Federal Reserve Bank of St. Louis Review, Third Quarter 2015, 97(3), pp

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1 Moneary Policy in Small Open Economies: The Role of Exchange Rae Rules Ana Maria Sanacreu Undersanding he coss and benefis of alernaive moneary policy rules is imporan for economic welfare. Wihin he conex of a small open economy model and building on he work of Mihov and Sanacreu (2013), he auhor analyzes he economic implicaions of wo moneary policy rules. The firs is a rule in which he cenral bank uses he nominal exchange rae as is policy insrumen and adjuss he rae whenever here are changes in he economic environmen. The second is a sandard ineres rae rule in which he cenral bank adjuss he shor-erm nominal ineres rae o changes in he economic environmen. The main finding of he analysis is ha, if he uncovered ineres pariy condiion ha esablishes a igh link beween he ineres rae differenial in wo counries and he expeced rae of depreciaion of heir currencies does no hold, he exchange rae rule ouperforms he sandard ineres rae rule in lowering he volailiy of key economic variables. There are wo main reasons for his: Firs, he acual implemenaion of he exchange rae rule avoids he overshooing effec on exchange raes characerisic of an ineres rae rule. And second, he risk premium ha generaes deviaions from he uncovered ineres pariy condiion is smaller and less volaile under an exchange rae rule. (JEL E52, E58, F41) Federal Reserve Bank of S. Louis Review, Third Quarer 2015, 97(3), pp The objecive, eiher explici or implici, for mos cenral banks is o keep inflaion low and sable while avoiding large flucuaions in real economic variables (i.e., oupu and unemploymen). 1 To achieve heir objecive, cenral banks use an insrumen, ypically he nominal ineres rae, ha is adjused when here are deviaions of inflaion from an explici or implici arge or deviaions of oupu from is poenial (i.e., significan deviaions in he oupu gap). Mos cenral banks adjus heir ineres rae in a manner consisen wih he so-called Taylor rule an ineres rae rule (IRR) ha specifies by how much he moneary auhoriy increases (decreases) he shor-erm nominal ineres rae when inflaion is above (below) he arge or he oupu gap is posiive (negaive). 2 In small open economies, however, he exchange rae is an imporan elemen of he ransmission of moneary policy (Svensson, 2000). Cenral banks in such economies generally Ana Maria Sanacreu is an economis a he Federal Reserve Bank of S. Louis. This aricle is based on a research projec wih Ilian Mihov eniled The Exchange Rae as an Insrumen of Moneary Policy. The auhor hanks Fernando Leibovici, Ilian Mihov, Paulina Resrepo-Echevarria, Yi Wen, and Seve Williamson for helpful commens and Usa Kerdnunvong for research assisance. 2015, Federal Reserve Bank of S. Louis. The views expressed in his aricle are hose of he auhor(s) and do no necessarily reflec he views of he Federal Reserve Sysem, he Board of Governors, or he regional Federal Reserve Banks. Aricles may be reprined, reproduced, published, disribued, displayed, and ransmied in heir enirey if copyrigh noice, auhor name(s), and full ciaion are included. Absracs, synopses, and oher derivaive works may be made only wih prior wrien permission of he Federal Reserve Bank of S. Louis. Federal Reserve Bank of S. Louis REVIEW Third Quarer

2 Sanacreu prefer o mainain igh conrol over he exchange rae. Several auhors have analyzed he performance of moneary rules ha explicily ake ino accoun he exchange rae in he conex of general equilibrium models. In paricular, wo exchange rae siuaions have been analyzed: (i) flexible exchange raes in which he moneary auhoriy follows an exended IRR ha reacs o deviaions of inflaion, oupu, and he exchange rae (De Paoli, 2009) or (ii) fixed exchange raes in which he cenral bank pegs he exchange rae o he currency of anoher counry and commis o defending such a peg by losing is abiliy o conrol he nominal ineres rae (Schmi-Grohé and Uribe, 2011). The Unied Saes, Canada, and Japan, for insance, follow a flexible exchange rae regime. Hong Kong, Denmark, and Bulgaria follow a fixed exchange rae regime. There is a hird possibiliy ha has no been analyzed exensively in he conex of a general equilibrium model. The cenral bank could use he exchange rae as an insrumen in he same way i uses he ineres rae in he IRR ha is, by adjusing he exchange rae o flucuaions in economic condiions. This is known as an exchange rae rule (ERR) and is he policy followed by he Moneary Auhoriy of Singapore (MAS) since Indeed, 98 percen of he asses held on he MAS balance shee are foreign asses. Therefore, in conras o oher small open economies in which he cenral bank inervenes mainly in he domesic bond marke o conduc moneary policy while sill paying aenion o flucuaions in he nominal exchange rae (as in New Zealand, Ausralia, and Canada), he MAS inervenes mainly in he foreign exchange marke o conduc moneary policy. (This scenario differs from siuaion (i) menioned earlier.) Thus, heir insrumen is he nominal effecive exchange rae, which is allowed o flucuae whenever here are changes in economic condiions. (This scenario differs from siuaion (ii) menioned earlier.) In a recen aricle, Mihov and Sanacreu (2013) aemp o fill his gap in he lieraure by analyzing a small open economy model of moneary policy o compare he implicaions of wo ypes of rules for economic volailiy. Firs, hey examine a model in which he cenral bank uses he shor-erm nominal ineres rae as he insrumen and allows he exchange rae o adjus from he decisions of economic agens (IRR). Then, hey sudy a model in which he cenral bank uses he exchange rae as he insrumen and allows he ineres rae o adjus from he decisions of economic agens (ERR). They ask he following quesion: Under wha condiions can a cenral bank achieve lower economic volailiy by using an ERR raher han an IRR? Mihov and Sanacreu (2013) argue ha he coss and benefis of an IRR versus hose of an ERR depend on wo facors: he acual implemenaion of he policy and wheher he uncovered ineres pariy (UIP) condiion holds. Firs, he acual implemenaion of he rule is imporan. While he cenral bank echnically can replicae any IRR by moving he exchange rae oday and announcing depreciaion consisen wih UIP, his is no how he rule operaes. In Mihov and Sanacreu (2013), he exchange rae oday is predeermined and he cenral bank announces he depreciaion rae from ime o +1. This implies, for example, ha he model may no feaure he sandard overshooing resul as he currency rae boh oday and a +1 are deermined by he moneary auhoriy. However, hey find his feaure is insufficien in generaing significan differences beween he wo rules. Therefore, he only way he 218 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

