How could we forget the convergence?

Transcription

1 Ho could org h convrgnc? Rasmus Kaai Bank o Esonia Summar his aricl ocuss on h convrgnc inconsisnc problms ha ma occur in h scond-gnraion applid srucural macroconomric modl o a ransiion or a caching up conom. W sho basd on h Esonian conom as an xampl ha i h rlaiv incom o a counr is iniiall ar blo h lvl i ill ulimal convrg o, h inrcps o h suppl sid bhavioural quaions mus b rsricd b h im dpndn dnamic homogni condiion in ordr o guaran ha h modl conom ill convrg xacl o ha is projcd b h producion uncion. aking car o his issu rquirs prior drminaion o h convrgnc pah. his could b basd on an xrnal ool such as a small cor modl. Alrnaivl a simpl calculus could b usd as shon in h currn papr. Idniing h problm In h olloing a simpl scond-gnraion srucural macro-conomric modl is considrd, hich has Noclassical suppl drmind long run bhaviour and Knsian dmand drivn shor run adjusmn. h modl consiss o a producion uncion, svral bhavioural quaions ha ar groupd ino dmand and suppl sid quaions, and idniis. 1 Ponial groh is givn b h Solo groh modl s Solo 1956, mor prcisl considr h Cobb-Douglas p labour augmning producion uncion Y K, A L, hr Y is h oupu, K is h phsical capial sock, A sands or h lvl o chnolog availabl in h conom, L is labour and dnos im. Ls assum or simplici ha hr is onl on suppl sid bhavioural quaion in h modl h ral ag quaion, rin don in h orm o h rror corrcion modl. In ordr o nsur consisnc bn h producion uncion and h ral ag s bhavioural quaion, irs nd o drmin ho hs pars o h macro modl ar rlad o ach ohr. In h Solo groh modl, hich is usd as an undrling long run groh pah drminan, ach producion acor arns is marginal produc. Ral ag is a marginal produc o labour and is xprssd as: K, A L. 1 L Labour has a posiiv, diminishing marginal producivi: K, A L / L 0 K, A L / L 0,. Simpl pu, h ral ag groh slos don h closr h conom gs o h sad sa. Evnuall, in h sad sa ral ag gros a 1 h xac srucur is no givn hr bcaus i is no rlvan or addrssing h convrgnc inconsisnc issu in h rmindr o h papr. On could s Willman and Esrada 00, Vlov 004, Sidris and Zonzilos 005 and Kaasik al. 004 or an dails o inrs. 1

2 h ra o chnological progrss sad sa and Figur 1. / g, hr dnos h irs ordr dirnc is h ral ag in h d / d also s g Figur 1. h ral ag groh ra h aim o h papr is o sho, undr hich circumsancs h coniguraion o h ral ag s bhavioural quaion dos no viola h ral ag s long run groh pah ha is drivd rom h producion uncion. W sar o b consrucing h olloing rror corrcion modl o h ral ag: ln ~ k ln k v ln ~ c ln, hr ln ~ is h lag polnomial o h obsrvd ral ag groh acual daa, c is h inrcp, ln is h lag polnomial o labour producivi as shon in quaion 1. For h sak o simplici producivi groh is h onl includd xognous variabl, alhough h urhr oucom could b gnralisd o an quaion ih an numbr o xplanaor variabls, as shon lar. h xprssion ln ~ k ln k is h rror corrcion mchanism and v is h disurbanc rm v ~ iid 0,. W dno h sad sa valus o ~ ih ~ and xpc h olloing rlaionship o hold onc h conom has convrgd: ~ ~ / / ln ~ c ln. 3 In h sad sa h ral ag quals o is long run arg ln ~ ln, impling ha ~ ~ / /, hr 1. As a rsul, g ha h shor run dnamics o h rror corrcion modl ar consisn ih h long run par o i onl i c /. his quali mus also hold on h pah o h sad sa, hror rri i in ordr o obain a mor gnral orm o h rsricion and g ha c /. h implicaion o h lar is ha h inrcp canno b rad as a consan anmor bu as a im dpndn

