1 Communicaion, Decision Making, and he Opimal Degree of Transparency of Moneary Policy Commiees Anke Weber Inernaional Moneary Fund This paper develops a heoreical model of a moneary policy commiee wih heerogeneous members whose decisions and public communicaions are observed by he financial markes. I hereby provides a link beween he lieraures on moneary policy commiees and cenral bank communicaion. The resuls show ha ransparency abou he differen views among commiee members surrounding he economic oulook is beneficial. However, communicaing he diversiy of views abou he moneary policy decision may no be welfare enhancing, a leas in he shor erm. These resuls suppor previous empirical findings and have srong implicaions for how commiees should communicae. JEL Codes: E50, E52, E58.. Inroducion The conduc of moneary policy has changed markedly since he 990s. Over he pas wo decades, a number of cenral banks have shifed responsibiliy for ineres rae seing o a moneary policy I would like o hank Alan Blinder; Pera Geraas; Pera Gerlach-Krisen; Sefan Gerlach; Heinz Herrmann; Sean Holly; Wolfgang Lemke; Jerome Vandenbussche; wo anonymous referees; paricipans a he Research Workshop on Moneary Policy Commiees a Norges Bank, Sepember 2007; and seminar paricipans a he Bank of Canada, he Bank of England, and he Federal Reserve Board for heir commens. This paper was wrien whils I was a Cambridge Universiy prior o joining he Inernaional Moneary Fund. The views expressed in his paper are hose of he auhor and do no necessarily represen hose of he IMF or IMF policy. Auhor conac: 700 9h Sree NW, Washingon DC, 2043, USA.
2 2 Inernaional Journal of Cenral Banking Sepember 200 commiee (MPC). In addiion, cenral banks have become more independen and now pay close aenion o explaining wha hey do and wha underlies heir decisions. Greaer ransparency and increased communicaion are consequences of hese developmens (de Haan, Eijffinger, and Rybinski 2007). 2 This paper provides a link beween he lieraures on moneary policy commiees and cenral bank communicaion, boh of which are imporan elemens in modern cenral bank design. I develops a heoreical model of a moneary policy commiee whose decisions and public communicaions are observed by he financial markes, and hereby analyzes how commiees should communicae. The model conrass in several ways wih previous work on cenral bank ransparency and communicaion. Firs, decisions are se by a moneary policy commiee wih heerogeneous members raher han by a represenaive cenral banker. I is assumed ha policymakers face uncerainy in assessing he sae of he economy. 3 They receive differen signals on he sae of he economy and face uncerainy abou he precision of hese observaions. They also have differen preferences regarding he opimal level of he oupu gap. In addiion, wo sources of asymmeric informaion beween he commiee and marke paricipans are inroduced. I is assumed ha marke paricipans have imperfec informaion abou he precision of public informaion on he sae of he economy and abou he policy preferences of commiee members. Several ineresing insighs are obained. I is shown ha here is a decreasing marginal benefi of increasing he commiee size. I is also found ha communicaion maers for financial markes expecaions of inflaion and fuure shor-erm ineres raes. Commiee members should communicae heir views on he sae of he economy wihou error, as his reduces inflaion and oupu-gap A recen survey by Pollard (2004) shows ha seveny-nine ou of eighy-eigh cenral banks conduc moneary policy by commiee. 2 Eijffinger and Geraas (2006) provide an index of ransparency for a se of developed counries ha includes some inflaion argeers (Unied Kingdom, Sweden, Ausralia, and Canada) as well as non-argeers (Japan, Unied Saes, and Swizerland). They show ha beween 998 and 2002 ransparency increased for virually all of he cenral banks hey sudied. 3 The fac ha cenral banks do no know he curren sae of he economy wih cerainy has been sressed by Orphanides (2003) and Aoki (2006).
3 Vol. 6 No. 3 Communicaion, Decision Making 3 variabiliy. Communicaion of a divergence of views by commiee members regarding he moneary policy decision (as, for example, he publicaion of voing records) may lead o greaer variabiliy in inflaion and he oupu gap in he shor run. In he long run, welfare is enhanced, as financial markes are able o infer members preferences from voing records once hey have a beer esimae of he precision of public informaion. This paper conribues o he previous heoreical and empirical lieraure on moneary policy commiees and cenral bank communicaion. 4 Blinder (2007) argues ha delegaing moneary policy o a commiee leads o superior policy for a number of reasons, such as he abiliy o pool judgmens of differen members and he possibiliy of learning from oher members. The finding ha commiees make superior decisions o individual policymakers has been confirmed by he experimenal lieraure (Blinder and Morgan 2005; Lombardelli, Proudman, and Talbo 2005). Furhermore, he heoreical lieraure has concluded ha a commiee of limied size is opimal due o he coss of acquiring informaion abou differen members and coordinaion coss (Siber 2006). This paper argues ha commiee members are no efficien a pooling differen informaion ses when hey do no know heir precision and ha his implies ha here are decreasing marginal benefis of increasing he commiee size. An increasing number of papers have examined he opimal communicaion sraegy of cenral banks. Some economiss sress he imporance of communicaion in providing cenral banks wih he means o influence key asse prices in he economy (Blinder 998; Bernanke 2004). However, ohers, such as Morris and Shin (2002), argue ha oo much communicaion may no be desirable. Morris and Shin (2002) develop a model in which welfare decreases when privae agens rely on a sufficienly noisy public signal o coordinae heir acions and hus disregard heir own privae informaion. Ehrmann and Frazscher (2005) invesigae communicaion by hree major cenral banks (he Bank of England, he Federal Reserve, and he European Cenral Bank) empirically and evaluae he effeciveness of cenral bank communicaion on financial 4 Vandenbussche (2006) and Blinder (2007) provide comprehensive overviews of he lieraure on cenral bank commiees whils Blinder e al. (2008) provide a survey of he lieraure on cenral bank communicaion.
