QUANTIFYING THE SECOND-ROUND EFFECTS OF SUP- PLY-SIDE SHOCKS ON INFLATION

Transcription

1 QUANTIFYING THE SECOND-ROUND EFFECTS OF SUP- PLY-SIDE SHOCKS ON INFLATION Tibor HLÉDIK * Absrac: This paper uses a small-scale dynamic raional expecaions model based on an openeconomy version of Fuhrer Moore-ype saggered wage seing o quanify he secondround effecs of seleced supply-side shocks and of shocks o he nominal exchange rae on wages and subsequenly on inflaion. In order o analyse he desired reacion of he cenral bank o hese shocks, opimal ime-consisen policy rules are derived wihin he presened New-Keynesian framework. The conclusions presened in he paper sugges ha he second-round effecs of shocks o impor prices and he nominal exchange rae on inflaion should no be ignored in pracical policy-making. Keywords: moneary policy, opimal policy rules, inflaion argeing JEL Classificaion: E52, E31, F41 1. Inroducion The Czech Republic inroduced is inflaion argeing regime a he beginning of Being a small open economy under ransiion, he Czech economy has experienced several quie significan exernal and inernal supply-side shocks and changes in he nominal exchange rae over he las few years. These have exered a srong direc influence on inflaion. Sudden changes in impor prices and changes in adminisered prices largely explain he volailiy of inflaion (measured by CPI consumer price index) since The direc effecs of hese supply-side shocks on inflaion are fairly easily idenifiable. However, i is more difficul o quanify some of he indirec effecs of hese supply-side shocks on inflaion and o derive how cenral banks should reac o hem. The main goal of his paper is o quanify he second-round effecs of some seleced supply-side shocks and a shock o he nominal exchange rae on wages and subsequenly on inflaion measured in erms of boh he gross domesic produc *) Czech Naional Bank, Na Příkopě 28, CZ Prague 1 ( Tibor.Hledik@cnb.cz). **) This aricle has been elaboraed wihin he Czech Naional Bank s Economic Research Programme. I would like o express my graiude o A. Blake for his assisance during he work on previous versions of he model on which his paper is based. In addiion, I would like o hank A. Bulíř, V. Kolán, D. Laxon, M. Mandel, J. U. Södersröm and J. Vlček for heir useful commens and suggesions. Of course, all remaining errors and omissions are solely mine. PRAGUE ECONOMIC PAPERS, 2, 2004 l 121

2 (GDP) deflaor and he CPI. The moivaion o do so sems from he auhor s aemp o explain he deerminans of he GDP deflaor in he Czech Republic and find a behavioural link beween he GDP deflaor and he labour marke. The analysis is carried ransparenly wihin a simple srucural model framework based on raional expecaions. I is assumed ha nominal wage conracs are se according o he corresponding specificaion of he open economy version of he Fuhrer, Moore (1995) model. In he Fuhrer Moore model i is assumed ha nominal wage conracs are se in order o keep he resuling real wage close o he weighed average of he pas and anicipaed fuure level of real wages. In order o define he second-round effecs arising from various shocks on inflaion, i is assumed firs ha nominal wage conracs are derived similarly o he prevailing pracice in he Czech Republic wih respec o he real wage deflaed by he CPI. By assuming ha a firm s compeiive posiion is more closely linked wih real wages deflaed by he GDP deflaor, for he model wih an alernaive wage conrac specificaion i is assumed ha nominal wages are negoiaed wih respec o real wages deflaed by he GDP deflaor. For he purposes of his paper he second-round effecs on inflaion (and oher model variables) arising from any shock are defined as he difference beween he dynamics of he models corresponding wih hese wo alernaive wage-conracing specificaions, oher hings held equal. Given he high aggregaion of he model and he fac ha he equaions are no derived wihin a dynamic general equilibrium framework, some imporan second-round effecs of supply-side shocks and shocks o he nominal exchange rae on inflaion such as he income effec are ignored. The paper is srucured ino seven secions. The inroducion is followed by a descripion of he main behavioural equaions, including a discussion of some of he model-relaed specifics of he Czech economy. The nex secion is devoed o presening he sae space represenaion of he model. This is necessary for deriving he analyic soluion of he model in erms of opimal rules and jump variables. The fourh secion repors on he parameerisaion of he model. Special emphasis is given in his secion o he calibraion of he Phillips curve for domesic prices. Knowledge of model equaions and numerical values for elasiciies makes i possible o presen he soluion of he model in he nex secion. In order o evaluae he dynamic properies of he model, he sixh secion invesigaes he resuls based on impulse responses for seleced supply-side and asse-price shocks for hree opimal policy rules corresponding o differen ad-hoc loss funcions of he moneary auhoriies. The las secion summarises he resuls. 2. The Model A New-Keynesian small open-economy raional expecaions model is used for he analysis. This is very similar in srucure o he models presened in Blake, Wesaway (1996), Baini, Haldane (1999), Baini, Yaes (2001) and Svensson (1999). The model was calibraed on quarerly seasonally adjused daa and specified in gap form. This means ha all variables are defined as deviaions from heir longrun equilibrium values 1) or, in he case of inflaion, as deviaions from he inflaion arge. The model equaions are as follows: 1) Equilibrium values were deermined using a generalised version of he Hodrick Presco (HP) filer in he case of non-saionary variables and se o long-erm averages in he case of saionary variables. The generalised HP filer in comparison wih he ordinary HP filer includes a penaly weigh for a deviaion of he filered value of he examined variable from is exogenously deermined long-run (seady-sae) growh rae. This modificaion makes i possible o miigae he well-known poor end-of-sample properies of he HP filer by seing he parameers of he filer o reflec some judgemen abou he long-run growh rae and cyclical posiion of he economy. 122lPRAGUE ECONOMIC PAPERS, 2, 2004

