnal deprecaon of he home currency. 7 The seres were derended by means of an OLS regresson on a consan and a lnear me rend. Each derended seres was compued as he dfference beween he orgnal seres and he rend erm mes s esmaed coeffcen. 6

8 Fgure : Deprecaon rae and home vs. foregn neres rae spread Deprecaon rae Ineres spread Deprecaon rae Ineres spread, derended Source: IMF Inernaonal Fnancal Sascs, Naonal Bank of Poland, own calculaons The hrd condon o look a s he RIP, posulang ha he devaon beween he real neres raes n he wo counres should be saonary. Fgure 3, especally he boom panel depcng he seres smoohed by akng -monh movng averages, shows ha hs s probably no he case, as he devaons beween he wo seres are raher perssen. Recall ha usng he Fsher decomposon, he RIP condon could also be wren n he form (9),.e. as a relaon beween he nomnal neres raes and he nflaon dfferenal, whch are graphed n Fgure 4. Here, he mpresson s ha he dfference beween he wo seres s I(0). To summarse, he mpresson from he graphcal analyss s ha he hree pares presened n Secon do no hold. Obvously, a vsual nspecon s only an nformal way of nvesgang wheher he gven relaons are saonary. The resuls of formal ess wll be dscussed n Secon 5; before ha, he nex secon wll presen he conegraed VAR model. 7

9 Fgure 3: Real neres raes Real neres rae Poland Real neres rae Germany Real neres rae Poland, -monh movng average Real neres rae Germany, -monh movng average Source: IMF Inernaonal Fnancal Sascs, Naonal Bank of Poland, own calculaons Fgure 4: Home vs. foregn neres rae spread and nflaon dfferenal.06 Ineres spread Inflaon dfferenal Ineres spread, -monh movng average Inflaon dfferenal, -monh movng average Source: IMF Inernaonal Fnancal Sascs, Naonal Bank of Poland, own calculaons 8

10 4 The conegraed VAR model 8 The j-dmensonal conegraed VAR(k) model n he vecor equlbrum correcon (VEC) form s gven by he followng equaon: x = Πx + Γ x Γk x k+ + ΦD + ε (0) where x s a j vecor of endogenous varables, D s a b vecor of deermnsc componens (such as a consan, a lnear me rend, seasonal or nervenon dummes, or srcly exogenous varables), ε s a j vecor of..d. Gaussan error erms, and Π, Γ ( =,..., k ), and Φ are coeffcen marces of approprae dmenson. Based on he assumpon ha all varables n (0) are a mos I(), he conegraon hypohess can be formulaed as a reduced rank resrcon on he marx Π : Π = α β () where α and β are j r coeffcen marces wh full column rank and r j, whch mples ha he rank of Π s also r. As he varables n x are I(), her frs dfferences on he lef hand sde of (0) are saonary; herefore, all erms on he rgh hand sde of he equaon mus also be saonary. Thus, he marx Π ranslaes he non-saonary vecor x, no a saonary one, x. More precsely, s he expresson β x ha defnes he saonary lnear combnaons Π (conegraon relaons) of he I() vecor x, whereas he marx α descrbes how he varables n he sysem adjus o he equlbrum error from he prevous perod, β x. The rank r of he marx Π gves he number of conegraon relaons (seady saes, long-run equlbrum relaons) beween he j varables of he VAR sysem, whereas j r gves he number of common sochasc rends ha drve her behavour. The former can be nerpreed as he pullng forces and he laer as he pushng forces of he sysem; each me a varable s pushed away from he seady sae, s pulled back o. The analyss n he nex secon ams a fndng conegraon relaons beween he varables of neres ha can be gven a meanngful economc nerpreaon, and a denfyng he common sochasc rends. x The vecor of varables ha are relevan for our analyss s defned as follows: [ p p s ] = where p = he Polsh ( home counry ) consumer prce ndex, () p = he German ( foregn counry ) consumer prce ndex, = he Polsh Treasury bll rae, = he German Treasury bll rae, 8 The conegraed VAR analyss s dscussed n deph n Juselus (006). 9

