Noise Trading and the Effects of Monetary Policy Shocks on Nominal and Real Exchange Rates

Transcription

1 Kiel Iniue for World Economic Dueernbrooker Weg Kiel (Germany) Kiel Working Paper No 1140 Noie Trading and he Effec of Moneary Policy Shock on Nominal and Real Exchange Rae by Chriian Pierdzioch January 2003 The reponibiliy for he conen of he working paper re wih he auhor, no he Iniue. Since working paper are of a preliminary naure, i may be ueful o conac he auhor of a paricular working paper abou reul or cavea before referring o, or quoing, a paper. Any commen on working paper hould be en direcly o he auhor.

2 Noie Trading and he Effec of Moneary Policy Shock on Nominal and Real Exchange Rae Chriian Pierdzioch Kiel Iniue for World Economic, Dueernbrooker Weg 120, Kiel, Germany Abrac A number of empirical udie have repored he reul ha exchange rae how a delayed overhooing in repone o moneary policy hock. Thi reul i puzzling. Economic heory ugge ha he overhooing hould occur immediaely afer he hock, no wih a delay. Thi paper ue a new open economy macroeconomic model wih pricing-o-marke o analyze wheher he aumpion of noie rading in he foreign exchange marke help o reolve he delayed overhooing puzzle. The implicaion of noie rading for he effec of moneary policy hock on he nominal and on he real exchange rae are analyzed. Keyword: Moneary Policy; Noie rading; Exchange rae overhooing JEL claificaion: F31, F32, F41 Addre: Kiel Iniue for World Economic Dueernbrooker Weg Kiel Germany Telephone: Telefax: c.pierdzioch@ifw.uni-kiel.de Acknowledgmen: Thi paper wa wrien during a reearch vii of he auhor a he Naional Bureau of Economic Reearch (NBER), Cambridge MA. The hopialiy of he NBER i graefully acknowledged. I would like o hank Claudia Buch and Joerg Doepke for helpful commen. The uual diclaimer applie.

3 1 1. Inroducion Influenial empirical reearch in inernaional macroeconomic ha eablihed he puzzle ha exchange rae ofen how a delayed overhooing in repone o moneary policy hock (Larape 1992, Clarida and Gali 1994, Eichenbaum and Evan 1995; ee, however, Fau and Roger 1999). The delayed overhooing of he exchange rae decribe a iuaion in which a moneary expanion rigger an immediae depreciaion of he exchange rae ha hen, however, gradually coninue for ome monh or quarer before he exchange rae ar appreciaing o i long-run po-hock level. Thi hump-haped paern of exchange rae dynamic in repone o a moneary policy hock i in harp conra o he predicion of he claical icky-price model pioneered by Dornbuch (1976). Thi workhore model of inernaional macroeconomic implie ha he exchange rae overhooing riggered by an unanicipaed expanionary permanen moneary policy hock hould occur immediaely afer he hock, no wih a delay. In hi paper, I analyze how he delayed overhooing of he exchange rae can be modeled wihin he conex of a dynamic opimizing new open economy macro (NOEM) model of he ype recenly developed by Obfeld and Rogoff (1995). A compared o he Dornbuch (1976) model ofen ued in previou heoreical reearch on exchange rae overhooing (ee, e.g., Levin 1994, Kempa and Nelle 1999), a major advanage of uing a NOEM model o reae he effec of moneary policy hock on exchange rae dynamic i ha NOEM model are full-fledged micro-founded general equilibrium model. NOEM model, herefore, allow aking ino accoun he ineremporal budge conrain and he dynamic opimizaion of he privae ecor when analyzing he effec of moneary policy hock in open economie. Wihin a NOEM model, I explore he implicaion of an explanaion for he delayed overhooing puzzle ha i baed on he noion ha ome agen who rade in he foreign exchange marke ue imple rule of humb when forecaing exchange rae and, hu, fail o form raional exchange rae expecaion. In he conex of he Dornbuch (1976) model,

4 2 Levin (1998) ha pelled ou he implicaion of relaxing he aumpion of raional expecaion for he overhooing phenomenon. In my model, hoe agen who ue imple rule of humb form heir foreca of exchange rae by comparing he acual exchange rae wih ome kind of medium-run arge exchange rae. A ime evolve, hey updae heir compuaion of he medium-run arge exchange rae. Thu, he agen who ue a imple rule of humb o foreca exchange rae learn over ime abou he naure of exchange rae movemen and updae heir foreca correpondingly. Thi idea ha he gradual accumulaion of informaion in an environmen in which agen need ome ime o learn abou he way heir environmen change ha araced aenion in he recen lieraure on he delayed overhooing puzzle. In a recen conribuion o hi lieraure, Gourincha and Tornell (2002) have hown ha delayed overhooing can arie in a model of exchange rae deerminaion in which agen learn abou he perience of moneary policy (inere rae) hock and inere rae reac only gradually o he hock. In addiion, hey allow for he poibiliy ha agen miperceive he econd momen of he moneary policy proce. Anderon and Beier (2000) have made a furher recen conribuion o hi lieraure. Anderon and Beier have hown how learning abou he perience of moneary policy hock may generae delayed overhooing of he nominal exchange rae in a varian of he opimizing general equilibrium NOEM model developed by Obfeld and Rogoff (1995). Moreover, hey have demonraed ha learning may increae he perience of he effec of nominal hock and, in addiion, ha imporan implicaion for he dynamic of he curren accoun and, hu, for he long-run effec of moneary policy hock. The reearch I preen in hi paper can be viewed a an exenion of he work of Anderon and Beier (2000). My analyi cloely reemble heir analyi inofar a I build a learning mechanim ino a dynamic opimizing wo-counry NOEM model. However, here are ome ignifican difference beween heir reearch raegy and he reearch raegy I