3 y = α 11 y 1 + α 12 r 2 + α 13 q 1 + α 14 y * 1 + ε (1) π d = α + α E E 3 3 d d im im ( π + 1 ) + α 2 i + 1 π 1 + α 25 E ( e + 1π + 1 ) + α 2 j + 6 ( e j π j ) i = adm adm ( π + 1 ) + α 2 k + 11 π k + α l y 1 + ω π cpi k = 0 l = 0 j = 0 = α 31 π d + α 32 ( e + π im ) + (1 α 31 α 32 ) π adm + (2) (3) e = E p * (e +1 ) + α 41 i + α 42 i + ϕ (4) E p (e ) = α 51 E (e +1 ) + (1 α 51 ) e 1 (5) r = α 61 E P (r +1 ) + α 62 i + α 63 E (π d +1) + ι (6) E P (r +1 ) = α 71 E (r +1 ) + (1 α 71 ) (i π4 d ) (7) i = Ψ 1 y + Ψ 2 y 1 + Ψ 3 y 2 + Ψ 4 y 3 + Ψ 5 y Ψ 6 π d 1 + Ψ 7 π d 2 + Ψ 8 π d 3 + Ψ 9 π im + Ψ 10 π im Ψ 11 π im 2 + Ψ 12 π im 3 + Ψ 13 π adm + Ψ 14 π adm Ψ 15 π adm 2 + Ψ 16 π adm 3 + Ψ 17 e 1 + Ψ 18 e Ψ 19 e 1 + Ψ 20 e 2 + Ψ 21 e 3 + Ψ 22 q Ψ 23 ϕ + Ψ 24 y * df + Ψ 25 i 1 + Ψ 26 π + Ψ 27 r 1 + ϖ df d q = q 1 + e + π π (8) (9) ϕ = α 101 ϕ 1 + ξ (10) π im = α 111 π im 1 + κ (11) π df = α 121 π df 1 + ξ (12) where E ( ) = expeced value of variable based on he informaion se of economic agens available a ime 2) ; y = Czech GDP; r = proxy for he real ineres rae wih one year mauriy (see he descripion laer); q = real exchange rae; π d = quarerly percenage change in he GDP deflaor a facor cos 3) ; π4 d = year-on-year per- adm adm π = α 131 π 1 + τ (13) y * = α 141 y * 1 + γ (14) i * = α 151 i * 1 + θ (15) 2) The informaion se includes he specificaion of all model equaions, including he reacion funcion of he cenral bank and exogenous shocks up o ime. 3) The GDP deflaor a facor coss is calculaed direcly from he GDP deflaor by eliminaing he impac of indirec axes on he index. PRAGUE ECONOMIC PAPERS, 2, 2004 l 123

4 cenage change in he GDP deflaor a facor cos; π adm = adminisered price index; cpi df π = quarerly inflaion rae measured in erms of he consumer price index; π = quarerly percenage change in he German GDP deflaor; π im = quarerly impored price inflaion expressed in erms of he euro; e = nominal exchange rae of he Czech koruna agains he euro; i * = 3-monh money marke rae (Germany, laer eurozone); i = 3-monh PRIBOR; ϕ = risk premium; y * = foreign demand approximaed wih German GDP; ε, ω, ι, ϖ, ξ, κ, ς, τ, γ, θ = shock erms. Equaion (1) specifies a sandard open-economy backward-looking IS curve. Oupu is a funcion of lagged oupu, he real ineres rae wih a wo-quarer lag, he lagged real exchange rae and foreign demand (boh wih a one-quarer lag). From he specificaion of equaions (6) and (7) i is clear ha he real ineres rae deerminaion is based on a risk-neural arbirage condiion on he financial markes and privae agens form boh forward-looking and adapive expecaions. In his way i is possible o examine he impac of a change in ineres raes wih longer mauriy on aggregae demand and implicily ake ino accoun expecaional yield-curve effecs on he dynamic properies of he model. Equaion (2) is a Phillips curve for domesic inflaion derived from a Fuhrer Moore-ype (F M) wage-conracing specificaion 4) ha has been modified for a small open economy. This modificaion 5) is based on he assumpion ha wage seers do no derive heir nominal wage demand from a real produc wage, as i is he case in he F M specificaion, bu raher from heir real consumer wage. 6) This assumpion is very much in line wih he pas and curren pracice of how wages are negoiaed in he Czech Republic. Indeed, rade unions always communicae heir nominal wage demands in erms of some plausible fuure real wage growh increased by expeced inflaion. Equaion (2), as will be shown laer, gives rise o secondround effecs of some seleced supply-side shocks or nominal exchange rae shocks on domesic inflaion via he wage-conracing channel. The following hree equaions served as he basis for deriving equaion (2): p d = λ 1 w + λ 2 w 1 + λ 3 w 2 + (1 λ 1 λ 2 λ 3 ) w 3 (15) p cpi = α p d + β (e + p im ) + (1 α β) p adm (16) cpi w p = χ 0 E (w + 1 p cpi + 1) + χ 1 (w 1 p cpi 1) + + χ 2 (w 2 p cpi 2) + χ 3 (w 3 p cpi 3) + (17) + (1 χ 0 χ 1 χ 2 ) (w 4 p cpi 4) + Ω y Equaion (15) is a sandard mark-up equaion based on he assumpion ha prices are deermined as a weighed average of curren and pas nominal conrac wages. The mark-up was se o zero, and he number of lags was chosen so as o ensure ha he reduced-form equaion (2) for he calibraion/esimaion exercise is 4) See Fuhrer and Moore (1995). Of course, he F M wage-conracing specificaion is no based on an SDGE opimising framework and as such is no immune o he Lucas criique. I is, however, sill useful in deepening he Phillips-curve coefficiens in equaion (2) and linking aggregae price dynamics wih labour marke behaviour. 5) In Blake, Wesaway (1996) and Baini, Haldane (1999) he Phillips curves are derived from he same heoreical assumpions. 6) The real produc wage is defined as he nominal conrac wage deflaed by he GDP deflaor a facor cos. Similarly, he real consumer wage is defined as he nominal conrac wage deflaed by he consumer price index. 124lPRAGUE ECONOMIC PAPERS, 2, 2004