4 4 Inernaional Journal of Cenral Banking Sepember 200 markes in erms of heir abiliy o anicipae moneary policy decisions. They conclude ha a higher degree of communicaion dispersion among commiee members abou moneary policy worsens he abiliy of financial markes o anicipae fuure moneary policy decisions. They also find ha communicaion of he risks and diversiy of views of he commiee surrounding he economic oulook enhances he abiliy of he public o anicipae fuure moneary policy decisions, a leas in he case of he Federal Reserve. Gerlach- Krisen (2004), on he oher hand, invesigaes he voing records of commiee members a he Bank of England and finds ha hose records can convey informaion abou he views of individual members. Their publicaion may hence lead o greaer policy predicabiliy. The presen paper is bes seen as providing some heoreical underpinning o explain hose previous empirical findings. The remainder of his paper is srucured as follows. Secion 2 ses ou he basic model. The soluion of his model is discussed in secion 3. Secion 4 presens he resuls, and conclusions are summarized in secion The Model 2. The General Seup Inflaion is deermined by a New Keynesian Phillips-curve relaionship: π = E π + + y + s, () where π denoes inflaion and y is he oupu gap defined as he difference beween acual and poenial oupu, where he laer is convenienly normalized o 0. For convenience, he coefficiens of he New Keynesian Phillips curve are se o. This does no affec he qualiaive resuls. In addiion, s is a persisen supply shock, which follows a simple AR() process: s = αs + v, (2) where 0 <α< and v is i.i.d. whie noise wih variance σ 2 v.
5 Vol. 6 No. 3 Communicaion, Decision Making 5 Following Kozicki and Tinsley (2008), he oupu gap is deermined by he following simple relaionship: 5 y = R, (3) where R denoes he long-erm real ineres rae. The assumpion ha he oupu gap is decreasing in he long-erm real ineres rae can be jusified by he fac ha he ineres-rae-sensiive componens of aggregae demand generally depend on he yield on financial asses wih longer mauriy (Eijffinger, Schaling, and Tesfaselassie 2004). To faciliae he derivaion of closed-form resuls, we replace he n-period real ineres rae in (3) wih a wo-period rae. The woperiod real ineres rae, R, and he curren and fuure shor-erm real ineres raes, i E π + and E i + E π +2, are relaed by he expecaions heory of he erm srucure: 6 R = 2 (i E π + )+ 2 (E i + E π +2 ). (4) Replacing he n-period bond rae wih a wo-period bond rae could be inerpreed as describing a siuaion in which he cenral bank deals wih he curren siuaion given expecaions abou he near fuure (wo periods ahead) while oo lile is known abou he long run (Gosselin, Los, and Wyplosz 2008). The cenral bank conrols he shor-erm nominal ineres rae, i, and has exogenously given inflaion and oupu-gap arges, π and y. I also wans o minimize deviaions of inflaion and he oupu gap from hose assigned arges. The cenral bank can observe and respond direcly o privae-secor expecaions, and i ses is ineres rae afer privae expecaions are se in every period. This iming implies ha moneary policy is se under discreion. Since i affecs only y and π and here are no endogenous sae variables, he cenral bank will se ineres raes o minimize he following loss funcion: 5 This equaion can be derived from a forward-looking IS curve of he form y = E y + (i E π +). Afer recursive forward subsiuion, he relaionship can be approximaed as y E [ n n i= i+i n n i= π+i+], where i denoes he shor-erm nominal ineres rae. 6 Wihou loss of generaliy, he unobserved erm premium is se o 0.
6 6 Inernaional Journal of Cenral Banking Sepember 200 L = 2 [(π π ) 2 + μ(y y ) 2 ], (5) where 0 <μ< is he relaive weigh on oupu-gap sabilizaion. In order o find he opimal reacion funcion, (5) is minimized subjec o (), (2), (3), and (4). The cenral bank s reacion funcion can be wrien as ( i = + 2 ) E π + + E π +2 E i + +μ + 2 +μ (s π ) 2μ +μ y. (6) Hence, i is increasing in he curren supply shock because i deermines curren inflaion. Opimal policy is also inversely relaed o financial markes forecas of he fuure shor-erm real rae, since he higher E i + E π +2, he lower he opimal shor-erm real ineres rae can be. The higher he relaive weigh ha he cenral bank gives o oupu-gap sabilizaion, μ, he smaller is he response of i o changes in expeced inflaion and he aggregae supply shock. The wo-period real rae can be expressed as R = +μ (E π + + s π ) μ +μ y, where equaions (4) and (6) have been used. Inuiively, he woperiod real ineres rae is a posiive funcion of expeced inflaion and he supply shock and a negaive funcion of he inflaion and oupu-gap arges. The mehod of undeermined coefficiens is used o obain he public s raional expecaion of inflaion as 7 E π + = μ +μ( α) αs + π + μy. (7) Privae-secor inflaion expecaions are increasing in he curren supply shock and he inflaion and oupu-gap arges of he cenral 7 The soluion mehod is oulined in he appendix.
