Causes of Portuguese Inflation: An Econometric Application

Transcription

1 Causes of Poruguese Inflaion: An Eonomeri Appliaion Agosinho S. Rosa * Deparmen of Eonomis Universiy of Évora November 2006 ABSTRACT A sudy of he auses of Poruguese inflaion, based on annual daa from 1954 o 1995, using he Johansen Mehod, allows us o onlude ha variaion in Poruguese inflaion is deermined essenially by foreign inflaion and by variaion in he effeive exhange rae of he Poruguese Esudo (PTE). In he long-erm, he relaionship beween inflaion rae and he growh rae of uni labour oss is almos uniary. However, he response of inflaion hange o he equilibrium error beween inflaion rae and hanges in uni labour oss is slow and almos insignifian, while he response of uni labour oss o his disequilibrium is fas and signifian. Beause of he fa ha he variaion in nominal money sok, orreed by he growh rae of real GDP, as well as budge defii as a perenage of GDP, are no signifian variables in he shor run, in relaion o variaion in inflaion as a dependen variable, we an onlude ha inflaion is aused essenially by oss. The oss ha are highly signifian in he shor run are hose reaed by he rae of variaion in impor pries (deermined eiher by foreign inflaion or by variaion in he effeive exhange rae). JEL Classifiaion: C12, C13, C32, E31, E24 Key Words: Causes of Inflaion, Uni Roos, and Coinegraion. * Correspondene o: Deparameno de Eonomia, Universidade de Évora, Largo dos Colegiais 2, , Évora, Porugal. Telephone: (351) , Fax: (351) , [email protected]. 1

2 Inroduion The auses of Poruguese inflaion was he fous of he sudy of some auhors in he las quarer of he 20 h enury, inluding Abel Maeus (1980), Jose Girão (1984), Robalo Marques (1990), Jorge Sanos (1992) and more reenly Robalo Marques (1995), Cunha and Mahado (1996) and Caela Nunes (1998). The aim of his work is o give oninuiy o hese sudies, looking for he main auses of Poruguese inflaion in he seond half of he 20 h enury, using annual daa for he period Thus, in he firs sage an expliaive model of he inflaion will be onsidered, in he seond sage we will presen he hosen daa and he reasons for heir hoie, in he hird sage we will analyze he degree of saionariy of he used ime series and in he fourh sage we will esimae he expliaive model of he inflaion onsidered in he firs sage, using he mehod of Johansen o dee oinegraion relaions among he non-saionary series and applying he mehodology of Rahbek and Mosoni (1999), whih allows us o inrodue saionary regressors in he VAR of oinegraion hrough umulaed explanaory variables and simulaneously o use he rae or maximum eigenvalue ess. Finally in he fifh sage we will presen he main onlusions. 1. The Considered Model The onsruion of a model is always a simplifiaion of realiy, given he mulipliiy of variables ha influene inflaion, among hem an inrease in he remuneraion of produive faors, an inrease in he pries of impored produs, a variaion in he sok of money in irulaion, a variaion in he exhange rae, he budge defii, expeaions of inflaion and he level and/or he variaion in unemploymen. Considering he Phillips urve, he heory of mark-up, he monearis heory of inflaion 1 and he possibiliy of he budge defii being able o onribue o an inrease in inflaion, 2 we an onsider he model: ( + ) ( + ) ( + ) ( + ) P& = f W& Q&, P& M, DEF, M& y& [1.1] 1 See Surrey (1989). This auhor presens he model of inflaion for he oss (heory of mark-up) separae from he monearis model of he inflaion. We have joined he wo heories in a single model. 2 See Jorge Sanos (1992) and Carlos Vieira (2000) on he relaion beween budge defii and inflaion. 2

3 ( ) ( + ) e W & Q& = g U, P& [1.2] P& P& + E& [1.3] M F Equaion (1.1) onains he heory of mark-up where he firms se he prie of heir produs above he marginal produion os. However, when he average os is onsan, i has been proved ha he marginal os is equal o he average os, so ha he pries (P) will be given by one mark-up above he average oss (CM): P = θ CM, θ > 1 [1.4] If mark-up (θ) will be onsan, he inflaion rae ( P & ) will be equal o he rae of variaion of he average oss. The average oss will vary in aordane wih he wage variaion orreed by he variaion of he produiviy ( W & Q & ), whih orresponds o he variaion of he uni labour oss, and in aordane wih he impored inflaion in domesi urreny ( P & M ). 3 Beyond he inflaion for he oss, we also inlude in (1.1) he inflaion for moneary emission beyond ha neessary for ransaions ( M & y& ) and he budge defii in perenage of GDP (DEF). The growh of money supply beyond ha neessary for ransaions, onsidering he inome veloiy of money o be onsan, will have o imply an inrease in inflaion in aordane wih he monearis shool. In he inlusion of he budge defii, one admis ha an inrease in publi onsumpion gives rise o inflaion by demand, in virue of he propensiy of he governmen o onsume being greaer han he propensiy of households o onsume. The inlusion in he model of he wo variables (budge defii and variaion in he nominal sok of money) raises some problems, sine here are periods where he governmen uses he moneary emission o finane is defii, so here is he possibiliy of orrelaion beween hese variables. Thus, before analyzing his omplee model, we sudied wo sub-models, one wihou defii, 4 and anoher one wihou variaion of money supply. As he basi onlusions do no hange, we will sudy he omplee model. The signals beween parenheses on variables in equaions (1.1) and (1.2) orrespond o he signals expeed for he oeffiiens of he relaion. 3 I is assumed ha he "oher inernal average oss" are onsan. See Agosinho Rosa (2000). 4 See Agosinho S. Rosa (2003). 3