11 s = he spo exchange rae (defned as PLN/DM). The daa are monhly, no seasonally adjused, and cover he perod 994: o 006:. All seres excep for he exchange rae are aken from he IMF Inernaonal Fnancal Sascs whereas he exchange rae s he end-of-monh rae as announced by he Naonal Bank of Poland 9. From January 999 onwards, he PLN/DM exchange rae s represened by he PLN/EUR rae, dvded by he rrevocable DM/EUR converson rae. The Treasury bll raes are no he usual annualsed raes bu monhly raes so hey are drecly comparable o he monhly changes n he remanng varables. Our choce of he proxy for long-erm neres raes was no sraghforward. Ideally, we should have used long (e.g. en-year) governmen bond yelds. However, frs emssons of longer-erm governmen bonds n Poland ook place n 999 so he me seres are raher shor. 0 As he Treasury bll rae s he only neres rae ha has been avalable hroughou he whole sample perod, we could only use hs rae as a proxy for long bond yelds. The daa n levels and n dfferences are depced n Fgure A. n he Appendx. Boh he graphcal analyss of he me seres n he prevous secon and he formal ess o be dscussed n he nex secon sugges ha he prce varables are I(), whereas our model s based on he I() assumpon. Therefore, we ransformed he daa so ha he resulng seres are a mos I(), whle a he same me preservng nformaon abou he long-run rends drvng he prces. The ransformed vecor of varables whose jon behavour s o be explaned whn he conegraed VAR framework now becomes: x [ p p ppp ] ~ I( ) = (3) where ppp was defned n Secon. Noe ha he VEC model s defned for dfferenced daa, whch means ha he prce varables n he vecor [ p p ppp ] ~ I( 0) x are dfferenced wce: x = (4) The pon of deparure for our analyss s he followng sylsed scenaro. In a neoclasscal world we would expec prces of goods, capal and foregn exchange o be drven by no more han wo dfferen sochasc rends. These could be defned e.g. as cumulaed supply and demand shocks, or as cumulaed domesc and foregn shocks. Alernavely, one rend could be assocaed wh shocks o he curren accoun and he oher wh capal accoun shocks. Therefore, we would expec he rank of he marx Π o be equal o 3. However, n a world wh nomnal rgdes, barrers o rade wh goods and o capal and labour movemens across counres, asymmerc nformaon, rsk averson ec., here mgh be more han wo common sochasc rends drvng 9 When average monhly exchange raes are used nsead of end-of-monh raes, he qualave resuls of he analyss are dencal and he quanave resuls are very smlar. 0 Ths problem s ypcal of Cenral and Eas European former cenrally planned economes. See he dscusson n Juselus & MacDonald (004a). 0

12 our varables. In a smlar daa se for Germany and he US, Juselus and MacDonald (004a) denfy a hrd common rend assocaed wh he specal role of he US dollar n he nernaonal moneary sysem, whch manfess self n agens wllngness o hold dollars rrespecve of he developmens n he US economy. The presence of a smlar rend, whch he auhors erm a safe haven or porfolo balance effec, n he Polsh-German daa seems plausble because of he radonally mporan role of he German mark as a medum of exchange and, especally, as a sore of value n he formerly cenrally planned economes of Cenral and Easern Europe. In ha case he rank of Π would be equal o. To summarse, we expec o fnd wo or hree conegraon relaons, and, correspondngly, hree or wo common sochasc rends drvng he sysem. More specfcally, f he smple pares dscussed n Secon descrbe he varaon n our daa correcly, hen hey can be modelled ndvdually because he relaons defnng hem are saonary by hemselves. From he graphs n Secon 3, we reckon ha he pares do no hold for our daa se. Therefore, we am a fndng ou wheher here exs saonary lnear combnaons of he smple pares. In oher words, we seek o fnd parameer values for a, b and c such ha: a ( ) b( p p ) c ppp (5) or, alernavely: a ( p ) b( p ) c ppp (6) defne saonary equlbrum relaons whch pull he sysem varables whenever hey are pushed away from equlbrum. Noe ha he smple pary relaons are specal cases of he above equaons as hey resul from seng wo of he parameers a, b, c o zero and normalsng he remanng parameer. We expec he seady-sae relaons found n our daa o be specal cases of equaons (5) and (6), or perhaps he equaons hemselves. 5 The emprcal analyss A. Specfcaon and esmaon of he unresrced VAR model As a frs sep of our analyss, we specfed and esmaed he unresrced VAR model presened n Secon 4. By seng he maxmum lag lengh o wo, we were able o oban a parsmonous model wh well-behaved resduals. We based our choce of he lag lengh prmarly on resdual analyss, alhough we also checked he nformaon crera and performed lag reducon ess. 3 In erms of deermnsc componens, he model was specfed so as o nclude an unresrced consan, whch means ha he daa n levels show rendng behavour bu he All resuls presened n hs paper were obaned usng CATS n RATS, verson (see Denns e al. 005). 3 The Schwarz Creron poned o k = and he Hannan-Qunn Creron o k = ; he lag reducon ess, however, suggesed a longer maxmum lag lengh. The resuls are no repored here o save space bu, lke any oher resuls, are avalable from he auhor upon reques.

