The Uncovered Interest Parity Puzzle, Exchange Rate Forecasting, and Taylor Rules

Transcription

1 The Uncovered Ineres Pariy Puzzle, Exchange Rae Forecasing, and Taylor Rules Charles Engel * Dohyeon Lee Chang Liu Chenxin Liu Seve Pak Yeung Wu Universiy of Wisconsin ** January 2, 208 *Corresponding auhor: Charles Engel, Deparmen of Economics, Universiy of Wisconsin, 80 Observaory Drive, Madison, WI cengel@wisc.edu. ** Address: Deparmen of Economics, Universiy of Wisconsin, 80 Observaory Drive, Madison, WI of each auhor: Charles Engel, cengel@wisc.edu; Dohyeon Lee, dlee286@wisc.edu; Chang Liu, chang.liu@wisc.edu; Chenxin Liu, cliu274@wisc.edu; Seve Pak Yeung Wu, seve.wu@wisc.edu Declaraions of ineres: none. This research did no receive any specific gran from funding agencies in he public, commercial, or no-for-profi secors.

2 Absrac Recen research has found ha he Taylor-rule fundamenals have power o forecas changes in U.S. dollar exchange raes ou of sample. Our work cass some doub on ha claim. However, we find srong evidence of a relaed in-sample anomaly. When we include U.S. inflaion in he well-known uncovered ineres pariy regression of he change in he exchange rae on he ineres-rae differenial, we find ha he inflaion variable is highly significan and he ineres-rae differenial is no. Specifically, high U.S. inflaion in one monh forecass dollar appreciaion in he subsequen monh. We inroduce a model in which a Taylor rule deermines moneary policy, bu in which no only moneary shocks bu also liquidiy shocks drive nominal ineres raes. This model can poenially accoun for he empirical findings. Key words: Uncovered Ineres Pariy Puzzle, Exchange Rae Forecasing, Taylor Rules, Liquidiy JEL No. F3, F3, F4

3 . Inroducion Recen research has found consisen success forecasing changes in nominal exchange raes, especially for he U.S. dollar relaive o oher high-income counries, using variables ha help o deermine moneary policy. This work posis ha cenral bank policy can be described by a Taylor rule ha deermines he shor-erm nominal ineres rae as a funcion of he inflaion rae, he oupu gap and oher variables. These variables have been dubbed he Taylor rule fundamenals and evidence has been amassed ha hese variables can be used o produce forecass of he exchange rae ha ouperform he random-walk forecas (of no change in he log of he exchange rae) even a shor horizons of around one monh. Engel and Wes (2006) and Mark (2009) inroduce empirical single-equaion models of he exchange rae based on general equilibrium macroeconomic models in which moneary policymakers commi o an insrumen rule such as a Taylor rule. The models in hese papers build on New Keynesian models such as Clarida, e al. (998) and Benigno (2004). Subsequen work in his area has pursued he quesion of wheher hese models can be used o forecas changes in he exchange rae ouside of he sample of esimaion. A key work in his area is Molodsova and Papell (2009), who find ha he Taylor-rule fundamenals provide significanly lower mean-squared errors in ou-of-sample forecass relaive o he random walk model, using he Clark and Wes (2006) es for comparing model predicions. Oher conribuions include Engel, e al. (2008), Molodsova e al. (2008), Molodsova e al. (20), Wang and Wu (202), and Binici and Cheung (202). In his paper, we aemp o reconcile hree relaed puzzles, wo of which arise from he empirical work linking Taylor rule fundamenals and he exchange rae. The firs puzzle is well known and has been sudied exensively he uncovered ineres pariy (UIP) puzzle. If 2

4 uncovered ineres pariy held, he opimal forecas of he change in he exchange rae beween ime and ime + is he ineres differenial beween he home and foreign counry a ime. Under uncovered ineres pariy (UIP) beween he U.S. and anoher counry: () US * Es s = i + i, where i US is he one-period nominal ineres rae in he U.S., i * is he one-period ineres rae in a foreign counry, s is he log of he dollar price of foreign currency, and E represens he expecaion condiional on all informaion known a ime. In a simple regression of he change in he log of he exchange rae on he ineres-rae differenial: s s = a + a i i + ζ, US * (2) ( ) he lieraure has consisenly found an esimae of he slope parameer a ha is negaive (while he inercep coefficien a 0 is usually esimaed o be close o zero.) If UIP holds, we should find he esimae of a is close o one. These sudies very ofen rejec he null ha a =, and less ofen even find a is significanly less han zero. The second puzzle is ha he Taylor rule fundamenals help predic he change in he exchange rae, bu in he opposie direcion han would arise in a model in which UIP holds. In oher words, suppose ha he Federal Reserve followed a policy rule for he shor-erm ineres rae, US US US US US US (3) i γ0 γ π γ2 y = + +, where ππ UUUU is he inflaion rae in he U.S., and US y is he oupu gap in he U.S.. Suppose he foreign counry had a similar Taylor rule, excep wih possibly differen parameers: (4) i = γ + γπ + γ y. * * * * * 0 2 3

5 If uncovered ineres pariy, (), held, we would have: * * * * * ( ) Es s = γ + γ π + + γ y γ + γπ + γ y. US US US US US For example, higher U.S. inflaion should predic he dollar will depreciae ( Es s > + 0 ). However, Molodsova and Papell (hereinafer, referred o as MP) and ohers find ha he coefficien signs end o be he opposie of hose implied by uncovered ineres pariy and Taylor rules - he Taylor rule fundamenals forecas changes in he exchange rae in he wrong direcion. They noe especially ha he coefficien on U.S. inflaion is negaive and on foreign inflaion is posiive. Tha reversal of sign appears o be consisen wih he empirical finding of he uncovered ineres pariy puzzle. I seems ha he UIP puzzle and he finding ha he Taylor-rule fundamenals predic in he wrong direcion are simply manifesaions of he same phenomenon. Indeed, if equaions (3) and (4) were exacly he moneary policy rules, he ineres raes would be perfecly correlaed wih he Taylor-rule fundamenals and so if one is negaively correlaed wih s s, so mus be he oher. However, once we recognize ha (3) and (4) do no exacly capure moneary policy, i is hard o reconcile hese findings wih a hird puzzle: he Taylor-rule fundamenals do a beer job of predicing he exchange rae change han does he relaive ineres rae differenial. To see his problem, assume ha here are some variables ha influence moneary policy ha are no measured by he researcher, or here are moneary policy shocks. We can augmen he rules posied above: + (5) i US US US US US US US = γ0 + γ π + γ2 y + u (6) i = γ + γπ + γ y + u. * * * * * * 0 2 4

