Inflation Targeting and Inflation Persistence,

Transcription

1 Inflaion Targeing and Inflaion Persisence, George J. Brasiois School of Economic Sudies Universiy of Mancheser Dover Sree, Mancheser M3 9PL,UK. Jakob Madsen Deparmen of Economics Brunel Universiy Uxbridge Middlesex UB8 3PH, UK. Chrisopher Marin Deparmen of Economics Brunel Universiy Uxbridge Middlesex UB8 3PH, UK. May 00 Absrac This paper argues ha he adopion of an inflaion arge reduces he persisence of inflaion. We develop he heoreical lieraure on inflaion persisence by inroducing a Taylor rule for moneary policy ino a model of persisence and showing ha inflaion arges reduce inflaion persisence. We invesigae changes in he ime series properies of inflaion in seven counries ha inroduced inflaion arges in he lae 980s or early 990s. We find ha he persisence of inflaion is grealy reduced or eliminaed following he inroducion of inflaion arges. JEL: classificaion: D4, D5, E4, E5. Keywords: Taylor Rule, Inflaion argeing, Phillips Curve, Inflaion persisence.

2 . INTRODUCTION This paper argues ha he persisence of inflaion is lower when here is an inflaion arge. This implies ha inflaion is more responsive o moneary policy when inflaion is he main focus of policy. The idea ha inflaion persisence may depend on macroeconomic insiuions or policy regimes, of which inflaion arges are a recen example, is well esablished in he lieraure. Alogoskoufis and Smih (99) and Alogoskoufis (99) argue ha inflaion is less persisen wih fixed exchange raes. Oher auhors, for example Siklos (999) and Burdekin and Siklos (999), argue ha oher facors, such as wars, supply shocks or Cenral Bank reforms, also affec persisence. We exend he heoreical lieraure by inroducing a Taylor-rule represenaion of moneary policy (Taylor, 993) ino an oherwise sandard model of inflaion persisence, similar o Taylor (979), Alogoskoufis and Smih (99), Agenor and Taylor (99) and Alogoskoufis (99). We show ha inflaion persisence is affeced by he parameers of he moneary policy rule. An increased weigh on he price-level arge in he moneary policy rule reduces persisence. As a resul, persisence is lower when here is an inflaion arge. We es our model by invesigaing changes in he ime series properies of inflaion persisence in seven counries ha adoped inflaion in he lae 980s or early 990s (Ausralia, Canada, Finland, New Zealand, Spain, Sweden and he UK). We find ha he persisence of inflaion is grealy reduced or even eliminaed following he inroducion of inflaion arges. Using annual daa we canno rejec he hypohesis ha inflaion persisence has been eliminaed in any counry. Using quarerly daa, we can only rejec his hypohesis for he UK. The paper is srucured as follows. Secion ) conains our heoreical model. Secion 3) conains our empirical resuls. Secion 4) summarises and concludes.. THE MODEL

3 In his secion we presen our model. We begin by considering aggregae demand. We hen develop he supply side of he model before finally analysing inflaion persisence. a) Aggregae Demand We assume ha aggregae demand is given by () y = y γ( i E p+ + E p) + v where y is he naural logarihm of oupu, y is an exogenous componen of demand, i is he nominal ineres rae, p is he naural logarihm of he price level, E p+ is he expeced price level in period (+) using informaion available a ime -, v is a whie noise demand shock and indexes ime. We assume ha moneary policy is conduced hrough an ineres rae Taylor-ype rule, * () i = i + φ( p p ) + ψ ( y y ) * * where i* is a consan, p* is he log of he policymaker's arge for he price level and y* is he log of he policymakers arge level of oupu. The policy parameers φ and ψ describe he responsiveness of nominal ineres raes o deviaions of inflaion and oupu from heir respecive arges. Our model exends he lieraure by inroducing a familiar Taylor rule descripion of moneary policy (Taylor, 993). In he exising lieraure, Taylor (979) assumes aggregae demand depends on he real money supply and ha he nominal money supply is proporional o he price level. Alogoskoufis and Smih (99), Agenor and Taylor (99) and Alogoskoufis (99) have an aggregae demand relaionship similar o (), bu model ineres raes using a money demand equaion and again assume he nominal money supply is proporional o he price level. In essence, hese models are equivalen o ψ=p*=y*=0 in (). The inroducion of a Taylor rule allows us o analyse various policy regimes. If φ and ψ 0, he over-riding prioriy of moneary policy is o achieve a price level of p *. This is equivalen o an inflaion arge of π *, where p *=π *+p -. If ψ and φ 0,

