PANEL COINTEGRATION ANALYSIS TO EXCHANGE RATE DETERMINATION: MONETARY MODEL VERSUS TAYLOR RULE MODEL. A Master s Thesis.

Transcription

1 PANEL COINTEGRATION ANALYSIS TO EXCHANGE RATE DETERMINATION: MONETARY MODEL VERSUS TAYLOR RULE MODEL A Maser s Thesis by VESİLE KUTLU Deparmen of Economics Bilken Universiy Ankara January 2009

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3 To My Siser

4 PANEL COINTEGRATION ANALYSIS TO EXCHANGE RATE DETERMINATION: MONETARY MODEL VERSUS TAYLOR RULE MODEL The Insiue of Economics and Social Sciences of Bilken Universiy by VESİLE KUTLU In Parial Fulfillmen of he Requiremens for he Degree of MASTER OF ARTS in THE DEPARTMENT OF ECONOMICS BİLKENT UNIVERSITY ANKARA January 2009

5 I cerify ha I have read his hesis and have found ha i is fully adequae, in scope and in qualiy, as a hesis for he degree of Maser of Ars in Economics Assoc. Prof. Kıvılcım Mein Özcan Supervisor I cerify ha I have read his hesis and have found ha i is fully adequae, in scope and in qualiy, as a hesis for he degree of Maser of Ars in Economics Assoc. Prof. Fama Taşkın Examining Commiee Member I cerify ha I have read his hesis and have found ha i is fully adequae, in scope and in qualiy, as a hesis for he degree of Maser of Ars in Economics Assoc. Prof. Aslıhan Alay-Salih Examining Commiee Member Approval of he Insiue of Economics and Social Sciences Prof. Dr. Erdal Erel Direcor

6 ABSTRACT PANEL COINTEGRATION ANALYSIS TO EXCHANGE RATE DETERMINATION: MONETARY MODEL VERSUS TAYLOR RULE MODEL Kulu, Vesile M.S., Deparmen of Economics Supervisor: Assoc. Prof. Kıvılcım Mein Özcan January 2009 This hesis examines he validiy of he moneary model and he Taylorrule model in deermining exchange raes in he long run. The moneary model and he Taylor-rule model are esed using he US dollar exchange raes over 980:0-2007:04 periods for 3 indusrialized counries. Johansen Fisher Panel coinegraion echnique provides evidence ha here exis a unique coinegraion relaionship beween he nominal exchange raes and a se of fundamenals implied by he moneary model and he Taylor rule model. The coinegraing coefficien esimaes for he moneary model and he Taylor rule model are found by using panel dynamic ordinary leas square (DOLS) esimaor. The esimaion resuls show ha he effecs of he moneary and he Taylor rule fundamenals on exchange raes are no he same as wha he heory suggess. Overall, he findings of his hesis imply ha here is no suppor for he moneary model and here is lile suppor for Taylor-rule model in explaining exchange raes. Keywords: Exchange Raes, Moneary Model, Taylor Rule, Panel Uni Roo Tess, Panel Coinegraion iii

7 ÖZET DÖVİZ KURUNUN BELİRLENMESİNDE PANEL EŞBÜTÜNLEŞME ANALİZİ: PARASAL MODEL İLE TAYLOR KURALI MODELİ NİN KARŞILAŞTIRILMASI Kulu, Vesile Yüksek Lisans, İkisa Bölümü Tez Danışmanı: Doç. Dr. Kıvılcım Mein Özcan Ocak 2009 Bu ez, uzun dönemde döviz kurlarının belirlenmesinde parasal model ile Taylor kuralı modelinin geçerliliğini araşırmakadır. Parasal model ve Taylor kuralı modeli Amerikan doları döviz kuru kullanılarak 980: : 04 dönemleri arasında 3 sanayileşmiş ülke için es edilmişir. Johansen Fisher panel eşbüünleşme ekniği nominal döviz kurları ile parasal model ve Taylor kuralı modelinin emel değişkenleri arasında ek bir eşbüünleşme ilişkisi olduğunu kanılamakadır. Parasal model ile Taylor kuralı modeli için eşbüünleşme kasayı ahminleri panel dinamik en küçük kareler (DEKK) ahminleyicisi kullanılarak bulunmuşur. Tahmin sonuçları parasal model ile Taylor kuralı modelinin emel değişkenlerinin döviz kurları üzerindeki ekisinin eorinin öne sürdüğü eki ile aynı olmadığını gösermekedir. Genel iibariyle bu ezin bulguları parasal modelin döviz kurunu açıklama gücüne yönelik kanı bulunmadığını ve Taylor kuralı modelinin döviz kurunu açıklama gücüne yönelik az kanı bulunduğunu işare eder. Anahar Kelimeler: Döviz Kurları, Parasal Model, Taylor Kuralı, Panel Birim Kök Tesleri, Panel Eşbüünleşme iv