5 of a sufficienly general form. The nex equaion defines he consumer price index as a weighed average of he GDP deflaor a facor cos, impor prices and adminisered prices. Equaion (16) deserves some more aenion given ha i is based on an approximaion. The consumer price index in he Czech Republic measures he price level of a consumpion baske consising of approximaely 790 represenaive producs and services. The curren daa collecion pracice of he Czech Saisical Office does no make i possible o differeniae beween domesically produced and impored goods or services in he CPI. Therefore, he only price index on he righhand side of equaion (16) ha is unambiguously defined wihin he CPI is p adm, he price index measuring adminisered prices. The weighed average of he oher wo indices, he GDP deflaor a facor cos and he impor price index, is an approximaion for boh domesically produced goods wih some impor conen and impored final goods. Equaion (17) is based on he assumpion ha real wages oday depend on he weighed average of expeced real consumer wages one period ahead and lagged (1 4 quarers) real wages. Real wages are, mos imporanly, posiively relaed o he cyclical posiion of he domesic economy (approximaed by he oupu gap). Equaion (2) is derived by summing equaions (17) for ime indices + 1 i muliplied by λ i (i = 1 3) and equaion (17) for 3 muliplied by 1 λ 1 λ 2 λ 3 and by subsiuing ou w i and p i cpi (i = + 1,, 1, 2, 3, 4) using equaions (15) and (16). The reduced-form coefficiens expressed as a funcion of he parameers of equaions (15) (17) are available on reques from he auhor. 7) Equaion (3) is obained by aking he firs difference of boh sides of equaion (16). Equaion (4) is a sandard uncovered ineres-rae pariy arbirage condiion. The expecaion formaion of he privae secor is no assumed o be fully forwardlooking model-consisen, as is apparen from he specificaion of equaion (5). Privae agens exchange rae expecaions are modelled as a weighed average of forward-looking raional and backward-looking expecaions. This modificaion in he UIP condiion makes he nominal exchange rae, and consequenly he model s dynamics, less jumpy and herefore more realisic. Equaion (6) is derived from an approximaion of he risk-neural arbirage condiion on he financial marke for he real ineres rae wih one-year mauriy, as 1 4 n d capured by he following equaion: E ( i 4 π ) r = + s + 1+ s s= 0 4 n n + 1 where n is se o uniy. 8) Equaion (6) can be obained by applying he expecaion operaor E o r + 1 and using simple algebra. As in he case of he UIP condiion, i is assumed ha economic agens do no form fully forward-looking model-consisen expecaions. Equaion (7) explicily specifies he expecaion formaion of he privae secor. The share of agens ha form model-consisen forward-looking expecaions is α 71, while he res of he privae secor is assumed o approximae real ineres raes wih one-year mauriy wih a shor-erm real ineres rae based on backward-looking inflaion expecaions. Equaion (8) specifies he reacion funcion of he cenral bank in a fairly general form. The variables are deermined by he sae space represenaion of he model oulined above (see laer for deails). The coefficiens of he opimal policy rules s 7) These coefficiens can be obained by a generalisaion of he approach presened by Blake (2000). 8) See Söderlind (1999). The approximaion for ineres raes of such shor mauriy is, of course, very crude. PRAGUE ECONOMIC PAPERS, 2, 2004 l 125

6 corresponding o various loss funcions of policymakers 9) will be derived laer using dynamic programming. Equaion (9) is a recursive definiion of he real exchange rae. Equaions (10) (14) approximae, respecively, he risk premium, impored inflaion, foreign inflaion measured in erms of he GDP deflaor, adminisered price inflaion and foreign demand as simple AR(1) processes. 3. Sae Space Represenaion of he Model Given ha he model described above is log-linear, i can be ransformed ino he following sae-space form represenaion: 10) X X ε + E ( ) = 1 A B i x x 0 (1*) where X = [y y 1 y 2 y 3 y 4 π d 1 π d 2 π d 3 π im π im 1 π im 2 π im 3 π adm π adm 1 π adm 2 π adm 3 e 1 e 1 e 2 e 3 q 1 ϕ y * i 1 i * df π r 1 ] and x = [e r π d ]. A is a 30x30 marix, and B is a 30x1 vecor. Vecor X is someimes referred o as he sae vecor, and x is he vecor of forward-looking variables. One of he simples ways of seing up he sae space represenaion is o code up he model in he following form: X A1 E ε ( ) + 1 = A2 B1 i x x + 1 X 0 (1**) where A1 and A2 are 30x30 marices, and B1 is a 30 1 vecor. If A1 is a non-singular marix, (1*) can be obained from (1**) by simply muliplying boh sides of (1**) by A1-1. In order o derive he opimal moneary policy rules corresponding o alernaive loss funcions of he cenral bank, he cenral bank s preferences mus firs be deermined. For he purposes of his paper i is assumed ha he cenral bank s goal is o minimise flucuaions in inflaion around he inflaion arge and o minimise he volailiy of he oupu gap and he change in shor-erm ineres raes. The model specified above is consruced so ha various opimal 11) ineres rae rules can be derived (wih respec o he volailiy of inflaion, oupu, and he change in shorerm ineres raes) according o cenral bank preferences. 12) The mahemaical expression of he loss funcion L is herefore as follows: L ( i i ) 2 2 cpi 2 = w cpi π + + π w y y w i 1 9) The choice of he loss funcion will be discussed laer. 10) I primarily use symbols and derivaions according o Svensson (1999). 11) The word opimal in he sense above is normaive in naure. The cenral bank decides on preferences in his model (e.g. higher or lower volailiy of inflaion or produc when deriving moneary rules). The objecive funcion of he moneary auhoriies is no derived on he basis of knowledge of he economic agens uiliy funcion. For an example of a paper in which he loss funcion is derived from microeconomic principles, see Roemberg and Woodford (1998). 12) Of course, some oher variables, for insance he real exchange rae (one of he imporan deerminans of he curren accoun balance), could also be included in he loss funcion. 126lPRAGUE ECONOMIC PAPERS, 2, 2004