4 here is an oupu arge. If ψ=φ, here is a arge for nominal GDP. The parameers of he Taylor rule affec he exen o which moneary policy accommodaes inflaion. Wih an inflaion arge, policy does no accommodae inflaion as real ineres raes increase whenever inflaion rises above he arge. Wih an oupu arge, changes in he price level do no change he real ineres rae and so moneary policy fully accommodaes inflaion. Subsiuing () ino (), we can summarise aggregae demand as γφ γ v y = y p + ( E p E p ) + + γψ + γψ + γψ (3) c + where y = { y γ(* i φp* ψy*)}/( + γψ). The slope of his aggregae demand curve c depends on he policy regime. The curve is horizonal if here is an inflaion arge, is verical if here is an oupu arge and has a convenional negaive slope if here is no arge (see also, Taylor, 999a). b) Aggregae Supply We use a sandard model of aggregae supply. We assume here are a large number of idenical monopolisically compeiive firms. Each firm s echnology is described by a simple producion funcion, (4) yj = α+ j + ξ l, where l is employmen, ξ is a supply shock, α is a consan and j indexes he firm. We follow he lieraure (eg. Alogoskoufis, 99 and Bleaney, 00) in assuming ha he supply shock follows a random walk, ξ = d ξ + ξ + ε. The demand for each firm depends posiively on aggregae demand and negaively on is relaive price: (5) y = y η( p p) j j 3

5 where y is given by (3) From a sandard profi maximisaion problem and using equaions (4) and (5), he price chosen by each firm is: (6) pj = µ + wj α ξ where w is he nominal wage and µ = ( / η) is he mark-up of price over marginal j cos in firm j. We assume ha wage adjusmen is saggered and described by a discree ime, Calvo-ype uiliy-maximising wage conrac model, (Calvo, 983). A any given ime, he wage a each firm has a fixed probabiliy δ of being adjused o a new value of ŵ, and a fixed probabiliy, (-δ), of remaining fixed a he previous period s wage. The aggregae wage is given by he sum of all wage conracs sill in force. Wih δ( δ) s being he fracion of wage conracs adjused s periods before, he aggregae wage is given by: (7) w ( ) s ˆ ˆ = δ δ w s = δw + ( δ) w s= 0 The wage chosen when adjusmen occurs is forward-looking: (8) s s * * = [ ( δ) β] ( δ) β + s = [ ( δ) β] + ( δ) β + s= 0 wˆ Ew wˆ w Ewˆ where w * is he opimal wage common o all union ha adjus heir wage conracs in period. We assume ha his is given by, (9) * * * = ω + + σ w E p E ( y y ) 4

6 where ω* is desired real wage growh (assumed consan for simpliciy), * y is a reference level of oupu and σ measures he elasiciy of real wages wih respec o oupu. Equaion (9) can be derived from almos any model of wage formaion. We hen use (8) o express wage conracs in erms of w and use (6) o express w in erms of prices. This gives he following equaion for he aggregae price level, (0) * ( δδω ) ˆ( + µ α) ( δ) p ( ˆ = + p + δe p + βe p+ ) + ( δ) β + ( δ) β ( δδσ ) ˆ ( δ) + E ( y y ) + ( ξ + βe ξ ) ξ + ( δ) β + ( δ) β * + where δ ˆ = δ(/( δ) β) > 0 and increasing in δ. Defining inflaion as π = p p and aking expecaions, we can summarise he supply side of our model as () E π = βe π + δω ˆ( + µ α) + δσ ˆ E ( y y ) * * + + ( δ) β + ξ E ξ + βe ξ δ + This aggregae supply or Phillips curve is similar o ohers in he lieraure (e.g Taylor, 999b, Mankiw, 000 or Holden and Driscoll, 00). c) Inflaion Persisence We subsiue he aggregae demand curve, equaion (3), ino he aggregae supply curve, equaion (), o obain 5