8 ACKNOWLEDGMENTS I would like o express my sincere graiude o my supervisor, Assoc. Prof. Kıvılcım Mein Özcan for her excellen guidance, encouragemen, and paience hrough he developmen of his hesis. I am very graeful o Assoc. Prof. Fama Taşkın for her valuable suppor and advices. I would like o hank o Assoc. Prof. Aslıhan Alay-Salih for her valuable commens. I am very hankful o my family for heir encouragemen during my sudies. I would like o give my special hanks o Emre Koç for his love and invaluable suppor. Thank you for being beside me. Finally, I would like o dedicae his hesis o my deares siser, Selda Çimen. v

9 TABLE OF CONTENTS ABSTRACT..... ÖZET ACKNOWLEDGEMENTS TABLE OF CONTENTS... iii iv v vi CHAPTER I: INTRODUCTION CHAPTER II: LITERATURE REVIEW... 6 CHAPTER III: THEORETICAL BACKGROUND The Moneary Model The Taylor Rule Model.. 5 CHAPTER IV: METHODOLOGY. 9 CHAPTER V: EMPIRICAL ANALYSIS Daa Panel Uni Roo Tess Panel Coinegraion Analysis Esimaion and Resuls CHAPTER VI: CONCLUSION 40 BIBLIOGRAPHY APPENDIX vi

10 LIST OF TABLES. Table 5.2.: IPS Panel Uni Roo Tess for Saionariy Table 5.2.2: ADF Fisher Chi-square Panel Uni Roo Tess for Saionariy Table 5.3.: The Panula Principle Resuls using s, (m-m), (y-y) Table 5.3.2: The Panula Principle Resuls using s, (i-i), (p-p) Table 5.3.3: Johansen Fisher Panel Coinegraion Resuls using s, (m-m), (y-y) Table 5.3.4: Johansen Fisher Panel Coinegraion Resuls using s, (i-i), (p-p) Table 5.4.: Panel Dynamic OLS Esimaes of Moneary Model Table 5.4.2: Panel Dynamic OLS Esimaes of Taylor-rule Model vii

11 CHAPTER I INTRODUCTION During he pas wo decades, researchers have ried o es he empirical validiy of Frenkel s (976) flexible-price moneary model of he exchange rae by using differen samples and esimaion echniques. The earlier sudies searched a longrun relaionship beween exchange raes and he moneary fundamenals by employing an Engle Granger wo sep procedure on he ime series of he individual counries. Among hese sudies, paricularly Boohe and Glassman (987), Baillie and Selover (987), and McNown and Wallace (989) could no find much of an evidence for a coinegraion relaionship beween exchange rae and is main deerminans suggesed by he moneary model of Frenkel. The failure of he moneary model of exchange rae by using Engle Granger echnique has led many researchers o employ anoher mehodology namely, Johansen s mulivariae coinegraion echnique. MacDonald and Taylor (993, 994), McNown and Wallace (994), Diamandis e al. (996) find evidence in favor of he moneary model in deermining exchange raes by using

