A joint Initiative of Ludwig-Maximilians-Universität and Ifo Institute for Economic Research COMMON MONETARY POLICY WITH ASYMMETRIC SHOCKS

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1 A jont Intatve of Ludwg-Maxmlans-Unverstät and Ifo Insttute for Economc Research Workng Papers COMMO MOEARY POLICY WIH ASYMMERIC SHOCKS Danel Gros Carsten Hefeker* CESfo Workng Paper o. 705 (6) Aprl 00 Category 6: Monetary Polcy and Internatonal Fnance Presented at CESfo Area Conference on Macro, Money and Internatonal Fnance, February 00 CESfo Center for Economc Studes & Ifo Insttute for Economc Research Poschngerstr. 5, Munch, Germany Phone: +49 (89) Fax: +49 (89) e-mal: offce@cesfo.de ISS An electronc verson of the paper may be downloaded from the SSR webste: from the CESfo webste: * We thank Ka Konrad for helpful comments.

2 CESfo Workng Paper o. 705 Aprl 00 COMMO MOEARY POLICY WIH ASYMMERIC SHOCKS Abstract What polcy objectve should a common central bank n a heterogeneous monetary unon pursue? Should t base ts decsons on the EU-wde average of nflaton and growth or should t nstead focus on (approprately weghted) natonal welfare losses based on natonal rates of nflaton and growth? We fnd that a central bank that mnmses the sum of natonal welfare losses reacts less to common shocks. hs can lead to hgher average unon-wde expected welfare f the varablty of common shocks s large relatve to the nflaton bas and f dosyncratc demand shocks n the non-tradables sector are not too hgh. JEL Classfcaton: E5, E61, F33. Keywords: monetary polcy, monetary unon, transmsson mechansm. Danel Gros Centre for European Polcy Studes Place du Congrès 1 B-1000 Brussels Belgum Carsten Hefeker HWWA-Insttute of Internatonal Economcs euer Jungfernsteg Hamburg Germany Carsten.Hefeker@hwwa.de

3 1. Introducton he common monetary area n Europe reveals sgnfcant dfferences among ts member states n nflaton and growth, as Fgure 1 documents. Should the EU's monetary authorty, the European Central Bank (ECB), react to these dvergences? he standard answer s no and the ECB s held responsble only for the average performance of the entre euro zone. hs, at least, s the offcal mandate and poston of the ECB. However, as n some countres the performance starts to dverge consderably from the average ths answer s not satsfactory. It s not satsfactory because t does not take nto account that the EU was created to serve the nterests of ts member states, whch reman the basc poltcal unts n Europe. hs dstngushes the euro area from naton states, even very federally organsed ones, n whch the man poltcal unt concdes wth the monetary unon. Countres whose performance dverges a lot from the average are not served approprately by a one sze fts all polcy f the welfare loss s a convex functon of the output gap and nflaton, as s usually assumed. he average welfare loss of member states ncreases as the standard devatons of output and nflaton ncrease. But n a monetary unon t s mpossble to have a natonally dfferentated monetary polcy. One s thus tempted to conclude that the ECB mght bemoan natonal dvergences wthn the euro area, but that there s nothng t could or should do about them. hs concluson s, however, rash f one admts that monetary polcy, at least n the short run, can have output effects. Referrng to the current problems the queston s thus whether the nflaton rate of, say, Ireland should be consdered just as one element n the calculaton of the average area-wde nflaton rate or whether one should consder the hgh welfare losses t causes n Ireland separately. he stuaton n that partcular country would presumably affect decsons by the ECB much more under the second approach. What should the ECB do? Should t base ts decsons on the area-wde averages of nflaton and growth, or should t attempt to mnmse the (weghted) average of natonal welfare losses resultng from natonal nflaton and growth rates? We am to provde a frst step towards an answer by showng to what extend these two choces would lead to dfferent polces even n a world where the preferences regardng nflaton and unemployment are dentcal, but where there are dfferences n the monetary transton mechansm. 1

4 Fgure 1: CPI-Inflaton and Unemployment for EU Unemployment CPI In order to focus on ths ssue, we consder the ECB as a homogeneous body where all members of the governng body have the same objectve. hs s n contrast to recent work that focussed on the mpact natonally orented polcy makers wthn the ECB board have on the common monetary polcy n the Euro-area (Aksoy, de Grauwe and Dewachter 001; Berger and de Haan 001). However, we consder two dfferent objectve functons namely the mnmsaton of a smple euro-area wde objectve functon and the mnmsaton of a weghted sum of natonal welfare losses. Smlar approaches have been chosen before by De Grauwe (000) and Gros and Hefeker (00). We extend on the prevous work and are able to provde a closed soluton nstead of usng smulaton analyss for our welfare analyss. Moreover, we explctly consder the cause of dvergent rates of nflaton wthn the member countres, even f the rate of nflaton s the same throughout the area for traded goods. We ntroduce a non-tradable goods producng sector whch mples that hgher growth rates lead to hgher rates of

5 nflaton. hs s the short-run equvalent of the so-called Balassa-Samuelson effect (for emprcal evdence see De Grauwe and Skudelny 000; MacDonald and Rcc 001). 1 he remander s organsed as follows: he next secton presents the model used for the analyss. We use a standard Barro-Gordon model because we want to draw attenton to a general pont that arses n a standard model, namely that there s a dfference between area-wde welfare based on the (weghted) area-wde averages of natonal performances and the average area-wde welfare based on (also weghted) natonal welfare, whch arses n the standard approach but has been neglected so far. Secton 3 calculates the polcy resultng under both choces (n the form of reacton functons), whle secton 4 draws welfare conclusons. Secton 5 concludes.. he atonal Economy Consder the followng generalsed model. We consder an economy that produces two composte goods, a non-tradable good (ndexed ) and a tradable good (ndexed ). In both sectors producton s wth a Cobb-Douglas technology (where the captal stock s normalsed to one). 3 hen, output n the non-tradables sector s Y P = W so that output s declnng n real wages, where W s the economy-wde wage n country. E s a country and sector specfc supply shock. Lkewse, output n the tradables sector s Y P = W where Ξ s a supply shock to the tradables sector that affects all economes n the monetary unon n the same way. Arbtrage ensures that prces for traded goods are equalsed across the unon. Ε Ξ 1 hs s a standard phenomenon: as overall demand ncreases the demand for non-tradable goods ncreases as well. But gven that supply of non-tradables s less elastc (than that of tradables) ther relatve prce has to ncrease. he general prncple that takng country specfc effects nto account may be welfare ncreasng wll survve n more elaborate set ups as well. 3 For a dervaton such of a model, see Adran and Gros (1999). 3

6 otal output n economy s a weghted product of output n the two sectors: ( ) ( ) ( ) Y = Y Y 1 β β. he prce level n the economy s also a weghted product of the prce levels n the two sectors ( ) ( ) ( ) P = P P 1 β β, where β s the country specfc share of non-tradables n the economy's producton,.e. the sze of the non-tradables sector. Fnally, the market clearng condton n the non-tradables sector requres that the value of total output n the non-tradables sector equal the demand for non-tradabels n country, a functon of total output (or ncome): P Y = β P Y Φ where Φ s a sector and country specfc demand shock. It captures the nfluence of hgher ncome growth n some of the member states. We have used the same weght β n both producton and demand for non-tradables to ensure that n the absence of shocks the equlbrum mples a relatve prce of tradables to non-tradables of one. Wth Cobb-Douglas preferences the demand for non-tradables s a constant. We assume that labour s moble between sectors so that wages n the two sectors are equal. hey are set at the begnnng of the perod and fxed for the rest of the perod. Unons wsh to stablse current employment, so they wll set wages equal to the expected prce change e W = P P, t+ 1, t+ 1, t. Log-lnearsng, and transformng nto rates of changes, the above equatons and suppressng tme subscrpts, we can rewrte the system as (wth lower case letters denotng logarthms) ( ) y = p w + ε (1) ( ) y = p w + ξ () ( ) y = 1 β y + β y (3) 4

7 ( ) p π = 1 β p + β p (4) p + y = p + y + φ (5) e e w = ln p ln p π (6) where we have set, wthout loss of generalty, the constant ln β = 0. All shocks have an expected value of zero and a constant and equal varance of of them s assumed to be zero. σ ξ, σ ε and σ φ. he covarance between any two It s straghtforward to solve ths system. Frst use (1) and () n (5) and the result n (4) to get π = + +. (7) p x z β where x = + b g 1 ξ ε measures the relatve mportance of the shock to the tradables sector 1 β weghted by the sze of the non-tradables sector. z = φ measures the demand shock, 1 β 1+ agan weghted wth the relatve sze of that sector. In addton, the effectveness of monetary polcy plays a role because t determnes how much of an actve monetary polcy s needed to address shocks. otal output n the economy s obtaned by usng (1), () and (7) n (3) y = p w + z + ξ x c h. (8) As a bass for the evaluaton of the alternatve polcy regmes ntroduce socal welfare functons for t 1 each country. he natonal preferences are formulated as a loss functon Λ E t δ L, where L = 1 M L, t s the per perod loss functon of the monetary authorty, and δ s the common dscount factor. Because all perods are ex-ante dentcal we drop the tme ndex. he perod loss functon s specfed as t= 1 t O QP L = c y k + π, (9) 5

8 where c s the relatve weght country places on employment n comparson to nflaton π. k measures the output target n country. If output s below the target output, ths s usually due to dstortons n the labour market or dstortve taxaton (see Barro and Gordon 1983). axaton dstorts supply of and demand for labour servces, dependng on what taxes are charged. Also, strong labour unons may use ther power to push wages above the market clearng level. If labour unons are charactersed by a separaton nto nsders and outsders, the former wll set wages too hgh for full employment. ormalsng (the log of) natural output to zero, k > 0 measures the sze of ths dstorton. otce that equaton (9) s meant to apply to natonal governments, as well as to the common central bank. It s also used as the bass for the welfare comparson below. We therefore abstract from any problems of delegaton and dfferences n preferences that has been the focus of much of the lterature on central bank polcy. 3. Monetary Polcy We now proceed to calculate the optmal monetary polcy under two dfferent assumptons about the objectve of the ECB. It could ether mnmse the (weghted ) average of natonal losses, or alternatvely mnmse the loss functon calculated at the euro area level, usng the (weghted) averages of natonal nflaton rates and output gaps as nput. he frst case could represent the case where natonal representatves determne monetary polcy. Assumng that they only care for ther natonal developments, each of them would look at natonal welfare losses. Smply summng up these objectve functons would yeld such a polcy, where t has been assumed that the weght of any sngle country can dffer accordng to ts economc mportance. In addton, ths would correspond to a weghted welfare functon a la Bentham. he second case would be the case where the ECB board adopts a truly European perspectve by lookng only at EMU wde averages. hs, n contrast to the frst approach s what the ECB s expected to do accordng to ts statutes. 6

9 3.1. Mnmsng natonal welfare losses he unon's monetary authorty maxmses the weghted average of natonal utltes (ndexed ). hs leads to the followng programme: Mnmse LECB = µ c b y k g + π, (10) where the relatve weght of country s µ, wth µ = 1. otce that the ECB's nstrument p s not, as usually assumed, the rate of nflaton but the rate of nflaton (prce change) n the tradables sector because the ECB cannot drectly address the dfferent prce levels n the non-tradables sector of member countres. he common area wde rate of nflaton n tradable prces s equvalent to the weghted average of overall CPI. Inflaton wll dffer across countres only due to unequal demand (or productvty) developments n the G sector, whch we assume to cancel out on average. hs s ensured by the fact that all country specfc shocks cancel n the European aggregate,.e. µ x = x = 0 and µ z = z = 0, where a bar over a varable denotes ts weghted average. By constructon, any common component of asymmetrc shocks s contaned n the common shock. Usng equatons (7) and (8) n (10) the frst order condton s L p e [ c ( ( p π ) + z + ξ x k ) + ( p + x + z )] 0 ECB = µ = leadng to expectatons about nflaton that are equal across all countres as follows from (7) snce all e e shocks have an expected value of zero. hus π = π = c µ k. Usng ths n the above equaton and collectng terms, we have the monetary polcy of the ECB as 1 p = c µ k c c z c x + + d ξ µ µ. 1 c µ (11) 7

10 3.. Mnmsng average welfare losses Alternatvely the ECB mght base ts decson on an area wde utlty functon that uses the averages of natonal output and nflaton (ndexed A). Its problem then becomes A Mnmse L = µ y k + µ π ECB b g. (1) Usng weghted averages of varables n ths expresson and equatons (7) and (8) n (1), the frst order condton s A L p ECB c h 0. e = c p π + ξ + µ z k + p = e e Ratonal expectatons n the prvate sector mply π = π = ck. Usng ths n the above equaton and collectng terms, we have the monetary polcy of the ECB as p c = ck 1+ c ( ξ + µ z ) (13) 3.3. Comparng rates of nflaton o compare the polcy choces of the ECB board under the two alternatve regmes, we frst have to derve the rates of nflaton from the prce ncreases n the tradables sector. From (7) and (11) we can calculate the unon wde rate of nflaton as π = µ π = µ p,.e. t has the same value as (11) f we take nto account that average dosyncratc shocks are zero. By the same logc the rate of nflaton n the "average regme" π A s as n (13). For a drect comparson of the two rates of nflaton, t s convenent to rewrte expresson (11) wth the help of the followng defntons: otce that µ m, m m = θ + where m =k, x, z and where θ m, s the correlaton between varables m and. Defne θ m, = µ m m d d and 8

11 multply t out to confrm the result. Further, we defne the dsperson of the 's as θ = µ ( ) and have µ = θ +. Usng these result we can rewrte (11) as π = c ( θ + k),k 1+ c 1 ( θ + ) ( cξ + c µ z c( θ + x ), x Snce x = 0, the last term on the RHS of ths expresson vanshes. he last but one term on the RHS also vanshes f we assume that the correlaton between the shocks x and the transmsson of monetary polcy s zero. In fact, gven that the shocks have expected value of zero, there s lttle reason to expect that there s a any relaton between economc shocks and the transmsson of monetary polcy. We therefore set θ 0., x = However, as argued n Gros and Hefeker (00), ths reasonng does not apply to the correlaton between structural dstortons and the transmsson of monetary polcy. he effectveness of monetary polcy s lkely to depend on structural characterstcs of an economy and vce versa; hence the term s not necessarly zero. In an explct model of optmsng wage settng behavour of labour unons (that gve rse to k) t can be shown that t s lkely to be negatvely related to (Gros and Hefeker 00). 4 Wth these assumptons (14) smplfes to θ, k π = c ( ) µ z θ + Ω ξ +,k k (14) where = c /( 1+ c( θ + ) Ω. Usng our defntons the rate of nflaton under averagng (13) becomes 4 A smlar story could be told by assumng that hgh dstortons k are lkely to be related to a hgh degree of wage ndexaton whch mply a low value of. 9

12 π A 1 = ck 1 + c ( cξ + c( θ + z ), z Agan, ths smplfes further by notcng that z = 0 and assumng that the correlaton between the transmsson of monetary polcy and any dosyncratc demand shocks z s zero as well. hen (15) collapses nto π A A = c k Ω ξ (15) A wth = c /( 1+ c ) A Ω and thus Ω < Ω. Obvously, the next step s to compare the rates of nflaton that the two alternatve objectve functons for the ECB would produce. hs dfference s π π A ( ξ cθ µ z ( 1 + c ) c = c θ,k + (16) ω wth = ( 1 + c )( 1 + c( θ + ) ω. he comparson shows that the "natonal regme" wll produce a lower rate of nflaton f the correlaton between the dstortons and the transmsson of monetary polcy s negatve (as s lkely to be the case) and f the weghted sum of the demand shocks s large. In both cases the central bank wll set a more restrctve monetary polcy because t takes the negatve correlaton nto account and stablses demand shocks by restrctng monetary polcy. Only the common exogenous shock would push up the rate of nflaton n ths regme. It s obvously mportant that θ, k s non-zero for the rates of nflaton to be dfferent under the two regmes. One can ths be explaned? he ntuton behnd the result that the rate of nflaton s hgher 10

13 under the natonal welfare maxmsng monetary regme--f there s a postve relaton between the effectveness of monetary polcy and labour market dstortons--s the followng: he more effectve monetary polcy s (a hgh ) the lower the margnal costs of usng monetary polcy. If n ths stuaton, dstortons (k) are also hgh, the central bank has a hgher ncentve to use actve monetary polcy. hs problem s magnfed by the fact that the central bank cares for natonal welfare nstead of averages. In ths case, countres wth a hgh level of dstortons are strongly taken nto account. Gven that ths s known to ratonal prvate agents, the expected rate of nflaton ncreases, hence a hgher nflaton bas results. If, on the other hand, and k are negatvely related, the result s reversed and the nflaton bas s lower he mportance of dfferences n the transmsson mechansm It bears notng that dfferences n the transmsson mechansm are the only factor that drves dfferences n the polcy choce n the two regmes. Settng the transmsson mechansm n the countres equal ( = ), one notces that the dfference between the two rates of nflaton dsappears rrespectve of the decson makng system n the ECB. hs can be seen by settng = n equaton (14). In ths case, the constant can be put before the summaton sgn and thus the two expresson become smlar. Hence, we can establsh that the only factor that really matters are dfferences n the transmsson mechansm, and that demand shocks do not play a role n the decson makng mechansm of the central bank. Regardless of the partcular objectve functon of the central bank, they wll be taken care of n the same way. As dfferences n the transmsson mechansm play a key role n our results, the queston thus arses how mportant these are n realty. he lterature on ths pont s dffcult to nterpret because the underlyng queston has usually been dfferent from ours. Some mantan the dfferences n the transmsson mechansm are so large that they wll make the operaton of EMU dffcult (Cecchett 1999). Others argue that these dfferences are due to dfferences n fnancal structures, whch wll dmnsh over tme as countres share a common monetary polcy (Dornbusch, Favero and Gavazz 1998). Most emprcal studes concur, however, that at present there are stll large dfferences n the 11

14 transmsson mechansm, although they are dffcult to estmate precsely (see e.g. Boro 1995, Gerlach and Smets 1995, Ejffnger and de Haan 000, oolsema, Sturm and de Haan 001). able 1 reports the estmates from Cecchett (1999) whch suggest that the dfferences n the output multpler are consderable. he hghest coeffcent s over 3 tmes larger than the lowest. here s thus some evdence that dfferences n the transmsson mechansms are large. able 1: ransmsson of Monetary Polcy Country Impact on Output of a 1-Percent Increase n Interest Rates (absolute changes) EMU-Members Belgum 0.7 France 1.30 Germany 1.1 Ireland 0.76 Italy 0.64 Portugal 0.39 Span 0.46 EMU-onmembers Denmark 0.48 Sweden 0.56 Unted Kngdom 0.53 Source: Cecchett A welfare comparson 4.1 Indvdual countres Havng derved the dfference n nflaton and n the stablsaton of shocks under the two alternatve objectve functons for the common central bank, t remans to be seen what welfare mplcatons ths would have. Gven that the comparson of welfare under the alternatve regme should be done on an ex-ante A bass, we concentrate on expected welfare losses and summarse them as L = E L E L. We 1

15 start wth an evaluaton of the welfare dfference for a sngle country. Usng the rates of nflaton n the loss functon, we get L = A ( 1+ c ) ( Ω Ω ) σ ξ + Ω { θ },k + c ( + k) ( k ) θ + σ z (17) It s not a pror clear f the ndvdual country profts more from a natonal or an average regme. Gven that Ω A < Ω the frst term n curly brackets s negatve. hus the larger s the varance of the common shock the more the country profts from the natonal regme. he reason s that the natonal regme takes the larger varety of transmsson mechansm more nto account than the smple averagng does. hs s benefcal for country. On the other hand, the larger the varance of the weghted sum of the dosyncratc demand shocks s, the more the country would beneft from the averagng regme because then the monetary polcy would not react at all to demand shocks, gven that they cancel on average. Fnally, the larger the negatve correlaton between dstortons and transmsson of monetary polcy, the more attractve s the natonal regme. hus, f demand shocks are not too mportant, ndvdual countres are clearly better off f the common central bank follows a natonal regme. One mmedately sees that the natonal regme becomes less attractve f the varance of the demand shocks ncreases, L > 0, whch s due to the fact that n the alternatve regme these shocks σ z dsappear wth aggregaton. In the natonal regme they are responded to and ths affects ndvdual countres negatvely as monetary polcy reacts to the dosyncratc shocks n the other member states. However, the attractveness of the natonal regme ncreases f the (negatve) correlaton between L dstortons and transmsson becomes larger snce > 0 whch s due to the reasons dscussed above. θ,k Also, L < 0 so that a hgher varance of the common shock makes the natonal regme more σ ξ 13

16 attractve as Ω A < Ω. Agan, ths s due to the fact that n the natonal regme the dvergence n the transmsson of monetary polcy s taken nto account. Overall, and not surprsngly, the transmsson of monetary polcy s the crucal factor decdng on the relatve merts of each of the two regmes. o see n whch way, dsregard the second expresson n A (17) and set θ 0 for smplcty. If 0 the expresson s clearly negatve because Ω < Ω., k = hus, f monetary polcy s not effectve at all, the country s better off under the natonal regme. As monetary polcy s less actve under ths regme ths must be better for a country that does not beneft from monetary polcy. Otherwse nflaton varablty would ncrease wthout provdng any beneft at all for country. A If, on the other hand, L s a functon of ( Ω ) Ω σ θ + + Ω σ ξ z only. hus, the natonal regme s more attractve, L <0, f the varance of the common shocks s suffcently larger than the varance of the demand shocks. If, on the other hand the demand shocks are more mportant, the averagng regme s more attractve for a country wth a super-effectve monetary polcy. 4.. Average welfare n the monetary unon akng fnally the expected welfare comparson for the entre unon, L = L, we get L = A ( 1+ c ) ( Ω Ω ) σ ξ + Ω + c ( + k) ( k ) θ { θ },k + σ z (18) whch, lke above, shows the nfluence of the sze of the common shocks, whch would suggest the natonal regme, and the varance of the demand shock whch would suggest the average regme. In addton, we have the dfference between the tme consstency problem and the response to the shocks. Gven that Ω A < Ω, t s lkely that the overall expresson s negatve and that thus the countres wthn 14

17 the monetary unon would, on average, beneft f the ECB followed a natonal rather than an average polcy regme. 5. Concluson We have found that t makes a dfference whether the central bank of a monetary unon bases ts decsons on the average values of nflaton and employment for the entre area, or whether t recognses that dfferences n natonal performance can lead potentally to large dfferences n natonal welfare and therefore tres to mnmse the average of natonal welfare. If t mnmses the (weghted) average of natonal welfare t wll clearly stablse less than a central bank concerned wth unon wde developments would do. It mght, on the other hand, also produce a hgher nflaton bas, dependng on the relaton between the transmsson mechansm and the dstortons n member countres. Gven that such a central bank stablses common shocks less, member countres gan more f the varance of common shocks ncreases. hs s because the central bank takes nto account that stablsaton mght be too strong for some countres. he reason for the somewhat counterntutve result s that less stablsaton mght actually be welfare ncreasng. A result whch s usually not taken suffcently nto account when dscussng the decson makng of the ECB s that t becomes unmportant whch mechansm the ECB uses once the transmsson of monetary polcy s equal wthn the member states. he emprcal evdence that at present there are stll large dfferences suggests that t s far from rrelevant on what aggregaton procedure the ECB bases ts polcy decson. here mght, at the present, be thus large potental welfare mplcaton from a shft to another objectve functon. On the other hand, one mght expect that wth a common monetary polcy the dfferences n the transmsson mechansm mght be reduced over tme. At present however, and n partcular wth a vew on the upcomng enlargement not only of the EU but also of the EMU, the ECB should reconsder ts decson mechansm. he problem that we have ponted out here mght lose ts mportance for the current members of EMU over tme but wth the enlargement t s lkely to regan force. One can reasonably expect that newcomers to the EMU wll show consderable dfferences n ther transmsson of monetary polcy n comparson to the older members. hus agreeng on the 15

18 approprate decson makng process n the ECB upon ts enlargement should not only take nto account that too many members wll make t more dffcult to reach decsons (Buter and Grafe 00). It s also mportant that natonal asymmetres be taken nto consderaton. hs, however, rases a queston that we have not answered n ths paper. How could one desgn a mechansm and ensure that t s mplemented that pays more attenton the natonal developments than the current averagng does? 16

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20 oolsema, Lnda, Jan-Egbert Sturm and Jacob de Haan (001) "Convergence of Monetary ransmsson n EMU. ew Evdence", CESfo Workng Paper