4 The equaion (1.2) orresponds o he augmened Phillips urve wih expeaions, onsidering ha growh in wages is posiively relaed o growh in produiviy ( Q & ) in aordane wih Burda and Wyplosz (1993, p. 245). The equaion (1.3) is an ideniy. The foreign inflaion ( P & F ) plus he variaion of he effeive indire exhange rae ( E & ) 5 give he impor inflaion rae in erms of domesi urreny. The aim of his arile is o esimae he equaion (1.1), where we will subsiue he variable P & M for P & F and E & in aordane wih he equaion (1.3). 2. Daa We use annual daa whose jusifiaion in heoreial erms is given by Campbell and Perron (1991, p. 153) where, eiher due saionary analysis needs a long-erm period, or beause "seasonal adjusmen proedures ofen reae a bias oward nonrejeion of a uni roo hypohesis" (Campbell and Perron, 1991, p. 153). praial erms, i is diffiul o ge all he variables in quarerly erms in a ompaible form for he sudy desired in he period under onsideraion. However, his opion is no exemp from problems eiher, beause he majoriy of he available ompaible series finish in 1995 and afer 1995 hey do no presen a long enough number of observaions as would be desirable for an eonomerial sudy, so we oped o sudy he period As saed previously, we formulaed he model on he basis of raes of hange, so we oped o ransform he available annual daa ino raes of hange. 7 In Some auhors hink ha he model would be riher if we used he original daa, bu we oped for raes of hange beause he variable ha we inend o explain (he inflaion rae) is generally I(1), so i implies ha he onsumer prie index (CPI) will be I(2), and he model wih I(2) variables is no he aim of our sudy. Thus we seleed eigh annual variables for he period , whih we shall enumerae, presening beween square brakes is approahed equivalene wih variables of he heoreial model onsidered previously: P, inflaion rae [ P & ]; U, unemploymen rae (board sense) [U]; CTUPEV, rae of variaion of he uni labour oss in firms [ W & Q & ]; PM, rae of variaion in impor pries [ P & M ]; E, nominal effeive indire exhange rae of he Esudo [ E & ]; PF, 5 Indire exhange rae means in erms of domesi urreny, ha E & > 0 depreiaion. 6 And we use daa of he Hisorial Series for he Poruguese Eonomy, Bank of Porugal, 1999, whih finished in Wih he exepion of he variable SPA, whih is a sruure rae. 4

5 rae of variaion in impor pries in foreign urreny [ P & F ]; SPA, General Governmen Balane in perenage of GDPmp(p) [- DEF]; MY, rae of variaion of he nominal sok of money (M2 - ) orreed by he growh rae of he real GDPmp [ M & y& ]. These variables have been alulaed from he Hisorial Series for he Poruguese Eonomy (1999) elaboraed by he Poruguese Cenral Bank, wih he exepion of he inflaion rae (whose soure is he annual CPI for he mainland, exluding housing rens, elaboraed by Insiuo Naional de Esaísia, INE) and of he exhange rae (whose soure is he saisial daa of Abel Maeus(1998)). One variables are seleed, we will sudy heir saionariy, and he eonomerial mehodology o adop in he esimaion of he model formulaed in he equaion (1.1) depends on he order of inegraion of he ime series. The plos of variables (visual inspeion) poins o he saionariy of foreign inflaion (PF) wih hree ouliers (1974, 1980 and 1986) whih orrespond o he effe of he firs and he seond oil-prie shoks lagged by one year, and o he favourable oilprie shok of The unemploymen rae (U) seems o have suffered a sruural break around 1974/75, whih orresponds o he revoluion of April. The General Governmen Balane in perenage of he GDP also seems o have suffered a sruural break around he ime of he revoluion of April (beween 1972 and 1974). Relaive o he oher variables, he inflaion rae seems I(1), as we expe from sudies ha some auhors have arried ou. 8 The exhange rae is praially onsan up o 1974 due o he regimen of a fixed exhange rae, 9 and has wo very high peaks (1977, 1983) jusified by high depreiaion of he Esudo in periods of a high defii in he Curren Aoun, 10 wih he aim of improving exernal ompeiion. 8 See for example Cruz and Lopes (1999, p. 248). 9 See Boas and Sousa (1995, p. 14). 10 Noe ha hese wo years preede agreemens wih he IMF o finane he Curren Aoun defii ha had also reahed wo peaks. 5

6 3. Analysis of saionariy of he daa Firsly we arried ou ess on he exisene of wo uni roos (Table I - Annex), seondly we arried ou ess on he exisene of a uni roo (Table II - Annex), hirdly we arried ou ess on he exisene of a uni roo in he ime series under sruural hange wih endogenous hoie of he break poin (Tb) (Table III - Annex). 3.1 Tess on he exisene of wo uni roos The Dikey and Panula (1987) es allows us o reje he null hypohesis I(2) agains I(1) in all variables sudied o he level of signifiane of 1%, as we an see in Table I of he Annex (1 s sep). The number of lags (k) of he seond differene of eah sudied variable was seleed, saring wih k-max = 5 and removing sequenially he las lag if insignifian a he 5 % level unil geing one lag ha is signifian. In his es, as we use he firs differenes of variables, i is enough o make he es on he model wih a onsan, beause he visual inspeion of he firs differenes of he seleed variables indiaes learly he inexisene of any linear rend. Tess LM and Q of Ljung-Box assure he absene of residual auoorrelaion. The seond sep of he es of Dikey and Panula o es H0: I(1) agains I(0) only rejes H0 for variables CTUPEV and PF. The rejeion of H0 for he variable CTUPEV is sranger beause, in he ADF es for he exisene of a uni roo, i is no rejeed, as we will see. 11 One he hypohesis of he exisene of wo uni roos is rejeed, we will es he hypohesis of he exisene of one uni roo. 3.2 Tess on he exisene of one uni roo We applied he ADF es sequenially, saring wih a model wih a onsan and a rend (CT) and seleed k saring a k-max = 6 and removed he las lag if insignifian a he 5% level unil geing one lag ha is signifian (see Table II - Annex). We verified by he LM(1) of Godfrey and he Q(4) of Ljung-Box ess he absene of residual auoorrelaion neessary o be able o apply he ADF es. We applied he join ess Φ 3 and Φ 1 and he individual ess τ βτ, τ µτ, τ µµ of Dikey and Fuller (1981) o verify he exisene of a rend or a onsan in he ase of he exisene of a uni roo, and hus we elaboraed sequenial ess unil rejeing he null hypohesis of he exisene of a uni roo, in aordane wih he advisable sraegy for he use of he 11 And he same resul happens in ohers ess no presened here, as PP and KPSS. 6