13 dfferenced daa have no rend. Ths s exacly wha he graphs of levels and dfferences of our me seres show (see Fgure A.). Orgnally we ncluded a rend erm resrced o appear n he conegraon space n order o accoun for he possbly ha he rends n daa do no cancel ou n he conegraon relaons. Long-run varable excluson ess showed, however, ha he rend erm could be excluded from he conegraon space whou loss of nformaon. Apar from he consan, cenred seasonal dummes and oher dummes were ncluded. Specfcally, we used nnovaonal dummes o accoun for large nervenons as well as a shf dummy resrced o le n he conegraon space, C 995: 05. The laer pcks up a level shf n he equlbrum relaon nvolvng he Polsh bond rae, whch we beleve o have aken place n May 995. The shf, whose occurrence s suggesed by our daa, can be pu down o mporan srucural changes n he moneary regme n Poland. Specfcally, on 6 h May 995 here was a changeover o a crawlng bands exchange rae regme wh a ±7% flucuaon band. Moreover, sarng from s June 995 he Polsh zloy became converble n accordance wh Arcle VIII of he Arcles of Agreemen of he Inernaonal Moneary Fund (IMF 945). The unresrced esmae of he long-run marx Π, wh sgnfcan coeffcens yped n bold face, s gven n Table A..a n he Appendx. 4 B. Deermnaon of he conegraon rank The second sep of he analyss conssed n he deermnaon of he conegraon rank, r,.e. he number of seady-sae relaons beween he varables of he sysem. As he choce of he conegraon rank s crucal for all subsequen analyss, we used all nformaon ha was avalable from he daa before decdng upon he correc rank. 5 The only formal es ha we appled was he race es, or he Johansen es 6, whose resuls for he model descrbed above are repored n Table A..a n he Appendx. 7 The larges wo egenvalues are sgnfcanly dfferen from zero a every sandard sgnfcance level; he sgnfcance of he hrd-larges egenvalue s borderlne. The race es hus pons o r =, bu a hs pon we canno exclude he possbly ha he hrd conegraon relaon s also saonary. The reason s he fac ha he race es has low power o rejec he un roo hypohess when he rue roo s lower ha bu near one,.e. when s n he near un roo regon. The low power problem s aggravaed by our relavely small sample sze. Therefore, we need o use oher sources of nformaon concernng r. As a frs sensvy check, we recalculaed he race es for a dfferen model specfcaon, namely one ha ncludes 4 Pror o esmaon, addve oulers (measuremen errors) were removed from he me seres of he German prce level; he fgures n he prevous secon and n he Appendx depc he correced daa. 5 All he ess and procedures used here are dscussed a lengh n Juselus (006, ch. 6). 6 See Johansen (996). 7 We smulaed he asympoc dsrbuon of he race es sascs usng he auomac CATS procedure wh,000 random walks and 0,000 replcaons.