6 Here, US u and * u are exogenous random variables. When we subsiue for i US and i in equaions (5) and (6) ino equaion (2), we ge: (7) s s = b+ bπ + by + bπ + by + θ, US US * * US * where b0 a0 a( γ0 γ0) US US = +, b= aγ, b2= aγ 2, b = aγ, * 3 b = aγ and * 4 2 θ US * ( ) = ζ + a u u. In essence, he finding of MP is ha equaion (7) has a beer fi han + + he UIP regression (2). If i were he case ha equaion (2) could be inerpreed as implying: US * (8) Es s a0 a( i i) + = +, hen his finding of MP would be impossible o reconcile wih he saemen ha equaions (5) and (6) correcly describe moneary policy. These laer equaions in essence say ha he Taylor rule fundamenals (given by he righ-hand-sides of equaions (3) and (4)) measure ineres raes wih noise. If equaion (8) were rue, he ineres differenial is he bes predicor of he change in he log of he exchange rae, and so i could no be he case ha he Taylor rule fundamenals do a beer job han he ineres rae differenial in forecasing currency movemens. Bu here is no paradox here if we recognize ha equaion (8) is no implied by he familiar UIP regression, (2). The condiional mean of he regression error may no be zero we canno claim ha E ζ + = 0. Since i is false o conclude ha (8) is an implicaion of he finding of he UIP regression (2), hen we can admi he possibiliy ha he Taylor rule fundamenals have a beer fi han he ineres rae differenial. Here we inroduce a small variaion on he model presened in Engel (206) in order o explain hese empirical puzzles. Engel (206) builds a simple New Keynesian open-economy model, in which here is a deviaion from UIP ha arises because U.S. shor-erm dollar asses pay an unobserved liquidiy reurn. The acual, observed moneary reurn on foreign asses mus 5

7 rise as he liquidiy reurn on U.S. dollar asses rise in order for invesors o be willing o hold foreign asses in equilibrium. We inroduce moneary policy shocks ino ha model. We can show he model is able o accoun for he empirical puzzles ha he Taylor rule fundamenals forecas he change in he exchange rae beer han he ineres rae differenial, and wih he wrong sign. In secion 2, we replicae he findings of MP, who find ou-of-sample predicive power for he Taylor rule fundamenals in monhly daa. We find ha when we exend heir sample hrough 206, he Taylor-rule fundamenals sill have a significanly lower mean-squared error han he random walk forecas, using he Clark-Wes saisic. Nex, we noe ha he exchange rae used in MP is a monhly average of daily exchange raes. If he daily exchange rae followed a random walk, hen he monhly average exchange rae would no, and he change in he monhly exchange rae should be serially correlaed. We find ha if we replace he monhly average exchange rae wih he end-of-monh exchange rae o correc his problem, he resuls abou he forecasing power of he Taylor rule fundamenals relaive o he random walk model are no as srong as in MP. Indeed, using end-of-monh exchange raes, he Taylor rule fundamenals do no generally ouforecas he random walk, using he Clark-Wes saisic. Moreover, we show ha he Clark-Wes correcion is very imporan in reaching he conclusion ha he Taylor-rule fundamenals have significanly lower roo-mean-squared-errors han he random-walk forecas. Wihou he correcion, he Taylor rule fundamenal predicions would no be significanly beer. The moivaion for he Clark-Wes correcion is ha he Taylor-rule model requires esimaion of some parameers, while he random-walk model is nesed in he Taylor rule model and in fac requires no parameer esimaes. Hence, if he Taylor rule model were he rue model, he esimaed forecas of he change in he exchange rae would 6

8 be less accurae han he rue forecas of he model because of parameer esimaion error. The Clark-Wes saisic correcs for his problem so ha i gives a valid es of he ou-of-sample forecasing power of an esimaed model relaive o a nesed model. The parameers of he model are esimaed by regressions in rolling samples. We plo he parameer esimaes over hese rolling windows and find considerable variabiliy in he esimaes. We argue ha he changes over ime in he parameer esimaes are oo large o be accouned for by esimaion error of a model wih fixed parameers. This finding calls ino quesion he validiy of he Clark-Wes correcion, which is designed for models wih fixed parameers. In secion 3, we ake a differen ack. We focus on he in-sample predicive power of ineres raes and Taylor-rule fundamenals for exchange rae changes. The regression, (2), ha generaes he empirical UIP puzzle is a form of esing for in-sample forecasing power. If UIP held, he ineres-rae differenial should have a coefficien ha is significanly greaer han 0 ( a should equal.) In fac, he UIP lieraure has ended o find a significanly less han one, wih a poin esimae less han zero, implying ha an increase in he U.S. ineres rae porends a greaer fuure appreciaion of he dollar. We aemp o replicae his finding using monhly daa from We choose January, 999 as he saring dae for our analysis for wo reasons. Firs, he euro came ino exisence in ha monh, and he euro-dollar exchange rae is an especially imporan one on world markes. Second, he parameer insabiliy in he rolling regressions noed above is much more readily apparen in he long span of daa ha begins in 973. There is much less parameer insabiliy in shorer samples, including he pos-999 sample. We are no able o confirm he UIP puzzle in our sample for mos counries when we esimae equaion (2), bu we find a surprising resul when we add U.S. and foreign inflaion o ha equaion as independen variables. In ha case, U.S. inflaion a ime (ha is, he increase 7