7 Since he analyic soluion echnique o be applied laer requires he model o be expressed in a general marix form, 13) L mus be expressed as a funcion of he sae vecor. Since he variables enering ino he loss funcions are linear funcions of he sae vecor and he loss funcion iself is a quadraic funcion, he general represenaion of he loss funcion is given by he following wo equaions: Y = C Z (X ' x ' ) + C i i (2*) L = Y ' K Y (3*) cpi where Y ' = (π y i i 1 ), C z is a 3x30 marix, C i is a 3 1 column vecor, and K is a 3 3 diagonal marix wih diagonal ( w cpi w y w i ). π Minimising he loss funcion defined above is equivalen o finding he minima I TL = lime δ L + l (4*) δ 1 l = 0 where δ is a discoun facor. Equaions (1*) (4*) give a complee descripion of he model, and herefore he general represenaion of he soluion has he following form: X + 1 = M 11 X + M 12 ε + 1 (i) x = H X i = f X (ii) (iii) Y = (C 1 Z + C 2 Z H + C 1 f) X where M 11 and M 12 are 27x30 marices, H is a 3x27 vecor, f is a 1x27 vecor, and 1 C Z vecor C = 2 is pariioned according o (X i ' x '). C Z Equaion (i) describes he dynamics of he sae vecor, (ii) expresses he forward-looking variable as a linear combinaion of predeermined variables, (iii) is an opimal ineres rae rule and (iv) is an expression of he variables in he loss funcion as a linear funcion of he sae vecor. Equaions (i) and (iv) can be easily derived wih he help of (ii), (iii) and (1*) (2*). Equaions (i) (iv) deermine he dynamics of he whole sysem. The ineres rae rule (corresponding o he chosen loss funcion) ensures he model converges o he seady sae for any shock hiing he sysem. The soluion is obained by applying dynamic programming. A deailed descripion of he opimising algorihm used can be found in Svensson (1999). The program for solving he model was coded up by he auhor in GAUSS. 4. Parameerisaion of he Model In order o be able o solve he model and carry ou dynamic impulse response analysis, all parameers in equaions (1) (14) mus be deermined. For he calibraion exercise, he equilibrium values for he saionary variables were se equal (iv) 13) Simple marix algebra is needed o code up he opimising algorihm in GAUSS. PRAGUE ECONOMIC PAPERS, 2, 2004 l 127

8 o heir long-erm averages. For non-saionary variables a generalised form of he Hodrick-Presco filer (see Laxon, 1992) was applied in order o incorporae exper judgemen ino he calibraion process and miigae he poor end-of-sample properies of he HP filer. 14) The model parameers of equaions (1) (14) were se as follows: α 11 = 0.9, α 12 = -0.25, α 13 = 0.15, α 14 = 0.25; α 21 = 0.107, α 22 = 0.282, α 23 = 0.173, α 24 = 3, α 25 = , α 26 = , α 27 = 14, α 28 = 75, α 29 = -8, α 210 = 6, α 211 = 0.056, α 212 = 0.034, α 213 = 0.013, α 214 = , α 215 = 0.087, α 216 = 0.074, α 217 = 0.046, α 218 = 0.017, α 31 = 0.68, α 32 = 0.14; α 41 = -0.25, α 42 = 0.25; α 51 = 0.4; α 61 = 0.8, α 62 = 0.2, α 63 = -0.8; α 71 = 0.4; α 101 = 0.6, α 111 = 0.09, α 121 = 0.54, α 131 = 0, α 141 = 0.69; α 151 = 0.9. The IS curve elasiciies were obained by simple OLS for he period of 1994:Q1 2001:Q4 and are broadly in line wih similar esimaes repored in previous sudies for he Czech Republic (see, for insance, Kolán, 2002 or Isard and Laxon, 2000). The parameer values enering ino he Phillips curve, α 21 α 218, were calibraed using he heoreically derived deep parameers for α 21 α 218, expressed in erms of he coefficiens of, and derived from, equaions (15) (17). The calibraion of he parameers was obained by applying a numeric non-linear opimising algorihm in a sandard Excel spreadshee. The algorihm minimises 15) he square of he residuals in equaion (2) wih respec o linear resricions ha all parameers in equaions (15) (17) are posiive and he share of adminisered prices in he CPI baske is known (0.18). In addiion i is assumed ha he share χ 0 of forward-looking agens in wage-conracing equaion (17) is ) The main reasons for calibraing equaion (2) by means of consrained opimisaion are he following: o be able o derive he parameers of he wage-conracing equaion implicily wihou relying oo much on labour marke daa, which are very shor and subjec o changes in daa collecion mehodology over ime; o obain plausible parameer values ha are consisen boh wih he heory applied and wih he available daa as far as possible. The resuls of he consrained opimisaion in erms of he parameer values of equaions (15) (17) are as follows: λ 1 = 0.4, λ 2 = 0.33, λ 3 = 0.20; α = 0.68, β = 0.14; 14) The modificaion of he HP filer was coded up in GAUSS. 15) Of course, i migh be he case ha he minimum found in his way represens a locally minimal soluion and no a globally minimal soluion. The calibraed value of 0.10 assumes slighly less forwardlooking behaviour in wage negoiaions han he esimaes for developed indusrial counries would sugges. 16) Inflaion expecaions are no available for a long enough ime horizon o es economerically he share of forward-looking agens in he wage-conracing equaion. Of course, for sandard esimaion procedures insrumenal variables could be used. 128lPRAGUE ECONOMIC PAPERS, 2, 2004