7 Dikey and Fuller ess desribed by Robalo Marques(1998, pp ). In he ase of rejeion of he exisene of a uni roo, we an es he exisene of a rend or a onsan using he radiional Suden es: in his ase we presen he p-value beween square brakes in Table II of he Annex. The join and individual ess of Dikey and Fuller (1981), assuming from he ouse ha a uni roo exiss, are no ommonly used. I is more ommon o refer o he visual inspeion o see if a rend exiss or no. In aordane wih he individual es τ βτ (or βτ in he ase of rejeion of H0), we anno reje he null rend as foreseen in he visual inspeion, exep for variable SPA. Despie his resul, we disagree ha SPA has a rend, in erms of visual inspeion. Due o his disord, we iniiaed he seleion of k in a model wih a onsan, and he variable SPA is presened as I(1) [Table IIA-Annex]. We hink ha his srange behaviour of SPA is due o he sruural break foreseen for visual inspeion; herefore we will analyze i. From he resuls of Table II we onlude ha P, CTUPEV and U are I(1) and PF, E, MY and SPA are I(0). 12 Refering o Cruz and Lopes(1999), he fa of U and P being I(1) is in aordane wih hose auhors. Cruz and Lopes(1999, p. 248) also raise doubs relaive o he nominal sok of money being I(2), oping o onsidering i I(1), whih is in aordane wih our resul of he rae of variaion of he nominal sok of money orreed for he rae of growh of he produ being I(0), sine he growh rae of he real GDPmp is learly a I(0) variable Tess for a uni roo in ime series under sruural hange wih endogenous hoie of he break poin (Tb) Beause of he hypohesis of sruural break for variaion of he mean in General Governmen balane in he perenage of GDP (SPA) and in he unemploymen rae (U), we use he Perron and Vogelsang (1992) es. The break poin (Tb) is endogenously seleed by wo proesses: firs, minimizaion of saisi for esing α=1 [Min αˆ = 1 ], where α is he oeffiien of he lagged variable o es he exisene of a uni roo; seond, minimizaion of he saisi (ha is, saisi for esing θ = 0, where θ is he oeffiien of DU ha represens he hange in he mean of he ime 12 Alhough he SPA variable is presened as I(1) in he Table IIA. 13 Alhough we do no presen i here, he rae of variaion of he nominal sok of money is also rejeed as I(1), as well as he rae of growh of he GDPmp. 7

8 series) before one "rash" [Min ] or maximizaion of he saisi if we suspe an upward shif in he mean [ Max ]. In he firs proess, following he exposiion of Perron (1997), we onsider he hoie of Tb in he whole sample, alhough in he seond proess we resri i o he inerval (0.15T, 0.85T), as suggesed by Banerjee e al.(1992). In he endogenous seleion of k, we follow he firs mehod desribed by Perron (1997, p. 359), whih onsiss of a reursive proedure, where we sared wih k-max = 6 and we eliminaed lags suessively no signifian using a wo-sided es a 10 % level, whih Perron(1997) alls "-sig" and whih Perron and Vogelsang(1992, p. 313) onsider leads o ess wih greaer power in almos all he sudied ases. In Table III (Annex), we an observe he resuls of his es under he form of Innovaional Oulier (IO) and Addiive Oulier (AO) Models. In he IO model, he hange of he series for he new sruure beomes gradual, while in he AO model he hange is sudden. The ess for sruural hange, eiher by he IO model or by he AO model, onfirm he possibiliy of a sruural break for he unemploymen rae (from 1973 o 1975), and for variable SPA (from 1972 o 1974). 14 This denoes an inrease of he mean of U gradually from 1973 o 1975 or insananeously in 1975, his las year being mos likely for he break in aordane wih Cruz and Lopes(99); he same wih he mean of SPA from 1972 o Analysing he ADF and Perron and Vogelsang (1992) ess, we an say ha he inflaion rae (P) is I(1) for all he ess and he rae of variaion of he uni labour oss (CTUPEV) is also I(1) for almos all, so we mus onsider hese wo variables as I(1) in he inflaion model esimaion, invesigaing he possibiliy of exisene of relaions of oinegraion beween hem. The oher variables, even wih some doubs, are all onsidered I(0), he wo of hem (U and SPA) wih sruural break (hange in he mean) in aordane wih he Perron and Vogelsang (1992) ess. However, as he rejeion of I(1) in he SPA wih breaking in 1974 is signifian a 1% by wo mehods of seleion of he poin of breaking (Tb) and he rejeion of I(1) in he unemploymen rae wih breaking in 1975 is only signifian a 5% by one mehod of seleion, we an admi ha U is I(1) and ha SPA is I(0). 14 Noe ha he firs poin of breaking orresponds o he IO model and he seond o he AO model. 8

9 4. Esimaion of an expliaive model of he inflaion We use he Johansen mehod as being he one ha allows he deeion of he presene of more han one oinegraing veor among variables in sudy. There are saionary regressors in he VAR model, so we anno use he riial values of Johansen (1996). Therefore we follow he mehodology of Rahbek and Mosoni(1999), whih onsiss of adding o he VAR he umulaed explanaory I(0) variables as I(1) exogenous variables, and hus he riial values of he rae or eigenvalue ess of, among oher auhors, Pesaran, Shin and Smih(1999) an be used. 15 Firs, as we have exogenous variables, he oinegraed VAR model o use orresponds o he ondiional model: 16 Y = µ + δ + k 1 Ψi X i + Π y X i= 1 + ω Z + ε [4.1] where X is a N 1 veor of I(1) variables, whih we an divide ino N y endogenous I(1) variables (Y ) and N z exogenous I(1) variables (Z ), suh ha N y + N z = N. Π y is he long-run muliplier marix of order (N y N) given by Π y = α y β', where α y is a (N y r) marix and β a (N r) marix of r oinegraning veors. The null hypohesis of he oinegraion rank (exisene of r oinegraing veors) is wrien as: Hr: R [Π y ] = r, r = 0,..., N y ; [4.2] where "R" is he rank of he marix. In he esimaion of he ondiional model (4.1) we an onsider 5 ases (or models) onsonan wih he resriions imposed on he deerminisi erms. Following PSS(99) we have: 17 Case I (No inereps; no rends): k 1 = 0 Y = Ψi X i + Π y X + ω Z + ε i= 1 µ = δ [4.3] 15 Referred o as PSS(99), aferwards. 16 We assume ha he Z variables are weakly exogenous and hey are no oinegraed beween hem, whih implies ha we an effiienly deermine and es he parameers of long erm (α and β), bu wih resoure o he ondiional model [see PSS(99)]. 17 I orresponds o he 5 ases onsidered in he program Mirofi 4.0. On he differenes in ases III and V relaive o models 3 and 5 of Johansen (1996), when i does no have exogenous variables, see PSS(99). I is also useful o see Makinnon e al.(1999, p. 568) whih ompares he 5 ases of PSS(99) wih ables 9