7 ( δ) γσ( + φ) ˆ ˆ γσδ + β( δ) + γψ β( + γψ) () p = p+ δe p + + βe p+ + p + s where, * * ˆ( ( c )) p = δω + µ α+ σ y y and Forming expecaions and rearranging equaion () we obain, + β( δ) s = ξ ξ + βe ξ δ +. (3) + β( δ) γσ( + φ) p E p+ + δˆ( ) E p + θ ( δ) + γψ θ ( p+ E s) = θ where, θ γσδˆ = β + > 0. Equaion (3) can be wrien as + γψ (4) ( ) F ( λ + λ ) F + λλ LE p = λλ ( p+ E s ) where λ and λ are he smaller and larger roos respecively of (4), L is he lag operaor and F is he forward operaor. Expressing (4) as λ λ λ i (5) E p = p + p+ E s+ i i= 0 ( ) subsiuing (5) ino () and hen aking firs differences, we obain λβ λ θ( δ) ( δ) (6) π = λπ + d ξ + ε ε θλ θλ + β( δ) + β( δ) where 6

8 (7) + β( δ) ˆ γσ( + φ) 4 θ( δ) λ = δ θ ( δ) + γψ ˆ γσ( + φ) β( δ) ( δδ ) ( ) + + γψ From (7), we can show (see appendix for deails) dλ dλ (8) < 0; > 0. dφ dψ Equaions (6)-(8) comprise our model of he persisence of inflaion. We find ha he parameers of a Taylor rule for moneary policy affec he persisence of inflaion (alhough he arges p* and y* do no). Inflaion is less persisen when policymakers place a greaer emphasis on he price level or a lesser emphasis on oupu. We herefore predic ha inflaion will be less persisen wih an inflaion arge. 3) Empirical Evidence In his secion we presen evidence on how he persisence of inflaion is affeced by inflaion argeing. We consider hose OECD economies ha adoped inflaion arges in he lae 980s or early 990s, namely New Zealand (adoped inflaion argeing in 989Q3), Ausralia (993Q), Canada (99Q), Sweden (993Q) and he UK (99Q3). We also consider Finland and Spain, which adoped inflaion arges (in 993Q and 994Q, respecively) bu abandoned hese upon enering EMU in 998Q (see Bernanke a al, 999 for furher insiuional deails). We use he consumer price index o measure prices hroughou and use boh annual and quarerly daa o ensure our findings are robus. We firs examine he ime series properies of our daa, esing for uni roos. For our quarerly daa, we es for seasonal uni roos, using he HEGY es (Hylleberg e al, 990). The HEGY es idenifies he precise naure of seasonal inegraion and allows us o 7

9 model any seasonal uni roos accordingly. The following auxiliary regression is underaken: (9) ϕ ( L) z4 = π z, + π z, + π 3z3, + π 4z3, + ε where n L ) = j= ϕ ( ϕ is a saionary auoregressive polynomial of order n in L. L j j Deerminisic variables are lef ou of he equaion for simpliciy bu are included in he empirical esimaes. The z-variables are given by: z ) 3 = ( + L + L + L p z ) 3 = ( L + L L p z ( L ) 3 = p z ) 4 4 = ( L p where p is he log of consumer prices. One-period lags of he dependen variable are included in he ess. The resuls of he HEGY ess are presened in Table ). The null hypoheses of π = 0, and 0 π 3 π 4 = are rejeced a he 5%-level for all counries, implying he absence of semiannual, complex and annual uni roos. However, he null hypohesis of π = 0 canno be rejeced a he 5%-level for any of he counries. This suggess ha consumer prices in quarerly daa conain a zero-frequency uni roo and herefore ha firs-differences is he appropriae filer for making he series saionary. We examined he ime series properies of our annual daa using simple ADF ess. We found ha prices were clearly I() in each counry (he resuls are no presened o save space, bu are available from he auhors on reques). We herefore define he rae of inflaion using boh annual and quarerly daa as π = p -p -, where p is he log of he consumer price index. To examine he impac of inflaion arges on inflaion persisence, we consider simple regression models of he form 8