9 χ 0 = 0.1, χ 1 = 0.90, χ 2 = 0.0; Ω = 0.11; The obained parameer values λ 1 λ 3 of equaion (15) sugges ha wage coss are gradually ransmied ino he price of value added over ime. In addiion, his lag srucure is decreasing sep by sep. Parameers α 31 and α 32 were calculaed using he opimising algorihm briefly described above. The implied share of impor prices in he CPI baske is 14 %. This share is broadly in line wih esimaes obained for oher small open economies. 17) I is imporan o noe in his respec, however, ha aking ino accoun he impac of impor prices on he GDP deflaor iself (see equaion 2) he cumulaive impac of impor prices on he consumer price index is considerably higher. The parameers of he uncovered ineres rae pariy condiions are se exacly according o he arbirage condiion specified for quarerly daa. The share of he fully raional forward-looking agens (0.4) and ha of he backward-looking agens (0.6) were se so ha he model exhibis plausible dynamic properies. An assumpion of fully forward-looking agens in he exchange rae deerminaion would make he exchange rae channel very fas and he exchange rae iself very jumpy. Conversely, a very small weigh of forward-looking model-consisen agens in he UIP would weaken he immediae impac of moneary policy on he exchange rae. The parameers of equaion (6) are derived from he arbirage condiion on he financial marke for real ineres raes wih n years of mauriy. The decision on he one-year mauriy is purely judgmenal and based on he volume of exended loans wih various mauriies. The decision on he large share of agens who base heir decision on long-erm ex-ane real ineres raes relaive o hose who base heir expecaion on shor-erm ex-pos real ineres raes is also judgmenal and based on similar reasoning as in he case of he nominal exchange rae. The auoregressive coefficiens of α 101 α 141 were deermined by simple OLS. 5. Model Soluion for Phillips Curves wih Alernaive Wage Equaions and Policy Rules The main goal of his secion is o presen he soluion for he wo models corresponding wih he wo alernaive wage-conracing equaions. The firs Phillips-curve specificaion is he one specified by equaion (2) corresponding o parameers α 21 α 218. These parameers were obained by subsiuing he resuls of he consrained opimisaion exercise menioned above in erms of he parameers of equaions (15) (17) ino he funcional forms of α 21 α 218. The second specificaion is based on a heoreical assumpion ha in wage-conracing equaion (17), real wages are deflaed by he GDP deflaor a facor coss insead of he consumer price index. The coefficiens and he lag srucure in equaions (15) (17) are assumed o be he same in boh cases. Replacing CPI inflaion wih domesic inflaion in he wage-conracing equaion obviously eliminaes enirely he impac of impor and adminisered prices on domesic inflaion. The resuling Phillips curve will replace equaion (2) in he model and will have he following specificaion insead: π d = α 21 E (π d +1) + α 22 π d 1 + α 23 π d 2 + α 24 π d α 25 π d 4 + α 26 π d 5 + α 27 y + α 28 y 1 + (2 ) + α 29 y 2 + α 210 y 3 + ω 17) The calibraion value used for he Unied Kingdom is 0.2 (see for insance, Blake, Wesaway, 1996). PRAGUE ECONOMIC PAPERS, 2, 2004 l 129

10 where α 21 = 0.105, α 22 = 0.487, α 23 = 0.299, α 24 = 0.109, α 25 = 0, α 26 = 0.0, α 27 = , α 28 = , α 29 = 53, α 210 = 89. For boh Phillips-curve specificaions, hree opimal rules will be derived ha correspond o he following weighs in he loss funcion specified by equaion (3): w π cpi = 0.8, w y = 0.1, w i = 0.1, w π cpi = 0.45, w y = 0.45, w i = 0.1, w π cpi = 0.1, w y = 0.8, w i = 0.1. Again, he choice of he weighs in he loss funcion is arbirary and reflecs, respecively, a higher, equal and lower emphasis pu by he moneary auhoriies on inflaion smoohing relaive o oupu sabilisaion. The weigh pu on shor-erm ineres rae smoohing was chosen in order o obain a plausible neiher oo jumpy nor oo sluggish reacion of he cenral bank o various shocks. The analyic soluion of he models for he unknown policy rule and jump variable parameers corresponding o he wo ypes of wage equaion and various loss funcions of he cenral bank are repored in Table 1 and Table 2 below. The firs, very sraighforward, observaion is ha he model based on a wage-conracing equaion in erms of he GDP deflaor resuls in a much simpler soluion, including he funcional form of he policy rule, han he model wih a wage equaion based on he CPI. This is a sraighforward implicaion of replacing impor price and adminisered price inflaion and heir lagged values in equaion (2) wih domesic inflaion. The second observaion is ha in he specificaion of he reacion funcions of he cenral bank, all variables have he expeced signs on a cumulaive basis. 18) 6. Definiion of Second-round Effecs and heir Quanificaion hrough Impulse Responses As was sressed in he inroducion, he main goal of his paper is o quanify he second-round effecs of impor prices and adminisered prices on wages and subsequenly on inflaion measured in erms of boh he GDP deflaor a facor coss and he CPI. Since he paper concenraes solely on hose second-round effecs which arise from replacing he CPI in he wage-conracing equaion wih he GDP deflaor a facor cos, for he purposes of his paper he second-round effecs on inflaion (and oher model variables) arising from any shock are defined as he difference beween he dynamics of he models corresponding wih he wo alernaive wage-conracing specificaions, oher hings held equal. The inerpreaion of he ceeris paribus condiion deserves special aenion in he case of he policy rule. There were a leas wo possible ways of handling his problem. The firs opion is o assume ha he reacion funcion of he cenral bank is unchanged in erms of a simple backward-looking Taylor-ype rule. In his case, he change in he Phillips-curve specificaion would no have any effec on he funcional form of he reacion funcion of he cenral bank. I is sufficien, however, o include any jump variable in he reacion funcion 19) and he change in he Phillips 18) The sum of elasiciies for all curren and lagged variables. 19) For insance, a Taylor-ype forward-looking inflaion forecas based rule would be a good example of such a reacion funcion. 130lPRAGUE ECONOMIC PAPERS, 2, 2004