5 3 adop in hi paper. Thee difference regard boh he macroeconomic model I ue o deermine exchange rae dynamic and he learning mechanim I buil ino hi model o generae delayed exchange rae overhooing. To model he impac of moneary policy hock on exchange rae dynamic, I employ an opimizing dynamic NOEM model feauring icky good price and pricing-o-marke (PTM) behavior of firm. NOEM model buil on he aumpion of PTM have recenly araced much aenion in he inernaional macro lieraure (Be and Devereux 1996, 2000, Kollmann 2001, Senay 1998). PTM implie ha firm can e differen price for heir good acro egmened naional good marke. Combining PTM wih he aumpion of icky price implie ha he price of good are icky in he currency of he counry ha impor he good. In line wih he available empirical evidence (ee, e.g., Engel and Roger 1996, Kneer, 1993), auming icky price and PTM limi he exen of pa-hrough of exchange rae flucuaion ono good price and cuhion he expendiure wiching effec of exchange rae change. Furhermore, PTM re on he aumpion ha naional good marke are egmened, implying ha moneary policy hock in general lead o deviaion of he real exchange rae from purchaing power pariy (PPP). Thi ha he advanage ha, a in he radiional Dornbuch (1976) model, he implicaion of rule of humb forecaing for he dynamic of he real exchange rae can be udied. Becaue Anderon and Beier (2000) ue in heir analyi a cloe varian of he model pioneered by Obfeld and Rogoff (1995), a model in which purchaing power pariy alway hold, hey canno udy how moneary policy hock affec he dynamic of he real exchange rae. I how ha he join modeling of he delayed overhooing of he nominal and of he real exchange ha he advanage ha i provide addiional inigh ino he queion under which condiion learning in he foreign exchange marke implie a delayed overhooing of he nominal and of he real exchange rae. I how ha he analyi of learning for he join delayed overhooing of he nominal and of he real exchange rae i imporan becaue in my

6 4 PTM-NOEM model delayed nominal exchange rae overhooing doe no auomaically imply delayed real exchange rae overhooing. In fac, in my model iuaion can arie in which he nominal exchange rae exhibi delayed overhooing bu he real exchange rae doe no. Thi reul i counerfacual becaue, in he real world, nominal and real exchange rae end o be highly correlaed wih correlaion coefficien ypically around 0.9 or higher. In conequence, a delayed overhooing of he nominal exchange rae hould be mirrored in a delayed overhooing of he real exchange rae. I follow ha, if learning i a he roo of he delayed overhooing puzzle, i hould give rie o delayed overhooing of he nominal and of he real exchange rae. I find ha a imulaneou delayed overhooing of he nominal and of he real exchange rae arie if he parameer ha decribe he learning mechanim imply ha agen updae heir foreca relaively quickly and heir expecaion are relaively eniive o exchange rae movemen. Becaue a number of empirical udie ha repored evidence on hee parameer for differen ample period and differen currencie, hi reul can be ued in fuure empirical reearch o conduc furher yemaic reearch on he link beween learning, rule of humb forecaing, and he delayed overhooing puzzle. The learning mechanim I build ino my PTM-NOEM model o generae delayed exchange rae overhooing i differen from he learning mechanim advocaed by Anderon and Beier (2001) and Gourincha and Tornell (2002). In boh udie, agen eek o learn abou he naure of moneary policy hock. In my model, in conra, agen eek o learn direcly abou exchange rae dynamic. Furher, in boh udie agen rely on relaively complex forecaing and learning echnique. In he model ued by Anderon and Beier (2002), agen alo form raional expecaion. In my model, in conra, ome agen ue a imple rule of humb o form exchange rae expecaion. In he conex of my model, hi coniue a deviaion from he aumpion of raional expecaion. Specifically, o udy he implicaion of learning in he formaion of exchange rae expecaion for he effec of moneary policy hock, I follow DaSilva (2001) and Devereux and Engel (2002) and exend

7 5 an oherwie andard PTM-NOEM model by allowing for he ype of mall deviaion from raional expecaion dicued in he large and rapidly growing noie rader lieraure. The main difference beween he udy of Devereux and Engel (2002) and my udy i ha hey eek o explain are concerned wih he o-called exchange rae diconnec puzzle which decribe he ylized fac ha exchange rae are exremely volaile and ha, a he ame ime, exchange rae volailiy doe no affec he volailiy of macroeconomic fundamenal. In conra, I focu on he delayed overhooing puzzle. Thi difference in he focu of he analyi require ha I analyze he conequence of a form of noie rading ha i differen from he form of noie rading udied by Devereux and Engel. In he udy of Devereux and Engel, noie rader have condiionally biaed exchange rae expecaion. Thi aumpion mainly erve o amplify he volailiy of he exchange rae. In conra, in my PTM-NOEM model, noie rader employ, a in DaSilva (2001), a rule of humb provided by echnical char analyi o foreca exchange rae movemen. Thi implie ha noie rading ha imporan implicaion in a dynamic conex. The empirical relevance of he form of deviaion from raional expecaion I aume in my analyi ha been documened in numerou empirical udie of he exchange rae forecaing echnique ued by foreign exchange rader. A by no mean exhauive li of ignifican conribuion o hi lieraure include he udie of Allen and Taylor (1990), Frankel and Froo (1987a, 1987b), and Cheung and Chinn (2001). The reul of my udy are in line wih he reul derived in differen heoreical eing in he lieraure on he implicaion of learning for delayed exchange rae overhooing (i.e., I find ha hee reul are robu). In addiion, my reul offer ome inereing new inigh. I find ha, in he conex of a ochaic, dynamic, opimizing PTM-NOEM model, noie rading in foreign exchange marke help explaining he delayed overhooing of he nominal and of he real exchange rae in repone o an unanicipaed perien expanionary

8 6 moneary policy hock. Moreover, I find ha he form of noie rading I analyze in hi paper help explaining he delayed overhooing puzzle if noie rader updae heir exchange rae expecaion quickly and/or if noie rader exchange rae expecaion are relaively eniive o deviaion of he curren exchange rae from i medium-run arge value. In line wih he reul repored by Anderon and Beier (2000), I find ha noie rading ha implicaion for he dynamic of he curren accoun and lead o yemaic deviaion from he condiion of uncovered inere rae pariy (UIP). Furher, noie rading help explaining he delayed overhooing puzzle if moneary policy hock are relaively perien or even permanen a in he claic Dornbuch (1976) udy. The link beween noie rading and he delayed overhooing of nominal exchange rae weaken of moneary policy hock are no very perien. I organize he remainder of he paper a follow. In Secion 2, I lay ou he heoreical model I ue o udy he link beween noie rading, moneary policy hock, and exchange rae dynamic. In Secion 3, I ue impule repone funcion o analyze how he dynamic of he nominal and of he real exchange rae and of oher key macroeconomic variable in he afermah of a moneary policy hock depend upon he behavior of noie rader and he perience of moneary policy hock. In Secion 4, I offer ome concluding remark. 2. The Model To analyze how noie rading change he way moneary policy hock affec exchange rae dynamic, I ue an in many repec andard PTM-NOEM model. Thi guaranee ha I ue a conenu model and ha he reul I derive do no hinge upon uncommon and arbirary aumpion regarding houehold preference and firm price eing. Be and Devereux (1996, 2000) have done he pioneering work on PTM in NOEM-yle general equilibrium model, and he model I ue cloely reemble heir model.