10 (0) π = α + (β + β FX + β 3 IT ) π - + u where FX is an indicaor variable ha equals uniy during periods of fixed exchange raes and equals zero in oher periods; IT is an indicaor variable ha equals uniy during periods where an inflaion arge was in operaion and equals zero in oher periods and u is an error erm. We use he Whie (980) procedure o correc our esimaed sandard errors for heeroskedasiciy and he Newey-Wes (987) esimaor o adjus sandard errors for serial correlaion. Equaion (0) is similar o oher models in he lieraure on inflaion persisence. These models ypically inerac lagged inflaion wih indicaors of insiuional presence or economic evens. For example, Alogoskoufis and Smih (99), Alogoskoufis (99) and Bleaney (00) use indicaors of fixed exchange raes, corresponding o β 3 =0 in (0). Oher auhors, eg Burdekin and Siklos (999) also include indicaors of oher evens, for example oil shocks and srucural changes a Cenral Banks. Esimaes of (0) are presened in able ). In every counry, he esimae of β 3 is negaive and significanly differen from zero using boh annual and quarerly daa. Indeed, we can only rejec he hypohesis ha inflaion arges have eliminaed inflaion persisence (H 0 : β +β 3 =0) in he case of he UK using quarerly daa and canno rejec he hypohesis for any counry when using annual daa. These finding provide srong evidence in favour of our hypohesis ha adoping an inflaion arge will reduce he persisence of inflaion. The only oher evidence on his is in Siklos (999), who finds more ambiguous resuls using daa up o 997 (his may be because we have more observaions from he inflaion argeing regime). The impac of exchange rae regimes on inflaion persisence is less clear. We find a significanly lower rae of persisence during fixed exchange raes for Spain and he UK, which is consisen wih Alogoskoufis and Smih (99) and Alogoskoufis (99), bu no consisen significan effec in Ausralia, New Zealand, Finland and Sweden. This is broadly consisen wih he resuls in Burdekin and Siklos (999), who argue ha wars, oil shocks or changes in Cenral Bank saues have a leas as grea an impac on inflaion persisence as exchange raes regimes. 9

11 We invesigaed he robusness of hese findings in several ways (he resuls of hese lenghy experimens are no repored bu are available from he auhors). Firs, we used alernaive measures of inflaion. We esimaed (0) where inflaion was defined as π =p -p - and π =p -p -4. We found broadly similar resuls; in paricular, we coninued o find large and significan reducion in inflaion following he inroducion of an inflaion arge. Second, we esimaed an augmened model ha allowed he inercep o vary beween policy regimes, o allow for changes in he equilibrium inflaion rae beween regimes (Bleaney, 00). We coninued o find ha he persisence of inflaion was lower when here was an inflaion arge, alhough here was an effec on esimaes for he fixed exchange rae regime, similar o Bleaney (00). Third, we included he measures of oil shocks and changes in Cenral Bank saues ha were idenified as significan by Burdekin and Siklos (999) and Siklos (999). We again coninued o find ha he adopion of inflaion arges lead o a reducion in inflaion persisence, alhough mos our esimaes again became less well deermined. Fourh, we assessed he imporance of mispecificaion apparen in he esimaes in Table ). Such mispecificaion is no surprising as we esimae a very simple model; similar findings are repored in he lieraure (eg Burdekin and Siklos, 999). Our use of he Whie (980) and Newey-Wes (987) correcions should ensure ha our esimaes are robus o his. We found we could eliminae mispecificaion by including more lags of he dependen variable and by including dummies for ime periods associaed wih marked volailiy. We again coninued o find ha inflaion arges are associaed wih less inflaion persisence. Fifh, we esimaed he model π = α + β π - + u using boh Kalman Filer and rolling window echniques. Alhough our esimaes were no as precise as hose repored in Table, we coninued o find ha inflaion persisence was lower in he 990s han in he preceding wo decades. Overall, herefore, i seems ha our conclusions are robus. Finally, we summarise our findings by presening esimaes of he pooled model () π i = α + (β + β FX i + β 3 IT i ) π i- + u where i indexes he counry and indexes ime. Our esimaes, presened in Table 3, confirm he resuls of he counry-by-counry esimaes in Table. The inroducion of 0