7 Vol. 6 No. 3 Communicaion, Decision Making 7 bank. Subsiuing (4) and (7) ino () and (3) yields expressions for inflaion and he oupu gap: μ π = [ + μ( α)] s + π + μy and y = [ + μ( α)] s. Hence inflaion is increasing in he supply shock and he cenral bank s arges for inflaion and he oupu gap. Moreover, i is a posiive funcion of μ. Therefore, he greaer he preference of he cenral bank for oupu-gap sabilizaion, he sronger is he response of inflaion o supply shocks. If s > 0, he oupu gap is also a posiive funcion of he cenral bank s preference for oupugap sabilizaion. Furhermore, i is a negaive funcion of he supply shock. 2.2 Imperfec Informaion abou he Sae of he Economy The cenral bank and he public are assumed o face uncerainy abou he curren supply shock bu o have heir own bes esimae of s. Secions 3. and 3.2 show how such an esimae can be derived. The cenral bank and he privae secor know he srucural equaions of he economy, and he cenral bank coninues o observe perfecly he public s inflaion expecaions, which are se before he cenral bank makes an ineres rae decision. This assumpion is made in order o be able o derive closed-form soluions of he model under uncerainy abou he sae of he economy and asymmeric informaion beween he cenral bank commiee and he financial markes. If policy is se under discreion, hen he commiee does no need o consider he effec of is shor-erm ineres rae decision on financial markes expecaions of fuure inflaion and ineres raes, since hese are already se. As Svensson and Woodford (2004) show, under asymmeric informaion beween he cenral bank and he public and uncerainy abou he sae of he economy, cerainy equivalence coninues o hold under discreion; ha is, he commiee can coninue o se ineres raes as i would under cerainy abou he supply shock bu use is bes esimae of he supply shock insead. Furhermore, he signal-exracion problem of finding an opimal esimae of he supply shock can be reaed separaely from he opimizaion problem of finding an opimal response coefficien for he reacion funcion of he commiee. This is because
8 8 Inernaional Journal of Cenral Banking Sepember 200 he bes esimae of he supply shock does no depend on he curren nominal ineres rae, inflaion, or oupu and hus a separaion principle applies (Svensson and Woodford 2004). Furhermore, financial markes use heir bes esimae of he curren supply shock and ignore he uncerainy surrounding his esimae when forming expecaions abou fuure inflaion and ineres raes. I is assumed ha in he final sage of each period, he supply shock is realized and observed boh by he cenral bank and he public. This assumpion is made in order o simplify he analysis. Whils i would be more reasonable o assume ha a new and beer esimae of he supply shock becomes available a he end of each period, his would make he signal-exracion procedure significanly more complicaed. Using (6), he shor-erm nominal ineres rae under uncerainy is given by i = ( + 2 +μ ) E π + + E π +2 E i ( (CB) s π ) 2μ +μ +μ y, (8) where s CB denoes he opimal esimae of he cenral bank for he supply shock in period. Insering he cenral bank s reacion funcion (8) ino (4) and using (7), he wo-period real ineres rae under uncerainy can be wrien as μα R = ( + μ)[ + μ( α)] s(f ) + +μ s(cb), (9) where s F denoes he opimal esimae of he financial markes for he supply shock in period. Using (7) and (9), inflaion and he oupu gap in period will equal π = and μ 2 α ( + μ)[ + μ( α)] s(f ) +μ s(cb) + π + μy + s (0) μα y = ( + μ)[ + μ( α)] s(f ) +μ s(cb). ()
9 Vol. 6 No. 3 Communicaion, Decision Making 9 Thus, inflaion coninues o increase wih higher cenral bank arges for inflaion and he oupu gap. I is a posiive funcion of he rue supply shock and he esimaed supply shock by he public. The higher he perceived supply shock by he cenral bank, he lower will be inflaion. This is because he higher he curren esimae of he supply shock by he cenral bank, he higher will be he shor-erm nominal ineres rae ha i ses. The oupu gap, on he oher hand, is decreasing in boh he cenral bank s and he public s esimaes of he supply shock. This paper assumes ha α>0 and μ>0. From equaions (0) and () i can be seen why hese assumpions are made. If α = 0, hen he privae secor s esimae of he supply shock has no effec on inflaion or he oupu gap. In his case, if he inflaion and oupu-gap arges of he cenral bank are known o he public, here is no role for communicaion by commiee members regarding heir views on he innovaion o he supply shock. The same is rue for μ = 0. In his case, here is also no effec of he oupu-gap arge on inflaion. Thus, for he resuls in his paper o hold, he supply shock should be persisen and he cenral bank should no be a sric inflaion argeer. Empirical sudies ypically confirm ha supply shocks are persisen (Ireland 2004). In addiion, wheher hey explicily arge inflaion or no, he cenral banks of mos developed economies ac as flexible inflaion argeers (Cukierman 2007). 2.3 Transparency and he Moneary Policy Commiee This secion inroduces a model of a moneary policy commiee wih N members whose decisions and public communicaions are observed by he financial markes. Each commiee member, j, receives a signal on he innovaion, v, o he supply shock, s : v (j) = v + ε (j), (2) where ε (j) is i.i.d. wih variance σε,j 2 for j =, 2,...,N. Thus E(v (j) v ) 2 = σε,j 2. I is assumed ha he error erms of hose signals are uncorrelaed among commiee members. Furhermore, heir rue variance is unknown. The precision of commiee member j s observaion is esimaed in period by member k as σ 2(k,j) ε, for j =,...,N and
10 0 Inernaional Journal of Cenral Banking Sepember 200 k =,...,N. Whils commiee members may receive he same informaion on he sae of he economy, hey inerpre and process his informaion differenly, resuling in differen observaions on he sae of he economy. Furhermore, commiee members are likely o be uncerain abou he correc underlying model of he economy, and his is refleced in differen variances of observaion errors and uncerainy abou he precision of informaion. In addiion, commiee members are modeled as having differen preferences regarding he level of he oupu-gap arge, y. Even hough he objecives of a cenral bank are ofen assigned by law, hese are usually defined in erms of a specific inflaion arge, whereas he objecives regarding he opimal level of he oupu arge are less precisely defined (Cukierman 2007). Thus, i is likely ha commiee members have differen views abou he opimal level of he oupu-gap arge, and his is confirmed by he empirical lieraure (Chappell, McGregor, and Vermilyea 2005). The paper assumes ha hese oupu-gap preferences are consan and denoed by θ (j) for member j. This may no be he case in realiy. Cukierman (2007) argues ha hese preferences flucuae due o changes in he inensiy of poliical pressures on members. However, he assumpion ha he oupu-gap arge preferences are consan grealy simplifies he analysis of he paper. If hey were following an auoregressive process as in Faus and Svensson (2002), his would add anoher signal-exracion problem o he paper. However, he basic conclusions should sill hold. There are wo imporan informaion asymmeries beween he moneary policy commiee and financial markes. Firs, financial markes do no observe he signals ha individual commiee members receive on he innovaion o he supply shock. Insead, financial markes receive public informaion on he sae of he economy from commiee members for insance, in he form of speeches. This communicaion akes he following form for each commiee member j: where ϖ (j) x (j) = v (j) + ϖ (j), (3) is i.i.d. wih variance σϖ,j 2 for j =,...,N. I is assumed ha E (ϖ (F,j),ϖ (F,k) )=0forj k. Thus, each commiee member, j, communicaes his view on he innovaion o he supply shock
11 Vol. 6 No. 3 Communicaion, Decision Making o he financial markes, bu may do so imperfecly, which is refleced in he error erm ϖ (j). When σϖ,j 2 = 0, he signals x(j) communicae v (j) wihou noise and here is perfec acual ransparency abou commiee member j s observaion on he innovaion o he supply shock. In realiy, i will be difficul for he privae secor o esablish how ransparen he cenral bank is, and i is unlikely ha he privae secor will know he variance of he communicaion error, σϖ,j 2. Thus, he paper follows Geraas (2007) and inroduces he noion of perceived ransparency. Commiee member j is perceived o be perfecly ransparen abou his signal on he innovaion o he supply shock if σ 2(j) ϖ, =0. Equaion (3) can alernaively be wrien as x (j) = v + ε (j) + ϖ (j) = v + ζ (j), (4) where he variance of ζ (j) equals Var(ζ (j) ) = σε,j 2 + σ2 ϖ,j for j =, 2,..., N. There is no communicaion abou he esimaed precision of signals by commiee members, and financial markes are uncerain abou he variance of ϖ (j). The variance of ζ (j) is esimaed by financial markes as σ 2(j) = σ 2(F,j) ε, + σ 2(j) ϖ,. Financial markes also have imperfec knowledge abou he policy preferences of commiee members. As Beesma and Jensen (998) argue, policymakers are likely o have privae informaion abou heir preferences. Financial markes have a prior on he preferred oupu-gap arges of policymakers. 8 Denoe his prior for he preferred oupu-gap arge of commiee member j as z (j) = θ (j) + ψ (j), where ψ (j) is i.i.d. wih variance σz,j 2 for j =, 2,...,N. The variance of his prior is esimaed by he financial markes as σ z,j 2. I should be noed ha he paper follows he definiion of Geraas (2002) and defines ransparency as he absence of asymmeric informaion beween policymakers and financial markes. The paper focuses exclusively on wha Geraas (2006) refers o as he informaion effec of ransparency ha is, he effec of giving he privae secor new informaion o ac upon. I does no invesigae ζ, 8 This prior could have been derived as a resul of some previous communicaion by commiee members abou heir preferences.