10 Case II (Resried inereps; no rends): µ δ = Π = 0 y η k 1 1 * ' Y = Ψi X i + Π y ( X, ) + ω Z + ε i= 1 * where Π = Π (, η) y y I N wih I N = ideniy marix (N N). ' [4.4] Case III (Unresried Inereps; no rends): µ δ 0 = 0 Y = µ + k 1 Ψi X i + Π y X i= 1 + ω Z Case IV (Unresried inereps; resried rends): µ δ 0 = Π y γ ** where Π = Π (, γ) k 1 1 i= 1 + ε ** ' Y = µ + Ψi X i + Π y ( X,) + ω Z + ε y y I N. ' [4.5] [4.6] Case V (Unresried inereps; unresried rends): µ δ 0 0 The model of he equaion (4.1) will be esimaed. Firs, hese 5 ases are elaboraed for N z >0 (exisene of weakly exogenous variables), bu give resuls for N y =N as a speial ase when N z =0 (inexisene of weakly exogenous variables). Seond, as we follow he mehodology of Rahbek and Mosoni(1999), our I(0) variables are inluded in Z in equaion 4.1 or in one of he 5 ases (models) onsonan wih he hoie ha is made. The umulaive sum of hese I(0) variables are I(1) variables, orresponding o Z in he previous equaion, enlosed herefore in X. Afer his brief inroduion 18 we will ry o esimae he orresponding model o he equaion (1.1). 4.1 Esimaion of he Long Term Model In relaion o he Model P=f(CTUPEV, PF, E, My, SPA), orresponden o equaion 1.1 where we have wo I(1) variables (P and CTUPEV) and four I(0) variables (PF, E, My and SPA), we will apply he Mehodology of Rahbek and Mosoni(1999) inroduing he umulaed explanaory I(0) variables ino he oinegraion relaion and of Oserwald-Lenum(92). Makinnon e al.(1999) supplies more orre riial values for he 5 ases of PSS(99). 18 Among ohers, see Johansen (1996), Pesaran, Shin and Smih (1999) and Rahbek and Mosoni(1999). 10

11 laer we will es is exlusion from his relaion using he likelihood raio es. Thus, we will represen he model for sudy as: P CTUPEV; sumpf sume summy sumspa & PF E My SPA where here are wo endogenous I(1) variables (P, CTUPEV) and four exogenous I(1) variables (sumpf, sume, summy, sumspa) orresponding o he four I(0) variables (PF, E, My, SPA), whih are inrodued ino he shor-erm model. As we use he variable SPA and no he variable DEF as in equaion 1.1, he signal expeed in he relaion beween P and SPA will be negaive, ha is, when he budge defii inreases, he budge balane diminishes and one expes ha he inflaion rae will inrease oo. In erms of k order of he VAR, we seleed VAR(2), using eiher mulivaried saisis, or univaried saisis so ha he esimaed residuals have no serial orrelaion (LB and LM ess), no auorregressive ondiional heerosedasiiy (ARCH es) and hey do no deviae oo muh from normaliy (BJ es), as Johansen (1996, p. 20) reommends. Wih k=2, whaever he model of he Johansen mehod is in erms of he deerminisi erms, we anno reje he exisene of one oinegraning veor by he rae es, so we are going o hoose he bes model VAR(2) of oinegraion in aordane wih he deerminisi erms onsidering r=1. The mehodology of PSS(99) leads us o hoose model IV beause we anno reje he exisene of a rend in he long-erm relaionship a he 10% level (8% o be more aurae). Given VAR(2) and Model IV, one an onfirm ha he exisene of one oinegraning veor anno be rejeed, eiher by he rae es, or by he maximum eigenvalue es. The Shwarz Bayesian Crierion (SBC) also seles he model wih r=1. The veor normalized in relaion o P (and idenified) wihou resriions wih X' = [ P CTUPEV sumpf sume summy sumspa ] is given by: 19 ' β 1 = ( ) ( ) ( ) ( ) ( ) ( ) where one verifies ha he umulaed variables have a relaively high sandard error, and hen i is probable ha hey are no signifian in he long-erm relaionship. We anno reje he hypohesis H01: β 3 =β 4 =β 5 =β 6 =0, by he likelihood raio es wih χ 2 (4)=4.0361[.401]. And we anno reje he join es of H01 and rend=0 whose likelihood raio es follows χ 2 (5)=4.5391[.475]. Thus we have: 19 Beween round brakes in he oinegraing veor we have he sandard errors. 11

12 ' β = ( ) and herefore, he long-erm relaionship is: P= CTUPEV. So, in he long-erm, he relaionship beween inflaion rae and he growh rae of uni labour oss is almos uniary. 4.2 Esimaion of he Shor Term Model Iniial muli-varied model 0 The esimaion of he mulivaried model only wih variables inrodued iniially in VAR(2) allows us o ge: 1) Equaion of P: (period ) P = P [ ] [ ] [ ] [ ] 25939E 12325My CTUPEV 21235SPA [ ] [ ] [ ] [ ] PF E My SPA [ ] [ ] [ ] [ ] PF 21484ECM1 2 T = 40[ ]; R = ; SEE = ; DW = ; LM(1, 27) = [.599]; RESET(1, 27) = [.854] BJ(2) = [.920); HET(1, 38) = [.396]; ARCH(2, 26) = [.422] 2) Equaion of CTUPEV: (period ) CTUPEV = P [ ] [ ] [ ] [ ] 64378E 19223My CTUPEV SPA [ ] [ ] [ ] [ ] PF 14700E My SPA [ ] [ ] [ ] [ ] ECM1 2 T = 40[ ]; R = 0. 76; SEE = ; DW = ; LM(1, 27) = [.651]; RESET(1, 27) = E-3[.980] BJ(2) = [.982]; HET(1, 38) = [.602]; ARCH(2, 23) = [.452] PF 12