9 7 The rucure of he model i a follow: The world i made up of wo counrie, Home and Foreign. The wo counrie are of equal ize. Each counry i inhabied by infiniely-lived idenical houehold who maximize heir expeced lifeime uiliy. In addiion, each counry i populaed by a coninuum of profi maximizing firm. The houehold own he repecive domeic firm. The firm ell differeniaed produc in a monopoliically compeiive good marke. Firm have monopoly power and are, herefore, price eer. Becaue here are no poibiliie o arbirage away price differenial beween egmened naional good marke, firm can e differen price in heir repecive home counry and abroad. All firm e price in he local currency ued by heir buyer. Thu, here i complee PTM. A in he PTM- NOEM model developed by Senay (2001), Be and Devereux (2001), and Kollmann (2001), he price eing of firm i governed by a aggered-conrac mechanim a in Calvo (1983). The only producion facor ued by firm i labor. Firm hire labor in a perfecly compeiive labor marke. There i no migraion of labor acro counrie. The pecial feaure of my PTM-NOEM model i he rucure of inernaional financial marke. Three feaure of inernaional financial marke are worh menioning. Fir, he only inernaionally raded ae are nominal one-period bond. Second, while Foreign houehold hold only Foreign currency denominaed bond, Home houehold hold boh Home and Foreign currency denominaed bond. Thi i merely a modeling device ha alleviae he analyi. Third, Home houehold can direcly rade in Home currency denominaed bond bu all of heir rading in Foreign currency denominaed bond i, a in Devereux and Engel (2002), carried ou by pecialized foreign exchange dealer. Foreign exchange dealer ac in a compeiive marke and eek o maximize he dicouned expeced reurn of buying and elling Foreign currency denominaed bond. Becaue he dicouned expeced reurn of rading in Foreign currency denominaed bond are eniive o exchange rae change, foreign exchange dealer have o form exchange rae expecaion. To form exchange rae expecaion, hey conduc a queionnaire among

10 8 pecialized foreign exchange rae forecaer. Some of hee foreign exchange rae forecaer are noie rader who ue a imple rule of humb o compue exchange rae foreca. 2.1 Houehold Preference and Budge Conrain Home and Foreign houehold have idenical preference and maximize he preen value of heir expeced lifeime uiliy. In he cae of a Home houehold he expeced lifeime uiliy i given by ε 2 ( log( C ) + χ( M / P ) /(1 ε ) κn / ) U = E β = 2, (1) where he Greek leer are uch ha κ > 1, χ > 0, ε > 0, 0 <β < 1 and E are expecaion condiional on ime informaion. A regard he argumen enering ino he uiliy funcion, C denoe a real conumpion index, N denoe hour worked, and M / P denoe he endof-period real money holding of he houehold, where M i he upply of Home cenral bank money (here i no currency ubiuion) and P i he aggregae Home conumer price index (CPI). The real conumpion index, C, i defined over a coninuum of differeniaed, perihable Home and Foreign conumpion good of oal meaure uniy: C 1 θ /( θ 1) ( θ 1) / θ = c ( z) dz, (2) 0 where θ > 1 denoe he elaiciy of ubiuion and c (z) denoe conumpion of good z a ime. The Home conumer price index, P, i defined a he minimum expendiure required o buy one uni of he aggregae conumpion index, C : 1/ 2 1 1/(1 θ ) 1 θ 1 θ = p ( z) dz + q ( z) dz, (3) 0 1/ 2 P

11 9 where p (z) denoe he Home currency price of a Home-produced good and q (z) denoe he Home currency price of a Foreign PTM good. The Foreign price index i given by a imilar formula. In addiion o real balance, Home and Foreign houehold hold nominal bond. Foreign houehold only hold Foreign currency denominaed bond. Home houehold can ake poiion in boh Home and Foreign currency denominaed bond. However, hey canno rade direcly in Foreign currency denominaed bond. All rading in Foreign currency denominaed bond i carried ou by pecialized foreign exchange dealer which ac in he inere of Home houehold. The ne paymen (denominaed in Home currency uni) Home houehold receive for heir invemen accoun from he foreign exchange dealer i denoed by f Π. Depending on he good luck or bad luck of he foreign exchange dealer, hi ne paymen may be negaive or poiive. Houehold ake he ne paymen hey receive from he foreign exchange dealer a given. The ne paymen i defined a Π = S B d S B, (4) f * * * h, 1 h, where S denoe he nominal exchange rae defined a he amoun of Home currency uni required o buy one uni of he Foreign currency, B * h, denoe foreign exchange dealer holding of Foreign currency denominaed bond paying one uni of foreign currency in period + 1, and fir componen of * d denoe he period price of Foreign currency denominaed bond. The f Π denoe he amoun Houehold receive in period from he foreign exchange dealer. The econd componen of in period o he foreign exchange dealer. f Π denoe he new paymen Houehold make Home houehold receive inere income for holding Home bond, profi income for he ownerhip of Home firm, labor income for hour worked, and ranfer from he governmen.