3 variabl bcaus o h diminishing marginal labour producivi m / m /, m 1. his ilds c / and his is ha rr o as a im dpndn dnamic homogni condiion. h conomricall simad quaion aks h orm: ln ~ c ln ln ~ k ln k, 4 hr c. As ral ag is usuall no h onl suppl sid bhavioural quaion in h scond-gnraion macroconomric modls, similar rsricions mus b s on h rs o hm as ll. A gnralisd orm o h rsricion bcoms c, hr is h vcor o h long run groh ras o xognous variabls in h olloing bhavioural quaion: ln k ln x k v ln c ln x, 5 hr ln is h lag polnomial o ndognous variabl, ln x is h lag polnomial o xognous variabls vcor x and ln k ln x k is h rror corrcion rm. Having his, conclud ha hr mus xis a prior knoldg o ho / volvs ovr im and onl hn i bcoms possibl o conomricall sima quaion 4 in our small xampl modl. aking labour groh qual o zro in h Solo modl L / L 0 h groh o labour producivi quals oupu groh and ac h ncssi o drmin h pah o h ral convrgnc o h conom h undrling rnd o pr capia incom. Assumpions on h ral convrgnc In ha ollos rl on h Esonian conom as an xampl in ordr o prsn on possibl soluion ho o projc h ral convrgnc or h uur priods. As ar daling ih a vr long im horizon, a gra dal o uncrain is involvd. hror mus rl on crain assumpions on h convrgnc pah. Naml i is assumd ha Esonian incom convrgs xacl o h EU15 avrag lvl b ar. In addiion, h ras o h conomic groh ar assumd o qualis b h sam im. I implis ha h spd o convrgnc is diminishing h closr h Esonian incom lvl gs o h EU15 h slor h oupu groh s Figur. Knoing h iniial rlaiv incom lvl and h groh ras o Esonia and EU15, i is possibl o calcula h im i aks o rach h EU15 s incom lvl undr h assumpions ha r mad. I ma b argud, hhr EU15 is h righ rrnc group or no. Firsl, us a group o counris in ordr o hav a hrognous sampl. I is mor diicul o jusi convrging o som paricular counr s incom lvl. Bu vn in his cas, hn considr Finland and Sdn, h counris ha Esonian conom has ingrad h mos ih, h rlaiv incom lvl o hs counris is clos o 100% o h EU15. Anohr issu is hhr Esonian rlaiv incom lvl convrgs xacl o 100% or no. Lacking h inormaion on hhr h acual oucom ill b abov or blo I is noorh ha i h modlld conom is blivd o b in a sad sa alrad or airl clos o i hn sing h uppr rsricion on h inrcp o h simad quaion is no rlvan. 3

4 100%, mak his simpliicaion and assum hala soluion. On ma ind h assumpions bing oo binding and rsriciv, bu on h ohr hand a clarl dind arg givs a las a solid ground o urhr discussion. Incom pr capia in logs EU15 Esonia Figur. h ral convrgnc W assum ha EU15 is in h sad sa alrad. I Esonia s incom lvl rachs ha o h EU15 s and groh ras also qualis, boh conomis ould gro a h sam spd o orign chnological progrss ĝ ha indicas ha dal ih h prsumd valu o acual g. W disinguish bn o im priods. h irs priod covrs ars and is dnod ih = [0; ] = 003. h scond priod covrs ars rom 004 up o h nd o convrgnc procss, dnod as = [ + 1; ]. h oal lngh o h im priod bing undr obsrvaion is hus = [0; ]. h olloing quaion is applid o calcula : ˆ d ˆ d 0, 6 hr dnos h Esonian incom lvl oupu pr capia in priod las availabl acual daa obsrvaion, masurd a h purchasing por pari PPP. is h orign EU15 incom lvl a h sam priod, hich is in h uur assumd o gro a h consan ra ra in Esonia in ˆ. Paramr is h avrag obsrvd groh h quaion 6 xprsss linarl diminishing oupu groh ra h groh in h orcas priod sars rom h lvl and gos don o orign groh ra ˆ ĝ b h im priod. In ohr ords, do no ra producivi as a convx curv as shon on igur 1 bu approxima i b a linar rnd. h draback o using a linar uncion is ha i is valid onl in [0; ]. For h sak o simplici his approach is usd hr and no anion has bn paid on inconsisnc in h sad sa and 4

5 acual groh ras ar h ar on could hink ha hr is a kink in h groh ra in priod, saing consanl ĝ, hich is h ra o chnological progrss. sands or h dirnial in avrag oupu groh ra during [0; ] and h groh ra in priod. Using as h iniial groh ra hr o sar projcing h groh in h long run rom, rsul in having a linar rnd ovr h hol priod [0; ] and avoid having a kink in priod s Figur 3. ˆ ˆ ĝ 0 / Figur 3. Projcing diminishing groh ras I is also noorh ha h valu or dpnds ngaivl on h iniial groh ra. h groh dirnial is xprssd in h olloing a: ˆ. 7 As EU15 is assumd o b in h sad sa alrad, i gros a h spd o chnological progrss, hich is ĝ = ˆ = % pr ar. Esonia s iniial rlaiv incom in purchasing pari rms is 44% Eurosa daabas Ncronos and calibraion givs or h iniial incom groh = 5.6%. Appling hs numbrs in quaion 6, g ha is 48 ars or in ohr ords, incom lvls and groh ras ill, according o his purl mahmaical xprimn, qualis in 05. As a rsul hav drmind h long run rnd o h incom lvl convrgnc ha could b dircl applid o rsric h inrcp c in quaion 4. Assumpions on h nominal convrgnc In paralll ih h ral convrgnc also h nominal convrgnc is an imporan counrpar o a macro modl o h caching up conom. hror similar o ha as prsnd abov, a orsigh on ho h pric lvl volvs in h long run is 5