13 Analysing hese equaions, we verify ha he variaion of he inflaion relaes posiively and signifianly a 1% level o he foreign inflaion and he variaion of he exhange rae, and negaively, bu only a 10% level, o E -1 and M y -1. The long-erm relaionship (P - 0,84016 CTUPEV) represened by ECM1 presens an expeed signal bu in his iniial model his is no signifian even a 10% in onras o wha happens in Rosa(2003). 20 This srenghens he weak exogeneiy of he inflaion rae in his model. The posiive relaion of he variaion in inflaion wih foreign inflaion and he variaion in he exhange rae orresponds o wha would be expeed. The negaive relaion wih M y-1 (by he way, almos insignifian) is diffiul o explain, bu in he parsimonious model, he Wald es suggess is exlusion from he model. Thus, foreign inflaion and he variaion in he exhange rae seem o be he main auses of inflaion. Nor he variaion in nominal money sok, orreed by he growh rae of real GDP (My), nor he General Governmen balane in perenage of GDP (SPA) is signifian in he equaion of P. The CTUPEV variaion beomes relaed posiively and signifianly a 1% o ECM1-1 and PF and negaively a 1% o E -1 and SPA -1. The explanaion for he relaion wih he firs hree variables is in Rosa (2003, p. 148). Relaive o he negaive relaion wih SPA -1, a possible explanaion ould be he fa of a high budge defii in he previous period implying an inrease in he expeaions of inflaion, 21 whih aused wages o inrease in he following period. 22 The negaive and signifian relaion a 10% beween CTUPEV and My -1 is more diffiul o explain, bu we do no worry abou his, beause in he parsimonious equaion, he Wald es suggess he exlusion of his variable. The ECM1-1 is signifian a 1% level and lose o 1 in he equaion of CTUPEV and i is no signifian in he equaion of P, so we an onlude ha i is he variaion in inflaion ha auses variaion in uni labour oss and no he opposie; ha is, labour oss seems o respond quikly and signifianly o an inrease in inflaion. The diagnosi ess indiae ha he residuals are no auoorrelaed, are homoeskedasis, normal and we anno reje orre speifiaion of he model. The auorregressive ondiional heerosedasiiy is also absen unil he seond order. 20 However, we mus ake ino aoun ha he ECM1 is slighly differen from he one in Rosa (2003) s model, and herefore no omparable. 21 The inflaionary expeaions happened more in a ime when he governmen ould use he moneary finaning of he defii. 13

14 Relaive o he equaion of P, all he residuals are inside he line bands of double sandard deviaion 23 and CUSUM and CUSUMSQ ess do no ross any of he signifian bars a 5% level. We esimaed he model for period wih he aim of leaving an observaion for mulivaried dynami foreas. Boh he foreass of P and P, as well as of CTUPEV and CTUPEV for 1995 seem aepable Expliaive Parsimonious model of he inflaion We ried o remove from he equaion of P in he iniial mulivaried model he variables ha were no signifian a he10% level, using he Wald es on he join nulliy of is oeffiiens, o reesimae parsimonious equaions. The Wald es does no allow us o reje all he non-signifian variables, so, afer some aemps, we kep PF -1 and ECM1-1 in he regression of P, despie is non signifiane in he iniial regression. Thus, he Wald es already allows us o reje all he oher variables. As E and E -1 have symmerial oeffiiens, we subsiue hem for E and hus he ECM1-1 beomes signifian a 10% (equaion DPC1 - Table IV of he Annex) and PF -1 beomes signifian a 1%; and PF is signifian a 1%. Reesimaing he previous equaion for (equaion DPC2), we anno reje eiher he prediive apaiy afer 1988 or he sruural sabiliy before and afer CUSUM and CUSUMSQ ess do no indiae problems, moreover. 24 We ried some dummies, 25 from DPC3 o DPC5 equaions, bu only dummies Dum87 and Dum80 are signifian individually (a 5 and 10 % respeively). The inroduion of SME ogeher wih Dum87, or wih he oher wo, implies residual auoorrelaion (equaion DPC5). The Dum87 seems o be he bes, always signifian a 5% and allows he error-orreion mehanism (ECM -1 ) o beome signifian a 5% (see equaion DPC3). In he period wihou dummies (equaion DPC6), he ECM1-1 is no signifian, as in he iniial model, bu he exlusion of his variable (equaion DPC7) 22 Thus, indirely, he budge defii ould have a posiive influene on inflaion hrough oss, insead of being hrough demand, as was assumed from he ouse in he model. 23 Beer ha in he model of Rosa (2003). 24 Analysis in equaion DPC1. 25 Dum74 (value 1 in firs oil shok and April Revoluion), Dum79 (value 1 in 1979 seond oil shok), Dum80 (value 1 in 1980 Esudo Revaluaion), Dum87 (value 1 in favourable exernal 14