9 in prices beween monh and monh ) is a significan predicor of he change in he log of he exchange rae beween ime and ime +, for almos all counries. Foreign inflaion generally is no helpful for forecasing he change in he exchange rae. Moreover, when he inflaion raes are included in he regression, he ineres-rae differenial is no significan. This finding is very similar o he puzzle we originally pose he inflaion rae of he U.S. is significan in forecasing he change in he log of he exchange rae, bu no he ineres rae differenial. We hen consider he possibiliy ha he U.S. inflaion rae for monh really is no useful in predicing exchange raes a he end of monh +, because he consumer price index is no known a he end of monh. I is no announced unil he middle of monh +. I may be ha when he marke learns he level of he CPI a he ime of he announcemen of ha saisic, he exchange rae reacs. Our predicive regression may be misakenly picking up he reacion of he exchange rae o news abou he monh CPI ha is announced in he middle of monh +. However, marke paricipans surely have a good idea of wha he CPI rae will be, because he CPI is based on observable prices of goods and services. We can examine his possibiliy by looking a he Bloomberg survey of marke paricipans on heir expecaion of he value of he CPI. Tha is, a he end of monh, Bloomberg asks he marke wha hey expec he value of he monh CPI will be when i is announced in he middle of monh +. We find ha i is he expeced componen of he CPI, raher han he surprise, ha predics he change in he exchange rae. Secion 4 hen presens a sligh exension of he model of Engel (206) and shows how i may be capable of explaining hese findings. 8

10 2. Forecasing he Exchange Rae using Taylor Rule Fundamenals MP propose several varians of equaion (7) o forecas changes in he exchange rae. We will focus exclusively on he specificaion ha appeared o be mos successful. I augmens (7) wih lagged ineres raes, based on a version of he Taylor rule wih ineres-rae smoohing: (9) s s = b+ bπ + by + bπ + by + bi + bi + θ. US US * * US * This is called he heerogeneous, symmeric Taylor rule model. I is symmeric because i is based on Taylor rules ha have he same variables in each counry (inflaion, he oupu gap, and he lagged ineres rae), bu i is heerogeneous because he coefficiens in he Taylor rules are no assumed o be equal bu of opposie sign (so i does no impose b = b3.) Firs, we replicae he findings of MP, which uses monhly daa from March 973 hrough June Some of he daa comes from he IMF s Inernaional Financial Saisics (IFS). The price level daa used o consruc inflaion raes is he consumer price index from line 64 of he IFS. The ineres rae daa is he money marke rae from IFS line 60B, which is a monhly average of daily raes. We use indusrial producion as a proxy for GDP, aken from line 66 in he IFS. We consruc he oupu gap as deviaions from he Hodrick-Presco filered rend oupu rae, following he mehods described in MP. Tha mehod consrucs he HP-filered oupu level for dae using indusrial producion daa only hrough dae, raher han he whole sample. The exchange rae is he monhly-average exchange rae from he Federal Reserve Bank of S. Louis (FRED) daabase. To consruc one-monh-ahead forecass of he change in he exchange rae beween ime and ime +, we esimae equaion (9) using daa hrough ime, and hen produce he forecas using he esimaed equaion. Our firs forecas is for March 982, so we use a 20 monh sample (March 973 February 983) o esimae he parameers. We hen employ 9

11 rolling regressions keeping he esimaion sample a 20 monhs o updae our parameer esimaes0f When we use he daa available on Papell s websie, we are able o replicae he resuls in MP very closely. However, when we collec he daa from he sources cied in MP, we find a few differences. Table repors he p-values for he Clark and Wes (2006) saisic ha we calculae, and compares our calculaions o hose presened in MP. This model provides an exchange rae forecas ha has a significanly lower mean-squared error han he random walk forecas of no change in he exchange rae for eigh of he welve currencies. One difference in our daa is ha our measure of he oupu gap in some cases differs from MP s near he end of he sample, which may be aribuable o daa revisions. There were hree more significan divergences. Our daa for he Poruguese exchange rae differs subsanially from MP s. Our daa for he ineres rae in Swizerland diverges from MP s afer 984. And we find daa for indusrial producion for Sweden in he IFS saring only in 997. Wih our daase, we sill find ha he Taylor rule model has significan ou-of-sample forecasing power in he original MP sample period. Table also exends he sample hrough December 205 for he counries ha are no in he Eurozone. We can see ha, if anyhing, he predicive power of he Taylor rule fundamenals has increased in he updaed sample. The p-values for he es of he forecasing power relaive o he random walk null are lower for he Ausralian dollar, Canadian dollar, Danish krone, Japanese yen, Swiss franc and U.K. pound, compared o he sample in MP. These are all he non- Euro currencies. This is an especially sriking finding because generally when he lieraure finds The forecass for he European counries ha evenually adoped he euro go hrough December 998, as he euro was adoped in January

12 a model ha ou-predics he random walk, he resuls are fragile and do no exend when he sample period is changed.f2 Table 2 compares he ou-of-sample RMSE of he Taylor-rule model o ha of he random walk. The noable poin is ha he Taylor-rule model, in almos all cases, has a higher RMSE. Tha is, if one were o use he esimaes from his model o forecas exchange raes, one would do worse han using he forecas of no change in he exchange rae. The Taylor-rule model is found o produce beer forecass han he random walk indeed, saisically significanly beer because of he Clark-Wes correcion. Clark and Wes noe ha even if he Taylor-rule model were rue, he economerician may do worse a forecasing he exchange rae because he parameers may be esimaed wih error. Whenever we are comparing one model nesed in anoher, he nesed model has fewer parameers o esimae, so here is less esimaion error. Clark and Wes propose a simple way o ake accoun of he esimaion error a correcion o he RMSE of he more general model ha allows us o compare i o he RMSE of he nesed model. In Table, in parenheses under he p-values for he Clark-Wes es are repored he p- values for he Diebold-Mariano-Wes es ha does no correc for he fac ha he Taylor-rule model requires esimaion of parameers, while he random walk model is nesed and acually requires no parameer esimaion. Noe ha hese p-values are quie large, and he Taylor rule model would no be significanly beer han he random walk using his es. However, if he condiions of he Clark-Wes model are saisfied, hese es saisics are incorrec because hey do no correc for esimaion error as he Clark-Wes es does. We reurn o his poin below. As noed above, he exchange rae used in MP is he monhly average exchange rae from he FRED daabase. Typically sudies of exchange-rae forecasing use end-of-period exchange 2 On his poin, see Faus, e al. (2003) and Cheung, e al. (2005, 206)