12 inflaion arges leads o a large reducion in he persisence of inflaion. Using annual daa, he persisence of inflaion fell from 0.54 o 0.6 following he inroducion of inflaion arges. We canno rejec he hypohesis ha he persisence of inflaion was eliminaed. Using quarerly daa, he persisence of inflaion falls from 0.6 o 0., alhough in his case we can rejec he hypohesis ha inflaion persisence is eliminaed. 4) Conclusion This paper has argued he persisence of inflaion is lower when here is an finflaion arge, so inflaion is more responsive o moneary policy when inflaion is he main focus of policy. We presened a model in which inflaion argeing reduces inflaion persisence by reducing he exen o which moneary policy accommodaes inflaion. We hen presened evidence from seven counries ha adoped inflaion arges in he lae 980searly 990s. We showed ha he persisence of inflaion did indeed fall sharply afer he inroducion of an inflaion arge. Inflaion arges are a relaively recen innovaion in moneary policy. Over ime, as daa accumulaes, i will become possible o analyse he impac of inflaion arges in greaer deail, invesigaing differen aspecs such as he choice of a arge value as opposed o a arge range, or differen definiions of inflaion o be argeed. We inend o consider hese issues in fuure work

13 Table ) HEGY uni roo ess πˆ ) πˆ ) F π ˆ, π ˆ 3 ) ( ( Canada Ausralia New Zeal Finland Spain Sweden UK ( 4 A ime-rend, consan erm, seasonal dummies and a lagged dependen variable are included in he esimaes. Esimaion period: 946.Q-00.Q, which yields 0 observaions. Criical values for T = 00 a he 5% level are (see Hylleberg e al, 990: ( π ) = -3.49, π ) = -.9, and F π 3, π ) = ( ( 4

14 Table ) Parameer esimaes of inflaion persisence π = α + (β + β FX + β 3 IT ) π - + u (a) quarerly daa sample 945Q-00Q β β β 3 DW R HET RES SC Ho:(β =β 3 ) Canada 0.69(3.0) -0.40(5.0) -0.56(3.60) Ausralia 0.65(9.5) 0.03(0.44) -0.47(.68) New Zeal. 0.57(3.83) 0.4(0.95) -0.40(.44) Finland 0.5(6.8) -0.06(0.46) -0.76(3.9) Spain 0.6(9.6) -0.3(3.49) -0.79(4.4) Sweden 0.37(4.83) -0.05(0.49) -0.43(3.5) UK 0.68(6.09) -0.4(3.30) -0.30(.06) (b) annual daa sample β β β 3 DW R HET RES SC Ho:(β =β 3 ) Canada 0.88(5.38) -0.45(3.4) -0.57(.34) Ausralia 0.79(.) -0.9(0.99) -0.50(.06) New Zeal. 0.77(0.0) -0.(0.9) -0.54(.7) Finland 0.63(4.3) -0.34(.86) -.90(.93) Spain 0.7(0.3) -0.4(.83) -0.63(3.4) Sweden 0.68(7.48) -0.8(.93) -0.68(.64) UK 0.77(8.46) -0.44(3.6) -0.50(3.34)

15 Noes: The numbers in parenheses are absolue -saisics. Consans and seasonal dummies are included in he esimaes bu no shown. The -values are based on Whie s heeroscedasiciy consisen covariance marix. Esimaion period: 946.Q-00.Q. DW = Durbin-Wason es for firs order serial correlaion, HET = Breusch-Pagan LM es for heeroscedasiciy, and is disribued as χ (6) under he null hypohesis of no heeroscedasiciy, RES is Ramsey s RESET es wih he prediced value squared as addiional regressor, and is disribued as F(,3) under he null hypohesis of no funcional form problems, and SC is a LM es for -4 order serial correlaion and is disribued as (7) under he null hypohesis of no -4 order serial correlaion. Ho:(β =β 3 ) is a es of he null hypohesis β =β 3. I is disribued as χ () under he null

