UNCERTAINTY IN THE TAYLOR RULE AND MONETARY POLICY ASSESSMENT*

Transcription

1 UNCERTAINTY IN THE TAYLOR RULE AND MONETARY POLICY ASSESSMENT* Frnando Martins** Paulo Soars Estvs** 1. INTRODUCTION In rcnt yars, on has witnssd a widsprad attntion on th way montary policy is conductd and in particular on th rol of th so-calld montary policy ruls. Svral rasons sm to undrli this rnwd intrst. Prhaps th most important on is that sinc th scond half of th 1980s, a numbr of studis hav concludd that montary policy significantly influncs th short-trm prformanc of th ral conomy. A part of this strand of litratur tris to idntify simpl montary policy ruls that could rduc th liklihood of inflationary shocks similar to thos of th 1970s. Th convntional approach in th litratur consists in stimating raction functions for a montary authority (th Fdral Rsrv, in most cass) in which a nominal intrst rat, dirctly or indirctly controlld by that montary authority, is adjustd in rspons to dviations of inflation (currnt or xpctd) from targt and of output from potntial. Ths raction functions, usually calld Taylor ruls, following John Taylor s sminal papr publishd in 1993, sm to match a numbr of normativ principls st forth in th litratur for optimal montary policy (1). * Th opinions xprssd in this papr ar thos of th authors and not ncssarily thos of th Banco d Portugal. ** Economic Rsarch Dpartmnt. Th authors ar gratful to José Frrira Machado, who has significantly contributd to improv this papr. Th authors ar also gratful for th commnts and suggstions by Francisco Dias, Isabl Gamiro, Marta Abru and Maximiano Pinhiro. Th usual disclaimr applis. This sms to provid a good rason for th growing prominnc of indications givn by Taylor rul stimats in dbats about currnt and prospctiv stanc of montary policy. Howvr, ths indications should b intrprtd with prudnc. Indd, thy ar usually prsntd as point stimats for th intrst rat, giving a sns of accuracy, which may b vry mislading. Typically, no wight is placd on th discussion of th risks to such stimats and, at last to a crtain xtnt, th radr is ncouragd to concntrat on an apparntly prcis cntral projction, ignoring th wid dgr of uncrtainty and oprational difficultis surrounding ths stimats. As in any forcasting xrcis, thr is uncrtainty rgarding both th stimatd paramtrs and th way th xplanatory variabls volv during th forcasting horizon [s Martins (000)]. Our work aims to obtain a mthodology to stimat a probability dnsity function for th intrst rat rsulting from th application of th Taylor rul (th Taylor intrst rat) and assuming that not only th xplanatory variabls but also th paramtrs of th rul ar random variabls. Our ap- (1) Th usfulnss of Taylor ruls as instrumnts for montary policy analysis can b sustaind not only on normativ grounds, with many studis concluding that simpl montary ruls hav stabilising proprtis which ar clos to thos of optimal policy ruls, but also on positiv grounds, sinc ruls with this kind of formulation sm to dpict fairly wll th way th major montary authoritis hav bn conducting montary policy. Martins (000) provids a summary of th mpirical litratur on Taylor ruls as wll as a discussion on th oprational difficultis and limitations associatd with th us of this kind of instrumnt. Banco d Portugal / Economic bulltin / Jun 001 1