6 ndd. his is also ncssar o rsric ohr suppl sid quaions bsids h ral ag quaion in h mos sandard scond-gnraion macro modl hs ar GDP dlaor and labour dmand quaions. Pric inlaion is currnl highr in Esonia compard o EU15, consisn ih a coninual dcras in h gap bn Esonian and EU15 pric lvls. h driving orc is highr producivi groh in Esonia, hich lads o a convrgnc o srucur and pric lvl as ll. 3 h undrling assumpion or h nominal convrgnc is ha EU15 lvl should b rachd b h im o incom lvl qualisaion. Folloing h sam ramork as usd o drmin incom lvl convrgnc, i is possibl o calcula iniial domsic pric inlaion 4 ha nsurs nominal convrgnc also in rms o lvls and groh ras o nd a h sam im ih h ral convrgnc and compar i o acual daa o s, hhr h projcion xrcis is lad or no: P P ˆ d ˆ d 0. 8 aking h iniial orign pric lvl qual o on hundrd P = 100, Esonian pric lvl, xprssd in GDP dlaor, maks up 5% o i P = 5 Eurosa daabas Ncronos. Forign inlaion is akn o b ˆ = % or h uur priods. According o quaion 8 h iniial arl inlaion ra, hich nsurs ha pric lvl convrgnc nds a h sam im ih ral convrgnc is 4.7% analogousl o ha mans in quaion 8, rlcs h dirnc in avrag inlaion ra in [0; ] and poin valu in. his rsul is also consisn ih acual daa obsrvaions. W can conclud, as i as projcd in h cas o ral groh, also inlaion slos don and bcoms qual o EU15 ra b h im o raching h sad sa, i.. in 48 ars. Conclusions In his papr discussd ha appling h sandard modlling chniqus o modl a caching up conom in h scond-gnraion macroconomric modl ramork could caus an inconsisnc problm in rlcing h convrgnc procss o a counr. W sho using h Esonian conom as an xampl ha i h rlaiv incom o a counr is iniiall qui lo compard o h lvl i ill ulimal convrg o, h inrcps o h suppl sid bhavioural quaions mus b rsricd b h im dpndn dnamic homogni condiion in ordr o guaran ha h modl conom ill convrg o ha is projcd b h producion uncion. Simpl pu i mans ha h long run projcions long run rnds o incom and pric lvls ar rquird o s h rsricions. hr ar svral mhods ho o produc hs long run rnds. W usd a simpl approach in hich rlid on a numbr o assumpions ho h conom convrgs. Approximaing convx marginal producivi curv b a linar rnd i as calculad 3 his procss is blivd o caus prcnag poin inlaion dirnc compard o inlaion in advancd conomis, shon b Randvr 000. Égr sad ha his c had bn srongr in h bginning o h ransiion priod in Esonia, bu i sill rmains a signiican acor Égr W considr GDP dlaor as h main pric lvl indicaor. 6

7 ho long dos i ak o rach h pr capia incom lvl o h EU15. h obaind rsul or h convrgnc priod as hn applid o calcula h long run rnd o h nominal convrgnc. Mor advancd ool o g h long run groh rnds ould b using a small cor modl, hich is a urhr ara o h rlad rsarch. Rrncs Eurosa daabas Ncronos. [uropa.u.in/comm/urosa/ncronos/rrnc /displa.do?scrn=lcomr&opn=/&produc=eu_main_ree&dph=1&langu ag=n] Égr, B. Nominal and Ral Convrgnc in Esonia: h Balassa-Samulson DisConncion radabl goods, Rgulad Prics and Ohr Culpris. Working Paprs o Esi Pank, No. 4, 003, 66 p. Kaasik, U., Kaai, R., Randvr, M., Spp, U. h Monar ransmission Mchanism in Esonia. h Monar ransmission Mchanism in h Balic Sas, Bank o Esonia. Edior Mas, D. G., 004, pp Randvr, M. uluasm konvrgns Euroopa Liidu ja liiuda sooviva riikid vahl. Esi Panga oimisd, Nr. 6, 000, 34 p. Sidris, D., Zonzilos, N. h Grk Modl o h Europan Ssm o Cnral Banks Mul-Counr Modl. Bank o Grc Working papr, No. 0, Fbruar 005, 56 p. Solo, R. M. A Conribuion o h hor o Economic Groh. h Quarrl Journal o Economics, Vol. 70, No. 1, Fbruar 1956, pp Vlov, I. h Lihuanian Block o h ESCB Mul-Counr Modl. BOFI Discussion Paprs, No. 13, 004. Willman, A., Esrada, A. h Spanish Block o h ESCB Mul-Counr Modl. ECB Working Papr, No. 149, Ma 00, 149 p. 7