15 generaes auorregressive ondiional heeroeskedasiiy, so ha we oped o keep i. Also, in he period , we anno reje eiher he prediive apaiy afer 1988, or sruural sabiliy before and afer 1988 (equaion DPC8). In he inroduion of dummies from equaion DPC9 o equaion DPC11 allows us o onlude ha he Dum87 oninues o be signifian a 5 % (equaion DPC9), bu he Dum80 eases o be signifian (equaion DPC10) and he inroduion of he Dum87, ogeher wih SME, does no suffer from auoorrelaion (equaion DPC11) and he ECM1-1 beomes signifian in his las ase. The omparison of he period (equaion DPC9) wih he period (equaion DPC3) allows us o noie a small inrease in he absolue value of he oeffiiens of PF -1, PF and E in he period , o he derimen of he absolue value of ECM Final onlusions The main auses of he variaion in inflaion in he period seem o be foreign inflaion (or is variaion) and he variaion in he effeive exhange rae of he Esudo. There is a long-erm relaionship beween he inflaion rae and he growh rae of uni labour oss, almos uniary, bu he response of he variaion in inflaion o he equilibrium error beween he inflaion rae and he variaion in uni labour oss is slow and almos insignifian, while he response of uni labour oss o ha disequilibrium is fas and signifian, whih suggess ha he direion of ausaliy is muh more eviden from he effe of he inflaion rae on uni labour oss han he reverse. This seems o mean ha wages adjus o growh in inflaion quikly, while inflaion adjuss o growh in wages slowly. The variaion in nominal money sok, orreed by he growh rae of he real GDP, as well as he General Governmen balane in perenage of GDP, are no signifian in he shor-erm relaionship, so we essenially have inflaion aused by oss. The srongly signifian oss in he shor-erm relaionship are he inflaion of impored produs (due eiher o foreign inflaion or o he variaion in he effeive exhange rae). The omparison of our resuls wih hose of oher auhors allows us o verify ha our onlusions are idenial o hose of he majoriy of he auhors who have made onjunure), EN (value 1 up o New Sae), EEC (value 1 afer 1986 Member of he EEC), SME (value 1 afer 1992 Pariipaion in he ERM of he EMS). 15

16 sudies for he 1970s and 1980s, so ha one sub-period srongly influenes our onlusions. This fa is no srange, beause during he New Sae, 26 he exhange rae of he Esudo was virually onsan and in he 1990s we ook measures o onrol he fluuaion of he same, suh as joining he Exhange Rae Mehanism of he European Moneary Sysem. The non-influene of money oinides wih he onlusion of Cunha and Mahado (1996), bu is ompleely opposed o ha of Nunes (1998). However, as we use annual daa while Nunes uses quarerly daa, and he period is differen, any omparison is wrong. 27 Relaive o he earlies sudies, we mus ake ino aoun ha hey do no use he mehodology of oinegraion, whih invalidaes he omparison. Sanos (1992), onludes ha he budge defii seems o be inflaionary, bu only in 50% of he analyzed ounries, among hem Porugal, and Vieira (2000) onludes ha here is lile suppor for he idea ha budge defiis have onribued o inflaion in he majoriy of European ounries, 28 so we herefore do no find our onlusion srange in relaion o he non-influene of he budge defii on he variaion in inflaion. Referenes BANERJEE, Anindya, Robin L. LUMSDAINE, James STOCK (1992) - "Reursive and Sequenial Tess of he Uni-Roo and Trend-Break Hypohesis: Theory and Inernaional Evidene", Journal of Business and Eonomi Saisis, 10(3), BOTAS, Susana and Miguel Roha de SOUSA (1995) - "PPP in he Long Run - A Coinegraion Approah: The Poruguese Case from 1891 o 1992", Eonomia, 19(2), BURDA, Mihael and Charles WYPLOSZ (1993) - Maroeonomis: A European Tex, Oxford Universiy Press. CAMPBELL, John Y. and Pierre PERRON (1991)- Pifalls and Opporuniies: Wha Maroeonomis Should Know abou Uni Roos, NBER Maroeonomis Annual, CHOW, Gregory C. (1960) - "Tess of Equaliy Beween Ses Coeffiiens in Two Linear Regressions", Eonomeria, 28(3), CRUZ, Paríia Moura and Arur Silva LOPES (1999) - "Raízes Uniárias e Quebras de Esruura: Evidênia Empíria para a Eonomia Poruguesa", Esudos de Eonomia, 19(2), New Sae is he regimen before he April revoluion in See also Juselius (1992), who finds hree signifian soures of inflaion for Denmark (moneary, wages and impored), while for us, he moneary one is no signifian. 28 There is more evidene herefore ha in is model he inflaion has onribued owards defiis. 16

17 CUNHA, Luís C. and José F. MACHADO (1996) - Theoreial Irregulariies on he Spanish and Poruguese Inflaions, in Ensaios de Homenagem a Manuel Jaino Nunes, ISEG/UTL, Lisbon, DICKEY, David A. and Wayne A. FULLER (1981) - Likelhood Raio Saisis for Auoregressive Time Series wih a Uni Roo, Eonomeria, 49(4), DICKEY, David A and Sasry G. PANTULA (1987) - "Deermining he Order Differening in Auoregressive Proesses", Journal of Business and Eonomi Saisis, 5(4), FULLER, Wayne A. (1976) - Inroduion o Saisial Time Series, John Wiley & Sons, Chap. 8, pp GIRÃO, José A. (1984) Salários, Inflação e Moeda: A Experiênia Poruguesa, Working Paper nº 11, Bank of Porugal. JOHANSEN, Søren (1996) - Likelihood-Based Inferene in Coinegraion Veor Auoregressive Models, Oxford Universiy Press, Oxford. JUSELIUS, Kaarina (1992) - Domesi and Foreign Effes on Pries in an Open Eonomy: The Case of Denmark, Journal of Poliy Modeling, 14(4), MACKINNON, James G., Alfred HAUG and Leo MICHELIS(1999) - "Numerial Disribuion Funions of Likelihood Raio Tess for Coinegraion", Journal of Applied Eonomeris, 14(5), MARQUES, Carlos Robalo (1990) Inflação em Porugal: Um esudo eonomério para o período , om projeções para 1990 e 1991, Working Paper nº 2 (new serie), Bank of Porugal. MARQUES, Carlos Robalo (1995) - Evolução ambial, inflação e salários, Boleim Eonómio, Bank of Porugal, MARQUES, Carlos Robalo (1998) - Modelos Dinâmios, Raízes Uniárias e Coinegração, Edinova-Edições da UNL, Lisbon. MATEUS, Abel (1980) - Inflação, Salários e Desvalorização, Eonomia, 4(2), MATEUS, Abel (1998) - Eonomia Poruguesa: Desde 1910, Ediorial Verbo, Lisbon. NUNES, Luís Caela (1998) Foreasing he Poruguese Inflaion Rae, [on line] Working Paper nº 6, Direção Geral de Esudos e Previsão, Minisério das Finanças, 36 pp. [ied in 98/3/10]. Available in URL: hp:// OSTERWALD-LENUM, Mihael (1992) - A Noe wih Quaniles of he Asympoi Disribuion of he Maximum Likelihood Coinegraion Rank Tes Saisis, Oxford Bullein of Eonomis and Saisis, 54(3),

