The Natural Rate of Interest in a Small Open Economy. Fernando de Holanda Barbosa Getulio Vargas Foundation Graduate School of Economics

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1 Th Nul R of In n Smll Opn Eonom Fnndo d Holnd Bbo Gulo Vg Foundon Gdu Shool of Eonom Th gol of h pp o how h h nul of n n mll opn onom, wh o h wold pl mk, ul o h nnonl l of n. W how h pop b ung h nfnl-ld olppng gnon modl nd w u h modl o nlz boh fd nd flbl hng gm. Kwod: Smll opn onom; Nul of n; ompl nd nompl mk. JEL lfon: F4. Inoduon Obfld nd Rogoff (995) nd h pogm h h bom known Th Nw Opn Eonom Moonom (NOEM). Th h bd on dnm nmpol modl fung onl pon, mpf ompon nd nomnl-p gd. On gol of h h o buld modl o pl o o upd h wokho mll opn onom modl of Mundll-Flmng- Donbuh, whh h d h mo-foundon oluon, n p of h wll-known Lu u. Rn wok b Glí nd Monll (5), hnfoh GM, pn modl fo mll opn onom h do no nflun fogn oupu, fogn p ll nd fogn n, whh mp o fll h gp n h lu. GM modl u h nfnl-ld nmpol opmzng pngn modl. I ommon knowldg [ Bo nd Sl--Mn (995), hp 3] h h modl, fo mll opn onom wh pf o h wold pl mk nd fd of m pfn, ld wkwd onun h no Ln () pod omphn u of h l nw opn onom moonom lu. Fo oh onbuon o h lu on mon pol n mll opn onom, fo mpl, ld, Glí nd Gl (), Mllum nd Nlon (), Snon ().

2 nbl h fom hol o fom n mpl pon of w. If h wo w dffn, h would b oppoun fo bg nd pl flow h ld o pdol onluon, h h oun own h wold wlh o mogg ll of pl nd ll of wg nom. Th ul nompbl wh d. In lod onom, h l of n ul o h of m pfn n d. If h dffn, h ok of pl dju o mk up h dffn. In n opn onom, h l of n ul o h nnonl l of n n d. In h h no mhnm o mk h djumn bwn h nnonl l nd h of m pfn. Th dffn bwn h wo, whh po o ng, would mpl onun h ounful. 3 Fou modfon of h ndd nfnl-ld nmpol opmzng pn-gn modl h bn ud n h lu o ol h poblm [ Shm-Gohé nd Ub (3)]. Th : ) ndognou m pfn à l Uzw (968); ) ndognou k pmum; ) on pofolo djumn o; nd ) ompl mk. Th ndognou m pfn h o b uh h gn bom mo mpn whn onumpon n, whh ounnu hpoh. Th n pmum nd on pofolo djumn o hpoh d ho nd, uh, n b ddd bu lk moonom foundon. Th ddd hpoh of ompl mk o h ndd pn-gn modl ndd ong hpoh nd h bn jd b mpl dn [, fo mpl, Obfld nd Rogoff (), nd fn hn]. Thu, h fou modfon no pull ompllng fo mll opn onom wh pf o h wold pl mk. GM u h ompl mk hpoh nd h dd no h f h n h mll opn onom, wh pf pl mobl, h nul of n would no b ul o h nnonl l of n. Th nul of n n h pp ul o h nnonl of n plu onn of hng of h l hng. Undlng h nul h hghl ngn 3 Obfld nd Rogoff (995) up wo-oun modl, wh hom nd fogn nddul h dnl pfn nd h wo oun h h m hnolog. Th up od h poblm of nul nonn bu h wold lod onom. Thu, n uh h l of n ul o h of m pfn n d.

