W. E. P. Würzburg Economic Papers. No. 34. The BMW model: a new framework for teaching monetary macroeconomics in closed and open economies

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1 W. E. P. Wüzbug Economic Papes No. 34 The BMW moel: a new famewok fo teaching moneta macoeconomics in close an open economies Pete Bofinge, Eic Mae, Timo Wollmeshäuse, Olive Hülsewig an Robet Schmit Jul 22 Univesität Wüzbug Lehstuhl fü Volkswitschaftslehe, Gel un intenationale Witschaftsbeziehungen Saneing 2, D-977 Wüzbug pete.bofinge@mail.uni-wuezbug.e Tel.: +49/93/3-2945

2 The BMW moel: a new famewok fo teaching moneta macoeconomics in close an open economies Pete Bofinge, Eic Mae, Timo Wollmeshäuse, Olive Hülsewig an Robet Schmit Jul 22 Abstact While the IS/LM-AS/AD moel is still the cental tool of macoeconomic teaching in most macoeconomic textbooks, it has been citicise b seveal economists. Colane [995] has emonstate that the famewok is logicall inconsistent, Rome [2] has shown that it is unable to eal with a moneta polic that uses the inteest ate as its opeating taget, Walsh [2] has citicise that it is not well suite fo an analsis of inflation tageting. In ou pape we stat with a shot iscussion of the main flaws of the IS/LM-AS/AD moel. We pesent the BMW moel as an altenative famewok, which evelops the Rome appoach into a ve simple, but compehensive macoeconomic moel. In spite of its simplicit it can eal with issues like inflation tageting, moneta polic ules, an cental bank ceibilit. We exten the moel to an open-econom vesion as a poweful altenative to the IS/LM-base Munell- Fleming (MF) moel. The main avantage of the open-econom BMW moel is its abilit to iscuss the ole of inflation an the etemination of flexible exchange ates while the MF moel is base on fixe pices an constant exchange ates. JEL classification: A 2, E, E 5, F 4 Kewos: moneta polic, inflation tageting, optimal inteest ate ules, simple ules, IS/LM, Munell-Fleming iii

3 Contents Intouction... 2 Fou main flaws of the IS/LM-AS/AD moel... 3 The BMW moel fo the close econom Its main builing blocs An analsis of eman an suppl shocks une full iscetion Inflation tageting: moneta polic guie b of a loss function The Talo ule: moneta polic guie b a simple ule The BMW moel fo an analsis of moneta polic in an open econom Moifications in the basic builing blocs Thee vaiants of inepenentl floating exchange ates Moneta polic une flexible ates if PPP an UIP hol simultaneousl (long-tem scenaio) Moneta polic une flexible ates if UIP hols but not PPP (shot-un scenaio) Moneta polic une exchange ates that behave like a anom walk Moneta polic une fixe exchange ates Fixe exchange ates as a estabilising polic ule The impact of eman an suppl shocks Fixe ates can also be stabilising Summa an compaison with the esults of the Munell-Fleming (MF) moel Summa...34 Refeence List...35 iv

4 Intouction While the IS/LM-AS/AD moel is still the cental tool of macoeconomic teaching in most macoeconomic textbooks, it has been citicise b seveal economists. Colane [995] has emonstate that the famewok is logicall inconsistent, Rome [2] has shown that it is unable to eal with a moneta polic that uses the inteest ate as its opeating taget, Walsh [2] has citicise that it is not well suite fo an analsis of inflation tageting. In ou pape we stat with a shot iscussion of the main flaws of the IS/LM-AS/AD moel. In section 3 we pesent the BMW moel as an altenative famewok, which evelops the Rome appoach into a ve simple, but compehensive macoeconomic moel. In spite of its simplicit it can eal with issues like inflation tageting, moneta polic ules, an cental bank ceibilit. In section 4 we exten the moel to an open-econom vesion as a poweful altenative to the IS/LM-base Munell-Fleming (MF) moel. The main avantage of the open-econom BMW moel is its abilit to iscuss the ole of inflation an the etemination of flexible exchange ates while the MF moel is base on fixe pices an constant exchange ates. 2 Fou main flaws of the IS/LM-AS/AD moel The stana vesion of the IS/LM-AS/AD moel suffes fom seveal seious flaws, which we will iscuss in the following. As Colane [995] has shown, it suffes fom an inconsistent explanation of aggegate suppl. The moel is esigne fo a moneta polic that tagets the mone suppl. Thus, as emphasise b Rome [2], it is unable to cope with eal wol moneta polic, which is conucte in the fom of inteest ate tageting. As pointe out b Walsh [2], the moel has nothing to sa about the inflation ate. As a consequence, the expectations augmente Phillips cuve is not an integal pat of the moel. Futhemoe, the moel cannot eal with moen concepts such as inflation tageting, ceibilit, moneta polic ules an loss functions. Its open econom vesion (Munell-Fleming moel) is unable to eal with flexible pices an exchange ate paths. This implies that it cannot aequatel cope with the two basic theoies of open econom moneta polic, i.e. uncovee inteest pait theo an puchasing powe pait theo.

5 The fist flaw has been fomulate b Colane [995] as follows: Given that the Kenesian moel inclues assumptions about suppl, one cannot logicall a anothe suppl analsis to the moel unless that othe suppl analsis is consistent with the Kenesian moel assumption about suppl. The AS cuve use in the stana AS/AD moel is not; thus the moel is logicall inconsistent. (ibi., p. 76) Chat : The classical IS/LM-AS/AD moel i IS-cuve M LM P M LM P i i P Y Y i () () i Y P P AD Y Y F AD Y This agument can be emonstate with the help of a simple gaphical analsis. It stats with a slightl iffeent appoach to the IS cuve. As this cuve is the locus whee aggegate eman an aggegate suppl ae ientical, we can make both cuves explicit. Fist, we aw an aggegate eman cuve that epens negativel on the nominal inteest ate (uppe panel of Chat ). The aggegate suppl can be eive une the assumption that thee is a full emploment output which is etemine in a neoclassical labou maket (Y F ). Fom the logic of Kenesian economics the aggegate suppl is etemine b aggegate eman as long as it is 2

6 below Y F. This leas to an aggegate suppl cuve which is ientical with the aggegate eman cuve an which becomes vetical at Y F. In the lowe panel we have epicte the AS/AD moel i.e. a classical aggegate suppl cuve which has been eive in the same wa as Y F an a tpical aggegate eman cuve. The inconsistenc is obvious fo negative eman shocks, which shift both aggegate eman cuves to the left. The main message of the IS/LM-AS/AD moel is now that this shock leas to a fall of the pice level, which is cause b an excess suppl (Y F > Y ) at the ol pice level P. But this effect on the pice level is onl possible if the fims ae actuall suppling the full emploment output (Y F ). Accoing to the logic of the IS cuve the woul simpl ajust thei suppl to the given eman Y so that the pice level woul emain constant. Thus, the whole explanation of the pice level povie b the IS/LM-AS/AD moel ests on inconsistenc between a Kenesian etemination of eman in the IS/LM plane an a neoclassical etemination in the AS/AD plane. The secon main flaw of the IS/LM-AS/AD moel concens its appoach to the implementation of moneta polic. As Rome [2] has shown the LM cuve is eive une the assumption that the cental bank uses the moneta base as its opeating taget. With a constant multiplie this is automaticall tanslate into a tageting of the mone suppl. This appoach is not compatible with actual pactice of cental banks using a shot-tem inteest ate (o a set of shottem ates) as opeating taget. An aitional shot-coming of the stana eivation of the LM is the fact that the mone suppl pocess is iscusse in a completel mechanistic wa which oes not take into account the elevant inteest ates (cental bank efinancing ate an loan ate of banks); a pice-theoetic appoach is pesente in Bofinge [2]. Fo teaching puposes the LM cuve has the main isavantage that it can sa nothing about the impact of changes in the official inteest ates (the Feeal Funs Rate o the ECB s Repo Rate) on the econom. In aition, epesenting moneta polic b the LM cuve equies that one uses a nominal inteest ate. While the nominal inteest ate is the elevant oppotunit cost of holing non-inteest beaing mone aggegate eman epens on the eal inteest ate. In oe to make the two ates compatible the IS/LM-moel has to assume that the inflation ate is zeo an hence, that pices ae constant. 3

7 This leas to the thi flaw of the IS/LM-AS/AD moel. Due to its moelling of moneta polic via the LM cuve, its analsis is limite to one-time changes in the pice level. Thus, it can sa nothing about the etemination of the inflation ate although this vaiable is much moe elevant in the public ebate than changes in the pice level. As mentione b Rome [2], a ecline in the pice level, which is the consequence of a negative eman shock in the IS/LM-AS/AD moel has been ael encountee in the post-wa peio. Howeve, a ecline in the inflation ate is something ve common. As a consequence of its focus on the pice level, the IS/LM- AS/AD moel is also not able to integate the stana expectations-augmente Phillips cuve. Thus, the common textbook poceue is the pesentation of an aggegate suppl cuve base on pice levels an one o seveal chaptes late a sepaate pesentation of the Phillips cuve base on the inflation ate. 2 We will also see that this appoach is esponsible fo the inconsistent eivation of aggegate suppl. Because of its inabilit to inclue the inflation ate, the IS/LM- AS/AD moel is unable to iscuss new concepts such as inflation tageting, moneta polic ules, an loss functions which ae all base on the inflation ate. In the open-econom vesion (MF moel) the moelling of moneta polic in the fom of the LM cuve is even moe limiting. As a fix-pice moel the MF moel is unable to analse the etemination of the pice level in an open econom. Thus, it cannot be use fo an analsis of suppl shocks. In aition, as the moel is onl focussing on one-time changes in the level of the exchange ate, its iscussion of flexible ates is ve limite. Above all, the coe concepts of exchange ate theo, the uncovee inteest pait theo an the puchasing powe theo, ae not use fo a etemination of the flexible exchange ate. 3 The BMW moel fo the close econom 3. Its main builing blocs The close-econom vesion of the BMW moel consists of fou builing blocs: an aggegate eman equation, an aggegate suppl equation, an inteest ate equation, an a Phillips cuve equation. McCallum [989] pesente a moel which ties to eal with these two appoaches une a positive inflation ate. Howeve, it is much too complicate fo intoucto puposes. 4

8 Aggegate eman, which is pesente, in the fom of the output gap () epens on autonomous eman components (a), negativel on the eal inteest ate an a eman shock (ε ): () D = a b + ε. As Chat 2 shows, this appoach is ve much in line with Rome [2]. Chat 2: The aggegate eman cuve MP( ) () We assume fo ou shot-un analsis that aggegate suppl is etemine b aggegate eman an that thee ae no capacit constaints: (2) S = D =. Fo the sake of simplicit we o not iffeentiate between S an D in the following. As a thi builing bloc we assume fo moneta polic that the cental bank is able to etemine a eal inteest ate. In the most simplest vesion we assume that the cental bank ecies on inteest ates on a iscetiona basis: (3) =. 2 See fo instance Blancha [2], Abel an Benanke [2]. 5

9 In Chat 2 this is epicte as a hoizontal inteest ate line (MP). As the cental bank contols the nominal inteest ate on the mone maket, it etemines the equie nominal ate b aing inflation to the eal inteest ate: (4) i = +π. The fouth builing bloc is the expectations-augmente Phillips cuve (Chat 3) which we moel in a simila wa as Walsh [2]: (5) π = π e + + ε 2. The inflation ate is etemine b inflation expectations, the output gap, an a suppl shock. In the most simple vesion one can assume that the cental bank is ceible, i.e. that pivate inflation expectations ae ientical with the cental bank s inflation taget (π ). Thus, the Phillips cuve becomes (6) π = π + + ε 2. It is impotant to note that this cuve is not a shot-tem suppl cuve but simpl a evice fo calculating the inflation ate that is associate with an output gap, which is etemine in Chat 3. Chat 3: The expectations augmente Phillips cuve PC 6

10 3.2 An analsis of eman an suppl shocks une full iscetion With these builing blocs we can alea escibe funamental pinciples of moneta polic in a ve simple an at the same time ve compehensive wa. Stating with a negative eman shock (ε < ) we can see in Chat 4 that the eman cuve is shifte ownwas so that at constant eal inteest ates a negative output gap emeges. In the lowe panel this is tanslate into an inflation ate π that is below the cental bank s taget ate. If the cental bank lowes the eal ate fom to the output gap is close an the inflation ate is bought back on its taget level. Thus, the moel shows that thee is no tae-off between output an inflation in the situation of a eman shock. Chat 4: Deman shock an optimal moneta polic PC If the econom is confonte with a positive suppl shock (ε 2 > ), Chat 5 shows in the lowe panel that the Phillips cuve is shifte upwas. If the cental bank ecies to emain passive we can see fom the uppe panel that at a constant eal inteest ate the 7

11 output gap emains zeo. The inflation ate ises fom π to π. It is impotant to note that this equies an equivalent incease in the nominal ate since the inflation ate has gone up. Altenativel the cental bank can incease the eal ate in oe to keep inflation on tack. In this case, it has to accept a negative output gap (point A). Of couse, the cental bank can also ecie to taget intemeiate combinations of an π which lie on the Phillips cuve between point A an B. Chat 5: Suppl shock an optimal moneta polic () π PC PC π B π A Thus, the basic vesion of the BMW moel helps us to unestan the uneling pinciples of moneta polic in a ve simple wa. Since we have left it open so fa, how the cental bank ecies in tae-off situations, one can escibe this setting as a iscetiona polic. It is impotant to note that in this basic vesion no aggegate eman cuve is equie in the π/ iagam. In this espect ou appoach iffes fom the moel pesente b Rome [2]. Compae with the IS/LM-AS/AD moel the BMW moel is at the same time 8

12 simple since it oes not equie eajustments of the LM cuve that take place if the pice level changes the eal mone suppl, moe poweful since it allows to explain changes in the inflation ate, moe compehensive since it inclues the expectations-augmente Phillips cuve, moe consistent since, it avois an inconsistent etemination of aggegate suppl. The moel is also well suite fo iscussing inflationa pocesses whee inflation expectations shift the Phillips cuve upwas an whee the cental bank has to accept a negative output gap if it wants to keep inflation close to the taget level. In ou view fo an intoucto textbook this vesion of the BMW moel woul be completel sufficient. It goes without saing that the stana pesentation of fiscal polic can be easil inclue in the moel. It woul also be possible to pesent aggegate eman in tems of output levels instea of output gaps. In this case equation () can be state as (a) Y D = a b + ε. As a benchmak we woul then have to efine a full emploment output (Y F ), which can be eive fom a neoclassical labou maket. The Phillips cuve woul be fomulate as: (6a) Y Y e F π=π + +ε2 YF. Fo an intoucto text one coul also omit the shock tems ε an ε Inflation tageting: moneta polic guie b of a loss function The BMW moel allows a simple iscussion of the inceasingl popula stateg of inflation tageting within a simple macoeconomic famewok. Fo that pupose one has to intouce a loss function fo the cental bank. It is tpicall efine as: (7) ( ) 2 2 L= π π +λ with λ. 9

13 In the most simplest vesion we assume that cental bank gives an equal weight to the inflation gap an the output gap so that λ equals. Such pefeences ae efine as a polic of flexible inflation tageting (Svensson [999]). In the π/-space loss functions can be epesente b cicles aoun a bliss point (see Chat 6). The bliss point is efine b an inflation ate, which is equal to the inflation taget an an output gap of zeo. It epesents the optimal outcome. Chat 6: Bliss point an an isoquant of the loss function π PC π Bliss point In the case of a eman shock we have alea seen that moneta polic is able to maintain the bliss combination of π an at the cente of the cicle. In the case of a suppl shock the loss function helps us to ientif the optimum combination of π an. Hee the Phillips cuve seves as a estiction une which it has to be minimise. The optimum combination is given b the locus on the Phillips cuve that is tangent to an isoquant of the loss function (see Chat 7). We can eive the isoquant b tansfoming the loss function (7) into the nomal fom of a cicle. The isoquant can be witten as 3 : (8) ( π π ) 2 2 = opt opt ( L ) ( L ) whee (;π ) is the cente of the cicle an the aius is given b opt L.

14 Chat 7: Suppl shock an tangenc point of an isoquant with the Phillips cuve PC PC A B Algebaicall we eive the optimal inteest ate in esponse to eman an suppl shocks b inseting the Phillips cuve (6) into the loss function (7) an eiving it fo. This gives the optimum output gap: (9) = ε. 2 ( +λ) 2 The optimal inteest ate can be calculate b inseting equation (9) in (). This leas to () opt a = + ε + ε b b b 2 ( +λ) 2. 3 Fo the moe geneal case of an ellipse see Bofinge et al. [22].

15 It shows that moneta polic has to eact with an incease in the eal ate in a situations of positive eman an suppl shocks. Aitionall one can also easil see that the esponse to a suppl shock epens on the weight given to output stabilisation. In the case of a cental bank that onl caes about inflation, λ becomes zeo ( inflation nutte ), which equies a stong eal ate incease an accoingl a high output loss. If eman an suppl shocks ae absent the cental bank tagets opt neutal eal shot-tem inteest ate. = a/b. In line with Bline [998], p. 3 this ate can be egae as a 3.4 The Talo ule: moneta polic guie b a simple ule Given the pominence of simple ules in the conuct of moneta polic the BMW moel has the avantage that it can also analse them in a elativel eas wa. The most pominent vesion of a simple ule is the Talo ule (Talo [993]) accoing to which the eal inteest ate is etemine b a neutal eal ate ( ) an the weighte inflation gap an output gap. = + e π π + f with e,f > () ( ) Gaphicall this gives an upwa-sloping inteest ate line (MP) in the / iagam (Chat 8). Chat 8: Talo ule MP(π ) MP(π ) π The MP line is shifte upwas if the inflation ate inceases. In the π/ iagam the Talo ule leas to a ownwa-sloping aggegate eman function. This line can be eive gaphicall as 2

16 follows (see Chat 9). Initiall the inflation ate is equal to the inflation taget π. The MP line coesponing to this inflation ate is MP(π ) which is associate with = (Point A, lowe panel). If the inflation ate inceases to π the MP line is shifte upwas to MP(π ). This leas to an output ecline coesponing to a negative output gap ( ). In the π/ iagam this combination of inflation an output leas to point B which togethe with point A allows us to aw a ownwa-sloping (π) line. Chat 9: Deiving the aggegate eman cuve MP(π ) MP(π ) () π π π B A ( e,f,π ) With a Talo ule we get iffeent outcomes fo moneta polic in situations with shocks. Stating with a negative eman shock we get a ownwa shift of the ()-line in the uppe panel of Chat. In esponse to the ecease of the output gap fom to the cental bank lowes b moving along the MP(π )-line - eal inteest ates fom to. In the lowe panel the (π)-line shifts fom ( π ) to ( π ). 3

17 Chat : Talo ule an eman shocks MP(π ) MP(π ) π () () PC π π ( ) ( ) e,f,π e,f,π As the inflation ate initiall emains unchange the new ( π) cuve has to go though a point, which is a combination of the new output gap ( ) an an unchange inflation ate (π ). Howeve, with a negative output gap the Phillips cuve which is the inflation etemining elationship tells us that the inflation ate will stat to fall. The new equilibium is the intesection of the shifte () π line with the unchange Phillips cuve. It is chaacteise b a somewhat ampene output ecline that is ue to fact that the cental bank euces eal ates because of the lowe inflation ate. Thus, we also get a ownwa shift of the MP line so that it intesects with the () line at the same output level as the intesection of the () π line with the Phillips cuve. This souns athe ifficult but the mechanics of the shifts ae ientical with the shifts in the IS/LM-AS/AD moel in the case of the same shock which leas to a ownwa shiftof the IS-cuve: 4

18 In ou moel the incease in inflation has a estictive moneta impulse since it inceases the eal inteest ate. In the IS/LM-AS/AD moel the incease in the pice level euces the eal mone stock, which also has a estictive effect since it inceases the nominal inteest ate. It is impotant to note that compae with inflation tageting (iscetiona polic guie b a loss function) a simple ule leas to a sub-optimal outcome. It pouces a change of the eal ate that leas into the ight iection but the ecline of the eal ate is too weak to estoe the bliss point. This outcome is not implausible since it emonstates that a simple ule cannot be ientical with a polic of iscetion whee polic-makes have pefect infomation. In actual moneta polic, howeve, polic-makes have onl impefect infomation so that the can be bette off using a simple ule instea of ting to achieve a iscetiona solution. Chat : Talo ule an suppl shocks MP(π ) MP(π ) () π PC PC π π ( e,f,π ) 5

19 Fo the iscussion of a suppl shock we stat the analsis in the lowe panel of Chat. The Phillips cuve is shifte upwas which inceases inflation ate. Because of the highe inflation ate the Talo ule line in the uppe panel is also shifte upwas fom MP(π ) to MP(π ). The incease in eal inteest ates fom to pouces a negative output gap ( ) which coespons to the inflation ate π. Note, that again compae with inflation tageting (iscetiona polic guie b a loss function) a simple ule leas to a sub-optimal outcome. Optimal moneta polic woul choose the tangenc point of the inne ellipse with the Phillips cuve. As moneta polic is conucte accoing to a Talo ule the final outcome will be the intesection of the Phillips cuve PC an the aggegate eman cuve (e,f,π). The loss attache to this outcome is given b the oute isoquant of the loss function. The istance between the two isoquants is the welfae loss implie b sticking to a simple ule. We can see that in this case the Talo ule outcome closel matches with the optimal solution une iscetion (see Chat 2). Chat 2: Suppl shock: Suboptimal outcome of simple ules MP( ) MP( ) PC PC e,f, 6

20 4 The BMW moel fo an analsis of moneta polic in an open econom 4. Moifications in the basic builing blocs Fo a iscussion of moneta polic in an open econom we have to inclue the effects of the eal exchange ate on aggegate eman. Thus equation () becomes: (2) = a b+ c q+ε, whee q is the change of the eal exchange ate an a, b, an c ae positive stuctual paametes of the open econom. 4 Fo the etemination of the inflation ate we will iffeentiate between two pola cases. In the fist case which epesents a long-tem pespective especiall fo a small econom the omestic inflation ate is completel etemine b the foeign ate of inflation expesse in omestic cuenc tems (π f ), an hence b puchasing powe pait (PPP): (3) f * π=π =π + s. Because of the long-tem pespective we o not inclue a shock tem. Thus, the omestic inflation ate equals the foeign inflation ate (π * ) plus the epeciation of the omestic cuenc ( s). In othe wos, we assume that the eal exchange ate * q = s+π π emains constant. In the secon case we aopt a shot-tem pespective. We assume that companies follow the stateg of picing-to-maket so that the leave pices unchange in each local maket even if the nominal exchange ate changes. As a consequence, changes in the exchange ate affect mainl the pofits of entepises. One can ega this as an open-econom balance-sheet channel whee changes in pofitabilit ae the main leve b which the exchange ate affects aggegate eman. In this case the Phillips cuve is ientical with the omestic vesion (see Chapte 3.): (4) π=π + +ε 2. 4 As is usuall one in the liteatue, q > is a eal epeciation of the omestic cuenc. 7

21 Of couse, it woul be inteesting to iscuss an intemeiate case whee the eal exchange has an impact on the inflation ate. But using an equation like (5) π= ( e) π + eπ f =π + + e q+ε 2, woul make the pesentation ve ifficult, above all the gaphical analsis. 5 As a futhe ingeient of open econom maco moels we have to take into account the behaviou of intenational financial makets paticipants which is in geneal escibe b the uncovee inteest pait conition (UIP): (6) * s+α= i i. Accoing to equation (6) the iffeential between omestic (i) an foeign (i * ) nominal inteest ates have to equal the ate of nominal epeciation ( s) an a stochastic isk pemium (α). This basic moel can now be use to assess moneta polic une the options of inepenentl floating (4.2) an absolutel fixe (4.3) exchange ates. 4.2 Thee vaiants of inepenentl floating exchange ates Fo a iscussion of moneta polic une inepenentl floating exchange ates it is impotant to ecie how a flexible exchange ate is etemine. In the following we iscuss thee iffeent vaiants: PPP an UIP hol simultaneousl (4.2.), UIP hols, but eviations fom PPP ae possible (4.2.2), the exchange ate is a pue anom vaiable (4.2.3). 5 Accoing to (5) the oveall inflation ate woul be calculate as a weighte (b the facto e) aveage of omestic inflation π (etemine b (4)) an impote inflation π f (etemine b (3)). 8

22 4.2. Moneta polic une flexible ates if PPP an UIP hol simultaneousl (long-tem scenaio) As it is well known that PPP oes not hol in the shot-tem, the fist case can mainl be egae as a long-tem pespective. PPP implies that the eal exchange emains constant b efinition: (7) * q = s+π π=. Fo the sake of simplicit we assume a UIP conition that is pefectl fulfille an thus, without a isk pemium: (8) * s= i i, which can be tansfome with the help of the Fishe equation fo the omestic inteest ate (9) i= +π an the foeign inteest ate (2) i = +π, * * * an equation (3) into (2) * =. Thus, one can see that in a wol whee PPP an UIP hol simultaneousl thee is no oom fo an inepenent eal inteest ate polic, even une inepenentl floating ates. As the omestic eal inteest ate has to equal the eal inteest ate of the foeign (wol) econom, the cental bank cannot taget aggegate eman b means of the eal ate. This oes not impl that moneta polic is completel poweless. As equations (4) an (9) show, the cental bank can achieve a given eal ate (which is etemine accoing to equation (2) b the foeign eal inteest ate) with iffeent nominal inteest ates. Changing nominal 9

23 inteest ates in tun go along with vaing ates of nominal epeciation o appeciation of the omestic cuenc s, fo a given nominal foeign inteest ate (see equation (8)). If i * an * ae exogenous, then π * is exogenous as well, an the chosen (long-un) nominal inteest ate finall etemines via the elate s an the PPP equation (7) the (long-un) omestic inflation ate π. In sum, the long-tem scenaio with vali UIP an vali PPP leas to the conclusion that moneta polic has no eal inteest ate autonom fo tageting aggegate eman, but a nominal inteest ate autonom fo tageting the inflation ate. This comes athe close to the vision of the poponents of flexible ates in the 96s who ague that this aangement woul allow each count an autonomous choice of its inflation ate (see Johnson [972]). It can be egae as an open-econom vesion of the classical ichotom accoing to which moneta polic can affect nominal vaiables onl without having an impact on eal vaiables Moneta polic une flexible ates if UIP hols but not PPP (shot-un scenaio) In ou secon scenaio fo flexible ates we assume that the omestic inflation is not affecte b the exchange ate. This assumption coespons with empiical obsevation that in the shot-un the eal exchange is athe unstable an mainl etemine b the nominal exchange ate (see Chat 3). As a stating point we eive in a geneal wa the optimum inteest ate fo ou moel on the basis of equation (4). If we inset it in the loss function (7), we can eive the optimum output gap: (22) = ε λ Using equation (2) we calculate the optimum eal inteest ate: (23) opt = a c 2 q b + b ε + b ε + b. 2 ( +λ) 2

24 It shows that the cental has to eact to eman an suppl shocks an to changes in the eal exchange ate. Chat 3: Nominal an eal exchange ate of the euo aea Nominal Effective Exchange Rate Real Effective Exchange Rate 99M 99M 992M 993M 994M 995M 996M 997M 998M 999M 2M 2M Souce: IMF, Intenational Financial Statistics Fo the case of flexible ates whee UIP hols the eal exchange ate in (23) can be substitute as follows. The UIP conition with a isk pemium (24) * s+α= i i can be tansfome b subtacting π π * on both sies into a eal UIP equation (25) * q= α. Inseting (25) into (23) an solving fo (assuming that = opt ) iels: 2

25 (26) = a c b c + b c ε + ε b c +α opt * 2 2 ( b c)( +λ) ( ). Equation (26) povies the optimal eal inteest ate fo a cental bank in a sstem of floating ates whee UIP hols (with the possibilit of isk pemium shocks) while PPP oes not hol. It shows that eal inteest ate has to espon to the following tpes of shocks: omestic shocks: suppl an eman shocks, intenational shocks: the shock of a change in the foeign eal inteest ate an the shock of a change in the isk pemium. Since opt can be set autonomousl, the cental bank can taget the eal inteest ate in the open econom in the same wa as in a close econom. The functioning of the moel can also be emonstate gaphicall. Fo this pupose we have to constuct the ()-cuve in awa that it is not iectl affecte b the eal exchange ate. This can be achieve b eplacing q in equation (2) b the value fo q in equation (25). This leas to a eman cuve fo the open econom, which is onl etemine b omestic eal inteest ate: (27) () a ( b c) c( * ) = +α +ε. This cuve is chaacteise b two featues: the slope of the ()-cuve is negative as long as b > c, i.e. the inteest ate channel of aggegate eman pevails ove the exchange ate channel; we efe to this as the nomal case; the slope of the ()-cuve is steepe in an open econom compae to a close econom: ( b c) > b. That implies that an ientical change of the eal inteest ate has a stonge effect on aggegate eman in close econom than in the open econom since in the latte inteest ate changes ae accompanie b counteacting eal exchange ate changes. 22

26 We begin with Chat 4, which illustates the inteest ate eaction of the cental bank in the pesence of a negative shock affecting the eman sie of the econom. Fom equation (27) we can see that such shocks have thei oigin eithe in the behaviou of omestic actos such as the govenment o consumes (ε < ), o in the intenational envionment in the fom of an incease of the foeign eal inteest ate o the isk pemium. The latte goup of shocks affects omestic eman via the eal exchange ate. Thus, the aggegate eman cuve can now be shifte b omestic an foeign shocks. In the case of a negative shock it shifts to the left, esulting in a negative output gap ( ) an a ecease of the inflation ate (π ). As a consequence, the cental bank lowes the eal inteest ate fom to so that the output gap isappeas, an hence, the eviation of the inflation ate fom its taget. One can see that the gaphical solution fo the open econom is full ientical with the close econom case. Chat 4: Inteest ate polic in the case of shocks, which affect the eman sie π () () PC π π The same applies to the iscussion of a suppl shock. Chat 5 shows that the cental bank is again confonte with a tae-off between output an inflation stabilisation. A positive suppl 23

27 shock (ε 2 > ) shifts the Phillips cuve to the left. If thee is no moneta polic eaction (the eal inteest ate emains at ), the output gap is unaffecte, but the inflation ate ises to π (point B). If, on the othe han, the cental bank tightens moneta polic b aising the eal inteest ate to, the output gap becomes negative, theeb loweing the inflation ate to π (point A). As in the close econom case, the optimum combination of an π epens on the pefeences λ of the cental bank. If π an ae equall weighte in the loss function, the iso-loss locus is a cicle, an PC touches the cicle at (π 2, 2 ). Chat 5: Inteest ate polic in the case of a suppl shock 2 () π PC PC π 2 B π A Moneta polic une exchange ates that behave like a anom walk One of the main empiical finings on the eteminants of the exchange ate is that in a sstem of inepenentl floating exchange ates no macoeconomic vaiable is able to explain exchange ate movements (especiall in the shot an meium un which is the onl elevant time hoizon fo moneta polic) an that a simple anom walk out-pefoms the peictions of the existing 24

28 moels of exchange ate etemination (Messe an Rogoff [983]). In a ve simple wa such anom walk behaviou can be escibe b (28) q =η whee η is a anom white noise vaiable. Inseting equation (28) into (23) iels the following optimum inteest ate: (29) opt = a c 2 b + b ε + b ε + b η. 2 ( +λ) Ranom exchange ate movements constitute now an aitional shock to which the cental bank has to espon with its inteest ate polic. At fist sight, even une this scenaio moneta polic autonom is still peseve. Howeve, thee ae obvious limitations, which epen on the size an the pesistence of such shocks, an the impact of eal exchange ate changes on aggegate eman, which is etemine b the coefficient c in equation (2). Empiical evience shows that the vaiance of eal exchange ates excees the vaiance of uneling economic vaiables such as mone an output b fa. This so-calle excess volatilit puzzle of the exchange ate is excellentl ocumente in the stuies of Baxte an Stockman [989] an Floo an Rose [995]. Base on these esults we assume that Va[η]>>Va[ε ]. Thus if a cental bank woul t to compensate the eman shocks ceate b changes in the eal exchange ate, it coul geneate highl unstable eal inteest ates. While this causes no poblems in ou puel macoeconomic famewok, thee is no oubt that most cental banks t to avoi an excessive instabilit of shot-tem inteest ates ( inteest ate smoothing ) in oe to maintain soun conitions in omestic financial makets. 6 If this has the consequence that the cental bank oes not sufficientl eact to a eal exchange ate shock, the econom is confonte with a sub-optimal outcome fo the final tagets an π. 6 Howeve, most moels, as the one pesente hee, fail to integate the vaiance of inteest ates an its consequences into a macoeconomic context. 25

29 Fo the gaphical solution the ()-cuve is simpl eive b inseting equation (28) into (2) which eliminates q: (3) () = a b+ cη+ε. Exchange ate shocks η lea to a shift of the ()-cuve, simila to what happens in the case of a eman shock. In Chat 6 we intouce a smoothing ban that limits the oom of manoeuve of the cental bank s inteest ate polic. In oe to avoi unue fluctuations of the inteest ate, the cental bank efains fom a full an optimal inteest ate eaction in esponse to a anom eal appeciation (η < ) that shifts the ()-cuve to the left. As a esult, the shock is onl patiall compensate so that the output gap an the inflation ate emain below thei taget levels. Chat 6: Inteest ate smoothing an exchange ates that behave like a anom walk max smoothing min π () () PC π π 26

30 4.3 Moneta polic une fixe exchange ates With fixe exchange ates a cental bank completel loses its leewa fo a omesticall oiente inteest ate polic. In oe to avoi estabilising shot-tem capital inflows o outflows, the cental bank has to follow UIP in a ve stict wa. Fo s = the UIP conition becomes: (3) i * = i +α Inseting equation (3) into (9) shows how the eal inteest ate is etemine une fixe exchange ates: (32) * = i +α π Fixe exchange ates as a estabilising polic ule As the eal inteest ate is onl etemine b foeign vaiables an as it epens negativel on the omestic inflation ate, the cental bank can no longe pusue an autonomous eal inteest ate polic. In pinciple, equation (32) can be intepete as a special case of a simple ule. This becomes obvious if equation (32) is tansfome into * (33) ( ) ( )( ) = i +α π + π π +. Compae to a Talo ule (equation ()) this ule has the negative featue that the inflation ate entes with a negative sign (instea with a coefficient of geate than zeo which is equie fo a stabilising Talo ule, see ou extene iscussion of the moel in Bofinge et al. [22]) an that a weight of zeo is given to the output gap. Thus, if a positive eman shocks ives the inflation ate up, fixe exchange ates equie a ecline in the eal inteest ate. In othe wos, moneta polic tens to estabilise the econom une fixe exchange ates. This can also be shown with a gaphical analsis which follows the pesentation fo a Talo ule in Chapte 3.4. In the (,)-space we can eive a hoizontal moneta-polic line (MP) fom the inteest ate equation (32) since the eal ate is not affecte b the omestic output gap. As in the secon case of floating ates (Chapte 4.2.2) we can inset equation (25) into (2) which helps to eliminate q in the ()-cuve: 27

31 (34) () a ( b c) c( * ) = +α +ε The coesponing (π)-cuve in the (π,)-space is eive in a simila wa as in the case of a Talo ule fo the close econom. B inseting the inteest ate equation (32) in equation (34) we get: (35) ( ) a b( * ) ( b c) * ( b c) π = +α π + π+ε. Again, we assume that (b - c) is positive. This implies that the ()-cuve has a negative slope wheeas the slope of the (π)-cuve is positive. Compae with the negative slope of the (π)- cuve une a Talo ule (see Chapte 3.4), the positive slope of the (π)-cuve shows again the estabilising popet of the inteest ate ule geneate b fixe exchange ates. Fo the gaphical analsis it is impotant to see that the slopes of the ()-cuve an the (π)-cuve have the same absolute value, but the opposite sign., the slope of the (π)-cuve is ( b c) which excees one if c < b <. Thus, the (π)- cuve is steepe than the slope of the Phillips cuve with a slope of fo which we also assume that is positive an smalle than one. Moneta polic une fixe exchange ates can now be iscusse gaphicall using Chat 7. While the Phillips cuve an the ()-cuve ae ientical with the cuves we use une flexible exchange ates, we have now an aitional (π)-cuve, which is geneate b the polic-ule of fixe exchange ates The impact of eman an suppl shocks In Chat 7 we use this famewok to iscuss the consequences of a negative shock that affects the eman sie of the omestic econom. Accoing to equation (34) the souce fo such a shift in the eman cuve can oiginate eithe fom a omestic eman shock (ε ) o fom an incease in the foeign eal inteest ate ( * ) o the isk pemium (α). The esult is a shift of the ()-cuve to the left. Without epecussions on the eal inteest ate the output gap woul fall to an the inflation ate to π. Howeve, in a sstem of fixe exchange ates the initial fall in π inceases the omestic eal inteest ates since the nominal inteest ates ae kept unchange on the level of the 28

32 foeign nominal inteest ates. Thus, in a fist step, we use the new output gap ( ) an an unchange inflation ate (π ) to constuct the new location of the (π)-cuve in the (π/)- iagam. It also shifts to the left to ( ) π. 7 This finall leas to the new equilibium combination (π, ) which is the intesection between the Phillips cuve an the new (π)-cuve. This equilibium goes along with a ise of the eal inteest ate fom to, which is equal to the fall of the inflation ate fom π to π. It is obvious fom Chat 7 that the moneta polic eaction in a sstem of fixe exchange ates is estabilising since π <π an <. Chat 7: Fixe exchange ates an shocks affecting the eman sie MP(π ) (π -π ) MP(π ) π ( π ) () () ( ) π PC π π π In Chat 8 we iscuss the effects of a suppl shock. Initiall, the shock shifts the Phillips cuve to the left, which leas to a highe inflation ate (π ) with unchange output gap. Since the ise in inflation lowes the eal inteest ate, a positive output gap emeges which leas to a futhe ise 7 In fact, the escibe shift of the (π)-cuve is onl tue in the case of ε -shocks which affect the (π)-cuve an the ()-cuve b exactl the same extent (see equations (34) an (35)). If, howeve, the econom is hit b a α- 29

33 of π. The final equilibium is the combination (π, ). Again, one can see that the polic ule of fixe exchange ate has a estabilising effect. It causes an incease of the inflation ate, which is even highe than une a completel passive eal inteest ate polic in a close econom. Chat 8: Fixe exchange ates an suppl shocks (π -π ) MP(π ) MP(π ) () π ( π ) PC π PC π π Chat 9 shows that this combination is also sub-optimal compae with the outcome a cental bank chooses une optimal polic behaviou in a sstem of inepenentl floating exchange ates (see Chat 5). Assuming again that the cental bank equall weights π an in its loss function, the ge cicle (π if, if ) epicts the loss une inepenentl floating exchange ates. If the cental bank ha followe a polic of constant eal inteest ates (that is absence of an polic eaction) the otte cicle woul have been ealise with (π,). Une fixe exchange ates, howeve, the iso-loss cicle expans significantl, an the final outcome in tems of the final tagets is (π, ). shock o a * -shock, the (π)-cuve shifts b a lage amount than the ()-cuve as b > c. 3

34 Chat 9: Loss une iffeent stategies in an open econom π π ( ) PC π π π if PC if Fixe ates can also be stabilising Fom this analsis one coul come to the conclusion that a sstem of fixe exchange ates is alwas a ba thing. Howeve, this esult is ifficult to econcile with the empiical fact that counties like the Nethelans, Austia, an Estonia coul follow a ve successful macoeconomic polic une almost absolutel fixe exchange ates. Thee ae two possible explanations fo this obsevation. Fist, ou analsis leaves it open of how the foeign eal exchange ate is etemine. A stabilising movement of the omestic eal inteest ate can be geneate if the foeign cental bank is confonte with an eacts to the same eman shocks as the omestic econom. This was cetainl the case in the Nethelans an Austia, which pegge thei cuenc to the D-Mak until 998. The economies in both counties ae ve simila to the Geman econom. Thus, in the liteatue on optimum cuenc aeas the coelation of eal shocks plas a ve impotant ole (see e.g. Baoumi an Eichengeen [992]; we also simulate a two-count case with a vaing egee of coelation between eman shocks in Bofinge et al. [22]). A secon explanation efes to the size of counties, which follow a polic of fixe exchange ates. In geneal, one can sa that the pefeence fo fixe ates is high in ve small an open economies. In this case, one can assume that in equation (2) the impact of the eal exchange ate (c) on omestic eman is highe than the impact of eal inteest ates (b). Thus, the slope of the (π)-cuve in Chat 7 an Chat 8 woul become negative. The intuition uns as follows: As 3

35 mentione above, the negative eman shock euces the inflation ate. But now the negative impact of the highe eal inteest ate is ovecompensate b the positive effects of the eal epeciation, which is cause b a ecline of the omestic inflation ate. As a consequence, the fixe ate egime woul have simila stabilising popeties as a Talo ule in a close econom. 4.4 Summa an compaison with the esults of the Munell-Fleming (MF) moel Fo a summa of the open-econom vesion of the BMW-moel it seems useful to compae it with the main esult of the MF moel (see also Table ). Fo fixe exchange ates the MF moel comes to the conclusion that moneta polic is completel ineffective, while fiscal polic is moe effective than in a close-econom setting. The BMW moel shows that moneta polic is not onl ineffective but athe has a estabilising effect on the omestic econom. Compae with the MF moel the souces of eman shocks can be mae moe explicit (above all the foeign eal inteest ate an the isk pemium) an it becomes also possible to analse suppl shocks. It is impotant to note that the BMW moel can also show that fo small economies an in the case of ve simila economies fixe ates can also have a stabilising effect. As fa as the effects of fiscal polic ae concene the BMW moel also comes to the conclusion that it is an effective polic tool an that it is moe effective than in a close econom. If we teat a estictive fiscal polic as a negative eman shock we can use the esults of Chat 7. We see immeiatel that the initial effect on the output gap is magnifie b the estabilising featue of fixe exchange ates. In the case of a ve small econom the opposite is the case. Fo inepenentl floating exchange ates the MF moels povies two main esults: moneta polic is moe effective than in a close-econom setting, while fiscal polic becomes completel ineffective. It is impotant to note that the MF moel implicitl assumes that neithe UIP no PPP hol. As fa as UIP is concene, the MF moel assumes that a euction of the omestic inteest ate is associate with a epeciation of the omestic cuenc (because of capital outflows). Fo PPP 32

36 the MF moel must assume that it is alwas violate if the nominal exchange ate changes since the MF moel assumes absolutel fixe pices. Fo the thee vesions of flexible ates the BMW moels comes to esults that ae patl compatible an patl incompatible with the MF moel. Fo a wol whee PPP an UIP (long-tem pespective) hol the BMW moel pouces the contaicto esult that thee is no moneta polic autonom with ega to the eal inteest ate. Thus, the cental bank is unable to cope with eman shocks. Howeve, because of its contol ove the nominal inteest ate it can taget the inflation ate an thus eact to suppl shocks. Fo fiscal polic the BMW moel also iffes fom the MF moel. As it assumes an exogenousl etemine eal inteest ate, i.e. a hoizontal moneta polic line, fiscal polic has the same effects as in a close econom. B shifting the ()-cuve it can pefectl contol the output-gap an iniectl also the inflation ate. Une a shot-tem pespective (UIP hols, PPP oes not hol) the esults of the BMW moel ae ientical with ega to moneta polic as fa as the signs ae concene. The cental bank can contol aggegate eman an the inflation ate b the eal inteest ate. Howeve, because of the UIP conition a change in the eal inteest ate (i.e. a ecline) is alwas accompanie b an opposite change in the eal exchange ate (i.e. a eal appeciation), the effects of changes in the eal inteest ate ae smalle in the open econom than in the close econom. Fiscal polic is again effective an if one assumes that the cental bank oes not eact to actions of fiscal polic (constant eal ate) it is as effective as in a close econom. In the thi an most ealistic scenaio fo flexible exchange ates (anom walk) the esults of the BMW moel ae in pinciple ientical with those of the shot-tem pespective. Howeve, the abilit of moneta polic to eact to exchange ate shocks can be limite b the nee to follow a polic of inteest ate smoothing. Thus, thee can be clea limits to the pomise of moneta polic autonom mae b the MF moel. Again fiscal polic emains full effective. In sum, the BMW moel shows that fo flexible ates a much moe iffeentiate appoach is neee than une the MF moel. Above all, the esults of the MF moel concening fiscal polic ae no longe vali if moneta polic is conucte in the fom of inteest ate polic 33

37 instea of a moneta tageting on which the MF moel is base. In the BMW moel fiscal polic emains a poweful polic tool in all thee vesion of floating. Table : Summa of the esults in an open econom Moneta polic F i x e F l e x I b l e Fiscal polic MF moel Ineffective Moe effective than in a close econom BMW moel b>c: Destabilising b<c: Stabilising MF moel Moe effective than in a close econom Ineffective BMW moel I (PPP an UIP) BMW moel II (UIP onl) BMW moel III (anom walk) Real inteest ate: Ineffective Nominal inteest ate: effective Effective as in close econom, but with b>c eal inteest ate changes ae less effective Effective as in close econom, but with b>c eal inteest ate changes ae less effective. Limits b the nee of inteest ate smoothing b>c: Moe effective than in a close econom b<c: Less effective than in a close econom Effective as in close econom Effective as in close econom Effective as in close econom 5 Summa In sum, the BMW moel povies obvious avantages ove the IS/LM-AS/AD moel. As fa as the close-econom set-up is concene, the BMW moel is in most basic vesion moe simple an at the same time moe poweful than the IS/LM-AS/AD moel. In its moe complex vesions it can analse impotant concepts such as loss functions an moneta polic ules without getting moe ifficult than the IS/LM-AS/AD moel. With espect to the open econom vesion of the BMW moel the egee of complexit is moe o less simila to that of the MF moel. As the BMW moel assumes full capital mobilit, it can avoi a iscussion of the balance of paments ajustment pocess that equies an intensive iscussion in the MF moel. The BMW moel is somewhat moe complicate as fa as the etemination of the flexible exchange ate is concene. Howeve, this makes it much moe poweful than the MF moel. 34

38 Refeence List Abel, Anew B. an Ben S. Benanke (2), Macoeconomics, Reaing. Baxte, Maianne an Alan C. Stockman (989), Business ccles an the exchange-ate egime ; Some intenational evience, in: Jounal of Moneta Economics, 23, Baoumi, Tamim an Ba Eichengeen (992), Shocking Aspects of Euopean Moneta Unification, CEPR Discussion Pape No Blancha, Olivie (2), Macoeconomics, Uppe Sale Rive. Bline, Alan S. (998), Cental Banking in Theo an Pactice, Cambige. Bofinge, Pete (2), Moneta Polic: Goals, Institutions, Stategies, an Instuments, Oxfo. Bofinge, Pete, Eic Mae, an Timo Wollmeshäuse (22), The BMW moel: simple macoeconomics fo close an open economies a equiem fo the IS/LM-AS/AD an the Munell-Fleming moel, Wüzbug Economic Papes No. 35. Colane, Davi (995), The Stoies we Tell: A Reconsieation of AS/AD Analsis, in: Jounal of Economic Pespectives, 9, Floo, Robet P. an Anew K. Rose (995), Fixing exchange ates A vitual quest fo funamentals, in: Jounal of Moneta Economics, 36, Johnson, Ha G. (972), The Case fo Flexible Exchange Rates, 969, in: Ha G. Johnson (e.), Futhe Essas in Moneta Economics McCallum, Bennett T. (989), Moneta Economics, New Yok. Messe, Richa A. an Kenneth Rogoff (983), Empiical Exchange Rate Moels of the Seventies: Do The Fit Out of Sample, in: Jounal of Intenational Economics, 4, Rome, Davi (2), Kenesian Macoeconomics without the LM cuve, in: Jounal of Economic Pespectives, 4, Svensson, Las E. O. (999), Inflation tageting as a moneta polic ule, in: Jounal of Moneta Economics, 43, Talo, John B. (993), Discetion vesus Polic Rules in Pactice, in: Canegie Rocheste Confeence Seies on Public Polic, 39, Walsh, Cal E. (2), Teaching Inflation Tageting: An Analsis fo Intemeiate Maco, mimeo, Univesit of Califonia, Santa Cuz. 35