12 2 Inernaional Journal of Cenral Banking Sepember 200 he indirec incenive effecs of ransparency, whereby he commiee members would adjus heir behavior according o which informaion is disclosed. These incenive effecs are paricularly relevan for he quesion of wheher voing records should be published. There cerainly is a concern ha if he European Cenral Bank were o publish voing records, his would induce members of he Governing Council o voe for he opimal ineres rae of he counry hey represen (Issing 999; Gersbach and Hahn 2005). Sraegic voing behavior has received considerable aenion in he heoreical lieraure. 9 However, policymakers hemselves do no believe ha sraegic consideraions play an imporan role in policy meeings. For insance, Yellen (2005) claims ha in fac, I hink FOMC members behave far less individualisically and sraegically han assumed in some of hese models. The iming of evens in any period is as follows: Firs, each commiee member receives a signal on he innovaion o he curren supply shock (denoe his sage as firs ). Subsequenly, he financial markes receive he public informaion x (j) and raionally form expecaions of inflaion and shor-erm nominal ineres raes. The commiee hen mees, deliberaes, voes on an ineres rae by majoriy, and publishes is ineres rae decision ( hird ). The commiee may also publish is voing records ( fourh ). 0 Finally, and before he beginning of period +, he supply shock, s, is realized and observed by boh he commiee and he financial markes. 3. Solving he Model 3. Commiee Decision Making When he commiee mees and deliberaes, each commiee member combines his signal on he innovaion o he supply shock wih hose 9 An exensive overview of he game-heoreic lieraure ha includes an analysis of sraegic voing behavior of commiee members and is relevance for moneary policy commiees has been provided by Gerling e al. (2003). 0 We hence assume ha he publicaion of voing records occurs in beween policy meeings. In he case of he Bank of England, for example, voing records and minues are published a 9:30 a.m. on he Wednesday hireen days afer he monhly commiee decision, so ha hey are available o he public before he commiee nex mees.
13 Vol. 6 No. 3 Communicaion, Decision Making 3 of he oher members in order o form an assessmen of he sae of he economy in period. The opimal combinaion of signals for each commiee member j is a linear combinaion of all signals wih he weighs deermined by he precision of signals: ṽ (j) = v + B [ () j, ε ε (2)... ε (N) ] (5) for j =, 2,...,N. The weighs given o he differen signals, he vecor B j,, is given by (44). I follows ha E (ṽ j )=v and ha Var(ṽ j )=σ 2 v + B j, Ω B j,. Commiee members can form an opimal assessmen of he innovaion o he supply shock for period using (5) and he fac ha he innovaion o he supply shock has zero mean. This assessmen is given by 2 v (j) = σ 2 v σ 2 v + B j, Ωj, B j, ṽ (j), (6) where i is assumed ha σv 2 is known o all commiee members. An imporan characerisic of equaion (6) is ha he more precise he opimal combinaion of signals is perceived o be, he more weigh i will be given by commiee member j. In paricular, he signal-exracion parameer, 2 v σ σv 2+ B, will approach 0 j, Ωj, B j, as B j, Ωj, B j,.if B j, Ωj, B j, = 0 and he opimally combined signal is perceived o be fully accurae, he signal-exracion parameer will be equal o. The opimal predicion for he supply shock by member j in period is given by s (j) = αs + v (j), (7) where v (j) is given by (6). As long as B j, B k, for j =,...,N, k =,...,N, and j k, i is rue ha v (j) v (k). Thus, here will Signals are combined using he mehods developed by Baes and Granger (969) and Dickinson (973) on he opimal combinaion of forecass. 2 The basic Kalman filering formulae have been used wih (5) as he observaion equaion. For a derivaion of he Kalman filering formulae, see, for example, Hamilon (994).