3 Sanacreu new model can provide ineresing dynamics is by incorporaing a failure of UIP. UIP predics ha currencies wih high ineres raes will depreciae relaive o hose wih low ineres raes. Tha is, arbirage should ensure ha he following wo invesmen sraegies are equivalen: An invesor eiher buys a domesic asse a he curren domesic ineres rae and collecs he proceedings omorrow or exchanges domesic currency for foreign currency a he curren exchange rae o inves in an idenical foreign asse ha pays he ineres rae of he foreign counry and omorrow exchanges he foreign currency back o domesic currency. This sraegy implies ha if he domesic ineres rae is higher han he foreign ineres rae, one should expec he domesic currency o depreciae beween oday and omorrow. Alvarez, Akeson, and Kehoe (2007) argue ha in large par he impac of moneary policy on he economy proceeds hrough condiional variances of macroeconomic variables raher han condiional means. In erms of he UIP condiion, heir aricle implies ha he ineres pariy condiion has a ime-varying risk premium. Ineres in ime-varying risk premiums has been growing in recen years. In he conex of he ineres pariy condiion, Verdelhan (2010) shows how consumpion models wih exernal habi formaion can generae a counercyclical risk premium ha maches key sylized facs quie successfully. Mihov and Sanacreu (2013) adop a similar approach by allowing exernal habi formaion in consumpion. In a producion economy, Mihov and Sanacreu (2013) find ha an ERR achieves lower volailiy of boh nominal and real variables. Conrary o a fixed exchange rae scenario in which he cenral bank achieves lower volailiy of nominal variables a he expense of increasing he volailiy of he real variables (Schmi-Grohé and Uribe, 2011), an ERR can sabilize boh because i is an inermediae exchange rae regime. The reasons are wofold: Firs, he acual implemenaion of he policy avoids he overshooing effec of an IRR. Second, an ERR reduces he mean and he volailiy of he risk premium ha causes deviaions from UIP. The aricle proceeds as follows. Firs, I describe how an ERR operaes and use he case of Singapore o illusrae i. Then, I presen an endowmen economy ha feaures deviaions from UIP hrough he exisence of a risk premium. I show ha he risk premium responsible for hese deviaions depends on he paricular policy rule he cenral bank follows (IRR versus ERR) and he parameers of he moneary policy rule. In an endowmen economy, hese deviaions affec only nominal variables. To capure he effec of alernaive rules on boh nominal and real variables, I hen describe a small open producion economy in which consumpion and oupu are boh endogenous and repor he quaniaive implicaions of he model. EXCHANGE RATE RULES: SINGAPORE In his secion, I describe Singapore s moneary policy o illusrae how an ERR works. According o he MAS Ac, he main objecive of moneary policy in Singapore is o ensure low inflaion as a sound basis for susained economic growh (Moneary Auhoriy of Singapore). To do ha, since 1981, The MAS manages he Singapore dollar (S$) exchange rae agains a rade-weighed baske of currencies of Singapore s major rading parners and compeiors. The composiion of his baske is reviewed and revised periodically o ake ino accoun changes in Singapore s Federal Reserve Bank of S. Louis REVIEW Third Quarer