2 proach builds on th work by th Bank of England [s Whitly (1999) and Britton t al (1998)] and th Svrigs Riksbank [s Blix and Sllin (1998)] producd in th contxt of thir inflation forcasting xrciss. Th mthod has a Baysian natur in th sns that involvs a subjctiv componnt, through a prmannt assssmnt of th stat of th conomy, basd on a cntral projction and th risks surrounding it. This assssmnt givs ris to th adoption of asymmtric distributions both for th xplanatory variabls and th paramtrs of th Taylor rul. Howvr, unlik th approach followd by th aformntiond cntral banks, th rsulting distribution for th Taylor intrst rat is obtaind by numrical simulation in lin with Estvs, Machado and Martins (001). This articl is structurd as follows. Sction prsnts a brif outlin of th Taylor rul and dscribs th procdur usd to comput a probability dnsity function for th Taylor intrst rat. This procdur is thn applid to th uro ara in sction 3. Finally, sction 4 prsnts som concluding rmarks.. TAYLOR RULE: A DISTRIBUTION ASSUMPTION FOR THE EXPLANATORY VARIABLES AND THE SIMULATION OF THE JOINT DISTRIBUTION Th original formulation of th Taylor rul is th following: * * * i r X (1a) Tt t t whr i T is th intrst rat rcommndd by th Taylor rul (th Taylor intrst rat), t th avrag inflation rat ovr th prvious four quartrs (masurd by th GDP dflator), * th inflation rat targt, X t th output gap and r* th quilibrium (or nutral) ral intrst rat (). Formulation (1a) by taking into account only th contmporanous inflation rat and output () Not that if 1 and 0, th ral intrst rat adjusts in a way that stabiliss both inflation and output; if 1, som inflation is accommodatd. In this cas, th nominal intrst rat chang is not sufficint to caus th ral intrst rat to mov in th sam dirction. This also applis to, which has to b non-ngativ for th rul to b stabilising. In Taylor s sminal papr (1993), th rul argumnts wr st at * 15., 05., and r *.. gap ovrlooks th forward-looking natur of montary policy. To ovrcom this problm, a forward-looking vrsion of th Taylor rul is usd in lin with Clarida, Gali and Grtlr (1997): * * * itt r t Xt 1 (1b) Th diffrnt tim horizons considrd for th output gap and th inflation forcast (on and two yars, rspctivly), has implicit th stylisd fact that, at last in larg and rlativly closd conomis, montary policy affcts conomic activity fastr than it affcts inflation [s Ball (1997)]. As it was rfrrd abov, th stimation of Taylor ruls involvs uncrtainty rgarding not only th stimatd paramtrs ( and ) but also th way in which th xplanatory variabls volv ovr th forcasting horizon. As a rsult, in this articl all th argumnts of th Taylor rul, xcluding th inflation targt, ar assumd to b random variabls. It is also considrd that th probabilistic bhaviour for ach of ths variabls is charactrisd by a two-pic normal distribution (TPN) (3). This distribution, which is also usd by th Bank of England and th Svrigs Riksbank in thir inflation forcasting xrciss, provids a simpl way to introduc asymmtrical considrations in th analysis. A random variabl W has a TPN distribution if its probability dnsity function is givn by: 1 fw; C W w; w, 1 xp w, W w (a) w, 1 1 fw; C W w; w, xp w, W w (b) with w, 1 C w, 1 w,. This distribution can b undrstood as a mrg of two standard normal distributions with th sam mod w but with diffrnt standard dviations w, 1; w,, which wr adjustd in a way to nsur continuity at (4) w. Chart 1 provids an (3) S Johnson, Kotz and Balakrishnan (1994) for a brif dscription of this distribution. (4) Th factors of adjustmnt applid to th normal distribution ar, 1/, 1 to th lft of th mod and w, w, / / w, 1 w, to its right so a to nsur that th probability dnsity function is continuous and th intgral adds to 1. Banco d Portugal / Economic bulltin / Jun 001

