Should Central Banks React to Exchange Rate Movements? An Analysis of the Robustness of Simple Policy Rules under Exchange Rate Uncertainty

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1 This version: July 31, 3 Firs version: November 9, Commens are welcome Should Cenral Banks Reac o Exchange Rae Movemens? An Analysis of he Robusness of Simple Policy Rules under Exchange Rae Uncerainy Timo Wollmershäuser ifo Insiue for Economic Research * Absrac This paper evaluaes he performance of simple policy rules in an open economy model. By inroducing a high degree of exchange rae uncerainy we find ha policy rules wih an imporan feedback from movemens in he real exchange rae are very robus o uncerainy abou he rue exchange rae model. A closed economy rule performs badly in mos exchange rae specificaions. This is in sharp conras o he findings of many oher sudies according o which reacing o he exchange rae only slighly improves (if a all) he macroeconomic performance. In our view, his resul is due o he fac ha mos of hese sudies assume a known and reliable relaionship beween he exchange rae and he ineres rae and herefore neglec he poor empirical evidence on models of exchange rae behaviour in he shor and medium run. Keywords: Exchange rae uncerainy; Robusness; Simple policy rules JEL classificaion: E5, E58, F41 * Poschingersraße 5, München, Germany, wollmershaeuser@ifo.de, phone: , fax:

2 1 Inroducion In recen years here has been a considerable progress in he field of moneary policy analysis. A growing academic lieraure explores simple policy rules expressed in erms of ineres rae insrumens as guides for moneary policy under a sraegy of flexible inflaion argeing. Since mos inflaion argeing counries oday are small open economies he role of he exchange rae for he conduc of moneary policy is a cenral issue. In paricular, he uesion wheher he exchange rae (in whasoever form) should ener he policy rule or no is sill a maer of debae in he lieraure. Thus, he evaluaion of so-called open economy policy rules has become an imporan exension o he closed economy analysis of ineres rae rules. Empirically, he endency of cenral banks o indirecly influence he exchange rae by ineres rae adjusmens is largely confirmed (even for developed counries) by work on moneary policy rules. One srand of evidence resuls from he esimaion of srucural VARs in which, among oher dynamic relaionships such as aggregae demand, an euaion for he moneary policy insrumen has o be specified. For example, Clarida and Gerler (1997) repored esimaes according o which he Bundesbank responded o a depreciaion of he real exchange rae wih a rise in shor-erm ineres raes. Based on a small-scale model of he Ausralian economy, Brischeo and Voss (1999) and Dungey and Pagan () found ha he Reserve Bank of Ausralia reacs wih he shor-erm ineres rae o movemens in he exchange rae. Anoher srand of empirical evidence resuls from he direc esimaion of moneary policy rules. Clarida e al. (1998) found a small, bu significan reacion of he nominal ineres rae of he Bundesbank ( ), he Bank of Japan ( ) and he Bank of England ( ) o he real exchange rae. Gerlach and Smes () esimaed ineres rae policy rules according o which he Reserve Bank of New Zealand and he Bank of Canada respond significanly wih he shor-erm ineres rae o changes in he nominal exchange rae, whereas he Reserve Bank of Ausralia does no. Invesigaing he inflaion argeers Ausralia, Canada, New Zealand, Sweden, Unied Kingdom Hüfner (3) found ha he exchange rae erm in he policy rule is only significan for he Unied Kingdom and New Zealand. He explains he differences o he sudy of Gerlach and Smes () mainly by a somewha larger sample period. For emerging marke economies Ades e al. () and Mohany and Klau (3) also found significan (and, in comparison wih he developed economies of he aforemenioned sudies, larger) exchange rae coefficiens in he ineres rae policy rule. 1

3 In conras o he raher clear-cu resuls from empirical sudies, he resuls from numerical simulaions of calibraed open economy macro models are mixed. By adding an exchange rae erm o a simple policy rule, Ball (1999), Svensson (), Baini e al. (1) and Leiemo and Södersröm (1) find a small improvemen of he macroeconomic performance of a cenral bank s ineres rae policy. In conras o his, Côé e al. () come o he resul ha using an open economy moneary policy rule ofen increases he value of he loss funcion. Taylor (1999c) ges somewha mixed resuls in his muli-counry sudy, favouring open economy rules for some counries and rejecing heir usefulness for oher counries. In a recen overview, he finally comes o he conclusion ha research o dae indicaes ha moneary policy rules ha reac direcly o he exchange rae, as well as o inflaion and oupu, do no work much beer in sabilizing inflaion and real oupu and someimes work worse han policy rules ha do no reac direcly o he exchange rae (Taylor, 1, p. 67). In our view he problem of mos of heses numerical simulaion sudies is ha hey disregard he poor knowledge of he economic profession abou he deerminans of exchange rae movemens and he ineracion beween exchange raes and oher fundamenal variables. 1 Thus, he main objecive of his paper is o find ou wheher he empirically observable uncerainy abou he rue deerminaion of he exchange rae in a sysem of independenly floaing exchange raes has any influence on he srucure of he policy rules ha cenral banks should commi o in a small open economy. Following McCallum (1988) we seek o idenify policy rules ha possess a high degree of robusness agains hese uncerainies in he sense ha hey perform well across a range of alernaive models. Our resuls indicae raher clearly ha, due o he inroducion of a high degree of exchange rae uncerainy, open economy rules become superior o simple policy rules ha only reac o inflaion and oupu. By following an open economy policy rule a cenral bank adops a sraegy ha insulaes he economy from he uncerainies semming from he mosly unknown and unreliable relaionship beween he nominal exchange rae and he nominal ineres rae or oher macroeconomic variables. The remainder of his paper proceeds as follows. We begin in Secion by presening a sandard Neo-Keynesian open economy macro model ypically used by academics and cenral banks for he evaluaion of moneary policy rules. In his model, o which we refer as he baseline model, he pah of he nominal exchange rae is deermined according o uncovered ineres pariy. We will 1 A noable excepion is he paper of Leiemo and Södersröm (1).