14 4 Inernaional Journal of Cenral Banking Sepember 200 be disagreemen beween commiee members afer he deliberaion process when members voe on he ineres rae. Acual voing daa of MPCs (Gerlach-Krisen 2003, 2009) confirm his feaure of he model. The ineres rae ha will be voed for by each commiee member j will equal i (j) = ( μ +μ ) E π + + E π +2 E i + ( s (j) π ) 2μ +μ θ(j) (8) for j =, 2,...,N. Since moneary policy decisions are made by majoriy voing, he ineres rae se by he commiee is deermined by he median voer: 3.2 Financial Markes i (c) = median( i (),i(2),...,i(n) ). (9) This secion derives expressions for inflaion and ineres rae expecaions of financial markes. In order o fully undersand he role of he wo informaion asymmeries in he model, in secion 3.2. i is assumed ha policy preferences of commiee members are idenical (and equal o y ) and ha financial markes face only uncerainy abou he supply shock and he precision of public informaion. In secion 3.2.2, uncerainy abou commiee members preferences regarding he level of he oupu-gap arge, θ (j), is added Imperfec Common Knowledge abou Signals and Their Precision Financial markes solve a signal-exracion problem similar o ha faced by commiee members. The opimally combined public signal can be wrien as ṽ F = v + B [ () F, ζ ζ (2)... ζ (N) ], (20) where he vecor B F, is defined in equaion (49). I follows ha E (ṽ F ) = v and ha Var(ṽ F ) = σ 2 v + B F, Ω F B F,. Such a
15 Vol. 6 No. 3 Communicaion, Decision Making 5 combinaion of he public informaion implies ha he more accurae he public signal of a specific commiee member is perceived o be by he markes, he more weigh i will be given. This can provide an explanaion for he finding by Ehrmann and Frazscher (2007) ha financial markes reaced significanly sronger o saemens by Alan Greenspan han o saemens by oher FOMC members. Alan Greenspan migh have been viewed by he markes as a paricularly able policymaker wih a precise observaion on he sae of he economy. 3 Financial markes use (20) o form an opimal assessmen of he innovaion o he supply shock in period : v (F ) = σ 2 v σ 2 v + B F, ΩF, B F, ṽ F. (2) The assessmen of financial markes of he curren supply shock equals s (F ) = αs + v (F ). (22) The ineres rae se by he median commiee member is given by (8), where s (CB) = median ( s () ),s(2),...,s(n). Inflaion and he oupu gap are given by equaions (0) and () Imperfec Common Knowledge abou Commiee Members Preferences Financial markes coninue o form an opimal esimae of he curren supply shock as in secion However, financial markes also need o derive opimal esimaes of commiee members oupu-gap arge preferences. I will be shown how voing records provide financial markes wih parial informaion abou hose preferences. I is firs invesigaed how privae-secor expecaions are formed when voing records are no published. 3 An alernaive explanaion for his empirical finding lies in he insiuional power of he chairman.
16 6 Inernaional Journal of Cenral Banking Sepember 200 Voing Records Are No Published. In his case financial markes receive a signal on he oupu-gap arge of he median voer in period once he policy decision is published. However, in he nex period, +, he assessmens of he innovaion o he curren supply shock by commiee members have changed and he median voer is likely o be a differen commiee member han in period. Thus he usefulness of he policy decision for deducing preferences of commiee members is limied. Financial markes realize his and use heir priors on commiee members preferences. Privae-secor expecaions of he median member s preferences are hus given by z C = median(z (),z (2),...,z (N) ). Voing Records Are Published. Voing records provide financial markes wih informaion on he preferences of commiee members. Financial markes know ha he ineres rae voed for by commiee member j in period follows i (j) = ( μ +μ ) E π + E π + E i ( s (j) π ) 2μ +μ θ(j). (23) Thus, if marke agens were able o observe s (j), hey would be able o perfecly infer θ (j) from he individual voing records. Unless commiee members communicae heir opimal assessmen of he economy afer deliberaion has aken place, financial markes imperfecly. The esimae by financial markes of s (j) ) for all j =, 2,...,N is equal o s(f. Therefore he signal financial markes receive on θ (j) in period is given by observe s (j) ξ (j) = θ(j) + [ (F ) s μ ] s(j), (24) where E (ξ (j) )=θ(j) and E (ξ (j) θ(j) ) 2 =( μ )2 (E (s (F ) s (j) )2 ). I should be noed ha he rue variance of ξ (j) is unknown o financial markes. This variance is a funcion of he precision of commiee members observaions on he innovaion o he supply shock and he precision of he public informaion.
17 Vol. 6 No. 3 Communicaion, Decision Making 7 Financial markes can updae heir iniial prior and derive a new assessmen of θ (j). In period afer voing records have been published, he bes assessmen of θ (j) equals θ (F,j) = θ(f,j) 2 + Ṽar ( θ (F,j) ) 2 ) + Ṽar ( ξ (j) ) [ ξ (j) Ṽar ( θ (F,j) 2 2] θ(f,j), (25) where he weighs are wrien in perceived erms because he rue variances are unknown o financial markes. Equaion (25) shows ha he bes assessmen of θ (j) in period, θ (F,j), is a linear combinaion of he previous bes assessmen, θ (F,j) 2, and he signal on preferences conained in voing records, ξ (j). The more precise he signal on commiee member j s preference, ξ (j), is perceived o be, he more weigh i will be given in he signalexracion procedure. If his signal is perceived o be perfecly accurae, Ṽar(ξ (j) ) = 0, hen from (25) he bes assessmen of θ (j) will equal ξ (j). If, on he oher hand, Ṽar(ξ(j) ), hen θ (F,j) θ(f,j) 2 and hus he weigh given o he signal on preferences conained in voing records will urn o 0. The bes assessmen of he median member s oupu-gap arge in period before voing records in ha period are published is given by z C = median ( θ (F,),θ(F,2),...,θ(F,N) ). (26) I is assumed ha he public ignores he uncerainy surrounding is esimaes of he supply shock and he preference of he median policymaker and insead uses is own bes esimaes o form expecaions of inflaion and shor-erm nominal ineres raes. In order o be able o obain a closed-form expression for inflaion expecaions, he public is modeled as making he implici assumpion ha he median voer also has he median oupu-gap arge preference. This clearly need no be he case, since commiee members ineres rae recommendaions are deermined boh by heir bes assessmen of he supply shock and heir oupu-gap arge preference.