4 Sanacreu Figure 1 Singapore Dollar Nominal Effecive Exchange Rae SGD NEER Boom Band Middle Band Top Band Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 NOTE: Here, he Singapore dollar (SGD) nominal effecive exchange rae (NEER) is defined as he inverse of he usual NEER and in erms of rade-weighed rading parners currencies per he Singapore dollar. Thus, he decrease in he figure means an appreciaion of he Singapore dollar currency. The boom, middle, and op band indexes are esimaed by Ciigroup, based on MAS moneary policy saemens. SOURCE: Calculaions based on: Cii Research, SGD NEER Indices, Bloomberg Finance L.P.; accessed April rade paerns. This rade-weighed exchange rae is mainained broadly wihin an undisclosed arge band, and is allowed o appreciae or depreciae depending on facors such as he level of world inflaion and domesic price pressures. MAS may also inervene in he foreign exchange marke o preven excessive flucuaions in he S$ exchange rae. In he conex of Singapore s open capial accoun, he choice of he exchange rae as he focus of moneary policy would necessarily imply ha domesic ineres raes and money supply are endogenous. As such, MAS s money marke operaions are conduced mainly o ensure ha sufficien liquidiy is presen in he banking sysem o mee banks demand for reserve and selemen balances. (Moneary Auhoriy of Singapore) Specifically, he MAS announces a pah of appreciaion or depreciaion of is currency based on he expeced economic condiions. Figure 1 shows Singapore s nominal exchange rae wih respec o a baske of currencies since January As he downward rend reveals, he Singapore dollar has been appreciaing over ime, which reflecs Singapore s rapid economic developmen during his ime. (The definiion of he exchange rae in he figure is such ha a decrease implies an appreciaion of he Singapore dollar.) In he shor run, he exchange rae flucuaes. To avoid misalignmen and deviaions from he fundamenals, he MAS inervenes in he foreign exchange marke o keep he value of he exchange rae wihin a specified policy band. The moneary auhoriy may change he slope of he band when changes in he economic environmen call for i. As Figure 1 shows, he MAS has changed he slope of appreciaion of 220 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

5 Sanacreu Table 1 Reacion Funcion Consan Inflaion Oupu gap Lagged appreciaion (a) ( φ π ) ( φ y ) (r) (0.291) (0.120) (0.130) (0.052) NOTE: Sandard errors are shown in parenheses. and denoe significance a he 5 percen and 1 percen levels, respecively. SOURCE: Mihov (2013). Used wih permission. he insrumen several imes. The mos recen inervenion was in January 2015, when he MAS slowed he rae of appreciaion of he Singapore dollar. 3 Several auhors (see, for example, Parrado, 2004) have esimaed a reacion funcion for changes in he moneary policy insrumen as proxied by he change in he nominal exchange rae. Tradiional empirical reacion funcions have used he nominal ineres rae as he insrumen. Moneary policy in Singapore is unique in ha i uses he nominal exchange rae o achieve low inflaion and susained growh. In paricular, assume (i) ha he moneary auhoriy has a arge for he change in he nominal exchange rae De and (ii) ha i adjuss he arge based on deviaions of inflaion from a prespecified arge and deviaions of oupu from is poenial level as follows: ( ) y( ) e = e φ π π φ y y π, where De is he long-run equilibrium change in he nominal exchange rae consisen wih long-run purchasing power pariy, p is he inflaion rae a ime, p is a arge for inflaion, y is he level of oupu, and y is he poenial level of oupu he economy would produce if all he facors of producion were fully employed (i.e., y y is he oupu gap). Consisen wih he definiion of he nominal effecive exchange rae in Figure 1, an increase in he nominal exchange rae in he equaion represens a depreciaion of he Singapore dollar. I follow his convenion hroughou he aricle. To capure some degree of smoohing in he adjusmen of he nominal exchange rae o is arge level, e = ( 1 ρe) e + ρ e 1, where r e [0,1] is he degree of exchange rae smoohing. Combining he wo previous expressions yields he following equaion: ( ) y( ) = α φ π π e φ y y + ρ e, π 1 e Federal Reserve Bank of S. Louis REVIEW Third Quarer