11 Table 1 Model Soluion wih he Wage Conracing Equaion based on CPI Vecor Ψ 1 Ψ 2 Ψ 3 Ψ 4 Ψ 5 Ψ 6 Ψ 7 Ψ 8 Ψ 9 Ψ 10 Ψ 11 Ψ 12 Ψ 13 Ψ 14 Ψ 15 Ψ 16 Ψ 17 Ψ 18 Ψ 19 Ψ 20 Ψ 21 Ψ 22 Ψ 23 Ψ 24 Ψ 25 Ψ 26 Ψ 27 Shor-erm ineres rae (policy rule) w_cpi = w_y = 0.1 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Nominal exchange rae w_cpi = w_y = 0.1 PRAGUE ECONOMIC PAPERS, 2, 2004 l 131 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Long-erm real ineres raes w_cpi = w_y = 0.1 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Domesic inflaion For all loss funcions

12 132lPRAGUE ECONOMIC PAPERS, 2, 2004 Table 2 Model Soluion wih he Wage Conracing Equaion based on he GDP Deflaor Vecor Ψ 1 Ψ 2 Ψ 3 Ψ 4 Ψ 5 Ψ 6 Ψ 7 Ψ 8 Ψ 9 Ψ 10 Ψ 11 Ψ 12 Ψ 13 Ψ 14 Ψ 15 Ψ 16 Ψ 17 Ψ 18 Shor-erm ineres rae (policy rule) w_cpi = w_y = 0.1 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Nominal exchange rae w_cpi = w_y = 0.1 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Long-erm real ineres raes w_cpi = w_y = 0.1 w_cpi = w_y = 0.45 w_cpi = w_y = 0.8 Domesic inflaion For all loss funcions

13 curve would resul in a change in he rule iself, since he rule would be a funcion of all sae variables and model parameers. The second opion he one ulimaely chosen by he auhor is o assume ha he preferences of he moneary auhoriies expressed in erms of he loss funcion are unchanged. 20) However, given ha he opimal rules corresponding o an unchanged loss funcion are differen for differen Phillips-curve specificaions, his means ha he funcional specificaion of he opimal rule will be differen for all simulaions (see he resuls presened in Tables 1 and 2). In order o quanify he second-round effecs on inflaion and oher model variables arising from seleced supply-side and asse-price shocks, wo differen impulse response exercises were generaed for he hree policy rules corresponding wih he hypoheical loss funcions of he cenral bank specified in he previous secion. The firs impulse response includes a 100 basis poin shock o impor prices expressed in foreign currency; he second shock, of he same magniude, is generaed wih respec o he nominal exchange rae. There are wo good reasons for carrying ou impulse responses for hese variables. Firs, despie he fac ha boh shocks resul in a 100 basis poin change in impor prices, heir implicaions for he models dynamics are dramaically differen. A shock o impor prices (expressed in foreign currency) ransmis direcly ino consumer price inflaion and hrough wage conracs indirecly ino domesic inflaion. In he case of a shock o he nominal exchange rae, in addiion o he direc and indirec impor price effec here is a srong demand effec caused by he change in he real exchange rae. The wo impulse responses, herefore, illusrae how imporan i is for he moneary auhoriies o differeniae beween he shocks hiing he economy o be able o reac adequaely. The second reason for generaing a shock o impor prices (expressed in foreign currency) is moivaed by he almos idenical effec of his shock (alhough wih slighly differen magniude and ineria) on he models dynamics o he shock o adminisered prices. 21) Therefore, he impulse response exercise for impor prices resuls in a very similar dynamic response of he model as for a shock o adminisered prices. The dynamic properies of he models based on he wo Phillips curves corresponding wih he alernaive wage-conracing equaions are depiced in Figures 1 4 by generaing a 100 basis poin shock o impor prices and he nominal exchange rae. Figures 1 and 2 aim a comparing he dynamic response of he wo models o he wo shocks given a loss funcion wih fixed equal weighs for boh inflaion and oupu w π cpi = 0.45, w y = 0.45, w i = 0.1. As such, hese impulse response resuls are useful in erms of undersanding he dynamic response o he shocks of he models wih he wo alernaive wageconracing equaions and comparing he resuls for he same loss funcion of he cenral bank. Figures 3 and 4 concenrae solely on he second-round effecs arising from hese shocks for he hree models corresponding wih he considered alernaive loss funcions of he cenral bank. Therefore, hese simulaions are inended o illusrae he impac of he choice of a paricular loss funcion of he cenral bank on he magniude of he second-round effec for he main model variables. 20) The final choice beween he wo alernaives also reflecs he view presened by Svensson (2002), who prefers fixing a general argeing rule of he cenral bank insead of he moneary policy rule iself. A policy rule corresponding wih an unchanged loss funcion is an example of such a argeing rule. 21) I is easy o see ha adminisered and impor prices ener symmerically ino boh he CPI and Phillips-curve equaions. PRAGUE ECONOMIC PAPERS, 2, 2004 l 133