18 8 Inernaional Journal of Cenral Banking Sepember 200 Using (7), (22), and (26), we can derive privae-secor expecaions of inflaion in period +as E π + = μα +μ( α) s(f ) + π + μz C. (27) The public s expecaion of he fuure shor-erm nominal ineres rae can be wrien as E i + = 2α + μ( + α)α2 ( + α)[ + μ( α)] s(f ) + π + μz. C (28) Therefore, he wo-period real ineres rae is given by R = 2 ( i (c) E π + ) + 2 (E i + E π +2 ), (29) where i (c) is given by (9). Subsiuing for R and E π + in () and (3) hen yields inflaion and he oupu gap under he publicaion of voing records. I is sraighforward o derive inflaion and he oupu gap when voing records are no published, he only difference being he financial markes esimae of he median member s oupu-gap arge. 4. Resuls Secions 4. and 4.2 solve a version of he model wih a single cenral banker under boh perfec and imperfec knowledge of he cenral bank s oupu-gap arge. Secion 4.3 hen urns o he commiee case and invesigaes welfare when here is only uncerainy abou he sae of he economy and he precision of public informaion. Secion 4.4 inroduces imperfec informaion abou preferences of commiee members, and he desirabiliy of publishing voing records is analyzed when commiee members mee repeaedly over ime. The parameers and variances are se as follows: α =0.8, μ =0.5, and σ 2 v = and σ 2 z,j = for all j =, 2,...,N. In addiion, π and y are se o 2. For all simulaions, he rue variances, σ 2 ε,j and σ2 ϖ,j, and perceived variances, σ 2(k,j) ε, and σ 2(j) ϖ,, are randomly drawn for each commiee member j =,...,N. The perceived and rue variances are drawn as follows for each commiee member: σ 2 =(u (j) ) 2,
19 Vol. 6 No. 3 Communicaion, Decision Making 9 where u (j) N(0, 2 ) and σ2 can sand for he rue variances, σε,j 2 and σϖ,j 2, or he perceived variances, σ2(k,j) ε, and σ 2(j) ϖ,. This implies ha σ 2 is basically drawn from a χ 2 disribuion, which has a variance of. 4 The covariance marices Ω, Ω F, Ω j,, and Ω F, are hen compued. Given hese covariance marices, i is possible o draw random shocks wih he covariance properies of he sysem being modeled. In all simulaions, hose random shocks are generaed using 0,000 draws. The baseline parameers are chosen so ha he perceived and rue variances on he signals received on he innovaion o he supply shock are drawn from a disribuion wih a variance of. Given ha he variance of he innovaion o he supply shock, σv, 2 is also se o, his seems a sensible baseline parameer specificaion. Secion 4.5 considers he effecs of changing he variance of u (j). 4. A Single Cenral Banker: Perfec Common Knowledge of Policy Preferences I follows direcly from (2) and secion 3. ha he bes esimae of he innovaion o he supply shock by he cenral banker is given by v (CB) = σ 2 v σ 2 v + σ 2(CB) ε, v (CB) = τ CB v (CB). (30) Similarly for financial markes, i can be deduced from (4) and secion 3.2 ha v (F ) = σ 2 v σ 2 v + σ 2(F,CB) ε, x (CB) + σ 2(CB) = τ F x (CB). (3) ϖ, In wha follows, he opimal weighs ha should be given o he observaion on he innovaion o he supply shock by he cenral 4 I is possible o conver u (j) N(0,σ 2 u) ino a sandard normal random variable, Z N(0, ), where Z = u(j) σ 2 u. If a sandard normal random variable is squared, i follows a χ 2 disribuion wih variance 2. Thus, in order o find he variance of (u (j) ) 2, he variance of Z 2 needs o be muliplied by (σ 2 u) 2.
20 20 Inernaional Journal of Cenral Banking Sepember 200 bank and he public informaion are defined as τ CB = σ 2 v σ 2 v +σ2 ε,cb σ and τ F = 2 v, respecively. These are he weighs ha σv 2+σ2 ε,cb +σ2 ϖ,cb would be given o he signal by he cenral bank and he public informaion if heir precision were perfecly known. Furhermore, μ le A = 2 α (+μ)[+μ( α)] and A 2 = +μ. Using equaions (0) and () as well as (2), (4), (7), and (22), he following expressions for inflaion and he oupu gap are obained: π =(A A 2 +)αs +[A τ F A 2 τ CB +]v +[A τ F A 2 τ CB ]ε (CB) and ( y = μ A + A 2 ) αs ( μ A τ F + A 2 τ CB + A τ F ϖ (CB) + π + μy (32) ) (v + ε (CB) ) τf μ A ϖ (CB). (33) In he appendix i is shown he expeced loss can be wrien as ( ( ) ) A E(L) = 2 + α μ +2A A α ][ ] 2 [ ] 2 σ2 v +(A τ F ) [+ 2 μ τ F + A 2 τ CB 2 τ CB. (34) +2A τ F 2A 2 τ CB + I is possible o evaluae how he overall loss depends on τ CB and τ CB as well as τ F and τ F. I is sraighforward o deduce ha E(L) τ CB < 0. Thus i is opimal for τ CB =. This is inuiive, as in his case he rue variance of he signal received by he cenral bank is 0. Furhermore, ( ) E(L) τcb =2A 2. τ CB τ CB The sign of his derivaive is ambiguous. As long as τ CB τ CB, he loss will be a decreasing funcion of τ CB. Thus if he cenral bank receives a signal on he innovaion ha is fully accurae, τ CB =,
21 Vol. 6 No. 3 Communicaion, Decision Making 2 i should undersand ha his is he case and use his signal as an esimae of he innovaion o he supply shock. I can easily be derived ha E(L) τ F < 0. The derivaive of he loss wih respec o τ F equals ( ( E(L) τ F =2A +A + )) > 0. τ F τ F μ Thus i is opimal for he cenral bank o provide perfec ransparency, σϖ,cb 2 = 0, wih regard o is informaion on he supply shock and herefore maximize τ F, which is decreasing in σϖ,cb 2. However, since he expeced loss is increasing in τ F, perceived ransparency should be minimal in order o maximize σ 2(CB) ϖ, and hus minimize τ F. These resuls are summarized in he following proposiion. Proposiion. When he commiee consiss of a single cenral banker and here is perfec common knowledge of cenral bank oupugap preferences, (i) i is opimal for he cenral banker o be perfecly ransparen abou is observaion on he innovaion o he supply shock, and (ii) ransparency abou he innovaion o he supply shock as perceived by he financial markes should be minimal. These resuls correspond o he resuls by Geraas (2007), who in conras o his paper uses a model wih no long-erm ineres rae and no uncerainy abou he supply shock by he cenral bank. As Geraas (2007) explains, he inuiion for his resul is as follows: Acual ransparency abou he innovaion o he supply shock reduces he noise of he public informaion on he supply shock and hus makes inflaion expecaions more sable, hereby reducing he variabiliy in he oupu gap and inflaion. Lower perceived ransparency, on he oher hand, reduces he response of privae-secor expecaions o he supply shock (as he less precise he signal is perceived o be, he less weigh i will be given). This will lead o a smaller variabiliy in inflaion, and hus he cenral bank needs o adjus he shor-erm nominal ineres rae by less o offse his