3 ondon no obbl n h l wold, nml h h oun un bom wk f h oun gow g hn h wold onom. Fuhmo, GM modl mpl um pf nhonzon bwn dom nd nnonl bun l. Ohw, h wold onom h o follow n unbl Tlo ul. Th nul of n bnhmk o mu h n of mon pol. Fuhmo, o u mon pol ul, uh Tlo(993), n m of h nul ud. Th lu h dl wh h mumn of h nul [, fo mpl, Lubh nd Wllm (3), Gmmol nd Vll (4)] h ud lod onom modl, n bg opn onom d lod on, nd h no ddd h opn onom. Th pp fll h gp n h lu nd pod fmwok o onu nul fo h mll opn onom bd on onom ho. Th omplhd b ung n olppng gnon modl h ld unu d whn h of m pfn dffn fom h nnonl l of n. Th gol of h pp o how h h nul of n n mll opn onom ul o h nnonl l of n. W how h pop b ung h nfnl-ld olppng gnon modl [Wl (989)] nd w u h modl o nlz boh fd nd flbl hng gm. Th pp ognzd follow. Son d h IS u fom h nfnl-ld olppng gnon modl, n whh h nul of n ul o h nnonl l of n. In h on w u Mllum nd Nlon () fmwok h od h umbom lgb uull found n NOEM modl, whh llow mpl nd ghfowd don of h IS u, whou lo of gnl. W lo u dmn bl bu oh nonmn no n o how h nul onn mbddd n h olppng modl. Son 3 ppl h modl o fd hng m nd Son 4 dl wh h flbl hng m. Th modl n h wo on nno b dud o wo uon dnm m, n h of nflon nd oupu gp, lk h lod onom modl, bu h bho of h un oun ff n fogn nd hough h good mk oupu gp nd, hn, nflon. Son 5 onlud. 3

4 . Olppng Gnon Opn Eonom Modl funon, n gn bon m l fo nd mmz m h ul u, d ubj o h flow budg onn:,,, wh h of m pfn, u [ (, )] h nnnou ul funon, (, ) nd fo h onumpon m b n gn bon m, (, ) l fnnl, () h nom. Th nom no oho pf. In h modl mk nompl, gn h o fogn bond, h dom l of n, UIP ondon hold nd h nnonl of n ognou o h mll opn onom. Nwl bon gn no lnkd lull o ng oho nd h bon wh onl non fnnl wlh bu no fnnl. 4 Thu: (, ) =. Th f od ondon of h poblm ld h Eul uon:,, 4 Th olppng gnon fmwok w ud b llo nd Ghon () o dl wh ndmn of h d. How, h dd no dd h nul poblm of h nfnl ld pn gn modl. 4

5 Th ggg Eul uon onn n djumn m fo onumpon b h nwbon gnon ( (, ) ): 5 n (, ) ( ) Sn onumpon popoonl o ol wlh, NF, wh, dno h onom ol n fogn, NF nd fo non-fnnl wlh nd, NF NF, bu h gn bon whou fnnl. Thu, w h: h ul h ggg Eul uon gn b:,. Mkng u of n Th mll opn onom wh pf o h wold pl mk n h d fo ggg onumpon ( ) n whn h of m pfn dffn fom h l n. Th mll opn onom do oun whn h l n g hn h of m pfn nd dbo oun whn h of m pfn g hn h l n. B ddng nd ubng n / o h pon w g: n Th nul of n gn b: n 5 S Wl ((989), p.88. ml ul would b obnd b ung h olppng gnon modl of Blnhd (985), wh h nddul f onn pobbl of dng n momn of m nd nwlbon gn bon wh onl non fnnl wlh. 5

6 In h up h djumn bwn h of m pfn nd h nnonl l of n hough h onumpon o, whh n b po o ng dpndng on h dg of mpn of h mll opn onom ompd o h wold l of n. W u h followng noon / nd /, wh n fogn nd onumpon nomlzd b ponl oupu. Th f od ln pnon of f ( ) ul o: Th pon n b wn : / / Thu, h gp of h wlh/onumpon o dpnd on h wlh nd onumpon gp odng o: log B ubung h pon n h uon fo h of gowh of onumpon ( ), w obn n n Th mll l dno h loghm of onumpon: = log. Th IS u fo mll opn onom n b obnd fom n nfnl-ld olppng gnon modl b ombnng h ggg onumpon Eul uon wh Mllum nd Nlon () ppoh h um h ll mpo nd lbo ud npu n h poduon of dom good. Thu, oupu n h mll opn onom n b wn : 6, wh,, loghm of

7 onumpon, l oupu nd po, whl h d- o of h opondng bl. Oupu gp h dffn bwn l oupu nd ponl oupu (umd onn, fo mpl). B kng m d of h oupu gp w obn: Th po uon pfd b: wh wold oupu, h l of ubuon bwn mpod ml nd lbo n poduon, onn nd h m of d. B ombnng h uon of, nd, h po uon nd h UIP ondon w g h IS u: Th uon h h oupu gp of hng dpnd on h oupu gp ll nd h gp of h n, wlh nd h m of d. Thu, n fogn pl n pl ol n h IS u. Th pm of h u dpnd on uul pm odng o: n n ; n ; Th offn nd po. On h oh hnd, h offn nd n b h po o ng. Th po f h oun n do nd ng f h oun n dbo. 7