14 no dummy varables excep for seasonal dummes. The resuls of hs es are repored n Table A..b n he Appendx. The es hs me very clearly pons o r = : wh a p-value of over 0.8, he sgnfcance of he smalles hree egenvalues canno be rejeced. Secondly, we looked a graphs depcng he ndvdual conegraon relaons of he unresrced model (see Fgure A..a n he Appendx) o assess wheher hey look saonary. The frs wo conegraon relaons behave lke saonary processes, he oppose holds for he las wo. The hrd relaon s of specal neres because f looked saonary, hen we would consder r = 3 n spe of he above-repored resuls of he race ess. As can be seen from he fgure, hs s hardly he case. The wo conegraon relaons of he model where he conegraon rank was resrced o (see Fgure A..b n he Appendx) seem agan o be very saonary, whch agan pons o r =. Thrdly, we compued he roos of he companon marx for dfferen values of r (see Table A.3 n he Appendx). Noe ha choosng a gven r auomacally leads o j r un roos, whch does no necessarly mean ha here are j r sochasc common rends n he daa. Lookng a he larges egenvalues for dfferen choces of r reveals ha for r 3, he hrd-larges egenvalue s near uny, whereas he fourh and he ffh are dsncly far from he un crcle. Ths leads us o he enave concluson 8 conegraon rank. ha he race es has pcked up he correc A furher source of nformaon on he conegraon rank s he unresrced esmae of he marx α and more specfcally, he sgnfcance of s parameers. As can be seen from Table A.4 n he Appendx, whch gves he unresrced esmaes of α gven dfferen values of r, he coeffcens n he frs wo columns have generally hgh -raos, bu he hrd column conans only one coeffcen ha s borderlne sgnfcan. 9 Ths can agan be nerpreed as evdence ha he hrd conegrang relaon mgh be saonary, alhough raher borderlne so. Furhermore, we used he recursvely calculaed race es sascs (see Fgure A.3 n he Appendx) o draw conclusons on he conegraon rank. The upper wo lnes, depcng he race es sascs for he wo mos saonary conegraon relaons, exhb pronounced lnear growh, whereas he oher hree reman roughly consan as more and more observaons are added o he base perod. Ths resul agan suggess ha r =. Fnally, one can draw on economc heory o hypohesse abou he number of conegrang relaonshps n our model. As argued n Secon 4, we expeced he varables n our sysem o be drven by wo or hree sochasc common rends, and herefore he conegraon 8 The concluson s only enave because we do no know he dsrbuon of he egenvalues, whch makes mpossble o es whch values are sgnfcanly dfferen from uny. 9 Noe ha he exac dsrbuon of hese coeffcens s unknown. If he correspondng equlbrum relaons are saonary, he -sascs are dsrbued as Suden s and n he non-saonary case as Dckey-Fuller s τ. 3

15 rank o be equal o hree or wo, whch s conssen wh he resuls dscussed above. Thus, based on all sources of nformaon we conclude ha he rank of he marx Π and hus he number of seady-sae relaonshps beween our varables of neres s equal o wo. The esmae of Π based on hs reduced rank s gven n Table A..b. C. Specfcaon ess Pror o he acual conegraon analyss we performed varous specfcaon ess of he esmaed VAR model o check he assumpon of he error erms beng ndependenly normally dsrbued. The resuls of hese ess, boh for he full rank and he resrced rank VAR model, are repored n Table A.5 n he Appendx. An mporan pon o noe s ha vald sascal nference s sensve o volaon of ceran assumpons, such as auocorrelaed or skewed resduals and parameer nconsancy, and que robus o volaon of ohers, such as resdual heeroskedascy or excess kuross. The mos mporan assumpons regardng he resduals are herefore hose of no auocorrelaon and zero skewness. As can be seen from he able, none of he ess rejecs he former hypohess for he whole sysem. As for he laer, normaly s srongly rejeced for he whole sysem and for equaons explanng he Polsh nflaon rae and boh bond raes. Ths resul s, however, prmarly due o he fac ha he kuross of he respecve emprcal dsrbuons s oo large o be assocaed wh normal dsrbuon, whereas he skewness seems o be less of a problem. Table A.5 shows ha he resduals from he equaon explanng he Polsh neres rae exhb ARCH effecs, whereas no such effecs are deeced n any he oher equaon or he sysem as a whole. All n all, we conclude ha he assumpon of ndependen mulvarae normal dsrbuon of he resduals s by and large confrmed by he daa. Furhermore, Table A.5 repors goodness-of-f measures for he whole model (race correlaon) and for ndvdual equaons (deermnaon coeffcen, R ). The race correlaon s farly large and he same holds for R for he equaons explanng he nflaon raes and he Polsh bond rae. The low values of R for he remanng wo equaons can be explaned by he weak exogeney of he German bond rae and he devaon from PPP (see Secon 5.D). The hrd assumpon ha s crucal for vald sascal nference based on a VAR model s ha he sample perod defnes a reasonably consan parameer regme. To check hs, we performed varous recursve ess of parameer consancy for he reduced rank model ( r = ): he recursvely calculaed es for consancy of he log-lkelhood funcon, he recursvely calculaed race es sascs, egenvalues and ransformed egenvalues, he max es of consan bea, and he -sep predcon es. 0 Vrually all ess, whose resuls are no repored here o save space, 0 All ess are exensvely dscussed n Juselus (006). 4