6 Sanacreu where a is a consan, φ, and π = φ π ( 1 ρ. Table 1 repors he resuls from e ) φ = φ ( 1 ρ ) y y e he esimaion of he previous expression. 4 Table 1 shows ha he Singapore dollar appreciaes when inflaion increases or he oupu gap widens. In paricular, a 1 percen increase in inflaion implies a percen appreciaion in he Singapore dollar. Similarly, a 1 percen increase in he oupu gap implies a percen appreciaion in he Singapore dollar. The esimaion also shows some degree of exchange rae smoohing, wih an esimaed smoohing parameer of MONETARY POLICY AND THE UNCOVERED INTEREST PARITY CONDITION: AN ENDOWMENT ECONOMY Nex, I presen a model ha capures deviaions from UIP by inroducing an endogenous risk premium on foreign-denominaed asses. I sar wih an endowmen economy so ha I can derive an analyical expression for he risk premium. The economy is a small open economy in which here is a represenaive consumer who maximizes a uiliy funcion ha feaures exernal habi in consumpion. Consumpion follows an exogenous process, and here are complee inernaional markes. Inflaion is deermined by a cenral bank ha uses eiher he nominal ineres rae (he IRR) or he exchange rae (he ERR) as is insrumen. I assume ha, in he res of he world, he cenral bank follows an IRR, since i behaves as a closed economy and is no as srongly affeced by flucuaions in he nominal exchange rae as he small open economy. Afer deriving an analyical soluion for he risk premium under boh moneary policy rules (an IRR and an ERR), I show ha he risk premium responsible for deviaions from UIP depends on he paricular moneary rule followed by he cenral bank and he parameers of he rule ha is, on he magniude of he cenral bank s reacion o flucuaions in inflaion and he oupu gap. Theory Sandard asse-pricing models assume ha he UIP condiion holds. Tha is, he models predic ha high ineres rae currencies will depreciae relaive o low ineres rae currencies o saisfy an arbirage condiion. However, for many currency pairs and ime periods, he opposie seems o occur (Fama, 1984). In he lieraure, he inabiliy of asse-pricing models o reproduce he empirical evidence is referred o as he UIP puzzle. The UIP evidence is relaed o shor-erm ineres raes and currency depreciaion raes. Because moneary policy influences shor-erm ineres raes in he case of an IRR or nominal exchange raes in he case of an ERR, he UIP puzzle can be formulaed in erms of moneary policy (Backus e al., 2010). A radiional open economy model canno replicae he forward premium anomaly as i ypically assumes ha UIP holds. When invesors are assumed o be risk neural, any cross-counry differences in ineres raes are associaed wih offseing movemens in expeced depreciaion. Various approaches in he lieraure o accoun for he forward premium anomaly include assuming ha markes are incomplee (Benigno, 2009) and modeling he deviaions hrough 222 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

7 Sanacreu a risk premium ha generaes a wedge beween he ineres rae differenial and he expeced exchange rae depreciaion (Alvarez, Akeson, and Kehoe, 2009; Backus e al., 2010; Benigno, Benigno, and Nisicò, 2013; and Verdelhan, 2010, among ohers). The risk premium inerpreaion of he UIP puzzle assers ha high ineres rae currencies pay posiive risk premiums. Therefore, one could derive an expression for he risk premium ha depends on he moneary policy insrumen and ask he following quesion: Wha moneary policy generaes larger flucuaions of he risk premium and herefore larger deviaions from he UIP condiion? To answer his quesion, I derive an analyical soluion for he foreign exchange risk premium as a funcion of he moneary rule parameers for boh an IRR and an ERR. I follow he procedure described by Backus e al. (2010) for an endowmen economy wih complee markes bu wih one modificaion: Insead of using recursive preferences, I assume here is exernal habi in he uiliy funcion (as in Verdelhan, 2010). Exernal habi formaion, also known as caching up wih he Joneses (Abel, 1990), simplifies he consumer s opimizaion problem because he evoluion of he sock of habi is aken as exogenous by he consumer. The following seps are aken o obain an expression for he risk premium: Sep 1: Preferences. In each counry, here is a represenaive household ha maximizes lifeime expeced uiliy. The uiliy funcion of he household in he domesic economy is given by 1 γ ( C hx) (1) E0 β U( C hx) =, = 0 1 γ where g denoes he coefficien of risk aversion, h is he parameer of habi persisence, X is he level of habis defined below, and C is consumpion. The evoluion of habis follows an AR(1) process wih accumulaion of habis based on las-period consumpion: X = δx + ( 1 δ) C, 1 1 where d [0,1] capures he degree of habi persisence. In a model wih habi (h 0), he consumer cares abou deviaions of consumpion from a cerain subsisence level. In his case, he coefficien of relaive risk aversion (CRRA) is γc CRRA : = C hx. The CRRA is ime varying and counercyclical: In good imes, when consumpion is far from is subsisence level (i.e., C > hx ), he denominaor increases and risk aversion decreases. Good imes correspond o a posiive shock o consumpion growh. Following he lieraure, assume ha he log of consumpion follows he AR(1) process (2) log( C ) = λlog ( C ) + ε, + 1 c, + 1 where l [0,1] and e c,+1 is an i.i.d. process wih zero mean and sandard deviaion s e. Sep 2: The Sochasic Discoun Facor. In his economy, he sochasic discoun facor or pricing kernel is deermined by he following expression: Federal Reserve Bank of S. Louis REVIEW Third Quarer