22 22 Inernaional Journal of Cenral Banking Sepember 200 increased variabiliy in inflaion, hereby muing he variabiliy of he oupu gap. 4.2 A Single Cenral Banker: Asymmeric Informaion abou Policy Preferences The bes esimaes of he innovaion o he supply shock by he cenral bank and he financial markes coninue o be given by (30) and (3), respecively. However, in conras o secion 4., financial markes now need o derive an opimal esimae of he level of he oupu-gap arge of he cenral bank, θ (CB), in order o form expecaions of inflaion and nominal shor-erm ineres raes. Using equaion (25), and assuming ha voing records are published for he firs ime in period, financial markes form he following esimae of he oupu-gap arge for period given heir prior z (CB) : θ (F,CB) σ 2 z =( τ ξ )z (CB) + τ ξ ξ (CB), where τ ξ = Thus, he more accurae he informaion σ z 2+Ṽar(ξ(CB) ). on he cenral bank s policy preference conained in voing records is perceived o be, he more weigh i will be given by he financial markes. When he perceived variance of he signal on he cenral bank s oupu-gap arge conained in voing records is 0, Ṽar(ξ(CB) )=0, hen τ ξ =, so ha he esimae of he oupu-gap arge in period will be equal o he signal conained in voing records in ha period. If, on he oher hand, Ṽar(ξ (CB) ), hen τ ξ 0, so ha he weigh given o he prior, z (CB), will urn o. Using equaions (7), (22), and (24), and aking ino accoun ha here is only a single cenral banker, he variance of he signal on policy preferences, ξ (CB), can be wrien as follows: Var ( ( ) ξ (CB) ) 2 [ ( (F ) = E v μ v )] (CB) 2. Using equaions (30) and (3), his expression can be simplified o Var ( ( ξ (CB) ) 2 [ τ = σv μ) 2 2 F + τ ] CB [ τ CB 2 τ F ], τ F τ CB
23 Vol. 6 No. 3 Communicaion, Decision Making 23 where he fac ha Var(ε (CB) ) = τ CB τ CB σv 2 and Var(ϖ (CB) ) = ( τ F τ CB )σv 2 was used. Inuiively, when τ F = τ CB and τ F = τ CB, he variance of he signal on policy preferences, Var(ξ (CB) ), is equal o 0. In his case, i follows from he definiions of τ F and τ CB in secion 4. ha σϖ,cb 2 = 0 and ha he cenral bank communicaes is signal on he innovaion o he supply shock wihou any noise. In addiion, since τ F = τ CB, he cenral bank and he privae secor aach he same weigh o heir observaions on he innovaion o he supply shock. Thus, he informaion on preferences conained in voing records is perfecly accurae in his case. Given he esimae of he oupu-gap arge, θ (F,CB), and he resuling privae-secor expecaions, inflaion and he oupu gap can be derived using equaions (), (3), (8), (27), (28), and (29). Simplifying he resuling expression and subsiuing using he definiions of secion 4., inflaion can be wrien as follows: π =(A A 2 +)αs +[A τ F A 2 τ CB +]v +[A τ F A 2 τ CB ]ε (CB) + A τ F ϖ (CB) + π + μa 2 θ (CB) + A 2 μ 2 θ (F,CB). (35) Similarly, he oupu gap will be given by ( ) ( ) (v y = μ A + A 2 αs μ A τ F + A 2 τ CB + ε (CB) ) τ F μ A ϖ (CB) [ (F,CB) μa 2 θ θ (CB)]. (36) As shown in he appendix, he expeced loss funcion can now be wrien as E(L asym )=E(L)+ [ ( μ τ 2 σ2 v τ ξ 2 2 F +μ μα 2 + τ ξ ( τ F τ CB ) +μ( α) ) [ τ CB 2 τ F ] τ CB ] + μ3 +μ ( τ ξ) 2 σz. 2 τ F + τ CB
24 24 Inernaional Journal of Cenral Banking Sepember 200 This is clearly decreasing in τ F, making acual ransparency again opimal. Inuiively, if he cenral bank communicaes is observaion on he innovaion o he supply shock wihou error, hen his improves he esimae of he supply shock of financial markes, making voing records a less noisy signal on he cenral bank s desired level of he oupu-gap arge. Because he sign of V ar(ξ (CB) ) τ F will depend on he sizes of τ F, τ CB, τ F, and τ CB,how welfare depends on τ F is ambiguous. When he voe is no communicaed o financial markes, financial markes will use heir prior on he oupu-gap arge of he cenral bank and hus τ ξ = 0. The expeced loss will hen equal E(L asym/nc )=E(L)+ μ3 +μ σ2 z. When voing records are no published, he findings of secion 4. apply, and hus he expeced loss is decreasing in τ F and increasing in τ F. Therefore, he cenral bank should be ransparen abou he supply shock and minimize σϖ,cb 2. However, since he expeced loss is increasing in τ F, perceived ransparency should be minimal. I is sraighforward o deduce ha if τ F = τ CB and τ F = τ CB, he expeced loss when voing records are published becomes E(L asym, τf = τ CB,τ F =τ CB )=E(L)+ μ3 +μ ( τ ξ) 2 σ 2 z. In his special case, publishing he voe is always preferable as long as σ 2 z > 0. If σ 2 z = 0, hen he variance of he prior on preferences is 0, and hus he expeced loss when voing records are published will be idenical o he expeced loss when hey are no published. From he above analysis i follows ha as long as he difference beween he perceived variance of he innovaion o he supply shock of he cenral bank and he financial markes is sufficienly small and he cenral bank is ransparen abou is view on he innovaion o he supply shock, publishing voing records will lead o a smaller expeced loss compared wih he case when voing records are no published. The following proposiion summarizes hese findings.