16 show ha he model s parameers have been consan hroughou he sample perod. Ths s especally rue wh regard o he concenraed model,.e. one where he shor-run dynamcs, Γ x, and deermnsc componens, Φ D, have been concenraed ou. The resuls presened n hs secon and he prevous one sugges ha our VAR model sasfes he I() assumpons, whch posulae ha () he rank of he marx Π s equal o r, () he companon marx has exacly j r un roos, correspondng o he sochasc rends ha drve he sysem varables, () he resduals are ndependen, (v) he sample sze s large (our relavely small sample sze s accouned for by he Barle correcon of varous es sascs) and (v) he parameers of he VAR model are sable hroughou he sample. These condons are he prerequse for he Granger represenaon heorem o hold,.e. for he VAR model o have a movng average represenaon (see equaon (7) n he nex secon). D. Tesng resrcons on long-run parameers The nex sep s o es resrcons on parameers of he long-run srucure,.e. of he marces α and β. The pon of deparure for all ess dscussed below are he esmaes of α and β subjec o rank resrcon r =. The parameers of he former marx are ermed adjusmen coeffcens because hey descrbe how he varables of he sysem adjus when hey are pushed away from he seady sae. An mporan es s ha of a zero row n α, whch s anamoun o weak exogeney of he varable correspondng o ha row. The hypohess of long-run weak exogeney, or no levels feedback, of a varable x for he long-run parameers β means ha he varable x has nfluenced he long-run sochasc pah of he oher varables n he sysem bu has self no been nfluenced by hem. Ths can be seen from he movng average (MA) represenaon, whch n s smples form (whou shor-run dynamcs and deermnsc componens) s gven by: ~ x = β α ε s + C + s= ~ β α β where ( ) ( L) ( L) ε A β, α and (7) β are he respecve orhogonal complemens o α and β, C s a lag polynomal and A depends on nal values. The erm α ε s defnes he common sochasc rends drvng he sysem and ~ β her loadngs, descrbng how he common rends are ransmed o he sysem varables. The hypohess of a zero row n α corresponds o a un vecor n s complemen, α. Thus, f he hypohess of weak exogeney of a gven varable s acceped, he cumulaed shocks o ha varable alone defne one of he common rends drvng Wh he excepon of he recursvely calculaed race es sascs dscussed n he las secon, see Fgure A.3 n he Appendx. j j r I.e. ( ) marces of full column rank such ha ( α, α ) rank( β, β ) = j rank, α α = 0 and β β = 0. 5 =

17 he sysem. As here are j r common rends, he number of weakly exogenous varables canno exceed j r,.e. hree n our case. The ess resuls (see Table A.6 n he Appendx) show ha he German bond rae and he devaon from PPP are boh weakly exogenous when esed ndvdually. Moreover, he hypohess of he wo varables beng jonly weakly exogenous s also acceped. We can conclude ha he cumulaed shocks o each of hese varables defne wo of he hree common rends pushng he sysem. As wll be shown n Secon 5.E, he German bond rae s also srongly exogenous, whch means ha hs varable self, and no jus he cumulaed shocks o, represen a common rend. The hrd common rend s a lnear combnaon of cumulaed shocks o he Polsh and he German nflaon raes and o he Polsh bond rae (see also equaon () n Secon 5.E). Accepng he hypohess of no long-run levels feedback for he wo varables n queson means ha our VAR model does no explan he sochasc pah of he devaon from PPP, whch would be a problem f modellng hs pah was he goal of our analyss. From ha follows ha we could reduce he dmenson of our sysem o hree and only nclude he German bond rae and he devaon from PPP as weakly exogenous varables n he conegraon space. A second es nvolvng he adjusmen coeffcen marx s ha of a un vecor n α, meanng ha he varable correspondng o hs vecor s exclusvely adjusng (.e. shocks o ha varable have only emporary effecs on he oher varables of he sysem). Ths can agan be seen from (7): as a un vecor n he marx α corresponds o a zero row n α, shocks o he gven varable do no ener he erm α ε s,.e. do no nfluence he level of x n he long run. We performed he es for each of he endogenous varables n our sysem (see Table A.7 n he Appendx for resuls) and found no evdence of a un vecor n α a he 5 percen sgnfcance level. Thus, we conclude ha none of he varables n he sysem s exclusvely adjusng. When esng resrcons on he parameers of β, he am s o fnd ou whch of he model varables and whch lnear combnaons of hem are saonary. Ths leads o he denfcaon of he fnal se of conegraon relaons ha are, deally, economcally meanngful equlbrum relaons. As a frs sep, we performed ess of he long-run excluson of varables from all conegrang relaons,.e. ess of zero row resrcons on β. The resuls, repored n Table A.8 n he Appendx, show ha only he German bond rae (whch s also weakly exogenous o he sysem) can be excluded from he long-run equlbrum relaons. Ineresngly enough, he shf dummy, C 995: 05, canno be excluded from he conegraon space. We wll draw on hese resuls when formulang our fnal conegraon relaons. In a second sep, we esed he saonary of a varey of lnear combnaons of he sysem varables, sarng from he varables hemselves (see Table A.9 n he Appendx). We frs 6