3 Chart 1 PROBABILITY DENSITY FUNCTION OF A TWO-PIECE NORMAL DISTRIBUTION N( w ; w, ) w, 1 w, illustration with w, 1 w,. In this xampl, th probability mass to th lft of th mod is smallr than th probability mass to its right, so that both th man and th mdian xcd th mod (positiv asymmtry). Th man and th varianc for a random variabl with this distribution ar givn by: NS( w ; w,1; w, ) N( w ; w,1 ) EW w w w 1,, (3) VarW 1 w w 1 w w,., 1, (4) In our analysis, W dnots ach of th argumnts of th Taylor rul: inflation forcast, output gap, In ordr to obtain th thr paramtrs of th distribution W w, w, 1, w,, it is ncssary to assign valus to: (i) w, which rprsnts th cntral projction (i.. th singl most likly outcom); (ii) w h ww, which rprsnts th standard dviation calculatd using historical data w adjustd by a factor of additional uncrtainty h w ; iii) P w, rprsnts th subjctiv probability of W bing blow th cntral projction th downsid risk (5). This paramtr plays a ky rol in th analysis, sinc th asymmtry builds on th particular valu ofp w.notic that ifp w =0.5, th distribution collapss to th standard normal distribution. Givn th distribution for th argumnts of th Taylor rul, th qustion that ariss is how to dtrmin th distribution of th Taylor intrst rat itslf. Unlik th cas whn random variabls follow a normal distribution, th aggrgation of random variabls with a TPN distribution dos not rsult in nw variabl with a TPN or any othr known distribution. Contrasting with th Bank of England and th Svrigs Riksbank approachs, in our work th Taylor intrst rat distribution is obtaind by numrical simulation in lin with Estvs, Machado and Martins (001). On of th problms to b solvd bfor numrical simulation, is th likly statistical dpndnc among th Taylor rul argumnts. Whras rgarding most of thm it sms rasonabl to assum indpndnc, that would b littl ralistic vis-à-vis th inflation forcast and th output gap. To modl th dpndnc btwn ths two variabls in a simpl mannr, it is considrd that th inflation forcast can b xprssd as a linar combination of two random variabls and, which ar indpndnt of th output gap X, and follow TPN distributions with common mod NS ; ; i 1 ; i : IX 1IX x x (5) whr I(.) stands for th indicator function. In addition, it is assumd that, which 1,, mans that, 1, is rlativly mor skwd to th right than. As a rsult, if th output gap outcom xcds (falls bhind) its cntral projction, a highr (lowr) proportion of agnts will b optimistic (pssimistic) about th inflation prospcts, that is th mass of probability to th right (lft) of th modal inflation forcast will b gratr. In othr words, good nws in trms of output/unmploymnt will lad a highr proportion of popl sharing a lss favourabl outlook for inflation. (5) Baring in mind that P w fxdx 1, it is possibl to 1 show that th standard dviations of th TPN distribution ar givn by: 1 Pw 1 Pw 1, w, Pw hw 1 1 and Pw Pw 1 Pw Pw, w w, Pw hw w 1. 1Pw 1 Pw 1 Banco d Portugal / Economic bulltin / Jun 001 3

4 Tabl 1 THE EURO AREA TAYLOR INTEREST RATE: CENTRAL PROJECTIONS, UNCERTAINTY AND BALANCE OF RISKS Equilibrium ral intrst rat (r*) Inflation targt * Inflation forcast Output gap X Cofficint of th inflation gap Cofficint of th output gap Main assumptions: Cntral projctions w Adjustd standard dviation w Historical standard dviation w Additional uncrtainty h w Balanc of risks Upsid(1-P w ) Downsid(P w ) Mmo itm: Man (a) Not: (a) Computd by numrical simulation. Th distribution for th inflation forcast can b computd by numrical simulation on th basis of quation (5). To do that, it is ncssary to postulat som valus for th distribution paramtrs. Rgarding th X distribution, w hav to assign valus for th cntral projction X ; th historical standard dviation X and th factor of additional uncrtainty h X ; and th downsid risk P X. Concrning th inflation