25 Vol. 6 No. 3 Communicaion, Decision Making 25 Proposiion 2. When he commiee consiss of a single cenral banker and here is imperfec common knowledge of he cenral banker s preferred level of he oupu gap, θ (CB), (i) i is opimal for he cenral banker o be perfecly ransparen abou is observaion on he innovaion o he supply shock; (ii) if voing records are no published, ransparency abou he innovaion o he supply shock as perceived by he financial markes should be minimal; and (iii) publishing voing records will always be beneficial if he cenral bank is perfecly ransparen and he cenral bank and he financial markes share he same perceived variance of he signal on he innovaion o he supply shock. 4.3 The Commiee Case: Perfec Common Knowledge of Policy Preferences An ineresing aspec of commiee decision making is o analyze how he commiee size influences welfare. One issue ha can be evaluaed is he average difference beween he ineres rae se by a commiee of size N under uncerainy abou he sae of he economy and he ineres rae se by he commiee if he supply shock were perfecly known. This is depiced in figure for u (j) N(0, 2 ). Figure assumes ha here is no communicaion by he commiee wih he financial markes, so ha financial marke expecaions are independen of he commiee size. The figure shows ha a larger commiee ses ineres raes under uncerainy closer o he level ha would be se if he supply shock were perfecly known. However, when here is imperfec knowledge abou he rue variances of observaions, hen a commiee of size N will se an ineres rae furher away from he opimal ineres rae han a commiee ha is no facing such imperfec knowledge. This is because when commiee members are uncerain abou he precision of members observaions on he innovaion o he supply shock, hey are no efficien a pooling hose differen informaion ses, resuling in a welfare loss compared wih he case when he underlying variances of signals are known. In his case he policy error is no converging oward 0. Figure also shows ha he marginal benefi of having a larger commiee is decreasing wih he number of
26 26 Inernaional Journal of Cenral Banking Sepember 200 Figure. Policy Errors under Differen Commiee Sizes Noes: This figure depics policy errors for differen commiee sizes, under boh uncerainy and perfec knowledge of he precision of signals. Perceived and rue variances are randomly drawn for σ 2 =(u (j) ) 2, where u (j) N(0, ). 2 E (i C i ) 2 denoes he average squared deviaion of he ineres rae se by he commiee under uncerainy abou he supply shock from he ineres rae se if here was no such uncerainy. members. Given ha coordinaion coss are likely o be increasing wih commiee size (Siber 2006), his may provide a parial explanaion for he empirical fac ha he size of commiees is limied (Ehrhar, Lehmen, and Vasquez-Paz 2007; Berger and Nisch 2008; Berger, Nisch, and Lybeck 2008). Whils real-world MPCs vary grealy in size ranging from hree members a he Swiss Naional Bank o weny-one a he European Cenral Bank Berger, Nisch, and Lybeck (2008) show ha he median size is around seven o nine members. I is possible o derive a general expression for he expeced loss in he commiee case. The opimal esimaes of he innovaion o he supply shock of commiee members and financial markes are given by (6) and (2). Thus τ CB and τ F can be wrien as
27 Vol. 6 No. 3 Communicaion, Decision Making 27 τ CB = σ 2 v σ 2 v + B CB, ΩCB B CB, and τ F = σ 2 v σ 2 v + B F, ΩF, B F,, where τ CB denoes he weigh given o he opimally combined observaions by he median member and τ CB and τ F are he signalexracion parameers in equaions (6) and (2). The more accurae he opimally combined signal, ṽ (CB), is perceived o be by he median member, and hus he smaller is B CB, ΩCB B CB,, he larger will be τ CB. The same is rue for he signal-exracion parameer of he financial markes, τ F. In addiion, define τ CB = σ 2 v σ 2 v + B CB, Ω B CB, and τ F = σ 2 v σ 2 v + B F, Ω F B F,. The parameers τ CB and τ F are similar o he signal-exracion parameers of equaions (6) and (2). However, heir size will depend on he rue underlying variance of he combined signals on he innovaion o he supply shock, B CB, Ω B CB, and B F, Ω F B F,, raher han he perceived variances. Therefore, τ CB will be decreasing in B CB, Ω B CB,. If BCB, Ω B CB, = 0, hen τ CB =. If B CB, Ω B CB,, τ CB 0. The same applies o τ F, which is decreasing in B F, Ω F B F,. The expeced loss under he commiee case is derived in he appendix, and i is shown ha he expression is equivalen o he expeced loss in he single cenral banker case, given by equaion (34). The only difference is ha τ CB is a funcion of all he perceived weighs given o commiee members by he median given o commiee members by he median policymaker. Similarly, τ F will be a funcion of he perceived weighs given by he public o he communicaion of each member. Thus, he loss is decreasing in τ F and τ CB and increasing in τ F. Furhermore, if τ CB τ CB, he expeced loss will be a decreasing funcion of τ CB. Therefore, all commiee members should be acually ransparen and communicae heir signals on he innovaion o he supply shock wihou error (hereby minimizing B F, Ω F B F, and maximizing τ F ) bu perceived
28 28 Inernaional Journal of Cenral Banking Sepember 200 ransparency should be minimized. 5 These heoreical findings are summarized in he following proposiion. Proposiion 3. When he oupu-gap arges of commiee members are idenical and known o he public bu here exiss uncerainy abou he precision of commiee members signals and communicaion, (i) acual ransparency abou commiee members observaions on he innovaion o he supply shock leads o lower variabiliy in boh inflaion and he oupu gap and hus greaer welfare, and (ii) ransparency as perceived by he financial markes should be minimal. The inuiion for hese resuls is as follows. When commiee members are perfecly ransparen abou heir observaions on he innovaion o he supply shock, his reduces he noise in he public informaion on he supply shock. I can be easily inferred from equaion (2) ha he variance of he public s esimae of he innovaion o he supply shock is a posiive funcion of he variance of he combined public signals, i.e., B F, Ω F B F,. The variance of his opimally combined signal is given by (47). This is minimized when σϖ,j 2 = 0 for j =, 2,...,N. When he noise in he public informaion on he supply shock is smaller, his makes inflaion expecaions more sable, hereby reducing he variabiliy of inflaion and he oupu gap. Lower perceived ransparency, on he oher hand, reduces he response of he privae-secor expecaions o he innovaion o he supply shock. This again direcly follows from equaion (2). The larger is σ 2(j) ϖ,, he smaller is τ F, which is he weigh given o ṽ F in (2). This will lead o a smaller variabiliy in inflaion, and hus he commiee needs o adjus he shor-erm nominal ineres rae by less, also muing he variabiliy of he oupu gap. In order o evaluae how he expeced loss depends on he commiee size, i needs o be invesigaed how τ F, τ CB, τ F, and τ CB vary 5 The fac ha B F,Ω F B F, is minimized for σ 2 ϖ,j = 0 where j =, 2,...,N direcly follows from (47). Similarly, from expression (48) i can be deduced ha B F, ΩF, B F, is increasing in σ 2(j) ϖ,.
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