18 esed for saonary of each sngle varable (hypoheses H o H 5 ), comng o he concluson ha only he German nflaon rae s by self I(0). However, he p-value assocaed wh ha laer es s so low ha we do no, n fac, beleve ha p s saonary. 3 Then we esed a number of relaons nvolvng he nflaon dfferenal p (H 6 o H 8 ), he neres spread p (H 9 o H 3 ), he domesc and he foregn real neres raes, p and (H 4 o H 8 ). We do no p repor he resuls of all performed ess bu raher presen he oucome for he gven smple relaon and all s saonary combnaons wh oher varables ha we have found. For each of he hypoheses we also esed wheher he relaons are saonary when he shf dummy s ncluded n he relaonshp bu we only repor he oucome when was changed by he ncluson of he dummy. The general oucome of hs exercse s ha none of he smple pary condons s sasfed by he daa. If PPP held, hen he real exchange rae should be saonary or a leas conegraed wh he nflaon dfferenal. However, he wo varables can only be made saonary f he German bond rae or boh bond raes are added o he lnear combnaon (see H 7 and H 8 ). If UIP held, hen he neres spread should be saonary or a leas conegraed wh he nomnal deprecaon rae. We were no able o es he laer hypohess drecly whn our VAR framework because he nomnal rae s no one of he sysem varables. 4 However, he saonary of he neres spread s decsvely rejeced (H 6 ). If RIP held, hen he real bond raes would be I(0) or a leas conegraed wh each oher, and he neres spread would be conegraed wh he nflaon dfferenal (we have already shown ha hese boh smple relaons are non-saonary). These hypoheses are also rejeced, hough (H 4, H 8, H 9, and H 0, respecvely). A lnear combnaon of he neres spread and he nflaon spread can only be made saonary by augmenng wh boh he real exchange rae and he shf dummy (H ); n case of he real bond raes saonary canno be acheved even n hs way (H ). Recall from Secon 4 ha we expeced our conegraon relaons o be specal cases of equaons (5) and (6), or hese equaons hemselves. Relaon (6) urned ou o be nonsaonary even when augmened by a shf dummy (H ); herefore, here s no equlbrum relaon beween real neres raes n boh counres and he real exchange rae. As for relaon (5), descrbng a lnear combnaon of he neres spread, he prce dfferenal and he real 3 If he German nflaon rae s saonary, canno be conegraed wh any non-saonary sngle varable or lnear combnaon of varables n he sysem so here was, heorecally, no pon n esng e.g. he hypoheses of he nflaon dfferenal or he German real bond rae beng saonary. However, he fac ha one canno rejec a hypohess does no necessarly mean ha he laer s rue: he probably of accepng a false hypohess s never zero (unless one adops he sraegy of never accepng he null). We hus decded o es such combnaons ha, from he purely heorecal pon of vew, could no be saonary f he German nflaon rae really was I(0). 4 We esed he hypohess of he nomnal exchange rae beng I(),.e. of s frs dfference beng I(0), usng a dfferen specfcaon of he VAR model where he vecor of varables ncluded he prce dfferenal, boh neres raes, he spo rae and he domesc nflaon rae, and could no rejec hs hypohess. 7

