Interest Parity Conditions. Interest parity conditions are no-arbitrage profit conditions for capital. The easiest way to

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1 World Economy - Inrs Ra Pariy (nry wrin for h Princon Encyclopdia of h World Economy) Inrs Pariy Condiions Th pariy condiions Inrs pariy condiions ar no-arbirag profi condiions for capial. Th asis way o undrsand his condiion is considr how a ypical invsor can sav in diffrn locaions. Suppos h hom currncy is a dollar, and h forign currncy is a uro. Thn, assuming a forward mark xiss, h invsor can ihr sav a hom, rciving inrs ra i, or convring by h xchang ra S, rciving inrs ra i* abroad, and hn convring back o hom currncy by h forward ra F obaining a im for a rad a im +. ( + i) vrsus ( + i * ) F S, + If h gross rurn on h lf grar han ha on h righ, hn invsors will plac hir capial in h hom counry; if i is lss, hn invsors will plac hir capial abroad. Wih infini amouns of capial moving in sarch of h highs rurn (and in his xampl, hr is no risk in nominal rms), hs rurns will b qualizd. F i i *, + ( + ) = ( + ) () S Afr manipulaion, ( i ( F * i ), = + * + i ) S S (2) This condiion is calld covrd inrs ra pariy, rflcing h fac ha invsors ar covrd agains nominal uncrainy by way of h forward mark. If h forward ra is qual o h fuur spo ra (s forward prmium ), such ha F, + S, + = hn (2) bcoms:

2 World Economy - Inrs Ra Pariy 2 (nry wrin for h Princon Encyclopdia of h World Economy) ( i ( S * i ), = + * + i ) S S (3) Whr h suprscrip dnos xpcd. Equaion (3) is rmd uncovrd inrs ra pariy. This xprssion holds whn invsors do no rquir compnsaion for h uncrainy associad wih rading currncis in h fuur. I sas ha xpcd nominal rurns ar qualizd across bordrs in common currncy rms. Whn inrs ras ar low, h following log approximaions ar ofn usd for quaions (2) and (3). ( i s (2 ) i * ) = f, + ( i s (3 ) i * ) = s, + Frankl (99) has labld condiion (2) holding as characrizing prfc capial mobiliy, whil condiion (3) is associad wih prfc capial subsiuabiliy. Ths rms aris from h viw ha if (2) dos no hold, hr mus b som sor of impdimn capial conrols or h hra hrof o h fr flow of financial capial. Bu vn if capial is fr o mov, invsors may sill rspond o risk; ha rspons o risk migh driv a wdg bwn h xpcd spo and forward ra. Whn invsors ar risk-nural in nominal rms, hn invsors will ra capial (say db insrumns issud in diffrn currncis) as prfcly subsiuabl. Th abov condiions prain o financial capial. In ordr o considr h mobiliy of physical capial, on has o bring ino play h prics of commodiis. Ingraion of goods marks ar ofn dfind as rlaiv purchasing powr pariy holding. Ex an rlaiv PPP can b wrin as: * * s, + s = ( p, + p ) ( p, + p ) (4) 2

3 World Economy - Inrs Ra Pariy 3 (nry wrin for h Princon Encyclopdia of h World Economy) Whr p is h log pric lvl. Equaion 4 sas ha xpcd dprciaion quals h xpcd inflaion diffrnial. Combining (4) wih h uncovrd inrs ra pariy condiion (3 ) lads o ral inrs pariy. i ( p * * * + p ) = i ( p, p ) (5), + This says h xpcd ra of rurn on capial, xprssd in physical unis, is qualizd across bordrs. To h xn ha in noclassical modls h marginal produc of capial quals h ral inrs ra, his condiion is quivaln o h qualizaion of marginal producs of capial qualizd across bordrs. Covrd Inrs Pariy Assssd For dvlopd conomis sinc h dismanling of capial conrols, covrd inrs pariy holds fairly wll. I should b nod ha mos ss ar conducd using offshor ras, in which cas (2) is somims rmd closd inrs pariy, alhough covrd inrs pariy is ofn usd as a rm ncompassing his concp. Early ss wr conducd by Frnkl and Lvich (975). Thy found ha, afr accouning for ransacions coss, covrd inrs pariy hld for 3 monh horizons. Offshor ras somims divrg from onshor ras, so ha h findings of covrd inrs pariy ar somwha wakr. Th qusion of whhr covrd inrs pariy holds for longr horizons is an opn on. Poppr (993) concluds ha covrd inrs diffrnials a long mauriis ar no apprciably grar han hos for shor (up o on yar) mauriis. This is a surprising rsul givn ha hr ar likly a numbr of rgulaory impdimns ha would nd o inroduc fricions ino h arbirag procss. Daa from long-da currncy swaps confirm his finding. 3