12 10 In addiion, hey receive fund from or, in bad ime, are required o pay fund in o heir foreign exchange dealer. Given he variou componen of heir income, Home houehold deermine heir opimal conumpion, decide on heir opimal Home bond holding, and deermine he opimal holding of domeic ouide money. Their period budge conrain can be wrien a P C 1 + w N + Π + Π + PT, (5) + d B + M = B + M 1 f where B and for he quaniy of Home currency denominaed nominal bond paying ou one uni of Home currency in period + 1, d and for he period price of hee bond, T and for real lump-um ranfer (denominaed in erm of he conumpion aggregae, w and for he nominal wage rae, and houehold receive from domeic firm. C ), Π and for he nominal profi income he Uing imilar argumen, i can be hown ha he period budge conrain for a Foreign houehold obey he following difference equaion: P C + w N + Π + P T, (6) * * * * * * * + d B f, + M = B f, 1 + M 1 * * * * * where B give he Foreign houehold holding of Foreign currency denominaed bond * f, and an aerik denoe a Foreign variable. The fir-order condiion for a Home houehold can be wrien a (he uual ranveraliy condiion applie): C P d = β E, (7) C+ 1P + 1 w N = κ C, (8) P

13 11 M P γ C 1 = d 1/ ε. (9) Following he ame ep ha led o equaion (7) - (9), analogou fir-order condiion can be derived for he Foreign houehold. 2.3 Foreign Exchange Dealer A in Devereux and Engel (2002), Foreign exchange dealer ac in a compeiive marke and maximize he dicouned expeced reurn of inveing in Foreign bond: max E fx * * * ( d S B d S B ) +, (10) 1 h, h, where fx E denoe foreign exchange dealer condiional expecaion and d i he ae coningen value of domeic currency delivered in period + 1. Thi equaion i a zeroexpeced-profi condiion ha can be ued o derive he following form of he no-arbirage condiion of uncovered inere rae pariy (UIP): fx = E d S / S ]. (11) * d [ + 1 Equaion (10) and (11) how ha he opimal invemen raegy he foreign exchange dealer chooe depend upon exchange rae expecaion. To form exchange rae expecaion, foreign exchange dealer conduc a queionnaire among foreign exchange rae forecaer. There are wo group of foreign exchange rae forecaer. The fir group coni of foreign exchange rae forecaer who apply a imple rule of humb o foreca exchange rae flucuaion. In he following, I ue he erm noie rader o refer o hi group of exchange rae forecaer. The econd group of exchange rae forecaer form model-conien raional expecaion o foreca exchange rae flucuaion. The exchange rae expecaion of hi econd group of forecaer are given by:

14 12 E Sˆ Sˆ ) E ( Sˆ Sˆ + = + ). (12) f ( 1 1 The erm f E denoe he condiional expecaion operaor applying in he cae of exchange rae forecaer forming raional expecaion and a variable wih a ha denoe percenage deviaion from he eady ae. A regard he noie rader, I aume ha hi group of exchange rae forecaer derive exchange rae foreca from he following imple rule of humb : E ˆ ˆ ) ( ˆ ˆ T S + S = φ S S ). (13) n ( 1 The parameer φ denoe he elaiciy of noie rader expecaion wih repec o he deviaion of he acual exchange rae change from a medium-run exchange rae arge, T Ŝ. The erm n E denoe he condiional expecaion operaor applying in he cae of noie rader. Noie rader calculae he medium-run exchange rae arge, T Ŝ, a he geomerically-weighed moving average of he exchange rae oberved during he la ma > 0 period: ˆ ma T = (( ma + 1 j) / J ) Sˆ, wih ma j J = j= 1 j= 1 S j. (14) Equaion (13) and (14) how ha noie rader ue a imple echnical rading rule o foreca exchange rae flucuaion. Varian of he imple echnical rading rule given in equaion (13) and (14) have ofen been udied in he heoreical noie rader lieraure. Becaue uch rule have been eimaed in he empirical noie rader lieraure, i i raighforward o calibrae hee rule. Of coure, more ophiicaed forecaing rule for he expecaion formaion of noie rader could be analyzed. However, he imple forecaing rule given in equaion (13) and (14) uffice o derive he main reul of hi paper. Moreover, uing more complex exchange rae forecaing rule o decribe he behavior of noie rader would

15 13 conflic wih he idea ha noie rader ue imple rule of humb o foreca exchange rae change. Guided by he reul repored in he empirical noie rader lieraure, I aume ha he elaiciy, φ, of noie rader expecaion wih repec o he deviaion of he acual exchange rae change from i medium-run exchange rae arge i poiive. Thi aumpion implie ha noie rader form regreive exchange rae expecaion. The empirical evidence repored by Frankel and Froo (1987a, 1987b, 1990) and oher ugge ha exchange rae forecaer form regreive raher han exrapolaive exchange rae expecaion a forecaing horizon of everal monh. Thee forecaing horizon are he relevan one for buine cycle analye. Finally, o cloe he model, I invoke he aumpion ha foreign exchange dealer form heir exchange rae expecaion upon compuing he weighed arihmeic average of he exchange rae foreca of noie rader and raional rader E ˆ ˆ n ˆ ˆ f S S ) ge ( S S ) (1 g) E ( Sˆ Sˆ + = ), wih g [,] 0 1. (15) fx ( See, for inance, DeGrauwe and Dewacher (1993) and DaSilva (2001) for imilar approache o aggregae he exchange rae expecaion of heerogeneou agen. 2.4 Pricing-o-Marke Firm maximize expeced profi. To maximize expeced profi, firm hire labor in a compeiive labor marke in order o produce a differeniaed good. The producion funcion of firm i given by y ( z) = N ( z). The nominal profi of a Home firm producing good z coni of profi from ale a Home and of ale in he Foreign economy and can be D F * expreed a Π ( z) = y ( z)[ p ( z) w ] + y ( z)[ S p ( z) w ], where p * ( z ) denoe he Foreign PTM price of a Home produc and y D (z) and y F (z) denoe he demand for he

16 14 produc of he firm a Home and abroad. Becaue price are icky, oupu i demand deermined in he hor run. The demand funcion are given by: y D θ ( z) = ( p ( z) / P ) C, (16) y F * * θ * ( z) ( p ( z) / P ) C =. (17) Becaue each firm ha monopoly power on he Home and Foreign marke for i differeniaed good, i rea he price, p (z) and * ( z ), i charge for i produc a choice variable. A in p Senay (1998), Be and Devereux (2001), and Kollmann (2001), firm price eing i ubjec o a dicree ime verion of he luggih price-eing mechanim developed by Calvo (1983). According o he Calvo-yle price-eing mechanim, when maximizing i expeced profi each firm ha o ake ino accoun ha here i a poiive probabiliy 0 <γ < 1 ha i canno revie he price p (z) and p * ( z ) i e in period < in period. In conequence, firm e he curren Home and Foreign price of heir produc, p (z) and ( ) p * z, o a o maximize he expeced preen value, V (z), of curren and fuure profi, where period, >, profi are weighed by he probabiliy ha he curren period price, p (z) and p * ( z ), will ill be in force in period. Firm maximize max V ( z) = E R *, p ( z), p ( z) = γ Π ( z), (18) where R, Π j= d j i he marke nominal dicoun facor. The fir-order condiion for hi maximizaion problem are: p ( z) = θ θ E 1 E γ = = γ R, R C (1/ P ), θ C (1/ P ) w θ, (19)