14 6. 1 Temporary 100 Basis Poin Shock o Impor Prices Comparing he Models Dynamics for he wo Phillips Curves Corresponding wih he Alernaive Wage-conracing Equaions The 100 basis poin shock o impor prices resuls in a jump of consumer price inflaion due o he direc impor price channel (see 1G) ha in urn iniiaes a reacion of he cenral bank by increasing shor-erm nominal ineres raes (see 1A). This reacion is slighly sronger when wage conracing is based on consumer wages. A he same ime, consumer price inflaion falls afer he one-ime jump almos immediaely back o arge when nominal wage conracs are derived from real produc wages. The alernaive wage specificaion resuls in considerably higher consumer price inflaion wih more ineria. This is simply a consequence of he Phillips-curve specificaions specified for domesic inflaion (equaions (2) and (2 )). When wage conracing is based on real wages in erms of domesic inflaion (equaion (2 )), impor prices do no direcly influence domesic inflaion. This is in conras wih he case where he Phillips curve is derived from a wage-conracing equaion based on real consumer wages (equaion (2)). Impor prices in his case do have a significan and inerial effec on domesic inflaion. Figure 1H depics he difference beween he wo cases. The oher significan difference beween he dynamics of he wo alernaive models involves he channels by which he inflaionary impac of he supply-side shock is reduced by he cenral bank. When wage conracs are based on consumer wages, moneary condiions are ighened hrough he real appreciaion of he exchange rae. Real ineres raes are for mos of he disinflaion process below heir equilibrium value. When, on he conrary, wage conracs are based on real produc wages, he eliminaion of inflaionary pressures is carried ou by means of an increase of real ineres raes above heir equilibrium level. The level of real ineres raes more han eliminaes he expansionary impac of he real exchange rae (see 1C and 1D). The combined effec of he real exchange rae and real ineres rae on demand is shown in 1B. In order o bring inflaion back o arge he moneary auhoriies mainain igher moneary condiions when impor prices do have a direc impac on nominal wage conracs (and subsequenly on domesic inflaion) in comparison wih he alernaive wage specificaion Temporary 100 Basis Poin Shock o he Nominal Exchange Rae Comparing he Models Dynamics for he wo Phillips Curves Corresponding wih he Alernaive Wage-conracing Equaions A 100 basis poin shock o he nominal exchange rae, similarly as in he previous case, resuls in a jump in impor prices and subsequenly in consumer price inflaion. The reacion of he cenral bank o he shock, however, is considerably sronger han in he previous case: he iniial jump in shor-erm ineres raes is abou five imes higher. I is imporan o bear in mind ha he change in he nominal exchange rae (see 2F) and real exchange rae (see 2D) in he iniial period afer he shock generaes a srong demand effec (see he specificaion of he IS curve capured by equaion (1)). Therefore, he cenral bank mus increase shor-erm ineres raes considerably in order o reac o inflaion being above arge and curb demand-led inflaionary pressures ha could accelerae inflaion in he fuure. There are a few ransmission channels, however, hrough which he disinflaion is achieved in he models. Firs, he reacion of he cenral bank resuls in an iniial rise of long-erm real ineres raes (see 2C), and he real exchange rae (see 2D) falls back o equilibrium oo. I should also be noiced ha he volailiy of boh he real ine- 134lPRAGUE ECONOMIC PAPERS, 2, 2004

15 Figure 1 A Temporary 100 Basis Poin Shock o Impor Prices 1A: Shor-erm Shor-Term Ineres Raes 1B: 1B: Oupu C: 1C: Long-erm Long-Term Real Ineres Raes 0.1 1D: Real Exchange Rae E: Quarerly 1E: Quarerly Change Change in in he he Nominal Nominal Exchange Exchange Rae Rae 0.8 1F: 1 : Nominal Exchange Rae Rae G: 1G: Inflaion Measured by by CPI CPI H: 1H: Inflaion Measured by by he he GDP GDP Deflaor Real wages deflaed by CPI Real wages deflaed by GDP deflaor PRAGUE ECONOMIC PAPERS, 2, 2004 l 135

16 Figure 2 A Temporary 100 Basis Poin Shock o he Nominal Exchange Rae A: Shor-erm Ineres Raes 2A: Shor-Term Ineres Raes 2B: 2B: Oupu Oupu C: Long-erm 2C: Long-Term Real Ineres Raes 2D: 2D: Real Real Exchange Rae Rae E: Quarerly Change in he Nominal 2E: Quarerly Change in he Nominal Exchange Rae Exchange Rae F: 2 : Nominal Exchange Rae Rae G: Inflaion 2G: Measured by CPI H: 2H: Inflaion Inflaion Measured Measured by by he he GDP GDP Deflaor Deflaor Real wages deflaed by CPI Real wages deflaed by GDP deflaor 136lPRAGUE ECONOMIC PAPERS, 2, 2004

17 res rae and he exchange rae is higher when he second-round effecs of impor prices are absen. The combined effec of he posiive real ineres rae and appreciaing real exchange rae gradually reduces he excess demand (see 2B). The magniude and dynamics of he oupu gap, despie he differences in he dynamics of he real exchange rae and real ineres rae, are similar for boh Phillips-curve specificaions. The visually mos significan difference beween he wo models dynamics emerges for domesic inflaion (see 2H). The difference in he specificaion of he Phillips curves corresponding wih he wo wage-conracing equaions largely explains why domesic inflaion is more volaile when wage conracs are derived from real consumer wages as opposed o he real produc wage. The reason is ha he exchange rae shock feeds ino nominal wage conracs and herefore causes greaer volailiy of domesic inflaion a he iniial sage. A he same ime he appreciaion following he shock exers an ani-inflaionary effec on wages and subsequenly on domesic inflaion. The difference beween he wo models is somewha smaller for consumer price inflaion (see 2G), which can be explained by he very same impac of he change of he nominal exchange rae (see 2E) on oal inflaion in he case of boh models Temporary 100 Basis Poin Shock o Impor Prices Quanificaion of Second-round Effecs for he Three Alernaive Loss Funcions of he Cenral Bank The firs very inuiive and sraighforward implicaion of he impulse response resuls depiced in 3A 3H is ha he magniude of he second-round effecs arising from a 100 basis poin shock o impor prices is direcly linked o he chosen loss funcion of he cenral bank. As one would expec, he volailiy of he second-round effecs for hose variables ha are included in he loss funcion of he cenral bank is negaively relaed o he weigh of ha variable in he loss funcion. Figures 3B and 3G clearly suppor his observaion. The volailiy of he second-round effecs for oupu is he highes for he loss funcion wih he smalles weigh for oupu, and, similarly, he volailiy of he second-round effecs for inflaion is he highes for he reacion funcion ha pus he smalles emphasis on inflaion relaive o oupu smoohing. I should be noiced ha when oupu smoohing is he main prioriy of he auhoriies, he second-round effec of he shock on oupu is close o zero (see 3B). On he conrary, he second-round effecs of he shock on CPI and domesic inflaion (see 3G and 3H) are posiive, differen from zero. This can be explained by he specificaion of he Phillips curve, namely, by he quick ransmission of impor prices ino CPI and domesic inflaion. The inflaionary impac of he shock can be eliminaed by moneary policy only wih some delay. The behaviour of he cenral bank and correspondingly he dynamics of he nominal exchange rae (see 3A, 3E and 3F) is very much in line wih simple inuiion. The higher is he weigh of inflaion in he loss funcion of he cenral bank, he larger is he iniial ineres rae hike and corresponding nominal exchange rae appreciaion o miigae he inflaionary pressures arising from he shock. The dynamics of he real ineres rae and exchange rae (see 3C and 3D) also correspond wih he loss-funcion specificaion. The highes preference for inflaion smoohing resuls in he lowes real ineres rae and mos appreciaed real exchange rae in he iniial period, and vice versa. PRAGUE ECONOMIC PAPERS, 2, 2004 l 137