12 Johansen s mulivariae coinegraion mehodology. Cushman (2000) also finds evidence in favor of coinegraion beween he US dollar-canadian dollar exchange rae and a se of moneary fundamenals by using Johansen s mehodology; however, he esimaed coinegraing coefficiens differ widely from hose suggesed by he moneary model. Cushman (2000) herefore concludes ha here is no suppor for he moneary model in US-Canadian daa. Wih he recen developmens in panel uni roos and panel coinegraion analysis, hese new echniques are used o check he validiy of he moneary model of exchange rae in he log-run. Among he sudies which uilize panel daa echniques, paricularly Groen (2000, 2005) and Mark and Sul (200), and Rapach and Wohar (2004) provide noeworhy panel resuls. Their resuls sugges ha he moneary model migh explain nominal exchange rae rends during pos-breon Woods floa. All of he aforemenioned sudies using boh imes series and panel daa echniques which are esing he validiy of he moneary model assume ha cenral banks are using money supply as a moneary policy insrumen. However, especially in indusrialized counries modern cenral banks have used shor-erm ineres raes as he single moneary policy ool. In fac, Clarida e al. (998) observe ha, since 980 s, he cenral banks of Germany, Japan and U.S. have pursued inflaion argeing meaning ha in response o a rise in expeced inflaion relaive o arge, each cenral bank raises nominal raes sufficienly o push up real raes. 2

13 On he basis of he changes in moneary policy insrumens of he cenral banks, Clarida e al. (998) esimae moneary policy reacion funcions assuming ha cenral banks se he nominal shor erm ineres raes according o a simple ineres rae rule proposed by Taylor (993). They find ha he coefficien of real exchange rae in he ineres rae rule is saisically significan for Germany and Japan. The findings of Clarida e al. (998) gave rise o a new srand of lieraure, noably Engel and Wes (2005, 2006), Mark (2005), and Molodsova and Papell (2008), which examines he linkage beween he exchange raes and a se of fundamenals ha arise when cenral banks se he ineres rae according o he Taylor-rule. Engel and Wes (2006) and Mark (2005) finds evidence Taylor-rule fundamenals provide a plausible framework for undersanding real dollar-dm exchange rae dynamics. Molodsova and Papell (2008) assess he ou-of-sample performance of he moneary and he Taylor rule models and provide he evidence of predicabiliy is much sronger wih Taylor rule model han wih he moneary model a shor horizon. Among hem, Engel and Wes (2005) failed o find a coinegraion relaionship beween exchange raes and a se of fundamenals implied by he moneary and he Taylor rule models. Earlier sudies which use ime series and panel-based frameworks generally invesigae wheher he exchange raes are coinegraed wih moneary fundamenals. In he ime series lieraure, only he sudy of Engel and Wes (2005) examines he linkage beween exchange raes and Taylor rule fundamenals using coinegraion analysis. In oher words, he role of Taylor- 3

14 rule fundamenals in explaining exchange raes wih panel coinegraion echniques has no been sudied previously. Hence, his hesis inends o conribue o he exising lieraure by using a panel coinegraion echnique o examine he linkage beween he exchange raes and he Taylor-rule fundamenals. This hesis is also moivaed from he fac ha combinaion of crosssecional and ime-series informaion in he form of a panel daa se can grealy increase he power of he uni roo and coinegraion ess. We aimed o invesigae wheher he nominal exchange raes are coinegraed wih he moneary and he Taylor rule fundamenals in a panel based framework. All of he previous sudies on he moneary fundamenals uilize panel coinegraion ess based on Engle-Granger (987) framework which depends esing he saionariy of he residuals from a levels regression. Unlike he previous lieraure his hesis uses he panel coinegraion analysis by employing Johansen Fisher panel coinegraion echnique which is originaed from Johansen s mulivariae coinegraion mehodology. In his hesis, Johansen Fisher panel coinegraion echnique is applied o check for he validiy of he moneary and he Taylor-rule models of exchange rae in he long run. The moneary and he Taylor-rule models are esed using he US dollar exchange raes over 980:0-2007:04 periods for 3 indusrialized counries. In order o find suppor for he moneary and he Taylor-rule models, wo pieces of evidence are needed. The firs one is o find ha he US dollar exchange rae is coinegraed wih he moneary and he Taylor-rule 4