17 15 * p ( z) = θ θ E 1 E = = γ γ R R,, C (1/ P ) * * * C (1/ P ) * θ θ w S. (20) Similar expreion can be derived for he profi-maximizing price, q (z) and ( ) Foreign firm. q * z, e by 2.5 Governmen The Home and Foreign governmen finance real ranfer by eignorage. The period-budge conrain for he Home governmen can, hu, be wrien a T = ( M M ) 1 / P. (21) The Home money upply i governed by a imple AR(1) proce: ˆ = α ˆ + ε, (22) M M 1 M, where ε M, denoe a erially uncorrelaed ochaic diurbance erm and he parameer α [0,1] capure he perience of moneary policy hock. The Foreign governmen ecor i rucured in a compleely analogou way. 2.6 Definiion of Equilibrium, Model Soluion, and Model Calibraion Following he NOEM lieraure, I focu on a ymmeric monopoliic compeiion equilibrium in each counry. Thi equilibrium i defined a an allocaion for oupu, conumpion, he exchange rae, price, inere rae, wage rae, and bond holding uch ha he following ix condiion are aified: (i) he labor marke in each counry clear, (ii) he fir-order condiion for houehold ineremporal uiliy maximizaion are aified, (iii) he conolidaed budge conrain for each counry i aified, (iv) he bond marke are in

18 16 equilibrium and he expeced profi of foreign exchange dealer are zero, (v) PTM firm e price according o equaion (19) and (20), and, (vi) he Home and Foreign money upply are given by equaion (22) and i foreign counerpar. To olve for he vecor of endogenou variable, I olve he model numerically. The oluion algorihm coni of hree ep. In a fir ep, I follow he NOEM lieraure and log-linearize he model around a ymmeric flexible-price eady ae in which Home houehold foreign ae poiion i zero. In a econd ep, I calibrae he model. The calibraion of he model i given in Table 1. All parameer value are wihin he range of empirical eimae. The parameer value I ue are a in Be and Devereux (2001). Oher auhor have ued imilar parameer value (ee, e.g., by Senay 1998). Following he model calibraion carried ou in hee udie guaranee ha he reul I repor in hi paper can be compared wih hoe repored in he lieraure. A regard he parameer decribing how noie rader form heir exchange rae foreca, I begin my analyi by auming φ = 0. 5 and ma = 2. The numerical value for he parameer φ lie wihin he range of empirical eimae (ee, e.g., Frankel and Froo 1987a, Cavaglia e al. 1993). Becaue he model i calibraed o quarerly daa, he numerical value for he parameer ma implie ha noie rader ue a geomeric moving average of lengh wo quarer (i.e., ix monh) o compue he mediumrun exchange rae arge value. In Secion below I analyze how he imulaion reul change if he parameer φ and ma are varied. In a hird ep, I imulae he model numerically in order o explore how he preence of noie rader in he foreign exchange marke change he impac of moneary policy hock on he dynamic of he nominal and of he real exchange rae and of oher key macroeconomic variable. I ue Klein (2000) algorihm in order o find he oluion of he yem. Thi oluion deermine he pah of he endogenou variable of he model in erm of he predeermined and exogenou ae variable of he model. For deail, ee Klein (2000).

19 17 Iner Table 1 abou here. 3. Noie Trading and he Propagaion of Moneary Policy Shock Thi ecion come in hree par. In he fir par, I analyze he implicaion of noie rading in he foreign exchange marke for he propagaion of a permanen Home moneary policy hock. I how ha noie rading can reul in he ype of delayed overhooing of he exchange rae documened in he empirical lieraure. I how ha noie rading implie deviaion from UIP and I alo analyze he implicaion of noie rading for he impac of a permanen Home moneary policy hock on he curren accoun. Moreover, I dicu he implicaion of noie rading for he real exchange rae. In he econd par, I analyze how variaion in he parameer ha decribe how noie rader form heir exchange rae foreca affec hee reul. In he hird par, I analyze he implicaion of noie rading for he propagaion of a emporary Home moneary policy hock. 3.1 The Effec of a Permanen Moneary Policy Shock Figure 1 depic he impac of a uni permanen Home moneary policy hock on key Home variable. To compue he impule repone depiced in he figure, I hold in line wih Dornbuch (1976) analyi he Foreign money ock conan. In order o ae he implicaion of noie rading for he propagaion of he moneary policy hock, I plo for each variable depiced in Figure 1 wo impule repone funcion: one impule repone funcion depic a iuaion in which noie rader play no role for exchange rae forecaing (olid line) and one impule repone funcion depic a iuaion in which foreign exchange rae dealer ake noie rader foreca ino accoun when forming exchange rae expecaion (dahed line). I ar wih he analyi of he impule repone funcion applying if here are no noie rader in he foreign exchange marke. Figure 1 how ha he Home moneary policy hock

20 18 reul in a emporary decline of he Home nominal inere rae. In conequence, he nominal inernaional inere rae differenial become negaive. In addiion, becaue PPP doe no hold in he hor run under PTM, real inere rae can differ acro counrie in he afermah of he moneary policy hock. The Home real inere rae, which i linked o he nominal inere rae by he Fiher pariy condiion, decline in he hor run. Thi ha he implicaion ha opimizing houehold increae heir conumpion pending in he afermah of he moneary policy hock. A furher effec of he abolue and relaive decline of he Home nominal inere rae i ha he nominal exchange rae mu depreciae in order o reore he condiion of UIP. The magniude of he required depreciaion of he nominal exchange rae depend upon he influence of noie rader on he exchange rae foreca of foreign exchange dealer. If here are no noie rader acive in he foreign exchange marke, he depreciaion of he nominal exchange rae come o a op only when he raional appreciaion expecaion of he foreign exchange dealer are large enough o cover he negaive inernaional nominal inere rae differenial. A a reul, he nominal exchange rae overhoo i long-run po-hock eadyae value. A in he model championed by Dornbuch (1976), he exchange rae overhooing can be oberved in he immediae afermah of he moneary policy hock. Thu, here i no delayed overhooing. A hown by Be and Devereux (2000), exchange rae overhooing will occur in he model o long a he elaiciy of money demand wih repec o real balance i maller han one. The depreciaion of he nominal exchange rae ranlae ino a correponding depreciaion of he CPI-baed real exchange rae. A furher effec of he moneary policy hock i ha Home firm expand producion in he hor run in order o mee he increaed demand for heir produc. Thi i profiable becaue price are above marginal co. Iner Figure 1 abou here.