18 Figure 3 A Temporary 100 Basis Poin Shock o Impor Prices 3A: 3A: Shor-erm Shor-Term Ineres Raes Raes 3B: 3B: Oupu Oupu C: Long-erm 3C: Long-Term Real Real Ineres Raes D: 3D: Real Real Exchange Exchange Rae Rae E: Quarerly Change in he Nominal 3E: Quarerly Change in he Nominal Exchange Rae Exchange Rae F: 3 : Nominal Exchange Rae Rae G :Inflaion Measured by CPI 3G: Inflaion Measured by CPI H: 3H: Inflaion Measured by he by GDP he GDP Deflaor w_pi=0.1 w_y=0.8 w_pi=0.45 w_y=0.45 w_pi=0.8 w_y= lPRAGUE ECONOMIC PAPERS, 2, 2004

19 Figure 4 A Temporary 100 Basis Poin Shock o he Nominal Exchange Rae 4A: 4A: Shor-erm Shor-Term Ineres Raes Raes 4B: 4B: Oupu Oupu C: 4C: Long-erm Long-Term Real Ineres Raes Raes E: Quarerly Change in he Nominal 4E: Quarerly Change in he Nominal Exchange Exchange Rae Rae G: 4G Inflaion :Inflaion Measured by by CPI CPI D: 4D: Real Exchange Rae Rae F: 4 : Nominal Exchange Rae Rae H: 4H: Inflaion Inflaion Measured by by he he GDP GDP Deflaor Deflaor w_pi=0.1 w_y=0.8 w_pi=0.45 w_y=0.45 w_pi=0.8 w_y=0.1 PRAGUE ECONOMIC PAPERS, 2, 2004 l 139

20 6. 4 Temporary 100 Basis Poin Shock o he Nominal Exchange Rae Quanificaion of Second-round Effecs for he Three Alernaive Loss Funcions of he Cenral Bank For mos variables a emporary 100 basis poin shock o he nominal exchange rae resuls in second-round effecs of similar magniude as in he previous case. The iming of he dynamic response for mos variables is, however, differen. The dynamic response in 4B illusraes ha he iniial second-round effecs on oupu are negaive 22) when he shock his impor prices and, on he conrary, he iniial secondround effec on oupu is posiive when he shock is generaed for he nominal exchange rae. This difference beween he impac of he wo shocks sems from heir differen origin. On he one hand he impor price shock has no direc effec on he real exchange rae and subsequenly on demand, hough i raises inflaionary expecaions hrough he direc exchange rae channel. On he oher hand he exchange rae shock resuls in a srong posiive impac on he oupu gap ha canno be enirely and immediaely eliminaed by he moneary policy reacion. The evaluaion of he second-round effecs for he hree considered policy rules gives similarly inuiive resuls as in he case of he previous 100 basis poin shock o impor prices. The volailiy of he second-round effecs for inflaion and oupu corresponds wih he chosen weigh of hese variables in he loss funcion of he cenral bank. The increasing of oupu relaive o inflaion in he loss funcion weigh (from 0.1 o 0.8) resuls in a decreasing volailiy of oupu relaive o he volailiy of consumer price inflaion. Figures 4G and 4H illusrae ha a small emphasis pu on inflaion smoohing resuls in a very gradual reurn of boh consumer and domesic inflaion o he seady sae. 7. Conclusion The main goal of his paper was o quanify he second-round effecs of seleced supply-side shocks on inflaion depending on alernaive assumpions made regarding wage-conracing specificaions. The wo alernaives included Fuhrer Moore-ype wage-seing behaviour, wih real wages being defined in he firs case in erms of he CPI and in he second case in erms of he GDP deflaor. A calibraed srucural model framework was used for he quanificaion ha incorporaes boh forward-looking model-consisen and adapive expecaions of economic agens on various markes. The models for he wo alernaive Phillips-curve specificaions specified in erms of domesic inflaion were solved for hree opimal policy rules corresponding wih hree differen (ad-hoc) loss funcions of he cenral bank. The dynamic properies of he models were analysed for a emporary 100 basis poin shock o impor prices and he nominal exchange rae. The impulse response resuls conained in he paper imply ha he second-round effecs of hese shocks on wages and subsequenly on prices are significan enough o be aken ino accoun in moneary policy decisions. The magniude of he second-round effecs of hese shocks on inflaion and oupu depends no only on he source of he shocks hemselves, bu also on he choice of reacion funcion of he cenral bank. The simulaion resuls also sugges ha he relaive magniude of he second-round effecs of he considered shocks on inflaion and oupu is posiively relaed o he weigh of hese variables in he loss funcion of he moneary auhoriies. 22) The only excepion is he dynamic response for he model wih he policy rule associaed wih he highes weigh for oupu smoohing. 140lPRAGUE ECONOMIC PAPERS, 2, 2004

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