4 World Economy - Inrs Ra Pariy 4 (nry wrin for h Princon Encyclopdia of h World Economy) Prior o h dismanling of capial conrols, and in many mrging marks oday, covrd inrs pariy is unlikly o hold. In ohr words, covrd inrs diffrnials could b inrprd as poliical risk, associad wih h possibiliy of govrnmnal auhoriis placing rsricions on dposis locad in diffrn jurisdicions (clarly his is somhing ha is no rlvan whn all h dposis ar offshor). Alibr (973) is crdid wih his inrpraion, whil Dooly and Isard (980) providd mpirical simas for h DM/dollar ra. Th Empirical Evidnc for Uncovrd Inrs Pariy Uncovrd inrs pariy is a mor difficul condiion o s, ssnially bcaus xpcd xchang ra changs ar unobsrvabl. In h liraur, mos ss of UIP ar acually join ss of UIP and h raional xpcaions hypohsis, i.., ha x pos ralizaions of h xchang ra ar a unbiasd masur of h x an xchang ra, viz., s =, + E( s+ I ). This assumpion combind wih quaion (2 ) yilds his sandard rgrssion quaion (somims calld h Fama quaion ): s + s = 0 + β( f, + s ) + υ+ β (6) Or by viru of covrd inrs pariy holding, s * + s = 0 + β( i i ) + υ+ β (7) Whr undr h join null hypohsis υ + is a man zro rror unprdicabl using pas informaion, and β =. Th vidnc in favor of his join hypohsis of UIP and raional xpcaions is qui wak. Th rgrssion of h x pos chang of h spo xchang ra on ihr h forward discoun (in quaion 6), or h inrs diffrnial (in quaion 7) ypically yilds a slop 4

5 World Economy - Inrs Ra Pariy 5 (nry wrin for h Princon Encyclopdia of h World Economy) cofficin sima ha is no only diffrn from uniy, bu in fac ngaiv and diffrn from zro a convnional lvls of saisical significanc. This is ru for rsrv currncis (h U.S. dollar, h yn, h Swiss franc, h duschmark, h franc, or hir succssor currncy, h uro) a horizons up o a yar. I is also ru for som mrging mark currncis (s Frankl and Poonawala, 2006). On inrsing characrisic of hs rgrssions is ha, alhough h cofficins ar ypically diffrn from zro in a saisical sns, h proporion of oal variaion xplaind is ypically vry small; i is no rar o obain ngaiv adjusd R-squard s. A longr horizons, (3, 5, 0 yars) h vidnc is mor supporiv of h combind UIPraional xpcaions hypohsis. Chinn and Mrdih (2004) documn ha simas of h β cofficin ar usually no significanly diffrn from h posid valu of uniy a 5 and 0 yar horizons. Th panl rgrssion cofficin a diffrn horizons in hs rgrssions is dpicd in Figur / Unbiasdnss cofficin valu mos. 6 mos. yar 3 yars 5 yars 0 yars Figur : Panl ba cofficins a diffrn horizons. Nos: Up o 2 monhs, panl simas for 6 currncis agains US$, urodposi ras, 980q-00q4; 3 yar rsuls ar zro coupon yilds, 76q-99q2; 5 and 0 yars, consan yilds o mauriy, 80q-00q4 and 83q-00q4. Sourc: Chinn (2006). 5

6 World Economy - Inrs Ra Pariy 6 (nry wrin for h Princon Encyclopdia of h World Economy) Th finding ha h join hypohsis of uncovrd inrs pariy and raional xpcaions holds br a long horizons han a shor appars o b robus. Nonhlss, som cauion is ncssary hr. Considr rgrssions involving n yar inrs diffrnials; by 2003, hr would only b hr non-ovrlapping obsrvaions availabl pr currncy. Inrsingly, Chaboud al. (2005) find ha UIP also holds a xrmly shor horizons of a fw minus. Ohr inrsing rsuls prain o priods of xrm mark urmoil. Flood and Ros (2002), following hir 996 work, find ha uncovrd inrs pariy holds br in rcn ims whn h sampl ncompasss succssful aacks on currncy pgs. Nonhlss, h sill find los of hrogniy in xprincs wih UIP. A diffrn prspciv on uncovrd inrs pariy is providd by dropping h raional xpcaions hypohsis. Froo and Frankl (989) rly upon survy-basd masurs of xchang ras o calcula xpcd dprciaion. Thy find ha for rsrv currncis (agains h U.S. dollar) i is much mor difficul o rjc h null hypohsis ha β =. Using a broadr s of currncis ovr a diffrn sampl priod, Frankl and Chinn (993) find ha whil h simas of h slop cofficin ar always grar han zro, h null of a uni cofficin is rjcd in on insanc. Hnc, for a widr s of currncis including som mrging mark currncis h uncovrd inrs pariy hypohsis dos sm o carry lss wigh. A nw ara of rsarch involvs invsigaion of whhr uncovrd inrs pariy holds for mrging marks. Bansal and Dahlquis (2000) found ha hr was a basic asymmry in whhr UIP holds. In paricular, hy find ha whn h U.S. inrs ra is lowr han forign counry ras, UIP holds, whil UIP fails o hold whn h U.S. ra is highr. Thy also find ha idiosyncraic facors, such as h GDP pr capia of h forign counry, ar imporan in drmining h dgr of failur of UIP o hold. 6