21 19 Wha are he implicaion of noie rading for he macro-dynamic effec of a permanen moneary policy hock? The impule repone depiced in Figure 1 highligh hree core reul. The fir core reul i ha noie rading allow generaing a delayed exchange rae overhooing in repone o a permanen moneary policy hock. The econd core reul i ha a negaive inernaional nominal inere rae differenial can arie alongide wih a depreciaion of he nominal exchange rae. The hird core reul i ha noie rading in he foreign exchange marke ha imporan implicaion for he repone of he curren accoun o moneary policy hock Noie Trading and Delayed Exchange Rae Overhooing The fir core reul highlighed by Figure 1 i ha noie rading can give rie o a delayed overhooing of he nominal exchange in repone o a permanen moneary policy hock. Why doe he nominal exchange rae exhibi a delayed overhooing raher han an immediae overhooing in he afermah of he permanen moneary policy hock? The key o he anwer o hi queion i he UIP condiion. Thi condiion can be wrien a ˆ * ˆ n ˆ f d d ge ( S ) = (1 g) E ( Sˆ ), (23) where he Greek leer denoe he fir-difference operaor. The key feaure of equaion n (23) i ha here i an addiional erm, E Sˆ ), in he UIP condiion if noie rader ( + 1 influence he exchange rae foreca of foreign exchange dealer. Thi erm capure he fac ha he depreciaion of he nominal exchange rae riggered by he Home moneary policy hock induce noie rader o compare he acually realized nominal exchange rae wih heir medium-run arge exchange rae. Becaue noie rader updae heir foreca for he mediumrun exchange-rae arge only gradually, he acual exchange rae lie above i arge rae in he immediae afermah of he moneary policy hock. Hence, noie rader expec a

22 20 reverion of he exchange rae rend in he medium run. In conequence, hey form n appreciaion expecaion: E ( Sˆ 1 ) < 0. + A wineed by equaion (23), he appreciaion expecaion of noie rader erve o miigae he effec of he negaive inernaional nominal inere rae differenial on raional forecaer exchange rae expecaion. I follow ha if he impac of noie rader on he formaion of exchange rae expecaion i rong enough (i.e., if he parameer g i large enough) he appreciaion expecaion of he noie rader will dominae he effec of he negaive inernaional inere rae differenial. In conequence, raional foreign exchange forecaer ake ino accoun he rong impac of noie rader and form correponding depreciaion expecaion. Becaue hee expecaion are raional, i follow ha he only viable oluion o he model in hi cae i one ha implie ha he exchange rae coninue depreciaing for ome period following he moneary policy hock. The reul i he delayed overhooing of he exchange rae hown in Figure 1. Becaue noie rader coninuouly updae heir expecaion regarding he medium-run arge exchange rae, he delayed overhooing phae ou gradually. In he long run, he medium-run arge exchange rae of noie rader i idenical wih he po-hock eady-ae exchange rae Noie Trading and Deviaion from UIP The econd core reul highlighed by Figure 1 i ha he inernaional nominal inere rae differenial i negaive in he afermah of he permanen moneary policy hock and, a he ame ime, ha he nominal exchange rae ar depreciaing. To hed furher ligh on hi reul, I plo in Figure 1 he deviaion from he condiion of UIP in he afermah of a moneary policy hock. I define he deviaion from UIP a he reidual ha obain if he inernaional nominal inere rae differenial i ubraced from he exchange rae foreca of raional rader. In oher word, I define he deviaion from UIP in erm of he exchange

23 21 rae foreca of noie rader. Hence, deviaion from he condiion of UIP can arie if he influence of noie rader on he formaion of exchange rae expecaion i erroneouly negleced. A can be een in Figure 1, if noie rader have no influence on he exchange rae foreca of foreign exchange dealer, he deviaion from UIP i idenically zero. However, once foreign exchange dealer ake ino accoun he exchange rae foreca of noie rader when forming exchange rae expecaion, he deviaion from UIP i in general non-zero. In paricular, noe ha a poiive deviaion from UIP (i.e., noie rader from appreciaion expecaion) arie in he fir period following he permanen moneary policy. Thee are he period during which he delayed overhooing occur. In conequence, he model implie ha in he afermah of a permanen expanionary Home money upply hock a depreciaion of he nominal exchange rae, a negaive inernaional nominal inere rae differenial, and a poiive deviaion from UIP can be oberved. Eichenbaum and Evan (1995) have decribed hi phenomenon in deail in heir empirical udy Noie Trading, Delayed Overhooing, and he Curren Accoun The hird core reul highlighed by Figure 1 i ha, a in he NOEM model ued by Anderon and Beier (2000), noie rading in he foreign exchange marke ha imporan implicaion for he impac of moneary policy hock on he dynamic of he Foreign bond holding of Home houehold and, hu, on he curren accoun. To ar he analyi of hi reul, I go one ep back and aume ha here are no noie rader in he foreign exchange marke. In uch a cenario, he model i imply a dynamic verion of he PTM-NOEM model developed by Be and Devereux (1996, 2000). From heir analyi, i i known ha moneary policy hock do no lead o change in he curren accoun and, hu, leave he bond holding of houehold unaffeced. The log-linear verion of he difference equaion governing he dynamic of he Foreign bond holding of Home houehold i given by