8 Sanacreu (3) M, + 1 ( ) ( ) U C hx = β U C hx C hx = β C hx c c γ. (4) Sep 3: The Risk-Free Rae. Define he risk-free rae R as R = E ( M, + 1) where R is he gross reurn on a riskless, one-period discoun bond paying off one uni of domesic currency in +1. The Euler equaion of a foreign invesor buying a foreign bond wih reurn R +1 is 1, (5) E( M, + 1R )= 1. The Euler equaion for a domesic invesor buying he same foreign bond is + (6) E M, + 1R Q 1 = 1, Q where Q is he real exchange rae expressed as he amoun of domesic good per uni of foreign good, defined as where P is he price of a baske of foreign goods and P ha of domesic goods. M,+1 and M,+1 are he domesic and foreign nominal pricing kernels, respecively. Sep 4: Inernaional Risk-Sharing Condiion. Households have access o a complee se of coningen securiies ha are raded inernaionally ha is, markes are complee. Wih complee markes, he sochasic discoun facor is unique and he following expression holds: Q = e P, P (7) Q Q M = M. + 1, + 1, + 1 We can now define he nominal ineres differenial i i, where i = log(r ) and i = log(r ), he expeced nominal depreciaion is E [de +1 ], and he exchange rae risk premium is fxp in erms of he domesic and foreign nominal pricing kernels, M,+1 and M,+1, respecively. From he previous expressions we find ha he ineres rae differenial has o equal he difference of he sochasic discoun facors in he foreign and domesic economies: Wih complee markes, ( ) ( ) i i = log E M M, + 1 log E, + 1. ( ) ( ) E[ de ]= M M + 1 E log, + 1 E log, Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

9 Sanacreu Combining he previous wo expressions and assuming log-normaliy of he pricing kernel, 5 (8) i i = de + fxp E [ ] + 1, wih he risk premium defined as 1 (9) fxp = Var log( M, 1) Var log( M, 1) The risk premium is equal o half he difference beween he condiional variance of he foreign and domesic sochasic discoun facors. The risk premium in equaion (9) capures deviaions from UIP. In he absence of a risk premium, if he domesic ineres rae were higher han he foreign ineres rae, he domesic currency would be expeced o depreciae over ime such ha an invesor would be indifferen beween holding a domesic or a foreign asse. However, wih a posiive risk premium, i is possible for high ineres rae currencies o appreciae over ime. This would happen if he invesor were risk averse and would demand a posiive premium o hold foreign currency. Sep 5: The Moneary Policy Rule. One can now derive an expression for he foreign risk premium when he domesic economy follows one of he wo rules: an IRR or an ERR. Assume ha he foreign economy follows an IRR (because i is a large economy and herefore is no as srongly affeced by exchange rae flucuaions as he small open economy): (10) i = φπ π + φc c, where i is he foreign nominal ineres rae, c is foreign consumpion, and p is foreign inflaion. In he domesic economy, we consider boh IRR and ERR, as follows: (i) IRR (11) IRR IRR i = φ π + φ c. π c The cenral bank increases he ineres rae whenever inflaion (p ) and consumpion (c ) increase, wih f p IRR and f c IRR indicaing he magniude of he adjusmen. (ii) ERR (12) ERR ERR de = φ π φ c. π c The cenral bank appreciaes he nominal exchange rae whenever inflaion (p ) and consumpion (c ) increase, wih f p ERR and f c ERR indicaing he magniude of he adjusmen. Sep 6: The Risk Premium. To derive an analyical soluion for he risk premium, I follow Backus e al. (2010) and use he mehod of undeermined coefficiens; hey assume ha inflaion follows a paricular funcional form. Then, using he firs-order condiions, he inernaional risk-sharing condiion, and he expression for he corresponding rule, I obain an expression for he risk premium ha can be expressed as Federal Reserve Bank of S. Louis REVIEW Third Quarer

10 Sanacreu Table 2 Calibraed Parameers Parameer Descripion Value h Habi 0.85 d Degree habi 0.97 g Coefficien of risk aversion 2.50 l Persisen shock 0.01 s e Sandard deviaion shock 2.50 SOURCE: Modified from Mihov and Sanacreu (2013). (13) fxp = κ κ c κ x, where x is he log of X and k 0 > 0, k 1 > 0, and k 2 > 0 depend on he paricular rule used and he parameers of he moneary policy rule (i.e., how srongly he cenral bank reacs o deviaions of inflaion from is arge and flucuaions of he oupu gap). 6 Noe ha he risk premium fxp is ime varying and counercyclical. In good imes, when consumpion is high, he risk premium decreases. I can also be shown ha if h = 0, hen k 1 = k 2 = 0, and here is a consan risk premium. Quaniaive Resuls Now, I analyze he effec of he wo alernaive rules on he mean and volailiy of he risk premium. Assuming a paricular process for consumpion growh in equaion (2), one can use equaion (13) o analyze he effec of he wo policy rules on he deviaions from UIP. Noe ha only he nominal variables are affeced because consumpion follows an exogenous process in his model. Simulaions of he endowmen economy described previously show ha he mean and he sandard deviaion of he risk premium differ depending on he paricular rule followed by he moneary auhoriy and he parameers of such a rule (i.e., how srongly he cenral bank reacs o deviaions of inflaion from is arge and flucuaions of he oupu gap). Table 2 shows he calibraed parameers (see Mihov and Sanacreu, 2013). Firs, impulse response funcions for a 1 percen sandard deviaion shock o consumpion show ha boh consumpion and inflaion increase in he case of an IRR (he solid line in Figure 2). 7 The cenral bank hen increases he ineres rae (see equaion (11)), and he currency depreciaes a +1. If he UIP condiion holds, he depreciaion is exacly equal o he iniial increase in he ineres rae. However, because now here is a decrease in he risk premium (hrough equaion (9)), he currency depreciaes by less han i would wih no risk premium. In he case of an ERR (he dashed line in Figure 2), afer a posiive consumpion growh he cenral bank reacs o he increase in boh consumpion and inflaion by appreciaing 226 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

11 Sanacreu Figure 2 Impulse Response Funcion o a Consumpion Shock: ERR Consumpion IRR ERR Inflaion Surplus Consumpion 0.8 Nominal Ineres Rae Depreciaion Rae 0 Risk Premium currency unil i reaches a new equilibrium. If he UIP condiion is saisfied, he ineres rae should decrease by exacly he same amoun, bu he ineres rae increases. As Figure 2 shows, boh inflaion and he nominal ineres rae respond less srongly o a consumpion shock when he cenral bank follows an ERR han when i follows an IRR, which suggess ha wih an ERR he moneary auhoriy is more successful in sabilizing he nominal variables. One of he main reasons is he acual implemenaion of he policy. The oher is ha he risk premium falls by less wih an ERR han wih an IRR. The fall in he risk premium afer a consumpion shock has consequences on he differing effec of he wo rules on he nominal variables. To beer undersand his poin, Table 3 repors he mean and variance of he risk premium under each rule (IRR versus ERR) and for differen values of he parameers of he reacion funcion (f p and f c ). In all cases, he ERR delivers a lower mean and lower volailiy in he risk premium. We also observe differences dependen on he magniude of he moneary auhoriy s reacion o flucuaions in inflaion and consumpion. These differences are more pronounced when he moneary auhoriy follows an IRR. Federal Reserve Bank of S. Louis REVIEW Third Quarer

12 Sanacreu Table 3 Risk Premium IRR ERR Parameer (f p, f c ) (1.5, 0.5) (1.05, 0.5) (1.50, 0.05) (1.5, 0.5) (1.05, 0.5) (1.50, 0.05) Mean Sandard deviaion Because in his exercise I have modeled an endowmen economy assuming he same consumpion pah under an IRR as under an ERR, he implied differences in he risk premium, alhough nonnegligible, are small and affec only nominal variables. To capure he effec of he differen rules on real variables as well, one should consider a producion economy in which consumpion is endogenous and is also affeced by he paricular rule he moneary auhoriy follows. In he nex secion, I describe a producion economy version of he endowmen economy jus presened and analyze he effec of each rule on he volailiy of economic variables. MONETARY POLICY AND THE UNCOVERED INTEREST PARITY CONDITION: A PRODUCTION ECONOMY Here I develop a producion economy in which consumpion growh is endogenous and depends on he paricular moneary policy rule followed by he cenral bank. In conras o he previous case of an endowmen economy, now I canno derive an analyical soluion for he risk premium. However, he advanage of a producion economy is ha he moneary policy rule has a sronger effec on he risk premium, which generaes larger differences beween he wo rules. Theory I follow he work of De Paoli and Søndergaard (2009) and Mihov and Sanacreu (2013) o develop a small open economy model wih wo alernaive rules: an IRR and an ERR. The small open economy, which is also he domesic economy, is modeled explicily. The foreign economy is assumed o be exogenous (foreign oupu, inflaion, and ineres raes follow an AR(1) process). In he small open economy, here is a represenaive consumer who chooses consumpion, labor, and savings subjec o a sandard budge consrain. There is exernal habi in consumpion, as explained in he previous secion: Consumers care abou heir consumpion relaive o a subsisence level. Markes are complee, and consumers have access o a complee se of coningen securiies ha are raded inernaionally. In his economy, consumpion is an aggregae of boh domesic and foreign goods (i.e., impors). There is home bias in consumpion, which deermines he degree of openness of 228 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

13 Sanacreu he economy. Consumers choose opimally how much o consume of each domesic and foreign good. On he producion side, each good is produced by a monopolisically compeiive firm ha uses labor according o a consan reurns-o-scale producion funcion. Producion of goods is subjec o an aggregae produciviy shock, which is he only source of uncerainy in his economy. Firms ake as given he demand by he final producer and se a price ha is a consan markup over heir marginal cos. In his model, prices are sicky à la Calvo. In each period, a consan fracion of firms se prices opimally, and he res se he price from he previous period. This resuls in a forward-looking process for inflaion: Inflaion oday depends on he oupu gap and expeced fuure inflaion. The model is closed wih an inernaional risk-sharing condiion ha (i) resuls from he assumpion of complee markes and (ii) deermines a relaionship beween he domesic and foreign ineres raes and he expeced rae of depreciaion of he currency. The cenral bank chooses a moneary policy insrumen o reac o flucuaions in inflaion and he oupu gap, which in his model is defined as he difference beween acual oupu and he oupu ha would be obained if prices were flexible. Consider, as before, wo cases for he moneary policy rule: (i) a rule in which he moneary auhoriy ses he ineres rae and les he exchange rae adjus wih he inernaional risk-sharing condiion ha arises from he assumpion of complee markes (IRR), and (ii) a rule in which he moneary auhoriy ses he exchange rae and les he nominal ineres rae adjus hrough he inernaional risk-sharing condiion (ERR). In his model, and o be more consisen wih he rule acually followed by he moneary auhoriy, I assume some degree of ineres rae smoohing for an IRR and some degree of exchange rae smoohing for an ERR. Tha is, he rules are modeled as follows: (i) IRR i = ρi 1 + ( 1 ρ) φy y y + φπ π π, where r (0,1) is he degree of ineres rae smoohing. (ii) ERR ( ( ) ( )) ( ) π ( ) e e e = e φ y y φ π π y where De is he depreciaion required o reach he long-run equilibrium nominal exchange rae. 8 I assume some smoohing in how he nominal exchange rae adjuss o is arge level: e = ( 1 ρe) e + ρ e 1. In conras o he endowmen economy in which I could obain an analyical soluion o capure flucuaions in he risk premium and, hence, deviaions from UIP he producion economy model has o be simulaed. Mihov and Sanacreu (2013) solve he model using a hird-order approximaion and compue second momens for he variables ha he moneary auhoriy cares abou: domesic inflaion, consumer price index (CPI) inflaion, and oupu. e Federal Reserve Bank of S. Louis REVIEW Third Quarer

14 Sanacreu Table 4 Second Momens: Producion Economy Variables IRR ERR Oupu Consumpion Oupu gap Domesic inflaion Depreciaion rae CPI inflaion Risk premium 1.09e e-05 Quaniaive Resuls Table 4 repors second momens of several economic variables and he risk premiums for he wo alernaive rules. The ERR generaes lower volailiy in he economy for boh nominal and real variables. By smoohing he flucuaions in he nominal exchange rae, he cenral bank achieves lower volailiy in boh domesic inflaion and CPI inflaion, which also akes ino accoun he inflaion of prices for foreign inermediae goods. The main difference beween his rule and one in which he exchange rae is fixed o he currency of anoher counry (i.e., pegged) is as follows: Because a cenral bank ha follows an ERR also reacs o flucuaions in real variables, such as he oupu gap, i can achieve less volaile nominal variables wihou increasing he volailiy of real variables, as would happen wih a peg. Oupu, consumpion, and he oupu gap are less volaile wih an ERR han wih an IRR. There are wo reasons for he lower volailiy: Firs, he acual implemenaion of he rule is imporan. In he model, he exchange rae oday is predeermined, and he cenral bank announces he depreciaion rae from ime o +1. This implies, for example, ha he model may no feaure he sandard overshooing resul because he moneary auhoriy deermines he currency rae boh oday and a +1. Second, deviaions from UIP are imporan. One way o measure hese deviaions in he model is by compuing he volailiy of he implied risk premium, which as Table 4 shows, is lower for an ERR han for an IRR. CONCLUSION Analyzing he properies of alernaive moneary policy rules is imporan from a welfare perspecive. In his aricle, I sudy he impac of an ERR on he volailiy of boh nominal and real variables. Simulaions of a producion economy show ha he ERR is more effecive in achieving lower economic volailiy han a sandard IRR. There are wo reasons for his: (i) The acual implemenaion of he policy maers, since he ERR avoids he overshooing in he nominal exchange rae, and (ii) he risk premium ha generaes deviaions from UIP is less volaile wih an ERR. Moreover, he ERR performs beer han a peg, since he moneary 230 Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW

15 Sanacreu auhoriy achieves exchange rae sabiliy wihou relinquishing is abiliy o reac o flucuaions of he economy. I have incorporaed several key issues in my analysis here. For insance, he credibiliy of he cenral bank is imporan for a policy such as he ERR o be successful and avoid large flucuaions in he nominal exchange rae. For a counry wih large capial inflows, lack of credibiliy in he moneary policy regime could rigger speculaive aacks on he currency. Furhermore, he moneary auhoriy s abiliy o adjus he exchange rae requires he auhoriy o hold sufficien foreign reserves on is balance shee. I have also absraced from balanceshee effecs. Finally, he iniial ne foreign asse posiion of he counry (wheher i has a surplus or a defici) maers for he performance of he rules ha aemp o sabilize he nominal exchange rae. I leave hese issues for fuure analysis on his opic. NOTES 1 The Federal Reserve s mandaes are maximum employmen, sable prices, and moderae long-erm ineres raes [wih] inflaion a he rae of 2 percen (year-on-year inflaion of personal consumpion expendiures, or PCE; see Board of Governors of he Federal Reserve Sysem, 2014). Moreover, he euro area mandae is []o mainain price sabiliy is he primary objecive of he Eurosysem and of he single moneary policy for which i is responsible (European Cenral Bank). And The Bank of Japan, as he cenral bank of Japan, decides and implemens moneary policy wih he aim of mainaining price sabiliy (Bank of Japan). 2 See Taylor (1993) for reference. 3 In is April 2015 moneary policy saemen, he MAS announced: MAS will herefore coninue wih he policy of a modes and gradual appreciaion of he S$NEER [Singapore dollar nominal effecive exchange rae] policy band. However, he slope of he policy band will be reduced, wih no change o is widh and he level a which i is cenered. This measured adjusmen o he policy sance is consisen wih he more benign inflaion oulook in 2015 and appropriae for ensuring medium-erm price sabiliy in he economy (Moneary Auhoriy of Singapore, 2015). 4 The reacion funcion esimaion is for Singapore wih he sample period 1981:Q1 2012:Q4. Insrumenal variable esimaion wih four lags of inflaion and four lags of oupu gap is used o insrumen for fuure inflaion and he fuure oupu gap. See Mihov (2013) for more informaion. 5 Under log-normaliy, ( E ) = E ( ) 1 log + ( ) M, + 1 log M, + 1 Var log M, The deails of his derivaion are provided in Mihov and Sanacreu (2013). 7 Along hese simulaion exercises, I se f p IRR = f p ERR = 1.5 and f c IRR = f c ERR = 0.5 o make he wo rules consisen. However, Mihov and Sanacreu (2013) find ha he ERR sill ouperforms he IRR for differen values of he coefficiens of he rules. 8 I follow he convenion ha an increase in he exchange rae implies depreciaion of he domesic currency. REFERENCES Abel, Andrew B. Asse Prices under Habi Formaion and Caching Up wih he Joneses. American Economic Review Papers and Proceedings of he Hundred and Second Annual Meeing of he American Economic Associaion, May 1990, 80(2), pp Alvarez, Fernando; Akeson, Andrew and Kehoe, Parick J. If Exchange Raes Are Random Walks, Then Almos Everyhing We Say Abou Moneary Policy Is Wrong. American Economic Review Papers and Proceedings, May 2007, 97(2), pp Alvarez, Fernando; Akeson, Andrew and Kehoe, Parick J. Time-Varying Risk, Ineres Raes, and Exchange Raes in General Equilibrium. Review of Economic Sudies, July 2009, 76(3), pp Federal Reserve Bank of S. Louis REVIEW Third Quarer

16 Sanacreu Backus, David K.; Gavazzoni, Federico; Telmer, Chrisopher and Zin, Sanley E. Moneary Policy and he Uncovered Ineres Rae Pariy Puzzle. NBER Working Paper No , Naional Bureau of Economic Research, July 2010; hp:// Bank of Japan. Ouline of Moneary Policy. hp:// accessed March 2, Benigno, Gianluca; Benigno, Pierpaolo and Nisicò, Salvaore. Second-Order Approximaion of Dynamic Models wih Time-Varying Risk. Journal of Economic Dynamics and Conrol, July 2013, 37(7), pp Benigno, Pierpaolo. Price Sabiliy wih Imperfec Financial Inegraion. Journal of Money, Credi, and Banking, February 2009, 41(Suppl. s1), pp Board of Governors of he Federal Reserve Sysem. Wha Are he Federal Reserve s Objecives in Conducing Moneary Policy? Curren FAQs, Sepember 19, 2014; hp:// De Paoli, Bianca. Moneary Policy Welfare in a Small Open Economy. Journal of Inernaional Economics, February 2009, 77(1), pp De Paoli, Bianca and Søndergaard, Jens. Foreign Exchange Rae Risk in a Small Open Economy. Working Paper 365, Bank of England, March 2009; hp:// European Cenral Bank. Objecive of Moneary Policy. hps:// accessed March 2, Fama, Eugene F. Forward and Spo Exchange Raes. Journal of Moneary Economics, November 1984, 14(3), pp Mihov, Ilian. The Exchange Rae as an Insrumen of Moneary Policy. Moneary Auhoriy of Singapore Macroeconomic Review, April 2013, 12(1), pp Mihov, Ilian and Sanacreu, Ana Maria. Exchange Raes as an Insrumen of Moneary Policy. Unpublished manuscrip, June Moneary Auhoriy of Singapore. MAS Moneary Policy Saemen. January 28, 2015; hp:// Saemens/2015/Moneary-Policy-Saemen-28Jan15.aspx. Moneary Auhoriy of Singapore. Moneary Policy. Undaed; hp:// accessed March 9, Parrado, Eric. Singapore s Unique Moneary Policy: How Does I Work? IMF Working Paper 04/10, Inernaional Moneary Fund, January 2004; hp:// Schmi-Grohé, Sephanie and Uribe, Marin. Pegs and Pain. NBER Working Paper No , Naional Bureau of Economic Research, March 2011; hp:// Svensson, Lars E.O. Open-Economy Inflaion Targeing. Journal of Inernaional Economics, February 2000, 50(1), pp Taylor, John B. Discreion Versus Policy Rules in Pracice. Carnegie-Rocheser Conference Series on Public Policy, December 1993, 39, pp Verdelhan, Adrien. A Habi-Based Explanaion of he Exchange Rae Risk Premium. Journal of Finance, February 2010, 65(1), pp Third Quarer 2015 Federal Reserve Bank of S. Louis REVIEW