8 8 Th umulon of n fogn n mll opn onom olppng gnon modl gn b h bln of pmn un oun: E n Th uon, whn h bl nomlzd b ponl oupu, n b wn : E n In d w g: E n Hn, E E n n Th f od pnon of boh n nom ( ) nd n po uon, pl: Subung h pon n h uon of ld: Th pm of h uon dpnd on h uul pm of h modl odng o: n, E S S S E S E E

9 Th offn nd po. Th gn of do o dbo. dpnd whh h oun 3. Fd Ehng R Rgm Th nw knn modl of mll opn onom und fd hng gm h n IS u dd fom h Eul uon, Phllp u (P) à l lo, n unod n p (UIP) uon, mon pol ul (MPR) wh h nl bnk pg h hng nd n uon fo h bln of pmn (BP) un oun. lo Phllp u onnuou m ggd p fomulon nd w kp h modl mpl ludng h hng of h m of d fom h u. Th nl ondon (I) of h modl uppo h h p ll, h m of d nd h n fogn pdmnd bl. Th oh bl f nd llowd o jump n pon o nw nfomon. Th modl h h followng pfon: IS: P: UIP: MPR: BP: I: Gn p, nd Th m of d dfnd b: p p Tkng m d on boh d of h pon nd kng no oun h h nomnl hng fd, w g: 9

10 Subung h nflon gp fo h l n gp n h IS u, h unod n p nd h un oun, w g, pl: wh nd. Th dnm m of h mll opn onom nw Knn modl, fo fd hng m, h fou dffnl uon n h followng bl: of nflon, oupu gp, m of d, nd n fogn wlh. Th l wo bl, h m of d nd n fogn wlh, pdmnd. Th ln ppomon of h dnm m ound h d gn b h fou-dffnl uon n,, nd : Th Jobn m of h m gn b: J Hn, h dmnn nd h of h m, pl: J J

11 Fo h m o hb ddl ph bl wh wo po oo nd wo ng oo h dmnn h o b po. Th dmnn wll lo b po f ll fou oo h h m gn (h po o ng). Thu, w h o po h ll oo h no h m gn. Fo h o b h h offn of of h h uon hould b ng [Sd, Som nd Bk (), p.8]: j j offn of I o f h f ll h oo h h m gn h offn of would b po. Th h uon of h dnm m gn b: Solng h dmnn b h ofo pnon long h f ln w g h h uon: 4 3 Th offn of hould b ng fo h dnm m o h ddl ph wh wo po nd wo ng oo. Th h f h followng nul hold: Thu, f h ondon hold h m hb ddl ph bl. Sng o zo h onn opondng o h unbl oo, h dnm m oluon, wh wo ng h oo,, gn b:

12 Th onn nd obnd fom h nl ondon wh h lmn j of h gno od o h ng oo om fom h oluon of h ln m: 4 3 Th f nd h hd uon of h m ld h nul: 3 Whn h fouh uon ombnd wh h hd w g h nul: 4 3 Th h nul wll pod ul nfomon o d h bho of h dnm m. Ddng h nflon gp b h l n gp nd kng lm whn m go o nfn w obn:

13 Whn lm lm, n, h m no bk, boh n h numo nd h dnomno, ong o on. Thu, lm Th uon nd h h nflon gp n h oupu gp, whn h m ong mpoll o h domnn [lo(987)], mo n h m don. W m u h m podu o po h: lm 3 lm 4 3 Th f nul how h h nflon gp nd h m of d mo n h m don, whl h ond nul how h h n fogn gp nd h m of d gp mo n oppo don. Th l n gp ul o h m d of h m of d. Thu, h oluon fo h l n gp gn b: 3 3 Ung h m podu w u fo h o bwn h nflon gp nd h oupu gp o f h: lm 3

14 Hn, h n gp nd h m of d gp mo n oppo don whn ongng o h d-. Fgu how n nflon g hng m zo, nnound b h fogn nl bnk o whh h dom un pggd, o b mplmnd m T. Th nflon g wll b dud fom o o. How h onom dju o n npd nd pmnn hng n h of wold nflon? W wll o o ph dgm o nw h uon. T m Fgu Fgu 4