24 22 βb ˆ * h x p z Pˆ * ( ˆ ˆ ( ) ) / 2 ( vˆ S pˆ ( z) Pˆ ) / 2 Bˆ *, = h, 1 ˆ Cˆ, (24) where xˆ ( vˆ ) denoe oupu old by Home PTM firm a home (abroad). If moneary policy hock do no reul in a change in ˆ * h, B, i mu hold ha in he immediae afermah of he hock, before firm begin adjuing price, he following equaion applie: y ˆ Sˆ Cˆ = 0. + Hence, he impule repone funcion depiced in Figure 1 how ha he curren accoun effec of he moneary policy hock i zero if g = 0. Wha change if noie rader ener he cene? The analyi of Figure 1 how ha he effec of allowing for noie rading on oupu and conumpion i relaively mall. In conequence, ŷ and Ĉ do no change ubanially. However, noie rader exer a ubanial effec on he nominal exchange rae. In conequence, i mu be he cae ha y ˆ Sˆ Cˆ + 0, implying ha moneary policy hock now rigger an adjumen of he ock of Foreign bond holding of Home houehold. In oher word, moneary policy hock affec he curren accoun. Thi implie ha money i no longer neural in he long run. In conequence, wha ha begun a a purely nominal phenomenon (noie rading and moneary policy hock) evenually reul in change in he allocaion of real reource. Of coure, he inerpreaion of hi reul hould no be reched oo far becaue, a poined ou by Obfeld and Rogoff (1995), he non-neuraliy of moneary policy in he longrun i proporional o he effec of he inere income on Foreign bond holding on he houehold opimizing behavior. For he aumed calibraion of he model, hi effec i fairly mall, implying ha money i almo neural in he long run. 3.2 Seniiviy Analye To analyze how change in he parameer ha govern he way in which noie rader form heir exchange rae foreca affec he reul repored in Secion 3.1, I ummarize in Figure 2

25 23 he reul of ome eniiviy analye. In he fir row of hi figure, I plo impule repone funcion for a model in which ma = 2 and he elaiciy of noie rader exchange rae foreca wih repec o he deviaion of he curren exchange rae from i medium-run arge value i equal o φ = 0. 5 (olid line) and φ = 0. 2 (dahed line). In he econd row of he figure, I fix he elaiciy of noie rader exchange rae foreca wih repec o he deviaion of he curren exchange rae from i medium-run arge value a φ = 0. 5 and increae he number of lagged exchange rae realizaion ued by noie rader o compue he medium-run exchange rae arge from ma = 2 (olid line) o ma = 4 (dahed line). Iner Figure 2 abou here. The figure how ha decreaing he elaiciy of noie rader exchange rae foreca wih repec o he deviaion of he curren exchange rae from i medium-run arge value implie ha he nominal exchange rae end o reach i maximum deviaion from he eady ae relaively rapidly. In conequence, he delayed overhooing of he nominal exchange rae end o be ranformed more and more ino an immediae overhooing a he numerical value aigned o he parameer φ decreae. Inereingly, he impule repone funcion graphed in he fir row of Figure 2 how a iuaion in which here i ill a delayed overhooing of he nominal exchange rae bu no longer a delay in he overhooing of he real exchange rae. While he nominal exchange rae gradually depreciae for ome period afer he moneary policy hock, he real exchange ar appreciaing in he immediae afermah of he hock. The main facor reponible for hi effec i ha in he iuaion depiced in he figure he delayed overhooing of he nominal exchange rae i overhadowed by he dynamic of he CPI. In fac, he Home CPI ar o rie relaively harply in he afermah of he moneary policy hock and converge hereafer rapidly oward i new eady-ae value. In addiion, becaue he Home moneary policy hock ha poiive emporary pillover effec on he Foreign economy (no depiced in

26 24 Figure 1), he CPI in he Foreign economy increae in he hor-run. Bu hi effec end o be maller han in he Home counry. The reul i ha he real exchange rae ar appreciaing immediaely following i impac devaluaion. Thi reul how ha he imulaneou modeling of he nominal and of he real exchange rae in a PTM-NOEM model provide imporan informaion on which numerical value for he parameer decribing how noie rader form heir exchange rae foreca hould be ued in he imulaion of he model in order o generae a delayed overhooing of he nominal and of he real exchange rae. The econd row of Figure 2 graph a iuaion in which noie rader ue a relaively long hiory of he exchange rae rajecory o compue heir medium-run exchange rae arge. In he depiced cenario, noie rading caue an underhooing of he nominal exchange rae. The reaon i ha if he number of lagged exchange rae ued by noie rader o compue he medium-run arge exchange rae i relaively large, hi arge exchange rae i updaed raher lowly. Thu, noie rader learn relaively lowly abou he naure of exchange rae change. Thi implie ha any depreciaion of he nominal exchange rae caued by he moneary policy hock give rie o relaively rong appreciaion expecaion of noie rader. In conequence, for he exchange rae o reach i po-hock eady-ae value, raional exchange rae forecaer have o form relaively rong depreciaion expecaion. The reul i ha he conemporaneou effec of he moneary policy hock on he nominal exchange rae end o be relaively mall in order o leave enough room for a furher gradual depreciaion of he nominal exchange rae. To um up, delayed overhooing of he nominal and of he real exchange rae in repone o a moneary policy hock end o occur whenever noie rader updae heir expecaion regarding he medium-run exchange rae arge relaively quickly. Moreover, delayed overhooing become more likely if he elaiciy of he foreca of noie rader wih

27 25 repec o deviaion of he curren exchange rae from hi medium-run arge value i ufficienly large. 3.3 The Perience of Moneary Policy Shock and Delayed Overhooing So far, I have analyzed how he preence of noie rader in he foreign exchange marke hape he dynamic effec of key macroeconomic variable in repone o a permanen Home moneary policy hock. Thi i he kind of analyi carried ou by Dornbuch (1976) and by he reearcher who have ued varian of hi model o udy he robune of he overhooing phenomenon. I now udy he implicaion of noie rading for he dynamic effec of a emporary Home moneary policy hock. To hi end, I compare in Figure 3 he implicaion of noie rading in he foreign exchange marke for he repone of he nominal exchange rae o a permanen and o a emporary uni Home money upply hock. Iner Figure 3 abou here. In he cae of a emporary moneary policy hock, boh noie rader and raional exchange rae forecaer expec ha he conemporaneou nominal depreciaion of he Home currency will be revered in he long run. In conequence, boh group of foreign exchange rae forecaer form appreciaion expecaion. Hence, here i no delay in he overhooing of he nominal exchange rae. Thu, a in he model developed by Gourincha and Tornell (2002) and Anderon and Beier (2000), he perience of moneary policy hock deerve pecial aenion in analye of he delayed overhooing puzzle. A expeced, he magniude of he acual depreciaion of he nominal exchange rae in he afermah of he emporary moneary policy hock become ronger he ronger i he influence of noie rader on he exchange rae expecaion of foreign exchange dealer. Alo noe ha even hough here i no delayed overhooing he preence of rule of humb forecaer implie ha, in line wih empirical evidence (Fau and Roger 1999), here are ill deviaion from UIP.