forcast, w also hav to assum valus for th cntral projction ; th historical standard dviation and th factor of additional uncrtainty h ; and th downsid risks P andp (6). Th simulation of th i inflation forcast distribution assums that, with bing a constant to b computd following th aformntiond assumptions 1, 1, 1 for th paramtrs [s Estvs, Machado Martins (001)]. Onc th distribution of th inflation forcast is dfind, on th basis of quation (1b), it bcoms (6) Givn quation (5), it is straightforward to dmonstrat that th downsid risks ar rlatd in following mannr: P 1P P P P. As a rsult, assuming valus for X X 1 P 1 and P for P 1 or P. is quivalnt to assum a valu for P and anothr possibl to obtain by numrical simulation a probability dnsity function for th Taylor intrst rat that taks into account th statistical dpndnc btwn th inflation forcast and th output gap. 3. AN APPLICATION TO THE EURO AREA Taking into account th abov procdur, this sction provids an assssmnt of th uro ara montary policy stanc on basis of data availabl in Dcmbr 001. Tabl 1 prsnts th cntral projctions for ach of th rlvant variabls of th Taylor rul, as wll as th dgr of uncrtainty and th balanc of risks. Th undrlying assumptions as wll as th rmaining calculations ndd to comput th Taylor intrst distribution ar listd blow. 3.1 Cofficints Tabl prsnts diffrnt stimatd valus for cofficints and. Evn though th rsults ar not qualitativly vry distinct, th conclusions drawn in ach modl could b quantitativly diffrnt. To dfin th baslin scnario and th standard dviations, w took th valus stimatd 4 Banco d Portugal / Economic bulltin / Jun 001

5 for Grmany in Clarida, Galí and Grtlr (1997), which ar similar to thos stimatd in Prsman and Smts (1998). W did not considr any additional uncrtainty. Against th backdrop that most stimats for th Unitd Stats point to highr cofficints than thos of Grmany, w considrd upsid risks gratr than 50 prcnt (60 and 70 prcnt, rspctivly for and ). 3. Equilibrium ral intrst rat W assum a valu of 3.0 prcnt for th uro ara quilibrium ral intrst rat. This figur is consistnt with stimats drivd from a raction function for th Bundsbank ovr th last two dcads and with th avrag ral intrst rats in G7 during th 1990s (7). Morovr, according to th wll-known goldn rul of capital accumulation, th marginal product of capital, which in quilibrium quals th ral intrst rat should not b lss than th growth rat of output (othrwis, th conomy would b dynamically infficint). Currnt stimats for th uro ara potntial growth rat suggst a lowr bound for th ral intrst rat of around.0 to.5 prcnt. For th historical standard dviation, w tak th valu drivd by Smts (1999) from a forward-looking raction function for th Bundsbank ovr th priod In this work, th implicit quilibrium ral intrst rat for an inflation targt of 1.5 prcnt was 3.0 prcnt as wll. As rgards th balanc of risks, diffrnt stimats put forward by th litratur for th quilibrium ral intrst rat for Grmany fall ovrwhlmingly in th rang of.5 to 3.5 prcnt, with a slight bias on th uppr half. This last vidnc sms to indicat that th balanc of risks is on th upsid, thus justifying th attribution of a 60 prcnt probability to upsid risks. Finally, th possibl ffcts of th so-calld Nw Economy induc som uncrtainty ovr th currnt potntial output stimats (7) Th calculation of th quilibrium ral intrst rat for th uro ara on th basis of th avrag ral intrst rats prvailing, for xampl, ovr th last dcad is likly to show an upward bias. Indd, ovr this priod, th disinflation procss in th currnt uro ara countris, may hav causd ral intrst rats to stand abov thir quilibrium lvl. Against this background, it sms mor appropriat to tak past Grman intrst rats as a bnchmark for comparison with today s uro ara. and consquntly ovr th quilibrium ral intrst rat. As a rsult, w dcidd to includ a factor of additional uncrtainty of 10 prcnt. 