15 Fgu how h ph dgm fo h pmn. B h Phllp u w n dmn h don of momn of h nflon n h on of h wo zon ddd b h ln, hown n Fgu. W know h h lop of h domnn gno po,.g., whn bom lg, nflon nd oupu ong o h d- lu fom h m don ( lm ( ) / / ). Thu, whn h nw nflon g nnound h nflon nd h oupu gp jump m zo o pon. Fom m zo on h onom follow h ph dpd b h owd u n Fgu. Th pdon of h fd hng gm h nflon dud wh no oupu gn. Whn h nflon g hng mplmnd h m m nnound h no oupu gn, n nflon jump mmdl o nw. 4. Flbl Ehng R Rgm Th nw Knn modl und flbl hng m h h m uon h fd hng gm fo h IS u, h Phllp u, h unod n p nd h un oun of h bln of pmn. Th dffn h mon pol ul. Th nl bnk now onol h n nd llow h hng o b mk dmnd. To mplf h lgb w um Tlo ul whou h oupu gp m. Th nl ondon of h flbl hng m dffn fom h fd hng m. Th p ll nd h n fogn pdmnd bl. Th oh bl f nd n jump whn h nw nfomon. Th pfon of h modl gn b h followng of uon: IS: P: UIP: BP: MPR: 5

16 6 I: Gn p() nd () Th mon pol ul n b wn : Subung h l n gp of h pon n h h uon, nml h IS u, h unod n p nd h bln of pmn un oun, w g, pl: Th dnm m of h nw Knn modl, und flbl hng m, h fou dffnl uon n h followng bl: nflon, oupu gp, m of d nd n fogn. N fogn h onl pdmnd bl. Th ln ppomon of h dnm m ound h d gn b: Th Jobn of h m gn b: J

17 7 Th dmnn of h m n b ompud ung h ofo pnon long h f ln of h m, whh ld: J Hn, J Th of h m ul o: J W um ng dmnn: J. Th dnm m und h hpoh h h on ng h oo nd h po oo o h po oo nd on ng oo. In od o know f h oluon wh h ng oo w h o nlz h h uon of h modl. Th uon obnd olng h dmnn: Ung ofo pnon long h f ln w g h h uon: 3 4 Whn h numb of hng n gn n h un of offn [Sd, Som nd Bk (), p.8] 3 4,,,, nd ul o h h h po oo. Th un gn b:

18 8,,, 3 4 o nd W um h h offn n h un uh h h h po oo. Hn, h oluon fo h nflon, h oupu gp, h m of d nd h n fogn, pl: 3 4 wh h onn obnd fom h nl ondon of (), h ng h oo nd h lmn of h h o j h oluon of h ln m: 4 3 Tkng no oun h f h h oo ng, h f, h hd nd h fouh uon mpl h followng nul: 3 4 3

19 Ddng h nflon gp b h oupu gp ld: Hn, h nflon gp nd h oupu gp mo n h m don. Ddng h nflon gp b h m of d gp w g: 3 I follow fom h pon h h nflon gp nd h m of d gp mo n oppo don. h l n gp popoonl o h nflon gp odng o h mon pol ul, h l of n gp nd h m of d gp mo n oppo don. Th popoon n lo d dd ung h UIP ondon:. I o obn: 3, Ddng h n fogn gp b h m of d gp w g: 4 3 Hn, h n gp nd h m of d gp mo n h oppo don whn h onom ongng o d-. How h onom dju o n npd nd pmnn fll n h nflon g? Fgu n b ppld o h wll b hngng fo nflon jump mmdl o h nw g wh no hng n oupu. 9. Th nl bnk nnoun m zo h m T h nflon g wll b dud fom o. Fgu how h djumn dnm n h lop of h domnn gno po, h lop of h fd hng gm. In h flbl hng gm modl, nflon n b dud wh no gn n oupu. If h nw nflon g mplmnd h m nnound, h

20 Rh hn ummzng h ul obnd n h pol gm, uful o hghlgh h mn dffn bwn h fd nd h flbl hng gm. In h fd hng gm nflon nd h m of d ong o h d- fom h m don,.g., h lop of h domnn gno po. In h flbl hng gm ju h oppo, h nflon nd h m of d ong o h d- fom oppo don. 5. onluon Th lu ddd of h pp o how h n mll opn onom wh pf o h wold pl mk h nul of n ul o h l nnonl of n. Sondl, how h h pn- gn modl no h pop hol fmwok fo mll opn onom, bu h no h wh h olppng gnon modl. In h pn-gn fmwok, h nul of n nd h nnonl l of n would b ul onl und ngn ondon, nml h h of gowh of dom oupu ul o h of gowh of wold oupu. In h nfnl-ld olppng gnon modl h nul of n ul o h l nnonl of n wh no ng hd. Th ul pnd n h pp uful onpul bnhmk o mu h nul of n n mll opn onom. odng o GM (5) h lod onom pn gn nw Knn modl ppl, wh mno pm npon, o mll opn onom. Th no h wh h olppng gnon nw Knn modl pnd h n h un oun djumn nno b whd w. Th jon of h mll opn onom pn gn modl, bd on mpl gound, h f-hng mplon fo mon pol nl. Muh of h opml mon pol lu, ppld b GM nd oh [, fo mpl, Woodfod (3)], h ud h ud lo funon n ppomon o h nmpol ul funon of h pn gn h ol wlf o b mmzd. Th on no long uful fo h mll opn onom olppng gnon fmwok n ol wlf dpnd on h wgh o b gn o h gnon, n ho h unbon.

21 Rfn Bku, D. Smh, G. (993), onumpon nd Rl Ehng R n Dnm Ehng Eonom wh Nondd Good, Jounl of Innonl Eonom, 35, Bo, R. nd Sl--Mn, X. (995), Eonom Gowh (Nw Yok: MGw-Hll). Blnhd, O. (985), Db, Df nd Fn Hozon, Jounl of Poll Eonom, 93, Bngno, G., Thonn,. (8), onumpon nd Rl Ehng R wh Inompl Mk nd Nondd Good, Jounl of Innonl Mon nd Fnn, 7, lo, Gullmo. (983), Sggd P n Ul Mmzng Fmwok. Jounl of Mon Eonom,, lo, Gullmo. (987), Rl Ehng R Dnm Wh Nomnl P, Suul hng nd Ohoong, Jounl of Innonl Eonom,, llo, M. nd Ghon, F. (), N Fogn n h Ehng R: Rdu Rd, Jounl of Mon Eonom, 49, h, V. V., Kho, P., MGn, E. (), Mon Shok nd Rl Ehng R n Sk P Modl of Innonl Bun l, Rw of Eonom Sud, 69, ld, R., Glí, J. nd Gl, M. (), Opml Mon Pol n lod Vu Opn Eonom: n Ingd ppoh, mn Eonom Rw, 9, o, G., Ddol, L., Ldu, S. (4), Innonl Rk Shng nd h Tnmon of Podu Shok. EB Wokng Pp S 38. Glí, J. nd Monll, T. (5), Mon Pol nd Ehng R Voll n Smll Opn Eonom, Rw of Eonom Sud, 7, Gmmol, N. nd Vll, N. (4), Th Nul Rl In R nd Mon Pol: Rw, Jounl of Pol Modlng 6,

22 Kollmnn, R. (). Mon Pol Rul n h Opn Eonom: Eff on Wlf nd Bun l, Jounl of Mon Eonom, 49, Ln, P. (), Th Nw Opn Eonom Moonom: Su, Jounl of Innonl Eonom, 54, Lubh, T. nd Wllm, J.. (3), Mung h Nul R of In, Rw of Eonom nd S, 85, Mllum, B. nd Nlon, E. (), Mon Pol fo n Opn Eonom: n ln Fmwok wh Opmzng gn nd Sk P, Ofod Rw of Eonom Pol, 6, Obfld, M. nd Rogoff, K. (995), Ehng R Dnm Rdu, Jounl of Poll Eonom, 3, Obfld, M. nd Rogoff, K. (), Th S Mjo Puzzl n Innonl Moonom: I Th ommon u? In B. Bnnk. nd K. Rogoff (d.) NBER Moonom nnul (mbdg, M: MIT P). Shm-Gohé, S. nd Ub, M. (3), long Smll Opn Eonom Modl, Jounl of Innonl Eonom, 6, Snon, L. (), Opn-Eonom Inflon Tg, Jounl of Innonl Eonom, 5, Sd, Knu, n Som nd P Bk (999). Eonom Mhml Mnul. Bln: Spng-Vlg. Tlo, J.B. (993), Don u Pol Rul n P. ng-roh S on Publ Pol, 39, Uzw, H. (968), Tm Pfn, h onumpon Funon nd Opmum Holdng n J. Wolf (d.) Vlu, pl nd Gowh: Pp n Hono of S John Hk (Ednbugh: Th Un of Ednbugh P). Wl, P. (989), Olppng Fml of Infnl-Ld gn, Jounl of Publ Eonom, 38, Woodfod, M. (3), In nd P: Foundon of Tho of Mon Pol (Pnon: Pnon Un P).