16 Table 3) Pooled parameer esimaes of inflaion persisence π i = α + (β + β FX i + β 3 IT i ) π i- + u (a) quarerly daa sample 945Q-00Q β β β 3 DW R Ho:(β =β 3 ) (7.0) -0.(6.70) -0.4(4.85) (b) annual daa sample β β β 3 DW R Ho:(β =β 3 ) (50) -0.39(6.7) -0.38(.48) see noes o able ) Addiional Noes: R is based on Buse s raw-momen R.

17 Appendix Derivaion of equaion (8) From equaion (7) and using he definiions of λλ and λ + λ, we can show ha dλ δσγ ˆ λ + λ (A) = < 0 dφ θ γψ. + λ λ λ + λ Since λ > λ and λ + λ > λ λ we also have >. Therefore, for any λ λ value of δ <, we obain, ˆ dλ θδ > 0, and hence, < 0 dφ reduces inflaion persisence. and so inflaion argeing Conversely, we can show ha he effec of oupu sabilisaion on inflaion persisence is posiive, (A) dλ δσγ ˆ λ( λ + φ) = 0 dψ > ( + βψ) ( λ λ)( λ+ λ). Since for convergence he small roo of he dynamic equaion is required o be less han uni λ < hen λ + φ > 0 and so given λ > λ for any value of δ <, dλ > 0. dψ

18 References Agenor, P-R and M Taylor, 99, "Tesing for Credibiliy Effecs", IMF Saff Papers, 39, pp Alogoskoufis, G, 99, "Moneary Accommodaion, Exchange Rae Regimes and Inflaion Persisence", Economic Journal, 0, pp Alogoskoufis, G, and R Smih, 99, "The Phillips Curve, he Persisence of Inflaion and he Lucas Criique: Evidence from Exchange Rae Regimes", American Economic Review, 8, pp 54-7 Bernanke, B., T. Laubach, F. Mishkin and A. Posen, (999), Inflaion argeing: lessons from he Inernaional Experience, Princeon Universiy Press. Bleaney, M, 00, "Exchange Rae Regimes and Inflaion Persisence", IMF Saff Papers, 47, pp Burdekin, R and P Siklos, 999, "Exchange Rae Regimes and Shifs in Inflaion Persisence: Does Nohing Else Maer?", Journal of Money Credi and Banking, 3, pp Calvo, G, 983, "Saggered Conracs in a Uiliy-Maximizing Framework," Journal of Moneary Economics,, pp Holden, S and J Driscoll, 00, "A Noe on Inflaion Persisence", NBER working paper 8690 Hylleberg, S, R Engle, C Granger and B Yoo, 990, Seasonal Inegraion and Coinegraion, Journal of Economerics, 44, Mankiw, G, 000, ""The Inexorable and Myserious Tradeoff Beween Inflaion and Unemploymen", Economic Journal,, pp C45-6 Newey, W and K Wes, 987, "A Simple Posiive Semi-Definie Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix", Economerica, 55, pp Siklos, P, 999, "Inflaion-Targe Design: Changing Inflaion Performance and Persisence in Indusrial Counries", Federal Reserve Bank of S Louis Review, March-April, pp Taylor, J, 979, "Saggered Wage-Seing in a Macro Model", American Economic Review, Papers and Proceedings, 69, pp 08-3 Taylor, J, 993, "Discreion versus policy rules in pracice", Carnegie-Rocheser Conference Series on Public Policy, 39, pp 95-4.

19 Taylor, J, 999a, The Robusness and Efficiency of Moneary Policy Rules as Guidelines for Ineres Rae Seing by he European Cenral Bank, Journal of Moneary Economics Taylor, J, 999b, "Saggered Price and Wage Seing in Macroeconomics", in Taylor and Woodford (eds.), Handbook of Macroeconomics, Vol B, Elsevier, 999 Whie, H, 980, "A Heeroskedasiciy-Consisen Covariance Esimaor and a Direc Tes for Heeroskedasiciy", Economerica, 48, pp