19 exchange rae, s saonary when he level shf s accouned for (H ). Ths equaon hus became our prmary canddae for a conegraon relaon. However, when esng he resrcons mpared n relaon (5) jonly wh hose ncorporang any oher saonary combnaon of he sysem varables, we found ha he resrcons were only borderlne acceped. Moreover, prevous ess showed ha he German bond rae can be excluded from he conegraon space alogeher. These resuls made us look for oher saonary combnaons whch could be hough of as rreducble conegraon relaons and, deally, should have a plausble economc nerpreaon as long-run seady-saes. 5 One canddae for an rreducble conegraon relaon s he lnear combnaon defned by H 5, ( p ) a p bc995: 05, whch relaes he domesc real neres rae o he foregn nflaon. A relaon ha can be gven economc nerpreaon, on he oher hand, s he one defned by H 3, p a p ( a) b ppp cc995: 05, whch mposes a long-run homogeney resrcon (sum of he coeffcens equal o zero) on he domesc and foregn nflaon and he domesc neres rae. Is nerpreaon s as follows: he domesc nflaon s parly mpored and parly he resul of nflaon expecaons, refleced n he domesc bond rae; s also affeced by he real exchange rae. These wo lnear combnaons of he sysem varables are he ones ha we evenually adoped as our conegraon relaons. E. Idenfcaon of he long-run and he shor-run srucure In he prevous secon we esablshed wo saonary relaons lnear combnaons of he sysem varables ha are our poenal conegraon relaons. The resrced rank VAR model was hen esmaed subjec o resrcons defnng he wo relaons as well as wo zero row resrcons on he marx α (recall from he prevous secon ha and ppp are ndvdually and jonly weakly exogenous). The resul s gven n Table A.0 and he correspondng resrced esmae of he marx Π n Table A..c (boh ables are n he Appendx). The resrcons on α and β have hardly changed he esmae when compared wh prevous resuls. Our conegraon relaons are defned as follows: CR p p ppp C995:05 = (8) ( p ) 4.88 p 0.04C995:05, CR = (9) As can be easly seen, he frs relaon s jus denfed and he second s over-denfed. The sysem as a whole s herefore formally (genercally) over-denfed 6 and he resrcons are 5 An rreducble conegraon relaon s a saonary lnear combnaon of non-saonary varables ha becomes non-saonary once any of hem s dropped from he relaon; see Davdson (998). A heorecally meanngful equlbrum relaon can be a lnear combnaon of wo or more rreducble conegraon relaons. 6 See Juselus (006) for an nuonal exposon of generc denfcaon and Johansen (995) for echncal deals. 8

20 esable. The resrcons were acceped wh a farly large p-value based on a Lkelhood Rao (LR) es. Moreover, he conegraon relaons are also emprcally denfed,.e. he coeffcens whch have no been se o zero when formulang he resrcons are n fac sgnfcanly dfferen from zero n he esmaed sysem. As for economc denfcaon,.e. nerpreably of he resuls, we already dscussed hs ssue a he end of he prevous secon. From he economc pon of vew, no only he conegraon relaons bu also he adjusmen coeffcens are of specal neres. Based on he resuls n Table A.0, we have: p p 0 = ppp CR CR The zero coeffcen values n he las wo rows of α are he resul of he mposed resrcons; however, he unresrced coeffcens were nsgnfcanly dfferen from zero anyway. Ths means ha boh weakly exogenous varables, he German bond rae and he real exchange rae, do no equlbrum-adjus,.e. her change n he presen perod s unaffeced by he deparure from equlbrum n he prevous perod. The coeffcens α and α are nsgnfcan so we se hem o zero n he above equaon. The reacons of he ruly endogenous sysem varables o he deparure from seady-saes are plausble n he sense ha he respecve α coeffcens are sgnfcan, have he sgns conssen wh error-correcng behavour (.e. here s no overshoong n he sysem) 7, and are of magnude whch by and large makes sense. The Polsh nflaon rae adjuss o he frs conegraon relaon, CR, whch s he equlbrum relaon for hs varable. If he deparure from CR n a gven monh s posve, hen (0) p would fall n he followng monh, correcng approxmaely 9% of he equlbrum error, whch amouns o very fas adjusmen. The German nflaon rae exhbs equlbrum-correcng behavour wh respec o CR and he Polsh bond rae wh respec o boh relaons, alhough he adjusmen s much slower han ha of p. Apar from he surprsngly hgh speed of adjusmen of he Polsh nflaon rae, he esmaed sysem seems o be economcally plausble. The over-denfed long-run srucure descrbed above was he pon of deparure for he denfcaon of he shor-run srucure: when esng resrcons on shor-run parameers, we kep he parameers c βˆ fxed a her prevously esmaed values. 8 The VAR model dscussed so far 7 The -h conegrang relaon s sgnfcanly equlbrum-correcng f he parameers n he -h column of he marx α are sgnfcanly dfferen from zero and have he sgns conssen wh equlbrum-correcng behavour,.e. he sgns oppose o hose of he correspondng coeffcens n he marx β. 8 The sascal movaon for hs s he superconssency of he esmaor βˆ (or 9 c βˆ ).