7 World Economy - Inrs Ra Pariy 7 (nry wrin for h Princon Encyclopdia of h World Economy) Using h forward discoun in h sad of inrs diffrnials, Frankl and Poonawala (2006) find ha hr is subsanial hrogniy in h rsuls. Wha mars imporanly is h xchang ra rgim; highly managd xchang ra rgims ar associad wih currncis ha xhibi grar dviaions from UIP. Ral Inrs Pariy Masurd If uncovrd inrs pariy dos no sm o hold a shor horizons, i sms unlikly ha ral inrs pariy, dscribd as xac qualizaion of ral inrs ras, would hold. Howvr, on could sill s h wakr condiion ha movmns in ral ras in on counry would b m by on for on ral movmns in ohr counris. Th ky difficuly wih sing his condiion, lik ha of uncovrd inrs pariy, is ha mark xpcaions ar no dircly obsrvabl. Hnc, on can conduc only join ss for ral inrs pariy. In Fujii and Chinn (200), x pos ralizaions of inflaion, and x an masurs compud using rcursiv im sris modls, ar usd o calcula ral inrs ras. Thy find ha hr ral inrs pariy holds wih diffrn srngh a diffrn horizons. As in numrous prvious sudis (Cumby and Obsfld, 984; Mark, 985), h ral inrs pariy (RIP) hypohsis is dcisivly rjcd wih shor horizon daa. A fiv o n-yar horizons, howvr, h mpirical vidnc bcoms far mor supporiv and in som cass h RIP hypohsis is no rjcd. In gnral, RIP, up o a consan, holds br a long horizons han a shor. Ths rsuls ar robus o alrnaiv ways of modling xpcd inflaion ras. In rcn yars, svral counris hav bgun issuing inflaion-indxd db scuriis. Hnc, on can obain ral ral inrs ras for a slc numbr of counris, including h U.S., h U.K., Canada and Franc. A cursory invsigaion rvals ha hr is no vidnc of 7

8 World Economy - Inrs Ra Pariy 8 (nry wrin for h Princon Encyclopdia of h World Economy) qualizaion. Morovr, whil hr is som covariaion, i is no anywhr nar on for on. Howvr, h hinnss of h marks and h diffrncs in h mauriis of h rlvan db insrumns maks srong conclusions in ihr dircion difficul. Mnzi D. Chinn (/2/07) Profssor of Public Affairs and Economics Univrsiy of Wisconsin Rfrncs Alibr, R.Z., 973, Th Inrs Pariy Thorm: A Rinrpraion, Journal of Poliical Economy 8: Bansal, R. and M. Dahlquis, 2000, Th forward prmium puzzl: diffrn als from dvlopd and mrging conomis, Journal of Inrnaional Economics, Volum 5: Chaboud, A.P. and J. H. Wrigh, 2005, Uncovrd Inrs Pariy: I Works, Bu No For Long, Journal of Inrnaional Economics 66(2): Pags Chinn, Mnzi D., 2006, Th (Parial) Rhabiliaion of Inrs Ra Pariy: Longr Horizons, Alrnaiv Expcaions and Emrging Marks, Journal of Inrnaional Mony and Financ 25() (Fbruary): 7-2. Chinn, Mnzi D. and Guy Mrdih, 2004, Monary Policy and Long Horizon Uncovrd Inrs Pariy, IMF Saff Paprs 5(3) (Novmbr): Cumby, Robr E. and M. Obsfld (984) Inrnaional Inrs Ra and Pric Lvl Linkags undr Flxibl Exchang Ras: A Rviw of Rcn Evidnc, in J. F. O. Bilson and R. C. Marson (diors) Exchang ra Thory and Pracic (Univrsiy of Chicago Prss, Chicago, IL). Dooly, M.P. and P. Isard, 980, Capial conrols, poliical risk, and dviaions from inrsra pariy, Journal of Poliical Economy 88(2): Flood, R.P. and A.K. Ros, 996, Fixs: Of h Forward Discoun Puzzl, Rviw of Economics and Saisics:

9 World Economy - Inrs Ra Pariy 9 (nry wrin for h Princon Encyclopdia of h World Economy) Flood, R.B. and A. K. Ros, 2002, Uncovrd Inrs Pariy in Crisis, Inrnaional Monary Fund Saff Paprs 49: Frankl, Jffry and Jumana Poonawala, 2006, Th Forward Mark in Emrging Currncis: Lss Biasd Than in Major Currncis, NBER Working Papr No (Augus). Frnkl, J.A., and R.M. Lvich, 975, Covrd Inrs Pariy: Unxploid Profis? Journal of Poliical Economy 83(2): Froo, K.A. and J.A. Frankl, 989,"Forward Discoun Bias: Is I an Exchang Risk Prmium?" Quarrly Journal of Economics 04() (Fbruary): Fujii, Eiji and Mnzi D. Chinn, 200, Fin d Siècl Ral Inrs Pariy, Journal of Inrnaional Financial Marks, Insiuions and Mony (3/4): Poppr, H., 993, Long-Trm Covrd Inrs Pariy Evidnc From Currncy Swaps, Journal of Inrnaional Mony and Financ, Vol. 2, No. 4, pp