3.3 Inflation targt W assumd an inflation targt of 1.5 prcnt. Rcall that within th ECB montary policy stratgy, adoptd in Octobr 1998, pric stability was dfind as an annual incras in th Harmonisd Indx of Consumr Prics (HICP) of blow prcnt. In addition, th drivation of th rfrnc valu for th growth rat of th M3 montary aggrgat had implicit an inflation rat of 1.5 prcnt. W did not considr any uncrtainty rgarding this targt. 3.4 Inflation forcast Tabl ESTIMATED COEFFICIENTS AND Inflation gap Output gap Taylor (1993).... US Taylor (1999).... US Ball (1997)... US Christiano (1999)... US Clarida, Galí Grtlr (1998)... US Clarida, Galí Grtlr (1997)... Grmany Prsman Smts (1998).... Grmany Th cntral projction for th inflation forcast corrsponds to th mid-point of th Eurosystm s forcasting intrval for th HICP growth in 00 publishd in Dcmbr 000 i prcnt. Th historical standard dviation was computd taking into account th Eurosystm s forcasting intrval (1.3,.5) is qual to twic th absolut man rror of th forcasting xrciss undrtakn ovr th last yars [ECB (000)]. Considring a normal distribution, this lads to a standard dviation of W did not assum any additional uncrtainty vis-à-vis th historical standard dviation. Rgarding th balanc of risks, w took downsid risks of 60 prcnt, if th output gap ralisation Banco d Portugal / Economic bulltin / Jun 001 5

6 Chart PROBABILITY DENSITY FUNCTION OF THE TAYLOR INTEREST RATE Intrst rat in Dcmbr 000 ECB rfrnc intrst rat (Dcmbr 000) 4.75 Mod Man Mdian Standard dviation Asymmtry % Intrvals 75% Probability of an intrst rat incras % falls bhind th modal forcast, and of 40 prcnt, if th output gap ralisation xcds th modal forcast. 3.5 Output gap Th cntral projction for th output gap in 001 (0.3 prcnt) was obtaind with th Hodrick-Prscott filtr, using quartrly data sinc This stimat is in lin with th Europan Commission and th OECD projctions for 001, publishd in Octobr and Novmbr 001, rspctivly. Th historical standard dviation was computd baring in mind that th Eurosystm s forcasting intrval (.6, 3.6) for th GDP growth rat is qual to twic th absolut man rror of th forcasting xrciss undrtakn ovr svral yars. Taking into account th ffcts of th so-calld Nw Economy (8), w dcidd to includ a factor of additional uncrtainty of 1.1. As to th balanc of risks, w admittd a downsid (8) Estimats for th currnt output gap ar particularly uncrtain, both bcaus rcnt output figurs ar in most cass prliminar or bcaus many stimation tchniqus, namly univariat mthods such as th HP filtr, pos som nd-of-sampl problms. risk of 55 prcnt, givn th prospct that th conomic slowdown in th Unitd Stats could b mor pronouncd than th availabl projctions. 3.6 Rsults With th aformntiond assumptions, all th cntral statistical masurs for th Taylor intrst rat would b abov th ECB rfrnc intrst rat in Dcmbr 000 (s Chart ). Nvrthlss, givn th significant varianc implid by th Taylor intrst rat distribution, ths indications ar surroundd by considrabl uncrtainty, which ar confirmd by th width of th confidnc intrvals. Indd, th confidnc intrval for th Taylor intrst rat is (4.37;5.37) with a probability of 50 prcnt, and (3.8;6.19) if th confidnc lvl is incrasd to 75 prcnt. Th ECB intrst rat in Dcmbr 000 lid insid both intrvals. It is intrsting to assss th impact of ach argumnt of th Taylor rul on th distribution varianc. Chart 3 clarly shows that th gratst contribution is givn by th inflation forcast varianc, which accounts for 96 prcnt of total varianc (9). It is also shown that th impact of uncrtainty rlatd to th Taylor rul spcification (qui- 6 Banco d Portugal / Economic bulltin / Jun 001