18 PERRON, Pierre and T. J. VOGELSANG (1992) - "Nonsaionariy and Level Shifs wih an Appliaion o Purhasing Power Pariy", Journal fo Business and Eonomi Saisis, 10(3), PERRON, Pierre (1997) - "Furher Evidene on Breaking Trend Funions in Maroeonomi Variables", Journal of Eonomeris, 80(2), PESARAN, M. Hashem and Bahram PESARAN (1997) - Working wih Mirofi 4.0: Ineraive Eonomeri Analysis (Windows Version), Oxford Universiy Press. PESARAN, M. Hashem, Yongheol SHIN and Rihard J. SMITH (1999) - "Sruural Analysis of Veor Error Correion Models wih Exogenous I(1) Variables", [on line] Oober, 46 pp., [ied in 2000/04/07]. Available in URL: hp:// (version reviewed of DAE WP 9706 of 1997, Univesiy of Cambridge, e urrenly published in Journal of Eonomeris, 97(2), ). RAHBEK, Anders and Roo MOSCONI (1999) - "Coinegraion Rank Inferene wih Saionary Regressors in VAR Models", Eonomeris Journal, 2, ROSA, Agosinho (2000) - "Uma Análise Teória da Curva de Phillips", in Homenagem ao Prof. Auguso da Silva, Dep. Soiologia/Universiy of Évora, Évora, ROSA, Agosinho S. (2002) Os Deerminanes da Inflação: Apliação ao Caso Poruguês, vols. I and II, PhD disseraion, Universiy of Évora. ROSA, Agosinho S. (2003) Inflação Poruguesa: Pelos Cusos ou Moneária?, Eonomia e Soiologia, 75, SANTOS, Jorge (1992) - "Budge Defiis and Inflaion: Porugal and he Oher EC High Deb Counries", Esudos de Eonomia, 12(3), Séries Longas para a Eonomia Poruguesa - Pós II Guerra Mundial, Vol. I - Séries Esaísias (version reviewed and drawn ou for 1994 and 1995), Coordinaion of Maximiano Pinheiro, Bank of Porugal, [also ied as PINHEIRO, Maximiano e al., Hisorial Series for he Poruguese Eonomy - Pos II World War, Bank of Porugal, 1999; Available: SURREY, M. J. C. (1989) - "Money, Commodiy Pries and Inflaion: Some Simple Tess", Oxford Bullein of Eonomis and Saisis, 51(3), VIEIRA, Carlos (2000) - "Are Fisal Defiis Inflaionary? Evidene for he EU", Eonomi Researh Paper 00/07, Deparamen of Eonomis, Loughborough Universiy, April. ( 18

19 Annex Table I - Tess on he exisene of wo uni roos Variables Dikey-Panula (1987) es 1 s sep 2 nd sep k τ LM(1) Q(4) k ρ 2 1 (F version) τ ρ 1 1 U a [.384] 1.667[.797] P a [.084] 1.515[.824] CTUPEV a [.399] 6.510[.164] b E a [.958] 0.069[.999] PF a [.170] 4.820[.306] b SPA a [.092] 3.511[.476] MY a [.400] 1.458[.834] Noes: Model wih a onsan; annual daa: a = signifian a 1%; b = signifian a 5%; = signifian a 10%. Table II - Tess on he exisene of one uni roo: ADF ADF es Variables Mod. k τ ρ 1 Φ 3 Φ 1 τ βτ τ µτ ; τ LM(1) Q(4) µµ F version 1 (CT) [.881] [.981] U 2 (C) [.572] [.949] [.362] [.804] 1 (CT) [.241] [.905] P 2 (C) [0.79] [.874] [.068] [.879] 1 (CT) [.160] [.527] CTUPEV 2 (C) [.393] [.604] [.826] [.244] 1 (CT) [.134] [.767] E 2 (C) b [.101] 2.369[.668] b [.048] [.261] 1 (CT) b b [.125] [.556] PF 2 (C) a a [.118] [.558] a [.200] [.514] 1 (CT) b b a [.158] [.438] MY 2 (C) b b a [.050] [.298] 3 0 A (CT) b b a a [.945] [.811] SPA 2 (C) 6 B B Noes: beginning of he ess in models wih a rend; annual daa: a = signifian a 1%; b = signifian a 5%; = signifian a 10%. A we reje he null onsan of a ime series. B - we reje he null rend of a ime series. Table IIA - Tess on he exisene of one uni roo: ADF ADF es Variables Mod. k τ ρ 1 Φ 1 τ LM(1) Q(4) µµ F version 2 (C) [.239] [.853] SPA [.226] [.816] Noes: Beginning of he ess in models wih a onsan, wihou a rend. Annual daa: (1) We begun he seleion wih k-max=10. 19

20 Table III - Tess for a uni roo in ime series under sruural hange wih endogenous hoie of he break poin (Tb) IO Model AO Model Series Mehod Esimaed Esimaed Parameers Tb k Parameers 29 αˆ =1 Tb k αˆ = 1 (DU) δˆ (DTb) αˆ (DU) αˆ Min αˆ = a a a a U Min a b 0929 a P CTUP- EV E PF MY SPA Max a a b a a b Min a a αˆ = 1 Min a a Max a a a Min a a αˆ = 1 Min b a a Max a b a b Min b a a a αˆ = 1 Min b a a Max b a a a Min a b a b a αˆ = 1 Min b b b b Max b b Min a b b a a αˆ = 1 Min a a a Max a b b a b a Min αˆ = a b a b a a Min a b a b a a Max a a Signifiane level: a = Signifian a 1%; b = Signifian a 5%; = Signifian a 10%. Sample: Noes: The level of signifiane refers o he null hypohesis ha his oeffiien is zero, bu for αˆ = 1 i refers o he null hypohesis of a uni roo, aording o he Perron and Vogelsang (1992) models. αˆ = 1 in bold means ha we reje he exisene of a uni roo, a leas a 5 %. IO Model: AO Model: 1 s sep: k = µ + θdu + δd(tb ) + α y 1 + i y i i= 1 y = µ + θdu ~ + y y + e k 2 nd sep: y~ = wi D(Tb ) i + α y~ + i y~ i + e i= 0 1 k i= 1 29 However, we pu a, b or aαˆ, here is no mean, beause he model has no onsan. 20