28 26 4. Concluion The analyi in hi paper demonraed ha adding noie rading o an oherwie andard PTM-NOEM model offer a number of inereing inigh ino he impac of moneary policy hock on nominal and on real exchange rae dynamic. Specifically, I howed ha noie rading help o model a delayed overhooing of he exchange rae in repone o a moneary policy hock. Moreover, noie rading i imporan for he dynamic of he curren accoun and may be one of he modeling device ha could help generaing perien deviaion from UIP. Furher, he magniude of he parameer ha capure how noie rader form heir exchange rae foreca i imporan. Specifically, noie rading end o help generaing delayed overhooing of he nominal and of he real exchange rae if (a) noie rader updae heir medium-run exchange rae arge relaively quickly, and (b) he elaiciy of noie rader foreca wih repec o he deviaion of he exchange rae from hi medium-run arge rae i ufficienly large. The laer reul are inereing becaue hey imply ha he delayed overhooing puzzle can be linked o he parameer ha decribe how noie rader compue heir exchange rae foreca. From he reearch on exchange rae expecaion, empirical evidence on he magniude of hee parameer i available for differen ample period and for a cro-ecion of currencie. Given hi evidence, i would be inereing o ue he reul I repored in hi paper o udy empirically wheher he delayed exchange rae overhooing puzzle can be linked in a yemaic way o he rucural parameer ha capure how foreign exchange rader form heir exchange rae expecaion.

29 27 Reference Anderon, T.B. and N.C. Beier (2000), Noiy financial ignal and perien effec of nominal hock in open economie, Dicuion Paper No. 2360, Cenre for Economic Policy Reearch, London. Allen, H.L. and M.P. Taylor (1990), Char, noie and fundamenal in he foreign exchange marke, Economic Journal 100: Be, C. and M.B. Devereux (1996), The exchange rae in a model of pricing-o-marke, European Economic Review 40: Be, C. and M.B. Devereux (2000), Exchange rae dynamic in a model of pricing-omarke, Journal of Inernaional Economic 50: Be, C. and M.B. Devereux (2001). The inernaional effec of moneary and fical policy in a wo-counry model. In G.A. Calvo, R. Dornbuch, and M. Obfeld (ed.): Money, Capial Mobiliy, and Trade: Eay in Honor of Rober A. Mundell. Cambridge, MA: MIT Pre: Calvo, G., (1983), Saggered price in a uiliy-maximizing framework, Journal of Moneary Economic 12: Cavaglia, S., W.F.C. Verchoor, and C.C.P. Wolf (1993), Furher evidence on exchange rae expecaion, Journal of Inernaional Money and Finance 12: Cheung, Y.-W. and M.D. Chinn (2001), Currency rading and exchange rae dynamic: a urvey of he US marke, Journal of Inernaional Money and Finance 20: Clarida, R. and J. Gali (1994), Source of real exchange rae flucuaion: how imporan are nominal hock? Carnegie-Rocheer Conference Serie on Public Policy 41: DaSilva, S. (2001), Chaoic exchange rae dynamic redux, Open Economie Review 12: DeGrauwe, P. and H. Dewacher (1993), A chaoic model of he exchange rae: he role of fundamenali and chari, Open Economie Review 4: Devereux, M.B. and C. Engel (2002), Exchange rae pa-hrough, exchange rae volailiy, and exchange rae diconnec, Journal of Moneary Economic 49: Dornbuch, R. (1976), Exchange rae expecaion and moneary policy, Journal of Inernaional Economic 6: Eichenbaum, M. and C.L. Evan (1995), Some empirical evidence on he effec of hock o moneary policy on exchange rae, Quarerly Journal of Economic 110: Engel, C. and J. Roger (1996), How wide i he border? American Economic Review 86:

30 28 Fau, J. and J.H. Roger (1999), Moneary policy role in exchange rae behavior, Inernaional Finance Dicuion Paper No Board of Governor of he Federal Reerve Syem. Frankel, J.A. and K.A. Froo (1987a), Shor-erm and long-erm expecaion of he yen/dollar exchange rae: evidence from urvey daa, Journal of he Japanee and Inernaional Economie 1: Frankel, J.A. and K.A. Froo (1987b), Uing urvey daa o e andard propoiion regarding exchange rae expecaion, American Economic Review 73: Frankel, J.A. and K.A. Froo, (1990), Chari, fundamenali, and rading in he foreign exchange marke, American Economic Review 80, Gourincha, P.O. and A. Torrnell (2002), Exchange rae dynamic, learning and mipercepion, Working Paper No Naional Bureau of Economic Reearch, Cambridge, MA. Kempa, B. and M. Nelle (1999), Sicky price and alernaive moneary feedback rule: how robu i he overhooing phenomenon? Inernaional Economic Journal 13: Klein, P., (2000), Uing he generalized Schur form o olve a mulivariae linear raional expecaion model, Journal of Economic Dynamic and Conrol 24: Kneer, M.N. (1993), Inernaional comparion of pricing-o-marke behavior, American Economic Review 83, Kollmann, R., (2001), The exchange rae in a dynamic-opimizing buine cycle model wih nominal rigidiie: a quaniaive inveigaion, Journal of Inernaional Economic 55: Larape, W.D. (1992), Source of flucuaion of real and nominal exchange rae, Review of Economic and Saiic 74: Levin, J. H. (1994), On luggih oupu adjumen and exchange rae dynamic, Journal of Inernaional Money and Finance 13: Levin, J.H. (1998), Alernaive expecaion model and exchange rae dynamic, Inernaional Journal of Finance and Economic 3: Obfeld, M. and K. Rogoff (1995), Exchange rae dynamic redux, Journal of Poliical Economy 103: Senay, Ö., (1998), The effec of good and financial marke inegraion on macroeconomic volailiy, The Mancheer School Supplemen 66: