Trms-of-rad Shocks and Exchang Ra Rgims in a Small Opn Econom Wai-Mun Chia and Josph D. Alba Division of Economics, Nanang Tchnological Univrsi Absrac W xamin h impac of rms-of-rad shocks on imporan macroconomic variabls b numricall solving a dnamic sochasic gnral quilibrium modl of a small opn conom. Th modl considrs nominal pric rigidi undr diffrn xchang ra rgims. Th numrical soluions obaind ar consisn wih h mpirical rgulariis documnd b Broda (2004), in which oupu rsponss o shocks ar smoohr in floas han in pgs; in moving from pgs o floas, h ris in nominal xchang ra volaili is coupld b h ris in ral xchang ra volaili; and in boh xchang ra rgims, n forign asss is h mos volail variabl. JEL Classificaion: F32, F4 Kwords: Trms-of-rad; imprfc compiion; nominal pric rigidiis; xchang ra rgims This papr has bn accpd b h 2005 Ausralian Confrnc for Economiss for prsnaion a h Univrsi of Mlbourn, 26-28 Spmbr 2005. Corrsponding auhor: Wai-Mun Chia; Tl: (65)6790-4290; Fax: (65)6792-6559; Email: aswmchia@nu.du.sg Trms-of-rad shocks and Exchang Ra Rgims in a Small Opn Econom ACE Submission 8 Jul 2005
. Inroducion Th mri which is ofn aribud o flxibl xchang ra rgims ovr fixd xchang ra rgims is hir abili o insula h conom mor ffcivl agains ral shocks. This hpohsis was firs proposd b Fridman (953) in h arl 950s. Sinc hn h choic of h xchang ra rgim has bn an ara of gra conrovrs and dba. In hor, h prsnc of pric sickinss xplains wh h xchang ra rgim ma mar. Whn an conom is hi b ral shocks, h conom ha can chang rlaiv prics mor quickl will hav smallr and smoohr adjusmn in oupu. This is paricularl ru in an conom wih pric sickinss whr h spd a which rlaiv prics can adjus dpnds cruciall on h xchang ra rgim. Undr flxibl xchang ra rgims, rlaiv prics can adjus insanl hrough changs in nominal xchang ra; whil undr fixd xchang ra rgims, rlaiv prics can adjus onl a h spd ha is prmid b pric sickinss, which is usuall much slowr. Thrfor, flxibl xchang ra rgims allow smoohr adjusmn in oupu and quickr adjusmn in rlaiv prics han fixd xchang ra rgims. Th horical proposiion b Fridman has subsqunl prompd inrnaional conomiss o xamin h ffcs of shocks on conomic variabls of diffrn ps of xchang ra rgims. Whil som focusd on building horical modls (Pool, 970 and Dornbusch, 980), ohrs focusd on documning mpirical rgulariis (Baxr and Sockman, 989; Talor, 993; Dvrux, 999; Collard and Dllas, 2002; Blan and Filding, 2002 and Broda, 2004). From h horical prspciv, man conomiss sill bliv ha h rlaiv mris of h xchang ra rgims cruciall dpnd on h p and h naur of shocks hiing h conom. Whn h shocks ar nominal in naur, fixd xchang ra rgims auomaicall prvn hm from affcing ral oupu. For insanc, whn mon dmand incrass, undr fixd xchang 2
ra rgims, mon suppl incrass as h monar auhori bus forign currnc o prvn h apprciaion of h local currnc. This lavs ral oupu unchangd. In conras, undr flxibl xchang ra rgims, mon suppl is lf unchangd and h local currnc is allowd o apprcia so ral oupu falls and mon dmand rurns o is iniial lvl. Whn h shocks ar ral in naur, flxibl xchang ra rgims ar mor ffciv as h allow a smoohr adjusmn o ral shocks. For insanc, whn rms-of-rad drioras in an conom whr prics ar sick, undr flxibl xchang ra rgims, h nominal xchang ra dprcias. Th dprciaion of nominal xchang ra, in urn, rducs h pric of radabl goods which pariall offss h ffc of h ngaiv rms-of-rad shock. Howvr, undr fixd xchang ra rgims, mon suppl dcrass as h monar auhori conracs mon suppl o prvn a nominal dprciaion of local currnc. This rspons is inhrnl conracionar and inducs an addiional fall in ral oupu. Thrfor, fixd xchang ra rgims hav o rl on h adjusmn in domsic prics o pull h conom ou of rcssion. From h mpirical prspciv, h mpirical vidnc is far from conclusiv on h ffcs of shocks on ral oupu, ral xchang ra and nominal xchang ra. Baxr and Sockman (989) show mpirical insnsiivi of oupu volaili o h p of xchang ra rgim. Th also find ha a broad rang of ral macroconomic variabls ar indpndn of h undrling xchang ra rgims. Dvrux (999) analzs h ffcs of suppl, fiscal and mon shocks using a modl wih nominal goods pricd in h sllrs currnc and wih prics which ar sick ovr on priod. H finds ha h xchang ra dos no rspond o ihr suppl shocks or fiscal shocks so macroconomic volaili is h sam across fixd and flxibl ssms. In conras, Collard and Dllas (2002) suggs largr diffrncs in volaili across rgims. Th find ha oupu volaili is significanl highr undr fixd xchang ra rgims rlaiv o flxibl Pool (970) prdicd ha h sandard dviaions of oupu across xchang ra rgims cruciall dpnd on h naur of h shocks. Whn h shocks ar nominal (ral) in naur, hn h sandard 3
xchang ra rgims. Using daa from 80 dvloping counris, Blan and Filding (2002) also show ha counris wih fixd xchang ra rgim hav significanl grar oupu varianc han a pical floaing-ra counr. Whil h horical liraur mphasizs ha h rlaiv mris of fixd and flxibl xchang ra rgims dpnd on h naur of h shocks, h mpirical liraur dos no clarl disinguish bwn nominal and ral shocks. Hnc, i would b maningful for an mpirical sud o clarl idnif ral shocks from nominal shocks. This is paricularl ru if on can sud h ffcs of rms-of-rad shocks on macroconomic variabls undr alrnaiv xchang ra ssms. Thr ar wo rasons for choosing rms-of-rad shocks. Firsl, rmsof-rad disurbancs ar rgardd as a major sourc of oupu flucuaions in a small opn conom (Mndoza, 995 and Kos, 2002). Scondl, sinc mos dvloping counris xpor arnings ar dominad b a narrow rang of primar commodiis (Kos, 2002) and h prics of hs primar commodiis ar subjcd o larg pric flucuaions in h world mark, rms-ofrad flucuaions in dvloping counris ar obsrvd o b mor volail. Bcaus of h prominn rol plad b xchang ra rgims in dvloping counris, Broda (2004) xamins h ffc of a singl ral shock givn b rms-of-rad changs of a counr undr diffrn xchang ra rgims. Using daa from 75 dvloping counris from 973 o 996, h idnifis h rsponss of ral GDP, ral xchang ra and consumr prics o xognous rms-of-rad changs across diffrn rgims. His findings gnrall suppor Fridman s proposiion. Firs, h shor run ral GDP rspons o rms-of-rad shocks is significanl smallr in counris wih flxibl xchang ra rgims han hos wih fixd xchang ra rgims. Scond, h dprciaion of ral xchang ra is immdia afr a ngaiv rms-of-rad shock undr flxibl xchang ra whil h dprciaion is slowr undr dviaions in fixd (flxibl) is rlaivl smallr. 4
fixd xchang ra. Third, counris wih flxibl xchang ra rgims can absorb ral shocks br han hos wih fixd xchang ra rgims. Givn h significanc of rms-of-rad flucuaions on domsic macroconomic variabls, undrsanding h ransmission and propagaion of rms-of-rad flucuaions is crucial in h dsign and conduc of macroconomic policis in boh indusrializd and dvloping counris. In his papr, w us an inrmporal quilibrium framwork wih nominal pric rigidiis and imprfc compiiv marks o analz h dnamics of som macroconomic variabls arising from rm-of-rad flucuaions undr alrnaiv xchang ra ssms 2. W adap h modl of Lan and Milsi-Frri 3 (2004) and consruc an inrmporal framwork wih radabl and nonradabl scors. Th xisnc of radd and nonradd goods provids a richr framwork for analzing h dnamics of imporan macroconomic variabls rsuling from rms-of-rad shocks. Furhrmor, b incorporaing nonradd goods, h modl is xndd o involv boh inrmporal and inramporal subsiuion ffcs. In our modl, h nonradd scor is assumd o b a monopolisic compiiv mark 4 whr prics ar sick. Th radd scor, on h ohr hand, is assumd o b a prfcl compiiv mark whr prics ar full flxibl and h law of on pric holds. Th asmmric ramn of h wo scors allows us o show h link bwn h scors whn hr is a rmsof-rad disurbanc. W clarl show h propagaion mchanism of rms-of-rad shocks on h dnamics of som macroconomic variabls. 2 Monaclli (2004) uss a dnamic gnral quilibrium modl of a small opn conom combining nominal pric rigidi wih a ssmaic bhavior of monar polic. H considrs shocks du o producivi, domsic prfrncs, world inrs ra and world dmand bu no rms-of-rad shocks. 3 This modl was originall usd o show ha counris wih n xrnal liabiliis hav largr ral xchang ra dprciaion, in which h main channl of ransmission works hrough h rlaiv pric of nonradd goods rahr han hrough h rlaiv pric of radd goods across counris. 4 W follow h assumpion in Lan and Milsi-Frri (2004) ha h domsic aggrga dmand condiions mar mor for h nonradd scor han h radd scor. 5
W us numrical soluion mhods o dmonsra h impuls rsponss of macroconomic aggrgas inducd b a ngaiv rms-of-rad shock. W xamin h link bwn rms-ofrad shock and som macroconomic aggrgas b numricall solving a dnamic sochasic gnral quilibrium modl of a small opn conom. Th numrical soluions of h modl ar compard wih h mpirical rgulariis documnd b Broda (2004). Our rsuls ar broadl consisn wih h following mpirical rgulariis. Firs, h rsponss of shor-run oupu o shocks ar significanl smoohr in floas han in pgs; scond, in moving from pgs o floas, h proporional ris in volaili of h nominal xchang ra is coupld b a ris in volaili of h ral xchang ra; and hird, in all ps of xchang ra rgims, h mos volail variabl is h holding of n forign asss. Th papr is organizd as follows: scion 2 las ou a dnamic gnral quilibrium modl of a small conom ha combins nominal pric rigidi wih a rms-of-rad shock; h modl paramrizaion is providd in scion 3; h flucuaions of h oupu, h ral xchang ra and h pric lvl as a rsul of rms-of-rad shocks ar analzd in scion 4; and h conclusions ar in scion 5. 2. Th Modl W driv an inrmporal modl of a small opn conom o analz h wa in which rms-of-rad shock affcs som ral variabls in an conom wih diffrn xchang ra rgims. To addrss h inramporal aspcs of h problm, w mak hr main assumpions. Firs, h imporabl is consumd bu no producd, and h xporabl is producd bu no consumd. In ohr words, h imporabl and h nonradabl ar consumd domsicall bu h xporabl and h nonradabl ar producd domsicall. Scond, invsmn is hld consan and h capial sock is an ndowmn which is no affcd b h rms-of-rad shocks. Third, 6
h conom is small in h sns ha i canno influnc h rms-of-rad of h conom 5. W also assum ha h oupu of h radd goods scor is an ndowmn of h radabl good T, which is sold in h world marks a h xpor pric of P T x, whr P T x is masurd in unis of h impord consumpion good and h impord consumpion good is usd as h numrair. Sinc consumpion of h xpor goods is assumd o b zro, P T x, b dfiniion is h rms-of-rad and is xognous o h counr. 2. Th housholds Considr an conom populad b a coninuum of oman-farmrs along h uni inrval [0,]. Th rprsnaiv agn aims o maximiz h inrmporal uili funcion which is givn b: σ k β, σ σ j () 2 V = C σ N ( j ) whr β ( 0,), σ, k > 0 = 0 2. β is a prfrnc paramr which is known as h subjciv discoun or im prfrnc facor, σ is h inrmporal lasici of subsiuion, and k is h marginal disuili of work. N ( j) is h producion of j-h vari of h nonradd goods. Th subscrips N and rprsn nonradabl goods and im, rspcivl. Th scond rm in h objciv funcion capurs h disuili of work ffor. Th consumpion indx C, aggrgas h consumpion of radd goods ( C ) and nonradd goods ( C ): (2) θ θ = γ C + ( γ ) T θ θ θ θ N θ C θ T C, N 5 Man (Snhadji, 998 and Backus al., 994) hav modld rms-of-rad as an ndognous variabls. Howvr, b suding Grangr-Sims saisical causali, Mndoza (995) found ha xcp for h Unid Sas and a fw major ful xporrs, h null hpohsis of xogni of rms-of-rad for small opn conomis canno b rjcd. 7
whr θ > which is h inramporal lasici of subsiuion bwn h radd and nonradd goods, and γ [0,] is h shar of consumpion of radd good in oal consumpion. Th consumpion-basd pric indx is givn b: θ θ (3) [ ] θ P = γp + γ ) P T ( N whr P T is h pric of h radd good xprssd in unis of domsic currnc. P N is h pric of h nonradd good. Agn j is h monopol producr of vari j of h nonradd good and facs h dmand funcion: d p A (4) N ( j) N ( j) = C µ > N PN whr µ is h pric lasici of dmand facd b ach monopolis and µ A C is h aggrga N consumpion of nonradd goods. Th nonradd consumpion and pric can b wrin as: (5) (6) C P N N = = 0 0 c p N ( z) µ µ dz µ N ( z) dz µ µ µ., and Each domsic agn holds onl on p of ass, naml an inrnaionall radd bond, B. Th agn producs a singl nonradd good, N (j), in a monopolisic compiiv wa and h rcivs a consan ndowmn of T unis of radd good. Th flow of budg consrain facd b agn j is givn b: x (7) PT B+ = ( + r ) B + p N ( j) N ( j) + PT T P C, whr B (in unis of h radd good) is h numbr of ral bonds and r is h rurn of h inrnaional bond. Maximizaion of () subjc o (4) and (7) gnras h rlaionships: σ θ C σ P PT E +, CT P + PT + (8) T + σ = β E ( + r ) 8
(9) C N γ P = γ CT P N T θ, and µ + µ P = µ N C N C k P (0) µ N A σ ( ) µ, whr E is h xpcaion opraor. Equaion (8) is h Eulr quaion govrning h dnamic voluion of consumpion. Givn h inrs ra, if h aggrga pric lvl rlaiv o h pric of radd goods is currnl low rlaiv o is fuur valu, h prsn consumpion is ncouragd ovr h fuur consumpion. Howvr, i also ncourags subsiuion from radd o nonradd goods. Th formr ffc dominas if inrmporal lasici of subsiuion is grar han h inramporal lasici of subsiuion ( σ > θ ), and vic vrsa. Equaion (9) rlas consumpion of nonradd and radd goods. Th lasici of subsiuion bwn h wo goods is paramrizd b θ. Whn h rlaiv pric is uni, h rlaiv consumpion of nonradd good is largr h smallr h paramr γ. Finall, quaion (0) shows h quilibrium suppl of nonradd goods. Th highr is h consumpion indx,c, h lowr is h producion lvl. Addiionall, h largr is h rlaiv pric of nonradd good o h aggrga pric lvl, h largr is h producion lvl. 2.2 Domsic firms Th producion scor is characrizd b housholds ha ac as a monopol in h producion of a singl radd good. Each houshold maximizs profis b choosing h pric of h good j ha i producs subjc o h dmand for his good. Howvr, as in Calvo (983), h firms s prics on a saggrd basis whr φ is h probabili ha h firm kps is pric fixd in a givn priod and φ is h probabili ha h firm changs is pric. Th probabili draws ar assumd o b indpndn and idnicall disribud (iid) ovr im. This implis ha, whn allowd o rs is pric, domsic firm j will choos ( j) o maximiz: p nw N + k 9
() k nw E ( ) [ p ( j) MC ] subjc o h dmand schdul: βφ Λ, + + + ( j), k N k N k k = 0 nw p (2) N+ k ( j) A N+ k ( j) C, N PN+ k µ whr Λ, + k is h im-varing porion of h firm s discoun facor and MC is h marginal cos. Th ncssar firs-ordr condiion of his problm givs: (3) p nw N k E ( βφ ) Λ, + k MC+ k N+ k ( j) µ = k = 0 ( j). µ k E ( βφ ) Λ, + k N+ k ( j) k = 0 No ha if a firm was abl o frl adjus is pric ach priod, i will choos a consan markup ovr marginal cos, i.. φ = 0 implis: nw (4) µ pn ( j) = MC. µ Givn h pricing rul, in a smmric quilibrium whr h law of larg numbrs holds, h nonradabl aggrga pric indx volvs according o: µ (/( µ )) [ N N ] µ nw (5) = βφp + ( βφ )( P ) 2.3 Inrnaional capial mark P. N As in Soo (2003), w assum imprfc inrnaional capial marks whr h inrs ra dpnds on h sock of n forign db of h conom. In paricular, h inrs ra is givn b: ψ * B ~, (6) ( + r ) = ( + r ) * whr ( r ) B + is h risk-fr inrnaional inrs ra and ψ 0 is a paramr ha masurs h prmium h domsic conom mus pa. This xprssion implis ha a counr wih larg sock of db ovr a sock of minimum db, B ~, sars paing a prmium ovr h inrs ra ha 0
prvails in h inrnaional capial mark. Howvr, for sock of db blow his hrshold, h counr rcivs a discoun. 2.4 Prics and ral xchang ra Th nominal xchang ra is h pric of on uni of forign currnc xprssd in unis of domsic currnc. Th ral xchang ra is dfind as: (7) q P P * =. Th forign pric lvl is assumd o b givn and h forign currnc dnominad pric of radabl is normalizd o b on. Whn h law of on pric holds for radd goods, i implis ha q = P P. T 2.5 Monar polic and xchang ra rgims Th formulaion of monar polic b h domsic auhori follows a gnralizd rul, in which dviaions of inflaion, nonradd oupu and nominal xchang ra from hir long-run arg hav a fdback on shor-run movmns of h nominal inrs ra. As in man ohrs (Talor, 993; Clarida, Gali, and Grlr, 999; Rombrg and Woodford, 998 and Monaclli, 2004), h following quaion dscribs h arg for h nominal inrs ra: P + i = N P. (8) ω ω ( ) ω π From quaion (8) h monar auhori racs o h conmporanous lvl of inflaion, nonradd oupu and nominal xchang ra. Th drminaion of h acual shor-run inrs ra ha accouns for h dsir of h monar auhori o smooh changs in h inrs ra is: (9) ( ) ( ) ( ) χ + χ = + i + i ω i. 2.6 Sad sa quilibrium W firs considr h siuaion in which all prics ar full flxibl. All variabls ar assumd o b consan a h sad sa. W normaliz h ndowmn of h radd good so ha h
rlaiv pric of nonradd goods in rms of radd goods is uni in h sad sa, ( ) P. In his smmric quilibrium, 0 = C 0 = ( γ ) C 0 and C ( γ ) C 0 γ N 0 P T 0 = N N =. N 0 T Th aggrga pric lvl, h pric of radd good and consumpion of radd goods ar consan a h sad sa. A h iniial sad sa, w also assum ha h rms-of-rad is on, x P =. Thn, from quaion (8), h sad sa valu for h ral domsic inrs ra is: 0 T (20) r = β. 0 Givn h sock of minimum forign db B ~, a sad sa h following rlaionship is obsrvd: (2) + r ψ ~ B0 = B * + r If w assum * r = r, hn B B ~ =. From quaion (7), h consumpion of radd goods in sad sa saisfis: (22) C = rb0 +. 0 T 0 T Th sad sa consumpion and producion of nonradd goods is givn b: σ µ + σ = = γ N 0 C N 0. (23) ( ) + σ Th rm ( µ ) / µ µ k is h invrs of h markup for h full flxibl prics cas. From his xprssion, oupu of h nonradd goods will b largr, h mor compiiv is h nonradd goods scor (h largr is µ ), h lss axing is work ffor (h smallr is k ) and h largr is h wigh placd on h consumpion of nonradd goods in h uili funcion (h largr is ( µ )). 2.7 Th log-linarizd vrsion of FOC and ohr condiions Th modl is solvd b aking a log-linar approximaion around h sad sa. W l a variabl wih ha, Xˆ o dno h log-dviaion of a variabl from h sad sa and a variabl 2
wih bar, X o dno a variabl a sad sa. Thn, h modl can b dscribd b a ssm of linar quaions as discussd in h following subscions. 2.7. Aggrga suppl and inflaion L xˆ N b h oupu gap in h nonradd scor which is masurd as h dviaion bwn h sochasic componn of currn oupu and h ponial oupu. Th following quaion shows h inflaion of nonradd goods: (24) ˆ π ˆ ˆ N = λxn + Eπ, N+ whr ( φ)( βφ ) λ = φ and E is h xpcaion opraor. This quaion suggss ha inflaion is posiivl rlad o oupu gap. 2.7.2 Aggrga dmand B aking a log-linar approximaion of (8) and (7), h following quaion can b obaind: [ ] (25) E ( Cˆ Cˆ ) = E rˆ + ( θ )( qˆ qˆ ) σ. T T+ σ + This quaion shows ha h consumpion of radd goods adjuss according o h voluion of ral inrs ra and ral xchang ras. From h log-linar approximaion of (3), (9) and (7), an xprssion ha rlas h oupu gap in h nonradd scor wih h ral xchang ra and h consumpion of radd goods is drivd as: (26) θ xˆ N = qˆ + Cˆ T zˆ, γ whr h las rm dnos h ponial oupu which is assumd o follow a saionar sochasic procss. 2.7.3 Ral inrs ra and currn accoun Th log-dviaion of h ral inrs ra facd b domsic agns corrsponds o: * (27) rˆ = rˆ +ψbˆ. Using quaion (7), h linar xprssion of h sock of forign asss is: 3
CT T x (28) bˆ ( r )( r Bˆ 0 ) Cˆ 0 = + ˆ + + ( Pˆ Pˆ ) 0 T. + T B0 B0 2.7.4 Uncovrd inrs pari condiion wih nominal and ral inrs ras Th uncovrd inrs pari dfins a linar xprssion for h xchang ra which can b xprssd as: (29) iˆ iˆ * + E ( ˆ ˆ ) = + whr * i and i ar domsic and forign nominal inrs ra rspcivl and iˆ = log( + i / i ) Th rlaionship bwn h nominal inrs ra and ral xchang ra + can b shown as (30) r iˆ + E ( Pˆ Pˆ ) ˆ = + 2.7.5 Monar polic rul Equaion (9) is obaind b aking a log-linar approximaion of (7) and (8) (3) iˆ ~ ˆ ~ ˆ ~ ˆ ˆ = π + ω N + ω + χi ω π whr ~ ω π ( χ ) ω, ~ ( ) π ω χ ω, and ω ( )( ) χ ω / ω ~. Following Monaclli (2004), his spcificaion allows us o approxima h ssmaic bhavior of monar polic undr h floaing and h fixd xchang ra rgims. In paricular, ω = 0 dscribs h bhavior of h monar auhori pracicing h floaing xchang ra rgim; whras ω (0,] approximas h bhavior of h monar auhori pracicing policis ranging from managd o h fixd xchang ra rgims. 2.7.6 Exognous sochasic procss Th sochasic procsss for h world (forign) inrs ra, rms-of-rad and ponial oupu can b summarizd as i* * * ρ i* (32) ( + i ) = ( + i ) xp( ε ) 4
P T x x ρ PT (33) P = P xp( ε ) T T z z (34) z = z ( ε ) ρ xp u wih = u u Eε + 0, Eε + ε + = Σ whr * x u = i,, u P z whr ε ar iid wih zro mans. T 3. Modl paramrizaion Th modl is solvd numricall 6 and h paramr choics for h modl ar summarizd in Tabl. B following h businss ccl liraur, h discoun ra β is s a 0.99 and h marginal disuili of work ffor k is s a 3. Th pric lasici bwn nonradd goods or h sad-sa markup µ is s a.2. As i is now common in h liraur using Calvo pricing, h probabili of pric non-adjusmn φ is s a 0.75. In ohr words, his implis ha h avrag frqunc of pric adjusmn is four quarrs. Th lasici of inrmporal subsiuion σ is s a /4, whras h lasici of inramporal subsiuion θ is s a /6. This assums ha h inrmporal lasici dominas inramporal lasici of subsiuion. Following Soo (2003), hs valus ar no s basd on an simaion bu ar arbirar 7. Dgr of opnnss is allowd o var from compll closd o compll opn. This implis ha ( 0,) γ. As o h monar polic rul paramrs, w follow h bnchmark valus in Monaclli (2004), whr ω is s o.5, π ω is s o 0 and ω ( 0,). To calibra h sourcs of sochasic volaili, w assum US inrs ra is h driving forc dscribing h world (nominal and ral) inrs ra and h world pric is consan. As a rsul, b following from Monaclli (2004), ρ is 0.8 and σ i* is.0.0379. Following Mndoza's (995) sud on dvloping counris, h man ε i* 6 For h numrical soluion of h modl, w modif Uhlig s MATLAB program. Th program is implmnd using h mhods of undrmind cofficins. For dails of h program and h mhodolog, plas rfr o Uhlig (997). 5
srial corrlaion of h rms-of-rad PT ρ quals o 0.44 and h sandard dviaion σ PT ε quals o 0.77. Sinc h ponial oupu is nonobsrvabl, h srial corrlaion of h ponial z oupu ρ and h sandard dviaion σ is arbiraril fixd a 0.5 and rspcivl. z Tabl Calibraion of modl Paramr Dfiniion and Dscripion Valu θ Inramporal lasici of subsiuion ¼ σ Inrmporal lasici of subsiuion /6 φ Probabili of pric non-adjusmn 0.75 γ Dgr of opnnss 0.5 λ (- φ )(- β φ )/φ 0.0858 β Discoun ra 0.99 µ Elasici of subsiuion bwn nonradabls.2 κ Inrmporal lasici of labour suppl 3 ψ Elasici of n forign ass o inrs diffrnials 0.05 χ Inrs smoohing paramr 0.5 i* ρ Auocorrlaion of forign nominal inrs ra 0.8 σ i* ε Sandard dviaion of forign nominal inrs ra.379 P ρ T Auocorrlaion of rms-of-rad 0.44 σ ε P T Sandard dviaion of rms-of-rad.77 z ρ Auocorrlaion of ponial oupu 0.5 σ z Sandard dviaion of ponial oupu ω Rsponsivnss of monar polic o xchang ra 0.25 and 0.99 ω Rsponsivnss of monar polic o inflaion.5 π ω Rsponsivnss of monar polic o oupu 0 4. Th volaili of h oupu, h ral xchang ra and h pric lvl W conduc an xprimn o invsiga whhr h baslin modl illusrad abov can rplica h quaniaiv vidnc rpord in Broda (2004). To characriz a fixd (flxibl) xchang ra rgim, w l ω approach on (zro). Th bnchmark calibraion dscribd abov prmis us o choos ω = 0. 99 for fixd xchang ra rgim and ω = 0. 25 for a mor flxibl 7 Sinc h goal is no o addrss h quaniaiv rsuls abou h rspons of h rad balanc and h currn accoun, arbiraril slc h lasiciis of inrmporal and inramporal subsiuion will no 6
xchang ra rgim. W hn invsiga whhr h modl dscribd is abl o gnra similar volaili in oupu, ral xchang ra and pric lvl as documnd b Broda. Figurs a and b illusra h ffc of a ngaiv shock o h rms-of-rad. In his modl, a drioraing rms-of-rad gnras a dclin in ovrall pric lvl. Nonradd oupu falls wih Knsian pric rigidiis. Addiionall, nominal xchang ra dprciaion is also associad wih ral xchang ra dprciaion. 4. Snsiivi analsis: Diffrn dgr of rigidiis in nominal xchang ra Tabl 2 and Figur 2 summariz h sandard dviaions of k macroconomic variabls wih diffrn dgrs of rigidiis in nominal xchang ra whn h modl is drivn b h rms-of-rad shock. Tabl 2 Saisics for h calibrad conom wih diffrn dgrs of rigidiis in Variabl nominal xchang ra pric of nonradabls pric nominal xchang ra ral xchang ra n forign asss nonradabl oupu consumpion Sandard Dviaion HP-Filrd ω = 0.25 ω = 0. 50 ω = 0. 75 ω = 0. 99 0.3.020.055 0.627.474 2.824 0.642 0.446 0.804 0.420 0.384 2.638 3.73 0.778 0.503 0.70 0.67 0.300 3.275 4.046 0.820 0.53 0.647 0.007 0.266 3.69 4.225 0.602 Nos: Sandard dviaions ar obaind from Hodrick-Prsco filrd daa. ω shows h rsponsivnss of monar polic o xchang ra. Th highr h valu of ω, h mor rsponsiv is h monar polic o xchang ra impling h mor rigid h xchang ra rgim. Svral inrsing rsuls mrg. Firs, undr a flxibl xchang ra rgim, h ral nonradabl oupu has a smallr flucuaion whn counris ar hi b rms-of-rad shock whras h pric lvl, h nominal and h ral xchang ras hav largr flucuaions. On h hav significan influnc on h rsuls of h analsis. 7
ohr hand, undr a fixd xchang ra rgim, h ral nonradabl oupu nds o flucua mor whras h pric lvl, h nominal and h ral xchang ras hav smallr flucuaions. Ths obsrvaions ar consisn wih Broda (2004) and Mussa (986). Scond, in moving from fixd o flxibl, h proporional ris in volaili of h nominal xchang ra is coupld b a ris in volaili of h ral xchang ra. This obsrvaion implis ha nominal and ral xchang ras ar srongl corrlad. Counris, moving from fixd o floaing xchang ra rgim, will xprinc a dramaic ris in h volaili of h ral xchang ra. Th corrlaion bwn nominal and ral xchang ras is consisn wih h Mussa's (986) facs. Monaclli (2004) also shows ha his rsul is robus o ohr ps of shocks such producivi, prfrnc, world inrs ra and world dmand shocks. Third, small opn conomis ha pg hir xchang ras achiv lowr flucuaion in pric han hos whos xchang ras floa. Fourh, h volaili of h holding of n forign asss is alwas h largs in all ps of xchang ra rgims bu his flucuaion nds o b smallr undr a mor flxibl xchang ra rgim. Sandard Dviaions 4.5 4 3.5 3 2.5 2.5 Nonradabl oupu Nonradabl consumpion 0.5 Tradabl consumpion 0 0 Flxibl ras Fixd ras Sandard dviaions 3 2.5 2.5 0.5 0 Nominal xchang ra Pric Ral xchang ra 0 Flxibl ras Fixd ras Figur 2 Variabili of som macroconomic variabls in moving from flxibl o fixd 8
4.2 Snsiivi analsis: Diffrn dgrs of pric rigidiis W addrss h rol of pric rigidiis undr wo xchang ra rgims: h flxibl vs. h fixd xchang ra. W s h probabili of pric non-adjusmn φ, a 0.25, 0.50 and 0.75. Whn φ = 0. 25, φ = 0. 50 and φ = 0. 75, prics compll adjus afr approximal.3 quarrs, 2 quarrs and 4 quarrs rspcivl. Th simulaion rsuls ar summarizd in Tabl 3. Dspi h p of rgim adopd b a small opn conom, h volaili of h nonradabl oupu incrass whn h probabili of non-pric adjusmn incrass from 0.25 (flxibl prics) o 0.75 (rigid prics). This is paricularl ru undr h fixd xchang ra rgim. This rsul suppors h convnional wisdom ha ral oupu, afr xprincing a spcific p of ral shock, should hav smoohr rsponss if h pric adjusmns o shocks ar quickr. Tabl 3 Saisics for h calibrad conom wih diffrn dgrs of pric rigidiis Variabls Prcn of Sandard Dviaion (HP-Filrd) φ = 0.25 φ = 0. 50 φ = 0. 75 Fixd Floa Fixd Floa Fixd Floa Pric of nonradabls 3.007 2.269.592.080 0.53 0.3 Pric 0.638.3 0.639.07 0.647.020 Nominal xchang ra 0.008.74 0.008.08 0.007.055 Ral xchang ra.506.542 0.798 0.973 0.264 0.627 Bond 3.679.466 3.649.469 3.69.474 Nonradabl oupu 3.445 2.757 3.80 2.684 4.225 2.824 Consumpion 0.908 0.684 0.866 0.659 0.840 0.642 No: φ shows h probabili of non-pric adjusmn. Whn φ is 0.5, prics compll adjus afr 2 quarr and whn φ is 0.75, prics compll adjus afr 4 quarrs. In ohr words, h largr h valu of φ, h highr h dgr of rigidi in prics. 4.3 Snsiivi analsis: Diffrn dgrs of opnnss In his scion w s h snsiivi of h prdicions of h modl o alrnaiv valus of a criical paramr dgr of opnnss. Th rsuls ar shown in Tabl 4. A fw inrsing rsuls sand ou. Firs, whn h dgr of opnnss rachs is highs possibl valu, h ral xchang ra is almos wic mor volail undr flxibl han i is undr fixd. Scond, boh 9
xchang ras - nominal and ral - ar alwas mor volail undr flxibl. Third, nonradabl oupu is alwas mor volail undr fixd han floaing xchang ras. Tabl 4 Saisics for h calibrad conom wih diffrn dgrs of opnnss Variabls Prcn of Sandard Dviaion (HP-Filrd) γ = 0.25 γ = 0. 50 γ = 0. 75 Fixd Floa Fixd Floa Fixd Floa Pric of nonradabls 0.56 0.404 0.53 0.3 0.505 0.307 Pric 0.302.246 0.647.020 0.472.4 Nominal xchang ra 0.009 0.760 0.007.055 0.007 0.987 Ral xchang ra 0.388 0.88 0.266 0.627 0.27 0.298 Bond 6.892 8.27 3.69.474 8.096 6.46 Nonradabl oupu 3.833 3.880 4.225 2.824 4.029 3.00 Consumpion 0.78 0.865 0.840 0.642 0.78 0.684 No: γ masurs h dgr of opnnss whr h largr h valu of γ, h mor opn is an conom. 5. Conclusions W xamin h link bwn rms-of-rad shocks and som macroconomic variabls b numricall solving a dnamic sochasic gnral quilibrium modl of a small opn conom. Th modl combins nominal pric rigidi undr diffrn xchang ra rgims. Th numrical soluions ar compard wih h acual mpirical rgulariis. In h modl, housholds consum radabl and nonradabl goods. Th radd scor is viwd as a prfcl compiiv mark whr prics ar full flxibl and covrd b h law of on pric. Th nonradd scor, on h ohr hand, is assumd o b a monopolisic compiiv mark whr prics in his scor ar sick. Th conom is small in h sns ha i canno influnc h rms-of-rad of h conom. Gnrall, h simulaions show ha h modl duplicas man of h slizd facs documnd b Broda (2004). Firs, undr a mor flxibl xchang ra rgim, h ral nonradd oupu has smallr flucuaions bu h pric and ral xchang ra hav largr flucuaions whn counris ar hi b rms-of-rad shocks. This rsul is in favor of Fridman s prdicion ha shor run oupu rsponss o shocks ar significanl smoohr in floas han in 20
pgs. Scond, in moving from fixd o flxibl, h proporional ris in volaili of h nominal xchang ra is coupld b a ris in volaili of h ral xchang ra. This implis ha counris, moving from fixd o floaing xchang ra rgim, will xprinc a dramaic ris in h volaili of h ral xchang ra. Third, h volaili of h holding of n forign asss is alwas h largs in all ps of xchang ra rgims bu his flucuaion nds o b smallr undr a mor flxibl xchang ra rgim. Snsiivi analsis shows ha dspi h p of rgim adopd b a small opn conom, h volaili of h nonradabl oupu incrass whn h probabili of non-pric adjusmn incrass. Addiionall, dspi h dgr of opnnss, volaili of h nonradabl oupu is alwas highr undr fixd han floaing xchang ras. Th appaling rsuls obaind from h modl suggs ohr opics for furhr invsigaion. Th arificial conom and h numrical mhods mplod hr can b usd o xplor quaniaivl h ffcs of ohr conomic policis implmnd in small opn conomis. 2
Figur a Effc of ngaiv rms-of-rad shock undr fixd xchang ra rgim 22
Figur b Effc of ngaiv rms-of-rad shock undr flxibl xchang ra rgim 23
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