21 Table IV: Parsimonious Equaions of P Dependen Variable: P Esimaion Mehod: OLS. ECM1= *P *CTUPEV esimaed on model: P CTUPEV; sumpf, sume, summy, sumspa & PF E MY SPA DPC1 DPC2 DPC3 DPC4 DPC5 DPC6 Equaion/ Regressors T=41 T 1 =34, T 2 =7 T=41 T=41 T=41 T=22 [55-95] [55-88] [55-95] [55-95] [55-95] [74-95] Inp [.840].23312[.650].41478[.350].36737[.395].75194[.100] [.550] PF(-1) [.000] [.000] [.000] [.000] [.000] [.001] ECM1(-1) [.072] [.072] [.025] [.050] [.020] [.341] PF.35997[.000].34915[.000].37176[.000].39077[.000].38194[.000].39279[.000] E.43382[.000].48629[.000].43141[.000].38324[.000].37550[.000].47112[.000] Dum [.086] [.087] - Dum [.011] [.013] [.005] - SME [.041] - 2 R SEE DW LM(1, T-k-1) [.141] [.018]* [.150] [.227] [.015]*.56800[.462] RESET (1, T-k-1).92664[.342].99118[.328] [.319] [.229] [.228].52154[.481] BJ(2) [.246] [.242] [.158] [.212] [.235] [.524] HET(1, T-2).23804[.628].34342[.562].35303[.556].29783[.588].41628[.523] [.255] ARCH(2, T-k-2).55831[.577] [.484].96366[.392] [.290] [.110] Chow(T 2,T 1-k) [.358] Cov(k, T 1+T 2-2k) [.207] Beween square brakes: p-value. The null hypohesis is H0: β=0, and is he Suden es for he esimaed oeffiiens. * Diagnosi es signifian a some level indiaes he p-value. Table IV: Parsimonious Equaions of P (oninuaion) Equaion/ DPC7 DPC8 DPC9 DPC10 DPC11 T=22 Regressors T=22 [74-95] T 1 =15, T 2 =7 [74-88] T=22 [74-95] T=22 [74-95] [74-95] Inp [.220] [.613].23662[.754].20005[.780] [.118] PF(-1) [.001] [.004] [.000] [.000] [.000] ECM1(-1) [.479] [.128] [.189] [.026] PF.39254[.000].38648[.000].40524[.000].42756[.000].39262[.000] E.51320[.000].53826[.001].45951[.000].40938[.000].43000[.000] Dum [.113] - Dum [.031] [.032] [.006] SME [.042] 2 R SEE DW LM(1, T-k-1) [.289] [.075]*.3872E-3[.985].18104[.677] [.116] RESET (1, T-k-1).68751[.419].38285[.551].91104[.355] [.182] [.266] BJ(2) [.519].29978[.861] [.524].36885[.832].33943[.844] HET(1, T-2) [.172] [.154].86779[.363].30388[.588] [.171] ARCH(2, T-k-2) [.026]*.57106[.586].23590[.793].51311[.610] Chow(T 2,T 1-k) [.618] Cov(k, T 1+T 2-2k) [.391]

22 Noes abou Table IV Diagnosi ess: We use he F version of diagnosi ess beause Robalo Marques(98) iing Kivie(86) 30 said ha in small samples he F version is preferable. In BJ es we presen he LM version 2 following a χ (2), beause he F version does no apply in his es. The degrees of freedom of he F es are in round brakes, whih depend on he k and T: T=number of observaions used in regression; k=number of esimaed oeffiiens; T 1 =sub-sample used in esimaion; T 2 =Period pos-sample (foreasing es) or seond sub-sample (sabiliy es, only possible when T 1 >k and T 2 >k). Diagnosi ess desripion: LM saisi of Lagrange Muliplier es for serially orrelaed residuals [based in Godfrey(1978) 31 ]. RESET saisi of Ramsey (1969) 32 s RESET es of funional form misspeifiaion. BJ saisi of Jarque-Bera s es of normaliy of regression residuals [based in Bera and Jarque (1981) 33 ]. HET saisi of Heerosedasiiy es [see Pesaran e Pesaran(1997)] ARCH saisi of Auoregressive Condiional Heerosedasiiy es [Engle (1982) 34 s es] Chow-saisi of Prediive failure es (2 nd es of Chow(1960)). Cov saisi of Chow s es of sabiliy of regression oeffiiens (1 s es of Chow(1960)). 30 J. F. Kivie (1986) - "On he Rigour of Some Misspeifiaions Tess for Modelling Dynami Relaionships", Review of Eonomi Sudies, 53, L. G. Godfrey (1978) - "Tesing Agains General Auoregressive and Moving Average Errors Models When he Regressions Inlude Lagged Dependen Variables" Eonomeria, 46(6), J. B. Ramsey (1969) - "Tess for Speifiaion Errors in Classial Linear Leas Squares Regression Analysis", Journal of he Royal Saisial Soiey, Series B, 31, A. K. Bera e C. M. Jarque (1981) - "An Effiien Large-Sample Tes for Normaliy of Observaions and Regression Residuals", Ausralian Naional Universiy Working Papers in Eonomeris, 40, Canberra. 34 Rober F. Engle (1982) - "Auoregressive Condiional Heerosedasiiy wih Esimaes of he Variane of Unied Kingdom Inflaion", Eonomeria, 50(4) Julho,