15 fundamenals. The second one is o obain esimaes of he coinegraing coefficiens relaing he US dollar exchange rae o a se of fundamenals which agree wih he values suggesed by he moneary and he Taylor-rule models. The res of he paper is organized as follows: Secion 2 presens he previous sudies in he lieraure. Secion 3 gives he heoreical background for he moneary and he Taylor-rule models. The mehodology is explained in Secion 4. Empirical analysis including daa sources, panel uni roo and panel coinegraion ess, and he esimaion resuls are presened in Secion 5. Finally, Secion 6 gives he concluding remarks. 5

16 CHAPTER II LITERATURE REVIEW The roos of he moneary approach in deermining he exchange rae movemens go back o he early 970s. Frenkel (976) deals wih he deerminans of he exchange rae and develops a moneary view of exchange rae deerminaion. Afer saing he building blocks of he moneary model, which are purchasing power pariy (PPP), money demand funcion and expecaions, he provides empirical evidence for he moneary approach o exchange rae deerminaion using he German hyperinflaion case during On he basis of Frenkel s findings, many researchers have sared o invesigae he moneary approach o exchange rae deerminaion by using ime series analysis for differen counries and differen exchange raes. Using Engle-Granger coinegraion mehodology, Boohe and Glassman (987), Baillie and Selover (987) and McNown and Wallace (989) could no find much of an evidence for a coinegraion relaionship beween exchange rae and is main deerminans suggesed by he moneary approach. On he oher 6

17 hand, several sudies by MacDonald and Taylor (993, 994), McNown and Wallace (994), Diamandis e al. (996) employ Johansen s mulivariae coinegraion echnique and heir resuls show ha exchange raes are coinegraed wih moneary fundamenals in he long run. Alhough MacDonald and Taylor (993, 994) and Diamandis e al. (996) find coinegraing coefficien esimaes suggesed by he moneary model, McNown and Wallace (994) provide coefficiens esimaes which are no consisen wih he moneary model. Cushman (2000) also finds ha he US dollar-canadian dollar exchange rae is coinegraed wih a se of moneary fundamenals by using Johansen s mehodology; however, he esimaed coinegraing coefficiens differ widely from hose suggesed by he moneary model. Therefore, Cushman (2000) concludes ha here is no suppor for he moneary model in US-Canadian daa. Wih he developmens of panel uni roos and panel coinegraion analysis, researchers have sared o use hese echniques o find empirical evidence of moneary models in deermining exchange rae movemens for differen se of counries. Two recen sudies by Groen (2000) ad Mark and Sul (200) follow he PPP lieraure and es he moneary model using panels of pos-breon Woods daa. Groen (2000) considers a panel of US dollar nominal exchange rae, relaive money supply, and relaive real oupu level daa for 4 indusrialized counries covering he period 973:-994:4. He finds ha nominal exchange raes are coinegraed wih relaive money supplies and relaive oupu levels and panel coinegraion coefficien esimaes ha are 7

18 reasonably consisen wih he moneary model for his full panel and hree subpanels (G0, G7, and EMS). Mark and Sul (200) employ a panel of US dollar nominal exchange rae, relaive money supply, and relaive real oupu daa for 8 counries spanning 973:-997:. Their resuls sugges ha US dollar exchange rae is coinegraed wih moneary fundamenals and ha he moneary fundamenals conain significan predicive power for fuure exchange rae movemens. They also find evidence of coinegraion using Swiss franc or Japanese yen as he numeraire currency. Rapach and Wohar (2004) show how poorly he moneary model performs on a counry-by-counry basis for US dollar exchange raes over he pos-breon Woods period for a large number of indusrialized counries. In addiion, using panel analysis hey find ha panel coinegraion ess largely indicae he exisence of a long run relaionship beween nominal exchange raes and moneary fundamenals. Crespo-Cuaresma e al. (2005) use a panel daa se for six Cenral and Easern European counries o esimae he moneary exchange rae model wih panel coinegraion mehods including he Pooled Mean Group esimaor, he Fully Modified Leas Square esimaor and he Dynamic Leas Square esimaor. Their findings are in line wih he exisence of a long run relaionship beween nominal exchange raes and he moneary fundamenals. Groen (2005) invesigaes boh he in-sample as well as he ou-ofsample fi of moneary exchange rae model in order o assess wheher he Euro 8

19 exchange raes of Canada, Japan, and he Unied Saes have a long-run link wih moneary fundamenals. He finds ha he aforemenioned exchange raes are consisen wih moneary exchange rae model based on a common long-run relaionship, albei wih a long run impac of relaive income ha is higher han prediced by he heory. He also provides he evidence ha ou-of-sample forecasing evaluaions based on long-run moneary model are superior o boh random walk-based forecass and sandard coinegraed VAR model-based forecass, especially a horizons of 2 o 4 years. Tradiional exchange rae models assume ha cenral banks are using money supply as an insrumen or arge variable o implemen moneary policy, where money supply is exogenously deermined. However, since 980s, moneary policy insrumen used by modern cenral banks is shor erm ineres raes raher han money supply. In Taylor (993) original formulaion, he rule assumes ha he Fed ses he nominal ineres rae based on he curren inflaion rae, he inflaion gap-he difference beween inflaion and he arge inflaion rae, he oupu gap-he difference beween GDP and poenial GDP, and he equilibrium real ineres rae. Clarida e al. (998) esimae moneary policy reacion funcions for he US, Germany and Japan. They found he real exchange rae enered an ineres rae rule for Germany and Japan wih a coefficien ha is saisically significan, albei small. The lieraure on exchange rae models wih Taylor rule fundamenals is relaively new. Recen papers by Mark (2005), Engel and Wes (2005, 2006), and Engel e al. (2007), and Molodsova and Papell (2008), invesigae some of 9

20 he empirical implicaions for exchange raes if cenral banks follow Taylor rules for seing ineres raes. Engel and Wes (2005) find ha fundamenal variables such as relaive money supply, oupus, inflaion and ineres raes provide lile help in predicing changes in floaing exchange raes. In conras, heir Granger causaliy resuls show ha exchange raes should be useful in forecasing fuure economic variables such as money, income, prices and ineres raes. Mark (2005) examines he implicaions of Taylor-rule fundamenals for he Deusche mark-dollar exchange rae deerminaion in an environmen where marke paricipans are ignoran of he numerical values of he model s coefficiens bu aemp o acquire ha informaion using leas-squares learning rules. Tha is o say, he assumes ha Taylor rule coefficien values are changing over ime. Using quarerly daa from 976 o 2003, he finds evidence ha his simple learning environmen in he policy rule provides a plausible framework for undersanding real dollar-dm exchange rae dynamics. Engel and Wes (2006) also use Deusche mark-dollar exchange rae o es he Taylor rule fundamenals covering he period of Firs, hey borrow he parameers of Taylor-rule from he sudy of Clarida e al. (998). Then hey esimae VAR for he variables, namely expeced inflaion, oupu gap and ineres raes o consruc he expeced value of he fundamenals. Finally, hey use he correlaion beween he model based and acual real exchange rae as a measure, which is found o be approximaely 30 percen. 0

21 Engel e al. (2007) emphasize he poin ha beaing a random walk in forecasing is oo srong a crierion for acceping an exchange rae model. They propose a number of alernaive ways o evaluae hese models. Firs hey examine in-sample fi by emphasizing he imporance of he moneary policy rule and is affecs on expecaions. Then hey presen esimaes of exchangerae models in which expeced presen values of fundamenals are calculaed from survey forecass. Finally, hey show ha ou-of-sample forecasing power of models can be increased by focusing on panel esimaion and long-horizon forecass. Molodsova and Papell (2008) also use Taylor rule fundamenals for exchange rae deerminaion. They evaluae he performance of alernaive exchange rae models using Clark and Wes (2006, 2007) inference procedures and assess he ou-of-sample performance of he models a o 36 monh horizons for a se of 2 currencies over he pos-breon Woods floa. They provide he evidence of predicabiliy is much sronger wih Taylor rule models han wih convenional models a shor horizon, paricularly a he one-monhahead horizon for 8 ou of 2 currencies. However, hey do no find any saisical evidence of increased predicabiliy of he models relaive o a random walk a long horizons.

22 CHAPTER III THEORETICAL BACKGROUND 3.. The Moneary Model The early flexible-price moneary model (Frenkel, 976) relies on he win assumpions of purchasing power pariy (PPP) and he exisence of sable money demand funcions for he domesic and foreign economies. The firs building block of his model, PPP (absolue), saes ha exchange raes should equalize he naional price levels of differen counries in erms of a common currency. s = p p () where s is he logarihm of he nominal exchange rae expressed in unis of home currency per dollar, p and p are he domesic and foreign (US) price levels, respecively. The second assumpion of he model is he sable money demand funcion in boh counries. Moneary equilibria in he home and foreign counry respecively are given by: 2

23 m p = b y b2i, (2) m 2i p = b y b (3) where m is he logarihm of he domesic money supply, p is he logarihm of he domesic price level, y is he logarihm of he domesic income, i is he domesic ineres rae, and aserisks denoe a foreign counry variable. Noe ha income elasiciy denoed as b >0 and ineres semi-elasiciy denoed as b 2 >0 are assumed o be common across counries. Solving for p and p in (2) and (3) respecively and plugging ino () yields he basic exchange rae equaion deermined by moneary model: s ( m m ) b ( y y ) + b ( i i ) = (4) 2 According o equaion (4), an increase in domesic (foreign) money supply will lead he domesic currency o depreciae (appreciae). An increase in domesic (foreign) income will raise he money demand, causing he domesic currency o appreciae (depreciae). Finally, an increase in he domesic (foreign) ineres rae will resul in depreciaion (appreciaion) of he exchange rae via a reducion of he demand for money. A furher assumpion underlying he moneary model is ha domesic and foreign bonds are perfec subsiues so ha uncovered ineres pariy (UIP) holds. UIP suggess ha he difference beween he domesic and foreign ineres rae is jus equal o he expeced rae of depreciaion of he domesic currency: 3

24 i i = E ) + s ( s (5) where E ) denoes he expecaion of he nex period s level of he exchange ( s + rae condiional on informaion available in period. Then by combining (4) and (5), one reaches an equaion as following: b2 [( m m ) b ( y y )] + E ( s ) s = + (6) + b + b 2 For simpliciy se, ( m m ) b ( y y ) 2 = x. Under raional expecaions, by ieraing forward, i is easy o show ha (6) can be expressed in he forward soluion form as following: i [ b ( + b )] 2 ) 2 2 E ( x+ i ) i= 0 s = ( + b (7) where he ransversaliy condiion [ ( b )] E ( s ) 0 imposed. 2 lim b i = has been i As oulined in Macdonald and Taylor (993), he exchange rae should be coinegraed wih he variables conained in x. This is illusraed by i subracing x from boh sides of equaion (7) and by rearranging he erms o obain 3 : s x = i i= i [ b ( + b )] E ( Δx ) (8) See appendix for deailed soluion. 2 The case where he ransversaliy condiion does no hold has examined by MacDonald and Taylor (993) in deail. 3 See Appendix for deailed soluion. 4

25 Now, if he variables enering he x expression are firs-difference saionary, I(), hen righ hand side of equaion (8) mus also be saionary. If s is also an I() series, he exchange rae mus be coinegraed wih he variables m m and y y. 4 So, in he empirical modeling, he following long-run nominal exchange rae equaion is used: ( m m ) + ( y y ) u s = β + β + (9) 0 β 2 =,...T, where according o heory β and β 0. Based on he heoreical findings of he moneary model, panel coinegraion ess are employed. I provides evidence for he exisence of a long run relaionship among he nominal exchange rae, relaive money supplies and relaive income levels across counries. = 2 < 3.2. The Taylor Rule Model This subsecion examines he linkage beween he exchange raes and a se of fundamenals ha arise when cenral banks se he ineres rae according o a Taylor rule in a wo counry model. Le π denoe he inflaion rae in erms of deviaion from is arge level a ime, and y be he oupu gap or deviaion of log oupu from rend a ime. Following Engel and Wes (2005, 2006) and Engel e al. (2007), he moneary rules in he foreign and home counries can be described as 5 : 4 Under raional expecaions forecasing errors are saionary. See Taylor (99). 5 Consan erms are omied for convenience. 5