7 librium ral intrst rat and cofficints) is ngligibl. 4. CONCLUDING REMARKS Empirical vidnc suggsts that Taylor ruls dpict fairly wll th way major montary authoritis (in particular, th Fdral Rsrv and th Bundsbank) hav conductd montary policy ovr th last two dcads a priod during which montary policy is gnrally considrd to b hav bn rathr succssful in rducing inflation. In this contxt, it sms rasonabl to sustain that indications givn by Taylor rul stimations could b a usful rfrnc whn assssing th montary policy stanc. Howvr, th convntional approach, which consists in prsnting ths indications as point stimats for th intrst rat, sms to b lack prudnc, givn th high dgr of uncrtainty and oprational difficultis surrounding th drivation of a Taylor intrst rat. In particular, th us of Taylor ruls in a forward-looking prspctiv rquirs th inclusion of macroconomic forcasts ovr th priod rlvant for th montary policy transmission mchanism. Givn th forcasting rrors of th past, that rquirmnt provids an important sourc of uncrtainty. In our work, th informativ contnt of th Taylor rul was prsntd as a probability dnsity function for th intrst rat. This approach maks clar that montary policy dcisions ar takn in an uncrtain nvironmnt, which has to b takn into account xplicitly in th contxt of montary policy assssmnt. (9) Th contribution of ach argumnt is givn by th varianc of th Taylor intrst rat assuming that th varianc of othr argumnts is qual to zro. Chart 3 CONTRIBUTION TO THE VARIANCE OF THE TAYLOR INTEREST RATE Cofficints Equilibrium intrst rat Output gap Inflation forcast REFERENCES Ball, L. (1997) Efficint ruls for montary policy, National Burau of Economic Rsarch, Working Papr 595. ECB (000), Monthly Bulltin, Dcmbr. Blix, M. and Sllin, P (1998) Uncrtainty bands for inflation forcasts, Working Papr Sris, Svrigs Riksbank, 65. Britton, E., Fishr, P. and Whitly, J. (1998) Th inflation rport projctions: undrstanding th fan chart, Quartrly Bulltin, Bank of England, Fbruary. Christiano, L. Gust, C. (1999) Taylor ruls in a limitd participation modl, mimo. Clarida, R. and Grtlr, M. (1998) Montary Policy Ruls and Macroconomic Stability: Evidnc and Som Thory, National Burau of Economic Rsarch, Working Papr 644. Clarida, R., Galí, J Grtlr, M. (1997) Montary policy ruls in practic: som intrnational vidnc, Cntr for Economic Policy Rsarch, Discussion Papr Estvs, P., Machado, J., and Martins, F. (001) A simpl mthod for simulating th Taylor intrst rat, Banco d Portugal, Working papr, forthcoming. Johnson, N., Kotz, S. and Balakrishnan, N. (1994) Continuous univariat distributions, Scond dition, Wily. Banco d Portugal / Economic bulltin / Jun 001 7

8 Martins, F. (000) Taylor ruls, Banco d Portugal, Economic Bulltin, March. Prsman, G. and Smts, F. (1998) Th Taylor rul: a usful montary policy guid for th ECB?, mimo. Smts, F. (1999) Th quilibrium ral intrst rat, Europan Cntral Bank, mimo, March. Taylor, J.B. (1993) Discrtion vrsus policy ruls in practic, Carngi-Rochstr Confrnc Sris on Public Policy, 39. Taylor, J.B. (1999) Th robustnss and fficincy of montary policy ruls as guidlins for intrst rat stting by th Europan Cntral Bank, Journal of Montary Economics, Volum 43, 3, Jun. Wallis, K. (1999) Asymmtric forcasts of inflation and th Bank of England s fan chart, National Institut of Economic Rviw, January. Whitly, J. (1997) Forcast uncrtainty, Bank of England, mimo. 8 Banco d Portugal / Economic bulltin / Jun 001