4 reproduce he resul usually obained from numerical simulaions by evaluaing he performance of six simple policy rules. As he exchange rae mainly deermined by he ineres rae iself, a separae ineres rae reacion o exchange rae movemens is redundan. Secion 3 defines he ypes of uncerainy semming from he poor knowledge abou he deerminaion of exchange raes in he conex of small open economy models. In paricular, we will focus on deviaions from uncovered ineres pariy ha in spie of is poor empirical suppor sill consiues a major building block of radiional open economy models. As alernaives o UIP we propose exchange rae specificaions ha eiher show a much beer fi in empirical sudies, ha allow for deviaions from he raional expecaions hypohesis by inroducing backward-looking expecaions, or ha simply display purely random exchange rae behaviour. Apar from he exchange rae specificaion all he models are idenical wih respec o he IS curve and he Phillips curve. Secion 4 evaluaes he exen o which he performance of he six policy rules which are derived from he baseline model is affeced by he risk ha insead of uncovered ineres pariy anoher exchange rae model is a beer descripion of acual exchange rae behaviour. We will show ha his exchange rae uncerainy impacs on he conduc of moneary policy on wo levels. Firs, he exchange rae appears as an own source of shocks which conveys independen informaion o he policy maker. And second, he ransmission of ineres rae impulses on he cenral bank s final arges via he exchange rae channel is subjec o a high degree of uncerainy. We will hen idenify he characerisics of hose policy rules ha perform reasonably well over all exchange rae specificaions. Secion 5 summarises he main resuls. Moneary policy in a sandard open economy macro model.1 Presenaion of he baseline model The baseline model is a modified version of he backward-looking Neo-Keynesian Ball (1999) model for open economies. We have oped for he purely backward-looking specificaion of he inflaion and oupu euaion o ge dynamics ha mach hose of available economic daa mos consisenly. Acual daa usually shows a high degree of persisence in boh, inflaion and oupu (see Esrella and Fuhrer,, and he papers cied here). We hereby deliberaely absained from any opimising foundaions and he relaed forward-looking jump behaviour of inflaion and 3

5 oupu. According o Ball (1999, p. 18) he advanage of he backward-looking specificaion is ha i is similar in spiri o he more complicaed macroeconomeric models of many cenral banks. This superioriy of he backward-looking specificaion in pracical use is also confirmed by a sudy of he Bank for Inernaional Selemens (1995) in which 11 cenral bank models were compared o each oher, all of which were purely backward-looking. An addiional aspec ha conribued o his decision was sressed by Rudebusch and Svensson (1999) who also used a purely backward-looking model, albei for a closed economy. In heir view, a backward-looking specificaion of he behavioural relaionships is appropriae in paricular if he inflaion argeing sraegy has only been recenly inroduced, implying ha he public is sill learning abou he new moneary policy regime. And indeed, many small open emerging marke economies o which he presen analysis applies foremos swiched from moneary argeing or some form of exchange rae argeing o inflaion argeing no earlier han he lae 199s. The baseline model consiss of he following euaions: ( ) y y =β y β + i π +β +ε (1) + 1 y i 1 ( ) π = π +γ y +γ +ε π + 1 y () i = i + E s s + u f + 1 s (3) s s +π π f 1 1 (4) The nominal ineres rae i serves as he operaing arge of moneary policy. The real exchange rae and he nominal exchange rae s are expressed in logarihms. The rae of domesic and f foreign inflaion ( π and π ), he oupu gap y and he nominal ineres rae i are measured in per cen. All parameers are assumed o be posiive. The wo shocks ε and π + 1 ε are i.i.d. whie noise y + 1 shocks wih mean zero, whereas s u represens an auocorrelaed disurbance. The demand side of he Ball (1999) model is given by he open economy IS euaion (1) according o which oupu depends on lags of he real ineres rae and he real exchange rae, is own lag and Noe ha we defined he real ineres rae as he difference beween he nominal ineres rae i and he curren rae of inflaion π (insead of expeced inflaion for he nex period E π +1 as is for example common in purely forward- 4

6 a demand shock. The supply side is given by euaion (). The inflaion process is governed by a backward-looking acceleraionis Phillips curve in which he rae of inflaion is posiively relaed o he lagged value of inflaion, he lagged value of he oupu gap, he lagged rae of real depreciaion, and a supply shock. Boh euaions are idenical o he specificaions in he original Ball (1999) model. In marked conras o he Ball (1999) model, he nominal exchange rae is modelled as an asse price ha is inherenly forward-looking and expecaions deermined. The basic relaionship underlying he dynamics of he exchange rae is uncovered ineres pariy (UIP) given by euaion (3). We will come back o Ball s original exchange rae specificaion below in Secion 3 where i will be used as one alernaive o UIP. The deviaions from UIP which are modelled as an AR(1) process ( u s su 1 s =ρ +ε s ) are ypically referred o as he foreign exchange risk premium ha incorporaes any exogenous residual disurbances o he exchange rae, including changes in porfolio preferences, credibiliy effecs, ec. (Svensson,, p. 163). By forward ieraion, euaion (3) can be solved for he nominal exchange rae: s ( f = + j + j+ + j j= s E i i u ) (5) Accordingly, he fundamenal deerminans of s are curren and expeced fuure ineres rae differenials as well as curren and expeced fuure risk premia. This is he core relaionship of an efficien speculaive foreign exchange marke in which he exchange rae fully reflecs informaion available o marke paricipans and in which every new piece of informaion should be immediaely mapped ono prices. In he simulaions of his Paper we oped for he UIP cum persisen risk premium exchange rae specificaion as our baseline model for wo reasons. Firs, UIP relies on arbirage argumens which should be rue. Even hough we know ha arbirage is ofen subjec o limis (see Shleifer and Summers, 199, and Shleifer and Vishny, 1997), i is noneheless one of he basic building blocks of economic decision making. Quesioning he validiy of UIP wihou rejecing he underlying arbirage mechanism hen has o rely on misaken expecaions. However, raional expecaions are sill he predominan paradigm in macroeconomics oday. Second, from his follows ha in almos looking models). Ellingsen and Södersröm (1) showed ha his definiion of he real ineres rae is consisen wih a forward-looking definiion of he real ineres rae if he Phillips curve is purely backward-looking. 5

7 all open economy macro models UIP serves as he principal consiuen of describing exchange rae behaviour (see for example he models presened in Buier, 199, McCallum, 1996, and Svensson, ). Moreover, UIP is also a consiuen of virually all conemporary exchange rae models. McCallum (1994, p. 19) summarises he analyical imporance of he UIP condiion as follows: [T]he main fac o be kep in mind is ha i appears as a key behavioral relaionship in virually all of he prominen curren-day models of exchange rae deerminaion. These include no only small models used in heoreical analysis, bu also a number of he more ambiious and carefully specified of oday s array of mulicounry economeric models hose used by inernaional organizaions as well as individual open-economy policy analyss. Due o his populariy wihin he economic profession he exchange rae specificaion in our baseline model is similar o ha of numerous oher sudies. In paricular, we assumed a known and consan ρ s. However, as we will show below, he empirical deerminaion of he degree of persisence ofen leads o mixed resuls. The final relaionship of our open economy macro model is he link beween he real exchange rae and he nominal exchange rae which is given by ideniy (4) and which explicily akes ino accoun ha deviaions from purchasing power pariy occur in he shor-run. On he basis of he four euaions of he baseline model we can describe he ransmission channels of moneary impulses in a small open economy which can be divided ino an ineres rae channel and an exchange rae channel. Wih he ineres rae channel, moneary policy affecs aggregae demand via is effec on he shor-erm real ineres rae (euaion (1)). Subseuenly, aggregae demand affecs inflaion via he supply-side of an economy which is described by he Phillips-curve euaion (). In his respec we follow he curren mainsream in moneary macroeconomics according o which he money sock only plays a minor role in describing moneary policy effecs (see Romer,, for an illusraive paper). According o he UIP euaion (3), he exchange rae channel is riggered by changes in he nominal ineres rae (see also euaion (5)). I can be divided ino a direc and an indirec channel. The direc channel explains inflaion flucuaions via he passhrough of exchange rae flucuaions o impor prices, and hence on inflaion (euaion () in conjuncion wih euaion (4)). Indirecly, he real exchange rae affecs he relaive price beween domesic and foreign goods, which in urn has an impac on boh, domesic and foreign demand for domesic goods, and hence conribues o he aggregae demand channel for he ransmission of moneary policy (euaion (1) in conjuncion wih euaion (4)). 6

8 . Opimal simple rules in he baseline model As is common in he policy-oriened lieraure, he ineres rae policy is implemened by assuming ha he cenral bank follows a simple policy rule for is operaing arge which prescribes an adjusmen of he nominal ineres rae in response o only a small se of observable variables (see for example Rudebusch and Svensson, 1999). Depending on his se of variables he policy rules used in our simulaions below can be divided ino wo caegories: closed economy Taylor-ype rules and open economy policy rules. A cenral bank ha follows a closed economy policy rule ses shor-erm ineres raes exogenously and independenly of any direc exchange rae developmens. Policy rule R1 is ypical for such a policy since he cenral bank s operaing arge only responds o movemens in he domesic goal variables inflaion and oupu (see Table 1). By implemening moneary policy hrough an open economy policy rule he cenral bank no only reacs o conemporaneous movemens in inflaion and oupu, bu also o movemens in some measure of he exchange rae. There is a muliude of possible formulaions of such rules (see e.g. Baini e al., 1), depending on wheher one refers o he real or he nominal exchange rae, o he level or o changes in he exchange rae, or o conemporaneous or o lagged movemens of he exchange rae (see policy rules R o R7 in Table 1). Table 1 For he choice of he response coefficiens of he simple rules we performed a consrained opimisaion. We minimised he policy maker s ineremporal loss funcion on a resriced sae variable se i f π,f y,f,f( 1) δ ( λππ +λ y = ) min E y (6) subjec o he sae and he evoluion of he economy represened by euaions (1) o (4). The resricion on he response coefficiens is shown in brackes below he min operaor. Each of he rules shown in Table 1 has been opimised for he baseline specificaion of he open economy model for idenical preferences of he cenral bank owards inflaion and oupu ( λ π = λ y = 1) and 7

9 for a discoun facor δ approaching uniy. By scaling he ineremporal loss funcion in (6) by a facor (1 δ) Svensson (3) showed ha when δ approaches uniy, he scaled ineremporal loss approaches he weighed sum of he uncondiional variances of inflaion and he oupu gap: δ λππ +λ y = λπ π +λy = ( ) ( ) [ ] [ ] lim 1 δ E y Var Var y. (7) δ 1 For he numerical deerminaion of he opimum response coefficiens we have o calibrae he model. Given he ime lags in euaions (1) o (4) a period can a bes be inerpreed as a year. The parameer values of he aggregae demand euaion (1) and he Phillips curve () which are summarised in s Table were chosen in accordance wih Ball (1999). The variance of he i.i.d. shocks, ε and ε y + 1 π ε is normalised o uniy. As he original Ball (1999) specificaion of he exchange rae euaion (see Secion 3 below) neglecs any influence of he foreign real ineres rae on he exchange rae, f we se he variance of ε + 1 as well as he persisence parameer ρ f o zero. Addiionally, π f is assumed o be consan and zero. This simplificaion eually applies o all oher exchange rae specificaions discussed in Secion 3 so ha each ype of model is hi by he same number of shocks (exchange rae shock, supply shock, demand shock). In accordance wih many oher sudies (see Table 6 in Secion 3.1) he auocorrelaion coefficien of he shock is chosen so as o persis over several periods. Thus, in he baseline model, we somewha arbirarily se he degree of persisence of he UIP shock o.3. 3 However, as we will show below, he uaniaive resuls are uie robus agains variaions of he UIP persisence as long as he degree of persisence remains low (i.e. smaller han.5). Table 3 A persisence parameer of.3 signifies a decay for UIP deviaions caused by a risk premium shock of 7 per cen per period, implying a half-life for UIP shocks of.6 periods. 8

10 Table 3 provides he resuls for he opimised coefficiens and he relaed loss in absolue and relaive erms. The laer expresses he loss in per cen of he loss from he opimal unresriced policy under commimen which corresponds o he unresriced opimum policy and which amouns o 4.9. I shows ha he closed economy policy rule R1 performs on average.68 per cen worse han he opimal unresriced rule. Wih regard o he eually weighed goal variables inflaion and oupu his resul means ha he variance of boh variables is on average.68 per cen higher. The coefficiens on π and y are somewha larger han 1.5 and.5 which are he coefficiens of he original Taylor (1993a) rule bu his resul is in line wih many oher simulaion sudies (see e.g. Rudebusch and Svensson, 1999, and oher papers in Taylor, 1999b). In paricular, wih f > π 1 he so-called Taylor principle holds which saes ha in response o a rise in inflaion nominal ineres raes should rise sufficienly o increase real raes (Taylor, 1999a). Adding he curren movemen of he real exchange rae o he ineres rae rule (R) reduces he loss by one percenage poin. The cenral bank reacs more aggressively on deviaions of he inflaion rae and he oupu gap from heir arge levels, and i raises nominal ineres raes when he real exchange rae depreciaes. If he lagged real exchange rae is added (R3) insead of he curren exchange rae, he cenral bank lowers he nominal ineres rae in response o a real depreciaion in he previous period. While he value of he loss funcion is relaively close o ha resuling from R, he composiion of he loss has changed in favour of inflaion. In R4 and R5 he ineres rae reacs o he change in he exchange rae. On firs sigh, R5 seems o be uie differen from R4 since he nominal exchange rae eners he rule. However, wih euaion (4) i is possible o replace wih s π and o reformulae R5 as ( ) i = f f π + f y + f s R4 R4 R4 R4 π y (8) Thus, wih R5 R4 R4 R5 R4 f = f f, f = f, and π π y y f R5 s = f, R4 and R5 lead o euivalen resuls in erms R4 of he dynamics of he sysem, and hence in erms of he loss funcion. For his reason, we only calculaed he opimal parameers for R4. We hen derived he parameers for R5 on he basis of (8). Compared o he policy rules ha only reac o he level of he real exchange rae, R4 and R5 perform somewha beer so ha he loss is only.38 per cen higher han ha of he opimal unresriced rule. If we allow for a separae weighing of he curren and he lagged real exchange rae (R6) we ge he bes resul in erms of he loss funcion. Noe ha he improvemen of he las 9

11 hree rules mainly sems from a reducion of he variance of he inflaion rae. As for policy rule R7, according o which he nominal ineres rae responds o he level of he nominal exchange rae, he opimisaion resuled in a coefficien on he exchange rae of zero ( f s = ). Thus, he policy rule is idenical wih R1. This resul is no very surprising given he non-saionariy of he nominal exchange rae in open economy macro models. Table 3.3 Explaining he mixed resuls in favour of open economy policy rules from numerical simulaions of calibraed models The figures in Table 3 show ha he benefi from addiionally responding o exchange rae movemens is raher limied. The economic raionale behind his resul can be direcly derived from he exchange rae model underlying he open economy models. According o UIP he curren exchange rae moves in response o curren and fuure expeced movemens in he domesic and foreign nominal ineres rae as well as in response o disurbances o UIP (see euaion (5)). Le us assume for a momen ha, in addiion o a consan foreign ineres rae, here is no disurbance o UIP. Thus, he only remaining deerminan of he exchange rae is he domesic nominal ineres rae, and hence he operaing arge of he cenral bank. From his i direcly follows ha he conemporaneous movemen of he nominal exchange rae conains no exra informaion for he decision making process of he cenral bank. Thus, under such a seing policy rules R1 and R would be idenical, wih no feedback from on i (see Table 4). As a resul, if he exchange rae is no an independen source of disurbance, here is no addiional informaional value o be had from also responding o he exchange rae iself. The exchange rae is fully deermined by he policy insrumen, and hence endogenous wih respec o he decision-making process of he cenral bank. In he case of UIP disurbances, he informaional conen of he curren real exchange rae can even be uanified. Table 3 shows ha he use of R insead of R1 lowers he loss by exacly 1 per cen, given he calibraion of he UIP shock in he previous Secion. 1

12 Table 4 The improvemen of he performance when he cenral bank responds o he lagged exchange rae (R3 o R6 which all produce an idenical oucome) canno be explained by informaional advanages, bu by gains from commimen. Such gains ypically occur in models wih forwardlooking behaviour by improving he shor-run rade-off beween oupu and inflaion. For a closed economy Woodford (1999) showed ha under commimen he ineres rae response in he case of supply shocks is more gradual compared o ha associaed wih discreionary policy. 4 Specifically, he showed ha in order o manipulae privae secor expecaions opimal policy under commimen almos always involves responses o lagged saes of he economy (he so-called hisorydependence of opimal policy under commimen). On he level of simple policy rules his gain from commimen can be realised in approximaion by ineres rae rules which are no only a funcion of curren oupu and inflaion, bu also of he lagged ineres rae. In an open-economy seing his so-called ineres rae smoohing behaviour can be replicaed by responding o a lagged exchange rae erm. 5 Wih f ( 1) < an appreciaion in 1 leads o an increase in he ineres rae in. As UIP perfecly holds, he appreciaion in 1 has been riggered by an increase in he ineres rae in 1. Thus, responding o 1 is idenical o responding o i 1. This is also confirmed by he resuls shown in Table 4 according o which R3 produces he same economic oucome as he ineres rae smoohing policy rule presened in he las row of he Table. Noe ha R4, R5, and R6 only represen ransformaions of R3 (and hence he ineres rae smoohing policy rule) which yield exacly he same oucome in erms of he dynamics of he sysem. As has been sressed by Leiemo e al. () who use a model ha is idenical o our baseline model, he reason for ineria in our baseline model is ha inflaion is affeced by he change in he 4 In conras o his, if demand shocks occur (i.e. if complee sabilisaion of each of he goal variables is simulaneously possible) here is no difference in he opimal responses under discreion and under commimen (see also Clarida e al., 1999). In open economy models, his resul does no hold in general. A posiive demand shock, followed by an increase in he ineres rae, resuls in an exchange rae appreciaion, which in isolaion conribues o lower inflaion. Thus, in open economy models here is also a rade off beween inflaion and oupu sabilisaion when demand shocks occur. 5 Noe ha in our baseline model he only forward-looking agens are he foreign exchange marke paricipans, whereas price seers and consumers are assumed obe fully backward-looking. 11

13 exchange rae. In an alernaive specificaion, where only he level of he exchange rae eners he inflaion euaion π =π +γ y +γ +ε + (9) π + 1 y 1 he addiional gain from using an ineres rae smoohing policy rule disappears and he open economy policy rules is indeed idenical o he closed economy policy rule (see Table 5). Table 5 3 Uncerainy abou how he marke deermines he exchange rae A well-known resul of he empirical lieraure on exchange raes is ha he shor- and medium-run behaviour of exchange raes is no very well undersood. In paricular, he empirical evidence on he wo pariy condiions purchasing power pariy and uncovered ineres pariy which no only consiue a major building block for moneary and porfolio balance models of exchange rae deerminaion bu also for sandard open economy macro models is no very supporive in sysems of marke deermined exchange raes. This finding inroduces an imporan uncerainy for he moneary policy maker who has o ake decisions in an open economy environmen where he exchange rae influences inflaion and oupu. Thus, when seing up an economic model on he basis of which one implemens moneary policy, one has o be aware of he fac ha his model is no a rue descripion of privae agens behaviour. This concerns in paricular domesic (foreign) firms selling goods o he foreign (domesic) marke and inernaional invesors shifing funds from one currency ino anoher. In he presen sudy we assume ha he pricing behaviour of firms, and hence he degree of passhrough, is known by he moneary policy maker. Thus, deviaions from PPP do no inroduce any uncerainy ino he decision-making process (for a discussion of he impac of an uncerain degree of pass-hrough on he conduc of moneary policy see Adolfson, 1,, and Hun and Isard, 3). The focus of his paper raher is on uncerainy originaing from he inernaional financial markes. In his Secion we concenrae on how possible deviaions from UIP and he resuling uncerainy 1

14 abou he rue behaviour ener our open economy macro model. In his conex, exchange rae uncerainy is defined as he risk ha insead of UIP anoher exchange rae model is a beer descripion of exchange rae behaviour a a cerain momen in ime. We modify he baseline model so as o accoun for he possibiliy ha anoher exchange rae specificaion is a more realisic descripion of acual exchange rae behaviour. Specifically, we replace he UIP euaion (3) wih six alernaive exchange rae specificaions enumeraed by (3.i), wih i = 1,,...,6. These alernaives o UIP ha have been proposed in several papers dealing wih he evaluaion of moneary policy rules in an open economy environmen. Apar from he exchange rae model, he model s remaining euaions (he IS euaion, he Phillips curve and he relaionship beween he nominal and he real exchange rae) are always idenical wih he baseline model (euaions (1), () and (4)). One possibiliy is o model he empirical deviaions from UIP as hough hey are a srucural shock process, inerpreable as ime-varying risk premium (see Secion 3.1). This is he line mosly aken in open economy macroeconomics as i corresponds paricularly o he sandard approach o explaining he UIP puzzle by an inernaional asse pricing model wih risk averse agens. Anoher srand of research concenraes on models ha respond o he rejecion of UIP by replacing i wih an alernaive exchange rae euaion ha coninues o posi a relaionship beween ineres raes and exchange raes. And his relaionship is above all based on empirical findings which yield somewha more sable resuls han UIP esimaions (see Secions 3. and 3.3). As an alernaive o he efficien marke hypohesis, many sudies allow for deviaions from he raional expecaions hypohesis by inroducing he processes of backward-looking expecaions (see Secions 3.4 and 3.5). Finally, we inroduce a purely random exchange rae behaviour ha excludes any macroeconomic deerminan oher han is own lagged value (see Secion 3.6). 3.1 Exchange rae uncerainy 1 (U1): Time-varying and persisen risk premium shocks The sandard way of modelling deviaions from sric UIP in open-economy macro models is o include a foreign exchange risk premium s u ha follows an AR(1) process s u = ρ u +ε (3.1) s s s 1 Due o his populariy wihin he economic profession he exchange rae specificaion in our baseline model is similar o ha of numerous oher sudies. In paricular, we assumed a known and consan, aking a value of.3. However, he empirical deerminaion of he degree of ρ s 13

15 persisence ofen leads o mixed resuls. Table 6 summarises he UIP specificaions ha can be found in various simulaion sudies for he open economy. Table 6 Thus, as a firs ype of exchange rae uncerainy we allowed for variaions of ρ wihin a range from o.99. Noe ha he srucure of he model under exchange rae uncerainy 1 is similar o ha of he baseline model. The source of uncerainy solely arises from he esimaion of an imporan model parameer. Thus, while exchange rae uncerainy 1 can be aribued o parameer uncerainy, he oher ypes of exchange rae uncerainy o be presened in Secions 3. o 3.6 refer o srucural model uncerainy since we presen alernaive exchange rae euaions ha replace UIP. s 3. Exchange rae uncerainy (U): The original Ball (1999) model for open economies As an alernaive o UIP, Ball (1999) proposed a saic relaionship beween he real exchange rae and he real ineres rae r ( = i π ) of he following form: = α r + ε (3.) i I capures he idea ha a rise in he ineres rae makes domesic asses more aracive, leading o an appreciaion of he domesic currency. Albei simplified, his approach is mainly based on empirical findings on reduced-form exchange rae euaions (see Secion 3.3). Concerning he calibraion of euaion (3.), Ball (1999) assumed an ineres rae elasiciy of he real exchange rae α i of indicaing ha a one percenage poin rise in he ineres rae causes a per cen appreciaion. The origin of his value is discussed in more deail in Secion 3.3. Similar o exchange rae uncerainy 1 we even increase he degree of uncerainy in our simulaions by no only alering he exchange rae specificaion (from UIP euaion (3) o euaion (3.)) bu by allowing he parameer o vary wihin a range from o 4. α i ε is assumed o be an i.i.d. whie noise shock. 14

16 3.3 Exchange rae uncerainy 3 (U3): The empirical approach of Ryan and Thompson () In empirical models for small open economies researchers ofen found srucural reduced-form euaions of he exchange rae o be superior o UIP. In a recen sudy for Ausralia, Ryan and Thompson (, p. 13) summarise his resul as follows: A sandard, forward-looking inernaional arbirage condiion is conspicuous in is absence bu has repeaedly failed o replicae he observed behaviour of he Ausralian dollar. Insead, a lagged real ineres rae differenial has consisenly proved more successful. Thus, in heir uaniaive simulaions hey replace UIP by f ( ) = α r r α +ε (3.3) + 1 r + 1 f which can be solved for +1 : ( 1 ) ( r r ) 1 r 1 + = α α +ε +. Accordingly, he curren real exchange rae is deermined by is own lagged realisaion and he lagged real ineres rae differenial. r is he domesic real ineres rae and he foreign real rae. ε is a whie noise disurbance. Similar o he Ball (1999) approach higher domesic ineres raes lead o an appreciaion of he currency, however wih a lag of one period. Addiionally, he backward-looking elemens favour a more gradual adjusmen as opposed o (3.1). f r + 1 The parameers ha have o be deermined for a uaniaive analysis of uncerainy 3 are he ineres rae elasiciy αr and he exchange rae elasiciy α of he change in he real exchange rae. Ryan and Thompson () esimaed a macroeconomic model of he Ausralian economy on he basis of a single euaion framework. For a period from 1985:Q1 o 1998:Q4 hey arrive a he following specificaion for he real exchange rae euaion: f ( ) =.39 r 1 r o o 1 +ε where o is he erms of rade. Beechey e al. () who esimaed a model of he Ausralian economy similar o ha of Ryan and Thompson () (wih an esimaion period ending in 1999:Q3) find he following parameers: f ( ) =.59 r r o o +ε Boh sudies base heir esimaion euaions on a macroeconomic model for Ausralia ha was developed by de Brouwer and O'Regan (1997). These auhors ge he following esimaes: 15

17 f f ( ) ( )( 1) =.36dum r r.63 1 dum r r o o +ε where dum is a variable ha akes a value of one for 198:Q3 o 1984:Q4 and zero oherwise. The oal esimaion period ranges from 198:Q3 o 1996:Q3. The resuls of he hree sudies make clear ha he elasiciies are subjec o a considerable degree of uncerainy. Noe ha in all esimaions he ineres raes are expressed in per cen per annum while he change of he real ineres rae refers o a uarer of a year. Thus, if we wan o eualise he lengh of he underlying periods, he ineres rae elasiciy has o be muliplied by four which yields a value beween.5 and for he abovemenioned empirical sudies. 6 These are he values ha Ball (1999) had in mind when he se α r in his model o. The parameer α roughly ranges beween.3 and.5. Thus, in accordance wih he previous Secions, exchange rae uncerainy 3 no only refers o he possibiliy ha he UIP condiion of he baseline model is no he rue exchange rae euaion, bu also o uncerain parameers wihin his alernaive specificaion. For simpliciy we only allowed α r o vary beween f and 4; α was se o.5. For he reasons oulined in Secion. r has been se o zero. 3.4 Exchange rae uncerainy 4 (U4): Mixed expecaions I (Dennis, ) The problem wih he empirical approaches of he las wo Secions is ha hey fully rejec he hypohesis of he exchange rae as an asse price since raional expecaions are no longer par of he deerminans of he curren exchange rae. An aemp o simulaneously capure he feaures found in daa based models on he one hand and he reuiremens implied by raionaliy and efficien marke consideraions on he oher hand is o inroduce mixed expecaions. Dennis () uses he following modified UIP condiion: ( ) f s s =υ E s + 1 υ s i + i +ε (3.4) s The parameer υ defines he degree of forward-looking and raional behaviour and is a whie noise disurbance. If υ approaches uniy, expecaions are predominanly forward-looking. If υ approaches zero, expecaions are predominanly saic and backward-looking. In fac, (3.4) is a simplified version of he charis-fundamenalis model proposed by De Grauwe and Dewacher ε 6 Recall ha our model does no explicily refer o any specific freuency. Because of he scarce lag srucure i could a bes be inerpreed as an annual model (see Secion.). 16

18 (1993). Insead of using an elaborae moving average rading rule, however, he chariss in he specificaion of Dennis () simply forecas he exchange rae in + 1 by is realisaion in 1. Again changes in he foreign ineres rae are ignored in our simulaions. Uncerainy occurs wih respec o he degree of backward-looking behaviour (1 υ) in he foreign exchange marke. Dennis () only considered he exreme cases of υ = 1 and υ =. In our simulaions, however, we allowed υ o vary over he enire specrum from 1 o. 3.5 Exchange rae uncerainy 5 (U5): Mixed expecaions II (Leiemo and Södersröm, 1) A somewha more elaborae specificaion of backward-looking behaviour can be found in Leiemo and Södersröm (1). Insead of saic expecaions for he backward-looking par of he expecaions, hey assumed agens o form expecaions adapively. UIP hen becomes ( ) f s s =υ E s + 1 υ Ñ s i + i +ε (3.5) where Ñ is he adapive expecaions operaor and s ε a whie noise disurbance. The parameer υ again defines he degree of forward-looking behaviour on he inernaional financial markes. If expecaions are purely adapive ( υ=) agens updae heir exchange rae expecaions gradually in he direcion of he observed exchange rae. Thus, measures he rae of updaing. ( ) Ñs = 1 ξ s +ξñ s, where < ξ< Similar o he oher ypes of uncerainy, he foreign ineres rae is ignored. Uncerainy occurs wih respec o he degree of raionaliy υ and he rae ξ wih which agens wih adapive expecaions revise heir expecaions abou he fuure exchange rae. Again υ was allowed o vary beween and 1. Reasonable parameers for were chosen on he basis of a sudy by Frankel and Froo (1987). Using survey daa on exchange rae expecaions for he US dollar agains five major currencies hey found saisically significan values of ξ ξ ranging from.5 o.9. As he resuls of he simulaions in Secion 4 did no depend upon he value of ξ, we se i eual o Exchange rae uncerainy 6 (U6): The real exchange rae as a random variable In one of he mos widely cied papers in he inernaional economics lieraure Messe and Rogoff (1983) demonsraed ha a whole range of fundamenals-based nominal exchange rae models (flexible-price moneary models wih and wihou curren accoun effecs, and a sicky-price 17

19 moneary model) were unable o ouperform a simple random walk in an ou-of-sample forecasing exercise. Some years laer, in Messe and Rogoff (1988) hey regressed changes in he real exchange raes on real ineres rae differenials o forecas he real exchange raes of hree currencies agains he dollar. Again hey found ha he forecass from he random walk have lower roo-mean-suare error han hose from heir regressions in he majoriy of he pos-sample fi experimens. However, he pure random walk of he real exchange rae has recenly been rejeced by sudies using longspan daa ses in favour of an AR(1) process wih a high degree of persisence. Based on hese findings which are sill unconesed oday (see e.g. Kilian and Taylor, 3) we posi he following behavioural relaionship of he real exchange rae: α = α +ε (3.6) Accordingly, he real exchange rae only depends on is own lagged value and a whie noise disurbance ε + 1. In paricular, no oher macroeconomic variables, such as he domesic ineres rae, have an influence on he exchange rae. We allowed for addiional uncerainy by assuming α o ake values beween zero and uniy. For reasons of non-saionariy, however, he pure random walk scenario in which α = has o be excluded from he range of possible values. Thus, we only approximaed he random walk by defining he real exchange rae as a saionary AR(1) process wih an auocorrelaion coefficien approaching uniy Summary Table 7 summarises he exchange rae specificaions as well as he ranges of variaion of he uncerain coefficiens. Noe ha in all specificaions he variances of he whie noise shocks were se o uniy. Table 7 18

20 4 Moneary policy in an environmen wih exchange rae uncerainy In he previous Secion we presened various approaches o replacing UIP wih oher exchange rae specificaions ha he auhors of he cied sudies deemed o be a beer descripion of acual exchange rae behaviour. In his Secion we assume ha neiher of he exchange rae specificaions is perfecly rue, bu ha here is a cerain bu unknown probabiliy ha insead of baseline UIP anoher specificaion is more realisic a a cerain momen in ime. Despie his knowledge, he policy maker coninues o use he baseline model o deermine his policy rules. Thus, he deems his model o be he mos likely, even hough he is aware of he fac ha he UIP euaion (3) is only an approximaion of he rue exchange rae generaing model. The crucial uesion now is wheher he conduc of moneary policy is affeced by he uncerainy abou he rue exchange rae behaviour and wheher here is a difference in he performance of he six policy rules which are derived on he basis of he baseline model in Secion. 4.1 Conseuences of exchange rae uncerainy for he moneary policy maker In our model, uncerainy abou he rue exchange rae specificaion impacs on he performance of moneary policy on wo levels. On he firs level, he exchange rae can be regarded as an own imporan source of shocks which direcly (in he case of open economy policy rules) or indirecly (via inflaion and oupu) rigger moneary policy acions. Thus, he exchange rae is no predominanly endogenous wih respec o he ineres rae, bu vice versa. On he second level, he ransmission of ineres rae impulses via he exchange rae channel on he cenral bank s final arges is subjec o a high degree of uncerainy which enails he risk ha a cenral bank fails o pursue a successful sabilisaion policy. In he following we will illusrae he wo levels of uncerainy wih he dynamics of he sysem s variables following an exchange rae shock and an ineres rae shock for a cenral bank ha adoped R1. For he sake of comparabiliy, Figure 1 depics he impulse responses for he baseline model. The lef panel shows ha a posiive UIP shock leads o an immediae depreciaion of he nominal (and he real) exchange rae. The depreciaion simulaes inflaion and oupu in =, so ha he cenral bank rises ineres raes. Conseuenly, oupu and inflaion uickly reurn o heir arge levels. 7 In he case of a posiive ineres rae shock (righ panel), he nominal exchange rae 7 This example makes clear why in he baseline model open economy policy rules lead o slighly beer oucomes. By following a policy rule like R, he cenral bank already adjuss is ineres rae in = 1 (since i direcly responds o exchange rae movemens). By doing so, he impac of he depreciaion on π and y in = is miigaed, and hence 19

21 appreciaes in = 1. As he conracionary moneary policy sance dampens oupu in =, he cenral lowers ineres raes so as o sabilise he pah of he oupu gap. Figure 1 Under exchange rae uncerainy, he cenral bank also observes an exchange rae depreciaion following a posiive shock o he exchange rae euaion in = 1 which raises oupu and inflaion above heir arge levels in =. Again, he cenral bank pursues a conracionary policy, bu he reacion of he exchange rae in = crucially depends on he uncerainy scenario which is assumed o be in acion (see Figure ). Compared wih he baseline model, he nominal appreciaion is sronger under U and U5, weaker under U3 and approximaely he same under U1 and U4 (hough saring from a higher level under U1). Under U6 he iniial appreciaion is even followed by a furher rise in s. The differen exchange rae developmens in conjuncion wih he relaed ineres rae responses hen lead o fundamenally differen pahs for inflaion and oupu. Figure The differences in he ransmission of ineres rae impulses are depiced in Figure 3 which shows he impac of a one-ime uni shock o he ineres rae in = 1 on he model s macroeconomic variables. From = on i is assumed ha he cenral bank follows he opimal simple rule R1. The rise in he ineres rae leads o an immediae appreciaion under all exchange rae specificaions, excep for U3 and U6. However, he exen and he dynamics of he appreciaion vary considerably, so ha he ransmission on π and y as well as he relaed response of i are differen for each exchange rae specificaion. Under U3, he exchange rae reacs wih a one period lag, while under U6 he nominal exchange rae appreciaes gradually, alhough no direcly in response o he ineres rae impulse, bu indirecly as he resul of an inflaion rae ha is below arge for a prolonged he loss reduced. However, as has been shown in Secion.3, he informaional gain from responding o exchange rae movemens which are riggered by baseline UIP shocks was fairly small.

22 period of ime in conjuncion wih a consan real exchange rae. Noe ha under U1 and U6 he dynamics of he economy following an ineres rae shock are independen from he parameerisaion of he uncerainy scenario. Thus, he ransmission of ineres rae impulses under U1 is idenical o ha in he baseline model. Figure 3 4. Idenifying policy rules ha are robus o exchange rae uncerainy Secion showed ha he performance of opimised simple rules in our baseline specificaion of he open economy model improves when some weigh is pu on he exchange rae in he policy rule. However, he improvemen is only small compared o he oucome of he closed economy policy rule R1. This resul seems o confirm he relucance of many economiss owards making policy rules more complicaed by including exchange rae variables. While a basic assumpion underlying he analysis in Secion was ha he cenral bank knows he behaviour of he privae agens wih cerainy, now he cenral bank is assumed o operae in a world of uncerainy. The purpose of his Secion is o find among he se of rules he policy rule which always guaranees he policy maker he bes oucome, even hough he is uncerain abou he acual privae agens behaviour. The policy rule ha performs bes across a range of srucural models is hen called a robus policy rule since i bes possibly insulaes he economy from he negaive conseuences of boh, exchange rae shocks and uncerain ransmission of ineres rae impulses via he exchange rae channel. In he lieraure on model uncerainy one can ypically find wo mehods on how o evaluae he compeiive performance of simple ineres rae rules across several srucural models. Levin e al. (1999) ook simple ineres rae rules wih parameers ha were opimised in a baseline model for differen preferences of he cenral bank owards inflaion and oupu and compared he oucome of hese rules in erms of he variances of he goal variables and he value of he loss funcion in srucurally differen models. The baseline model is defined as he model ha he policy maker deems o be more likely han he alernaive specificaions. 1

23 The second mehod differs from he firs mainly in is reamen of he opimised policy rule. While in he firs approach he policy maker mus rely on a paricular parameerisaion of a rule (wih given numerical coefficiens resuling from he opimisaion in he baseline model) and hen consider he performance of ha given fixed rule across various models, Rudebusch (1) opimises a simple rule for each model specificaion. He hen calculaes he performance of each rule wihin he rule-generaing model and compares he resuls of one model wih hose of oher specificaions. In Rudebusch () he also assesses he performance of various srucurally differen opimised ineres rae rules by seing up a ranking in erms of loss wihin each model under consideraion. However, in he same paper he admis ha hese resuls do no capure he model uncerainy faced by a policy maker and ha he performance of a fixed rule across models is in he essence of he model robusness crierion championed by McCallum (1999) (Rudebusch,, p. 417). The same criicism has been pronounced by Sock (1999, p. 54) who argues ha he essence of policy robusness is wheher a specific uaniaive rule performs well under a model oher han ha used o develop he policy. We decided in favour of he firs mehod as our goal is o show how uncerainy abou he rue exchange rae deerminaion on he financial markes affecs moneary policy ha has commied iself o follow a ime-invarian simple ineres rae rule. In conras o he approach of Levin e al. (1999), however, we did our analysis for one specific preference srucure of he moneary policy maker, namely λ π = λ = y 1. The resuls are presened in Figure 4 which shows for each exchange rae specificaion he loss from all he policy rules in a single char. Figure 4 Wih a growing risk premium persisence (U1), he loss increases. While variaions of ρ beween and.5 do no have a major impac on he value of he loss funcion, a ρ s approaching uniy makes he loss grow progressively. 8 The empirical approaches o he deerminaion of he real exchange rae (U and U3) produce U-shaped loss curves. The loss reaches is minimum for an ineres rae s 8 This explains why he concree value of ρ s (which we se o.3 in he baseline model) plays only a minor role for he deerminaion of he policy rules provided ha ρ s does no a exceed a criical value.

24 elasiciy of he real exchange rae somewhere beween zero and wo. Wih a growing α he loss increases much faser han wih a falling α i/r. A noable excepion is he oucome of R6 under U. The resuling loss seems o be almos immune agains uncerainy abou α. The inroducion of mixed expecaions (U4 and U5) reduces he loss resuling from he policy rules relaive o he fully raional baseline case ( υ=1) up o a criical mass. The concree resuls, however, depend on boh, he policy rule and he exchange rae specificaion. Under U4, he performance of policy rules R and R6 becomes beer he higher he degree of saic (and hence backward-looking) expecaions. In conras o his, he loss curves of he oher rules have a minimum which is a υ=.5 for R1, υ=.7 for R3, and υ=.3 for R4 and R5. An examinaion of U5 shows ha for a growing degree of adapive expecaions (i.e. a lower υ) he behaviour of he loss curve of R1, R and R3 differs from ha of R4, R5 and R6. The firs group reaches a minimum loss a an i/r somewhere beween.4 and.7. If υ is furher reduced, he loss resuling from hese rules uickly explodes. In conras o his, he loss from he las hree rules remains relaively low. Wih regard o a purely random real exchange rae (U6), loss increases wih a growing high for a pure random walk. α. Excep for R and R6, he loss becomes very Significan differences in he performance of he rules only occur for a large risk premium persisence (U1), a high ineres rae elasiciy of he exchange rae (U and U3), a high degree of backward-looking expecaions (U4 and U5) and a near-random-walk behaviour of he real exchange rae (U6). In Table 8 we se up a ranking of he bes and second bes performing policy rule for each model specificaion. I shows ha R6 performs very well under all ypes of exchange rae uncerainy. R, R4 and R5 also seem o produce relaively good resuls. However, R performs wors under U3; and so do R4 and R5 under U. i υ Table 8 In shor, we ge he following resuls: 1. The closed economy policy rule R1 according o which he cenral bank ses independen of any exchange rae developmens performs badly under marke deermined exchange raes wih i 3