13 raes raher han period averages. If he null hypohesis were ha he daily exchange rae followed a random walk, hen he monhly average would no follow a random walk, bu insead have a high-order moving average componen. The fac ha he Taylor-rule fundamenals can ouforecas he random-walk model for he monhly average exchange rae may no be ha ineresing, because changes in he monhly average exchange rae may acually be serially correlaed. In Table 3, we repea he exercise of Table, bu using an end-of-monh exchange rae. These exchange raes are from he Federal Reserve daabase, H.0 release, and are measured as noon buying raes in New York on he las rading day of each monh. We show resuls wih a sample period ha is he same as in MP, and for our exended sample period. The able repors he p-values for he es of he null hypohesis ha he random walk forecas is no worse han he Taylor-rule model. In boh samples, wih few excepions we find ha he Taylor-rule model does no have significanly beer forecasing power han he random walk model. This is he reverse of he finding when we use monhly-average exchange raes, as in MP. These saisics embed he Clark-Wes correcion, bu he ou-of-sample forecasing power of he Taylor-rule model found by MP is apparenly an arifac of using monhly-average exchange raes. Anoher ineresing aspec of he forecass is he behavior over ime of he coefficien esimaes from he rolling regressions for he Taylor-rule model. Figure plos he coefficien on U.S. inflaion, from our regressions using end-of-monh exchange rae daa. We see ha here is considerable variaion of he parameer esimaes over ime. Could his variaion arise as a resul of esimaion error of a consan parameer? This seems improbable. The Figure also plos he 95 percen confidence inerval for he parameer esimae a each poin in ime. We can see by inspecion ha if we pick almos any poin in ime, ha he parameer esimae for mos of he 2

14 oher ime periods lie ouside he 95-percen confidence inerval for he parameer esimae a ime. This srongly suggess ha over he full sample, he parameers of he model are no consan. We noe ha we find he same hing when we plo he coefficien esimaes using he monhly-average exchange rae. Indeed, MP s Figure displays heir esimaes of his coefficien, and i shows similar ime variaion. Poenially his is a concern because he Clark-Wes correcion is developed under he assumpion ha here is a parameer a consan, no a ime-varying parameer ha is esimaed wih error. If he coefficiens in his regression vary over ime, hen he consanparameer model is misspecified, and so he Clark-Wes correcion is no valid. In his secion, we have seen a couple of reasons o be dubious abou he ou-of-sample forecasing power of he Taylor-rule model. When we use end-of-period raher han monhly average exchange raes, he Taylor-rule model no longer has significan forecasing properies relaive o he random walk, using he Clark-Wes correcion. And, in any case, he validiy of he Clark-Wes procedure is quesionable because he parameers of he Taylor-rule forecasing model appear o move grealy over ime. 3. In-sample Forecasing and an Exended UIP Tes In his secion, we focus on in-sample forecasing power of he ineres differenial and he Taylor-rule fundamenals. The well-known es for UIP, he regression (2), can be considered an example of an in-sample es. If one finds ha a 0, one can conclude ha he ineres rae differenial, i US i, has forecasing power for he change in he exchange rae, s + s. Under * he null of he UIP es, a =, so if uncovered ineres pariy holds, he ineres differenial should indeed forecas exchange rae changes. The UIP puzzle is he empirical finding ha he 3

15 slope coefficien is generally found o be significan, bu negaive. The ineres rae differenial has forecasing power, bu in he opposie direcion of he UIP hypohesis. The firs column of Table 4a repors he slope coefficien esimaes for his es of UIP.2F3 Our exchange rae daa is he end-of-monh daa described above: from he Federal Reserve daabase, H.0 release, noon buying raes in New York on he las rading day of each monh, for he Canadian dollar, Danish krone, he euro, Japanese yen, Norwegian krone, Swiss franc, Swedish krona, and U.K. pound. In his able, we also use one-monh ineres raes measured on he las day of each monh. They are he midpoin of bid and offer raes for one-monh Eurocurrency raes, as repored on Inercapial from Daasream. We begin he sample in January, 999, which corresponds wih he adven of he euro, and use daa hrough December, 205. Our choice of sar dae is dicaed by our concern abou parameer sabiliy. We have noed above ha in he ou-of-sample forecasing exercises, he parameers move considerably over he long sample. In conras o he usual es for UIP, we do no generally find a significanly negaive slope coefficien on he ineres rae differenial.3f4 The poin esimae is negaive for only four of he eigh currencies. In no case is he slope coefficien significanly differen from zero, in fac, indicaing ha he ineres rae differenial does no have in-sample forecasing power for he change in he exchange rae. Moreover, we canno rejec he UIP null ha he slope coefficien is equal o one for any of he currencies. In shor, in his daa, he UIP puzzle does no hold. The second panel of Table 4a ( Specificaion 2 ) includes U.S. and foreign inflaion in he sandard UIP regression. Tha is, we esimae he following equaion: 3 We do no use Ausralia in hese ess because inflaion daa is no available monhly. We add Norway, for which he relevan daa is available. 4 See Bussière e al. (207) for a similar finding. 4

16 s s = b + b i i + b π + b π + ζ (0) ( ) i US * US US * * This specificaion is moivaed by he observaion ha many cenral banks have adoped inflaion argeing rules for moneary policy. I may be, in fac, ha he inflaion rae is a good predicor of he sance of moneary policy, and so may capure informaion ha is no included in he ineres raes hemselves. Moreover, as discussed in he nex secion, ineres raes movemens may reflec no only he moneary policy sance, bu also percepions of he relaive liquidiy of shorerm ineres bearing asses across counries. We find ha for almos every currency, he coefficien on U.S. inflaion, and significanly differen han zero, he only excepion being in he regression for he dollar/japanese yen rae. In ha case, he poin esimae of US b, is negaive US b is negaive, bu i is insignifican. The coefficien on foreign inflaion is generally insignifican. There are a few excepions: for he euro, Swiss franc, and Swedish krona, * b is significanly posiive, and for he Norwegian krone, i is significanly negaive. The coefficien on he ineres differenial, cases, excep marginally for he euro. In no case is i b, is insignifican in all i b significanly differen han one.4f5 These findings remarkably overurn he UIP puzzle. I is no longer he case ha he ineres differenial predics he change in he exchange rae, bu wih he wrong sign. Insead, he U.S. inflaion rae has explanaory power. When U.S. inflaion is high in one monh, i appears ha we can reliably predic ha he dollar will appreciae in he subsequen monh. We have performed wo ypes of robusness ess. Firs, we exclude one or wo variables from he regressions repored in Table 4a. In he firs specificaion, we exclude each counry s 5 We include Denmark separaely from he Euro Area, even hough is ineres rae and exchange rae are very closely pegged o hose in he Euro Area. The esimaed coefficiens for Denmark in Table 4a differ noably from hose for he Euro Area. This arises almos enirely because Danish inflaion differs from Euro area inflaion. If only he ineres differenial and U.S. inflaion are included in he regression, he esimaed coefficiens are very similar. 5

17 inflaion rae, including only he ineres rae differenial and U.S. inflaion. In he second specificaion, we regress he change in exchange rae on U.S. inflaion only. The resuls are no repored here bu included in he Appendix (Tables A. and A.2). They are quie similar o our baseline resuls. The esimaed coefficien on U.S. inflaion is negaive for all counries, and for mos i is saisically significan under boh specificaions. Second, we perform a sub-sample analysis. In he pos-global financial crisis period, nominal ineres raes were near zero in many counries. I is hen naural o wonder wheher our resuls in Table 4 arise from he effecs of he pos-crisis period. Tables 4b and 4c perform he same regression as in Table 4a, bu on a sample spli a he end of The sriking finding is ha here is lile difference beween he wo subsamples. If anyhing, he resuls are slighly sronger in he sample. Again, he coefficien on U.S. inflaion is always esimaed o be negaive, and i is generally saisically significan, while he coefficiens on he oher wo variables are no consisenly of he same sign across counries, nor significan. One possible explanaion for his finding is ha he U.S. inflaion rae for monh is no really known a he end of monh. The CPI inflaion rae is announced wih a wo-week lag afer he end of he monh. I may be he case ha he news of he monh inflaion rae incorporaed in he CPI announcemen in he middle of monh + causes he exchange rae o move during monh +. So, our measured inflaion for monh migh acually no be known a he end of monh, and herefore is no legiimaely a predicor of he currency depreciaion in period +. To examine his hypohesis, we make use of he Bloomberg survey of commercial and invesmen banks ha collecs forecass of he announcemen of inflaion. To be clear, hese are no forecass of inflaion, bu insead hey are forecass of wha he Bureau of Labor Saisics 6

18 will announce. For example, in mid-april, he BLS may announce he measure of he CPI inflaion rae for March. Bloomberg surveys in-house economiss of financial insiuions a he beginning of April, and asks wha hey hink inflaion was for March wha hey forecas he BLS will announce. We ake he median of he Bloomberg survey as our measure of wha markes hink inflaion was for monh, as of he end of monh. The acual inflaion daa is released in he middle of he monh for all of he counries in our daase, and he survey is aken four o eleven days prior o he release of he daa. We call hese measures of expeced inflaion USe *e π and π, and ake hem o be proxies for wha he marke hough monh inflaion was a he end of monh. We esimae he equaion: s s = b + b i i + b π + b π + ζ () ( ) i US * US USe * * e Table 5 repors he esimaes of equaion (), and compares i o he esimaes of equaion (0). On he whole, here is very lile change. For hree of he counries in which he coefficien was negaive and marginally significan, we find he coefficien is sill negaive bu marginally insignifican. There is no much change in he esimaed magniude of he effec, bu a small increase in he sandard error of he coefficien esimae. For all of he counries excep Japan, he esimaed coefficien on U.S. inflaion is negaive. 4. A Proposed Soluion o he Puzzles Here we would like o develop a model in which he U.S. inflaion rae predics he change in he exchange rae (high inflaion predics a dollar appreciaion subsequenly), and ha when we conrol for he U.S. inflaion rae, he ineres rae differenial is no helpful in forecasing he rae of change of he exchange rae. The second fac requires ha UIP be violaed, because if UIP holds, only he ineres differenial can forecas he change in he log of he 7

19 exchange rae. However, i mus be he case ha he U.S. inflaion rae conains informaion no conained in he ineres differenial ha is helpful for predicing he exchange rae. We can exend slighly he model in Engel (206). Tha paper assumed a Taylor rule wih ineres rae smoohing. The model here has no smoohing, bu i does allow for serially correlaed moneary policy shocks, which are very similar in heir effec o including a lagged ineres rae. The advanage of he model here is ha here is a simple, closed-form algebraic soluion. The superscrip R refers o he value of a variable in he U.S. relaive o is value in he foreign counry. For example, π is U.S. minus Foreign inflaion, or i R is U.S. minus foreign R ineres rae. In all of he equaions, we assume he parameers are he same for he U.S. and he foreign counry, which allows us o simplify he sysem and wrie he equaions in relaive erms. The disadvanage of his simplificaion is ha, in he end, i will imply he coefficien on foreign inflaion in equaion (0) should be equal in absolue value, bu of he opposie sign, o he coefficien on U.S. inflaion. This model is clearly oo simple o fully explain he daa, bu we view i as providing inuiion o he elemens ha migh belong in a more complee model. The dynamic model has hree equaions. Firs, here is he Taylor rule for seing moneary policy. We assume ha each counry arges is own inflaion rae, and here is a serially correlaed error erm: (2) i = σπ + u, u = ρu + ν; σ > 0, 0< ρ < R R where ν a mean-zero, i.i.d. random variable. The second equaion is a model of liquidiy, which is a modificaion of he UIP equaion. Engel (206) derives a model, based on Nagel (206), in which he expeced reurns on U.S. bonds falls relaive o he reurn on foreign bonds as he U.S. ineres rae rises. Tha is, if he U.S. bond has some value for is liquidiy, hen he foreign bond mus be expeced o pay a 8

20 higher moneary reurn. Engel (206) shows ha when he U.S. ineres rae is relaively high, he U.S. bond s liquidiy reurn will be relaively high. Tha is because he U.S. ineres rae increases under a moneary ighening. The money supply is reduced, so agens value U.S. bonds more for heir liquidiy. If he U.S. bond pays an inangible liquidiy reurn, is moneary reurn will be lower han ha of he foreign counry. This means ha he excess moneary reurn on he foreign bond will be posiively relaed o he difference beween he U.S. and foreign ineres rae. We le α denoe he sensiiviy of he excess moneary reurn on he foreign bond o he i US i ineres differenial. In addiion, η is a mean-zero, i.i.d. random shock o he liquidiy * reurn, such ha he Home bond is more liquid as η is larger. We have: * US US * (3) i ( Es+ s) i α( i i ) + = + η, α > 0. US * The expeced reurn differenial beween U.S. and foreign bonds is i i ( Es s). + A firs glance, his equaion seems like i could no possibly deliver he UIP puzzle, because we have assumed 0 US * α >. Rearranging (3), we have Es s ( α)( i i ) = η, so i seems as if we regress s + s on US * i i, we mus ge a coefficien greaer han one, and cerainly no negaive. However, i US i is an endogenous variable, and i responds o liquidiy * shocks, η, so i US i and η are correlaed. Engel (206) shows ha he model is capable of * explaining a negaive slope parameer in he UIP regression (2). In any case, our regressions do no find evidence of he sandard UIP puzzle in daa since 999. We can add and subrac expeced Home relaive o Foreign inflaion o wrie his R R expeced reurn differenial as ( ) i Eπ + + Eq + q, where q is he real exchange rae: 9

21 R q = s p, and R R R R R = p p. i Eπ + is he difference in he real ineres rae in he π + + Home counry and he Foreign counry. The model of liquidiy described above hen says: i Eπ + Eq q = αi + η, α > 0. (4) ( ) R R R + + The hird equaion in he model is he Phillips curve ha relaes he relaive inflaion raes in he wo counries o he real exchange rae. This is a sandard New Keynesian Phillips curve ha says ha Home inflaion will end o be higher when q is high (which means relaive prices are low in he Home counry): = +, δ > 0, 0< β <. R R (5) π δ ( q q) βeπ + In pracice, i is reasonable o assume δ is small (ha is, close o zero, so perhaps somehing like 0.05 if a ime period is one-quarer long) and β is very close o one. q is an exogenously given long-run value for he real exchange rae, and i follows he serially-correlaed process: q = µ q + ε, 0< µ <, where ε is a mean-zero, i.i.d. random variable. Before considering he general soluion o his model, i is helpful o examine a simple special case. Se ( ) var q = 0, so here are only wo shocks, η and u. This simple case has he unaracive feaure ha Es + s should be perfecly explained by R π and i R in he model. Tha does no mean ha a regression of s + s on R π and i R would have a perfec fi, however, because he regression error would jus equal he forecas error, s+ Es +. Also assume he moneary shock, u, is i.i.d., so ρ = 0. We have already assumed ha η is i.i.d. In his case, we can wrie he soluions for Es + s, R π and i R as: 20

22 i σδ = u η + σδ + α + σδ + α R ( ) ( ) ( + ) u ( ) ( ) R δ α δ π = η + σδ + α + σδ + α + α Es + s= u+ η + σδ + α + σδ + α ( ) ( ) R By inspecion, we see Es + s= π, which means ha he relaive inflaion rae δ will predic he change in he log of he exchange rae, bu he ineres differenial will have no addiional predicive power. I is easy o see where his is coming from. Add and subrac expeced relaive inflaion o Es + s, so we have: Es s = Eq q + Eπ. R R Since shocks are i.i.d., we mus have Eq = Eπ = 0, so Es s = q. The Phillips curve R in his case is given by π = δq since q = 0 and Eq + = 0. Bu hen, Es + s= q= π. δ When here is a real appreciaion of he U.S. dollar, on one hand, i causes an expecaion of a nominal depreciaion o resore he real exchange rae o is equilibrium value (which is zero), because prices are no expeced o adjus. On he oher hand, he real appreciaion leads o lower curren inflaion, by he Phillips curve. So lower curren inflaion predics he depreciaion of he currency. The fi is perfec in his case. The ineres differenial, on he oher hand, is no perfecly correlaed wih Es + sbecause of he risk premium. The inuiion can be deepened by looking a he soluion for he real exchange rae: R (6) ( + α ) u σδ ( α ) σδ ( α ) q = η. 2

23 Boh a moneary ighening in he U.S. (an increase in u ) and an increase in he liquidiy value of U.S. bonds (an increase in η ) lead o a real appreciaion of he dollar, and a subsequen expeced nominal depreciaion. Boh of hese shocks also lower inflaion in he U.S. relaive o he foreign counry. I is clear ha he moneary ighening would have ha effec. The liquidiy shock also has ha effec because he real appreciaion leads o greaer relaive U.S. inflaion hrough he Phillips curve. The upsho is ha boh shocks lower U.S. inflaion, and hey boh cause a real U.S. appreciaion which foreells a nominal depreciaion. However, he wo shocks have opposie effecs on he relaive U.S. o foreign ineres rae. Ineres raes can rise eiher because moneary policy has ighened or because here is a shock ha makes U.S. bonds less liquid. Those wo evens have differen effecs on he value of he currency a U.S. moneary ighening appreciaes he dollar, bu when U.S. bonds are less valued for liquidiy, he dollar depreciaes. In urn, he expeced pah of fuure exchange raes is differen. High ineres raes predic a fuure depreciaion if here has been a moneary ighening, bu an appreciaion if here has been a denigraion of he liquidiy value of U.S. bonds. As a resul, he ineres differenial is no as useful in forecasing he change in he exchange rae as is he inflaion differenial. I may look as if his model delivers a posiive coefficien on he inflaion differenial in regression (0), if one ignores he fac ha inflaion and ineres raes are endogenous and respond o he shocks. From he Taylor rule, we have i R = σπ R + u. The risk premium definiion R R is given by i + E ( s s ) = αi + η. This gives us ( ) ( α) + R wrien as ( ) ( ) ( ) E s s = + i + η, which can be R + E s + s = σ + α π + + α u + η. This equaion migh give he impression 22

24 ha if we regress s + s on R π, we would ge a posiive coefficien. Bu ha is wrong, because π is negaively correlaed wih ( α) R + u + η. The full soluion o he model is given by: (7) (8) (9) (20) ( ) ( )( ) σδ µ ρ βρ δρ σδ i = q + u η R D D2 D3 ( ) ( ) δ µ q δ + π = α u δ η R D D2 D3 ( µ ) δσ ( α ) ( ) ( )( ) + + α ρ βρ ρδ Es s = q + u + η. + D D2 D3 ( + ) ( )( ) δ σ α µ + α βρ q = q u η, D D2 D3 where ( ) ( )( ) D = δ + α σ µ + βµ µ ( ) ( )( ) D2 = δ + α σ ρ + βρ ρ ( ) D3 = + σδ + α. This simple hree-equaion model canno be expeced o replicae he momens of many differen variables in he open economy. Bu i will end o deliver our finding ha he inflaion rae is a beer predicor of he change in he exchange rae han he ineres differenial under cerain assumpions. Firs, if he variance of he equilibrium real exchange rae is relaively low, hen moneary and liquidiy shocks are he key drivers of inflaion, ineres raes and exchange raes, as in he example above. Second, if he persisence of moneary policy shocks is low, he inuiion of he example goes hrough. I is possible, however, ha when moneary policy shocks are very persisen, a moneary ighening acually lowers nominal ineres raes. Tha could 23

25 occur because he effec on inflaion of a very persisen moneary ighening is o lower inflaion immediaely by a subsanial amoun. Sill, he more plausible case is he one in which moneary ighening raises he nominal ineres rae, which is also he case in which he conclusion from he simple example is mainained. To reierae he poin, ineres raes have an ambiguous effec on currency values. If he U.S. ineres raes rises because of a moneary ighening, he dollar appreciaes and is subsequenly expeced o depreciae. Bu if he ineres rae rises because U.S. ineres bearing asses have a lower liquidiy reurn, he dollar depreciaes, wih an expeced ensuing appreciaion. On he oher hand, shocks ha raise U.S. inflaion unambiguously lead o a dollar depreciaion on impac, and a subsequen expecaion of an appreciaion. Tha is, boh a moneary easing and a reducion in he liquidiy reurn lead o higher inflaion, currency depreciaion and an expecaion of an appreciaion. An ineresing feaure of he daa ha our model does no address is he finding ha U.S. inflaion is a much sronger predicor of he fuure exchange rae change han inflaion in he foreign counry. This may reflec some asymmery in he liquidiy of U.S. shor-erm ineres bearing asses relaive o hose in oher counries. Or perhaps his reflecs he dominance of U.S. moneary policy in deermining exchange raes, along he lines discussed in Rey (203). The U.S. migh be able o follow a Taylor rule, bu oher counries are more consrained in heir ineres rae seing, and adjus heir ineres raes in response o changes in he U.S. ineres rae. We leave his anomaly o fuure research. 24

26 5. Conclusions The key findings of his paper are conained in Table 4. When he sandard UIP regression is augmened wih U.S. and foreign inflaion, we find consisenly across all currencies ha higher U.S. inflaion predics dollar appreciaion in he subsequen monh. Secion 2 of his paper cass some doub on he evidence ha Taylor-rule fundamenals can consisenly ouforecas he random walk model of exchange raes ou of sample, bu he insample significance of U.S. inflaion is inriguing. There is acually no inernal conradicion beween he claim ha an economic fundamenal, like U.S. inflaion, is no useful in producing a superior forecas relaive o he random walk, bu is significan in regression (0). As Engel and Wes (2005) demonsrae, his is exacly he oucome ha arises in presen-value models of he exchange rae, when he discoun facor is close o one. We illusrae a model in which U.S. bonds pay a liquidiy reurn ha could poenially accoun for our empirical findings. The model is exremely simple, and inended o be illusraive. We believe our empirical conclusions presen a challenge for open-economy macroeconomiss. 25

27 Acknowledgmens We are graeful for commens from paricipans a he conference sponsored by he Global Research Uni of he Deparmen of Economics a he Ciy Universiy of Hong Kong, in May 207, Exchange Rae Models for a New Era: Major and Emerging Marke Currencies. We are especially graeful o our discussan, Daniel Law, and o an anonymous referee. References Benigno, Gianluca Real Exchange Rae Persisence and Moneary Policy Rules. Journal of Moneary Economics 5, Binici, Mahir and Yin-Wong Cheung Exchange Rae Dynamics under Alernaive Opimal Ineres Rae Rules. Pacific Basin Finance Journal 20, Bussière, Mahieu; Menzie Chinn; Lauren Ferrara; and, Jonas Heiperz The New Fama Puzzle. Working paper, Banque de France. Cheung, Yin-Wong; Menzie D. Chinn; and, Anonio Garcia Pascual Empirical Exchange Rae Models of he 990 s: Are Any Fi o Survive? Journal of Inernaional Money and Finance 24, Cheung, Yin-Wong; Menzie D. Chinn; Anonio Garcia Pascual; and, Yi Zhang Exchange Rae Predicion Redux: New Models, New Daa, New Currencies. Working paper, Universiy of Wisconsin. Clarida, Richard; Jordi Gali; and, Mark Gerler Moneary Rules in Pracice: Some Inernaional Evidence. European Economic Review 42, Clark, Todd E., and Kenneh D. Wes Using Ou-of-Sample Mean Squared Predicion Errors o Tes he Maringale Difference Hypohesis. Journal of Economerics 35, Engel, Charles Ineres Raes, Exchange Raes and he Risk Premium. American Economic Review 06, Engel, Charles and Kenneh D. Wes Exchange Raes and Fundamenals. Journal of Poliical Economy 3, Engel, Charles and Kenneh D. Wes Taylor Rules and he Deuschemark-Dollar Real Exchange Rae. Journal of Money, Credi and Banking 38, Engel, Charles; Nelson C. Mark; and, Kenneh D. Wes Exchange Rae Models are No as Bad as You Think. NBER Macroeconomics Annual 2007,

28 Faus, Jon; John H. Rogers; and, Jonahan H. Wrigh "Exchange Rae Forecasing: The Errors we've really made," Journal of Inernaional Economics 60, Mark, Nelson C Changing Moneary Policy Rules, Learning, and Real Exchange Rae Dynamics Journal of Money, Credi and Banking 4, Molodsova, Tanya, and David H. Papell Ou-of-Sample Exchange Rae Predicabiliy wih Taylor Rule Fundamenals. Journal of Inernaional Economics 77, Molodsova, Tanya; Alex Nikolsko-Rzhevskyy; and, David H. Papell Taylor Rules wih Real-Time Daa: A Tale of Two Counries and One Exchange Rae. Journal of Moneary Economics 55, S63-S79. Molodsova, Tanya; Alex Nikolsko-Rzhevskyy; and, David H. Papell.20. Taylor Rules and he Euro. Journal of Money, Credi and Banking 43, Nagel, Sefan The Liquidiy Premium of Near-Money Asses. Quarerly Journal of Economics 3, Rey, Hélène Dilemma, no Trilemma. The Global Financial Cycle and Moneary Policy Independence. in Global Dimensions of Unconvenional Moneary Policy (Federal Reserve Bank of Kansas Ciy, Jackson Hole Symposium) Wang, Jian, and Jason J. Wu The Taylor Rule and Forecas Inervals for Exchange Raes. Journal of Money, Credi and Banking 44,

29 Table : Replicaing Table 4 of Molodsova-Papell (2009) Specificaion: Heerogeneous symmeric Taylor rule model wih ineres rae smoohing and consan using HP filer for poenial oupu consrucion Counry Our Resuls (A) (daa end a Dec 205)^ Our Resuls (B) (daa end a Jun 2006)^ Molodsova-Papell (2009) Table 4, p. 74 (daa end a Jun 2006) Non Euro Zone Ausralia 0.002*** 0.044** (0.66) (0.834) 0.038** Canada 0.000*** 0.007*** (0.63) (0.548) 0.02** Denmark 0.032** 0.077** (0.962) (0.995) 0.032** Japan 0.02** 0.09** (0.886) (0.759) 0.0** Swizerland 0.069* (0.98) (0.98) 0.06** Sweden ^^ ^^ U.K. 0.06** (0.739) 0.33 (0.866) 0.033** Pre-Euro Zone (daa end a Dec 998)^ France 0.034** (0.93) 0.008*** Germany (0.97) 0.26 Ialy 0.000*** (0.432) 0.00*** Neherlands 0.09** (0.794) 0.009*** Porugal (0.974) Noes: The able repors p-values for -monh-ahead CW ess of equal predicive abiliy beween he null of a maringale difference process and he alernaive of a linear model wih Taylor rule fundamenals. DMW p-values wihou CW correcion are repored in parenhesis. The alernaive model is he model wih symmeric Taylor rule fundamenals wih smoohing, which is esimaed wih heerogeneous inflaion and oupu coefficiens, and wih a consan using HP rends o esimae poenial oupu. *, **, and *** indicae ha he alernaive model significanly ouperforms he random walk a 0, 5, and % significance level, respecively, based on sandard normal criical values for he one-sided es. Esimaion window is 20 monhs. ^The models are esimaed using daa from January 975 for Canada, Sepember 975 for Swizerland, February 983 for Porugal, January 989 for UK and March 973 for he res of he counries. The sample ends in December 998 for Euro Area counries and December 205 for column A (and June 2006 for column B) for he res of he counries. ^^In his exercise, we use he same daa source as Molodsova-Papell (2009). i.e. nominal exchange rae daa from FRED, all oher daa from IMF IFS. The recen IMF IFS daa has Sweden Indusrial Producion daa only sar from 997. Therefore, we are unable o do a meaningful comparison wih he p-value in Molodsova-Papell (2009). 28

30 Table 2: Comparison of he ou-of-sample RMSE of he Taylor-rule model (eq. 9) and he random walk Counry Taylor-rule model RMSE (daa end a Dec 205)^ Taylor-rule model RMSE (daa end a Jun 2006)^ Random walk RMSE (daa end a Dec 205)^ Random walk RMSE (daa end a Jun 2006)^ Non Euro Zone Ausralia Canada Denmark Japan Swizerland U.K Pre-Euro Zone (daa end a Dec 998)^ France Germany Ialy Neherlands Porugal Noes: The able repors roo-mean-square error (RMSE) for -monh-ahead forecasing wih he Taylor rule fundamenals model and he random walk. Esimaion window is 20 monhs. ^ The models are esimaed using daa from January 975 for Canada, Sepember 975 for Swizerland, February 983 for Porugal, January 989 for UK and March 973 for he res of he counries. The sample ends in December 998 for Euro Area counries and December 205 for column,3 (and June 2006 for column 2,4) for he res of he counries. 29

31 Table 3: Replicaing Table 4 of Molodsova-Papell (2009) using end of monh exchange rae daa Counry Our Resuls (daa end a Dec 205)^ Our Resuls (daa end a Jun 2006)^ Molodsova-Papell (2009) Table 4, p. 74 (daa end a Jun 2006) Non Euro Zone Ausralia 0.033** ** Canada ** Denmark ** Japan ** Swizerland ** Sweden ^^ ^^ U.K ** ** Pre-Euro Zone (daa end a Dec 998)^ France *** Germany Ialy 0.00*** 0.00*** Neherlands 0.027** 0.009*** Porugal Noes: The able repors p-values for -monh-ahead CW es of equal predicive abiliy beween he null of a maringale difference process and he alernaive of a linear model wih Taylor rule fundamenals. The alernaive model is he model wih symmeric Taylor rule fundamenals wih smoohing, which is esimaed wih heerogeneous inflaion and oupu coefficiens, and wih a consan using HP rends o esimae poenial oupu. *, **, and *** indicae ha he alernaive model significanly ouperforms he random walk a 0, 5, and % significance level, respecively, based on sandard normal criical values for he one-sided es. Esimaion window is 20 monhs. ^The models are esimaed using daa from January 975 for Canada, Sepember 975 for Swizerland, February 983 for Porugal, January 989 for UK and March 973 for he res of he counries. The sample ends in December 998 for Euro Area counries and December 205 for column (and June 2006 for column 2) for he res of he counries. ^^In his exercise, we use he same daa source as Molodsova-Papell (2009). i.e. all daa are from IMF IFS excep for he end of monh nominal exchange rae, which is from he Federal Reserve daabase, H.0 release. The recen IMF IFS daa has Sweden Indusrial Producion daa only sar from 997. Therefore, we are unable o do a meaningful comparison wih he p-value in Molodsova-Papell (2009). 30