21 s heavly overparamersed; especally he shor-run marx Γ and he deermnsc componens marx Φ conans many nsgnfcan coeffcens. Our goal s now o acheve a parsmonous paramersaon of he shor-run reduced-form VAR model. Based on parameer sgnfcance and he resuls of he LR es of over-denfyng resrcons, we were able o mpose a oal of 56 resrcons on he shor-run srucure. The resuls are repored n Table A. n he Appendx; he columns represen he equaons of he sysem. The unlagged endogenous varables 9 have only been ncluded n her own equaons and he correspondng un marx of coeffcens s no repored o save space. As can be seen from he able, mos of he coeffcens of he marx Γ could be se o zero whou sgnfcanly changng he value of he lkelhood funcon; only n he equaon of he Polsh neres rae and he devaon from PPP are he lagged dfferences of (some) sysem varables sgnfcan. A parcularly srkng resul s ha of all coeffcens n he German neres rae equaon equal o zero. Combned wh he resuls of he analyss n Secon 5.D, where was found o be weakly exogenous (ndvdually and jonly wh he real exchange rae), hs means ha he German bond rae s srongly exogenous o he sysem and ha he correspondng equaon could be excluded from he model wh no loss of nformaon. As already menoned n Secon 5.D, anoher concluson s ha one of he sochasc rends o he sysem s self, no jus shocks o. As for he adjusmen coeffcens, he resuls are smlar o hose descrbed above, wh he dfference ha he German nflaon rae now adjuss o boh conegraon relaons and he speed of adjusmen of he Polsh nflaon rae s somewha lower. All n all, our resrced reducedform VAR does no enal any resuls ha are nconssen wh economc heory or wh he oucome of our prevous analyss. Moreover, he resduals are essenally uncorrelaed, as can be seen from he boom panel of Table A.: only he correlaon coeffcen beween he resduals of he frs and he ffh equaon s sgnfcanly dfferen from zero. Thus, our reduced-form model can be nerpreed as a srucural VAR model. Based on he esmaed over-denfed sysem (0), he MA represenaon s as follows: 9 The erm endogenous s n quoaon marks because sands for he varables ha sand on he lef-hand sde of he sysem (ncludng he weakly exogenous ones, lke he real exchange rae and he German bond rae n our model), no necessarly hose ha are acually explaned by he sysem. 0

22 p p 0.06 = ppp s= ε p, s s= s= ε ε, s s= ppp, s ε p, s + s= ε, s +... () The esmaes of α, defnng he common rends, and ~ β, defnng her loadngs, are gven n Table A. n he Appendx; for smplcy we se nsgnfcan coeffcens o zero n he above equaon. Bearng n mnd he resul of srong exogeney of he German bond rae, we have: ε = (), s s=.e. he German bond rae self, and no jus shocks o, consues he second common rend, whch drves boh bond raes n he long run. The hrd common rend, drvng prces n boh counres and he real exchange rae, s he cumulaed sum o ha laer varable. The frs rend s a lnear combnaon of cumulaed shocks o he hree endogenous varables, and deermnes he levels of hese hree varables n he long run. We have no red o fnd he srucural MA represenaon or o gve he shocks labels,.e. o nerpre hem as srucural shocks; hs s a ask for our fuure research. However, we noe ha he second rend, he German bond rae, can be nerpreed as a safe haven or porfolo balance effec (see Juselus, MacDonald 004a), whch s relaed o he mporan role of he German mark or raher, he (fuure) EMU for whch Germany s a proxy for he Polsh economy. 6 Summary and conclusons In hs paper we red o denfy a se of economcally meanngful long-run equlbrum relaons ha would reflec he nernaonal pary condons: he purchasng power pary, he uncovered neres pary and he real neres pary. As hese smple pares seldom hold emprcally, he general dea was o model hem jonly n order o uncover he dynamc srucure underlyng he sochasc behavour of prces, neres raes and he real exchange rae n Poland versus he EMU, represened by Germany. The emprcal analyss, based on a conegraed VAR model, no only showed ha he smple pares are nconssen wh our daa se bu also faled o denfy conegraon relaons ha would be lnear combnaons of all hree pares. Therefore, he queson arses why he pares ha are so well-esablshed n he economc heory could no be pnned down when analysng he Polsh-German daa se, even when we analysed hem jonly and allowed for me rends and level shfs n he daa. We see he raonale for hs n he fac ha our sample was raher shor, and covered he perod of Poland s ranson from a cenrally planned o a marke economy. Therefore, he pares whch are supposed o hold