26 i = γ π E π + + γ y + u (0) y m q ( s s ) + γ Eπ + y y um i = γ π + γ + () where γ π >, γ y > 0, and γ q > 0, i is domesic ineres rae, s is he logarihm of he nominal exchange rae expressed in unis of home currency per dollar, s is a arge for exchange rae, E denoes mahemaical expecaions condiional on a period informaion se, Eπ + denoes deviaion of expeced inflaion from he cenral bank s arge in he domesic counry, y is domesic oupu gap, u m error erm in he moneary policy of domesic counry and aserisks denoe a foreign variable (US). Equaion (0) is a sandard Taylor rule and equaion () is a Taylor rule wih nominal exchange rae and is arge level included. Following Engel and Wes (2005, 2006) and Engel e al. (2007), i is assumed ha wo counries have he same moneary policy parameers, namely γ π and γ y. Equaion (0) for he foreign counry does no include he nominal exchange rae and is arge because here is no evidence ha he U.S. has adoped an exchange rae arge 6. Much of he Taylor rule lieraure pus expeced inflaion in he moneary rule. I is highly possible ha when choosing he arge ineres raes, i and i, he cenral banks may no have direc informaion abou he curren values of he price level. Adding expeced inflaion allows for his possibiliy 7. 6 See Molodsova and Papell (2007). 7 See Engel and Wes (2005) for deailed discussion. 6

27 To simplify he model, i is assumed ha he moneary auhoriies se he arge level of exchange rae o make PPP hold 8, ha is: s = p p (2) Since s is expressed in unis of home currency per dollar andγ q > 0, he rule () means ha home counry is assumed o raise ineres raes when he currency is depreciaed relaive o he arge. The mos imporan reference can be Clarida e al. (998), who find ha he coefficien of real exchange rae in Taylor rule, γ ^ q, is saisically significan and he esimaed values for Germany and Japan are equal o 0.05 and 0.09, respecively. Subracing he foreign from he domesic moneary rule, i is obained i ( s s ) + γ [ E π E π ] + ( y y ) + u u i = q + + γ y γ π (3) m m Nex, wrie uncovered ineres rae pariy as i i = E s + ) s ( (4) Now plug uncovered ineres rae pariy equaion ino boh sides of equaion (2) and use he definiion of he arge level of exchange rae o obain: s ( i i ) + γ ( p p ) γ ( Eπ Eπ ) γ ( y y ) u + u + ( γ ) E ( s ) = q q + + y m m q + γ π (5) Equaion (5) is he form of he expeced discouned presen value models where he discoun facor is given by ( γ q ). The observed fundamenal in he formulaion is given by ( i ) + ( ) i p. p 8 In Cho and Wes (2003), arge level of exchange rae follows an unobserved random walk. 7

28 Following Engel and Wes (2005), he remaining variables in equaion (5) are reaed as unobserved. Hence, he ineres rae and he price level differences as he Taylor rule fundamenals are used in order o esimae he nominal exchange rae based on he following equaion: ( i i ) + ( p p ) v s = α + α + (6) 0 α 2 =,...T, where α = α 0 according o previous sudies. 2 > Based on he heoreical findings of he Taylor-rule model, his hesis ess wheher he nominal exchange raes are coinegraed wih he relaive price levels and he relaive ineres raes across counries. 8

29 CHAPTER IV METHODOLOGY This secion describes a panel-based framework o conduc panel coinegraion analysis for he panel version of (9) and (6). Since a prerequisie for conegraion analysis is ha all variables are nonsaionary, several panel uni roo esing mehodologies are employed o deermine he order of inegraion of all variables under sudy. Tradiionally, DF (Dickey-Fuller) or ADF (Augmened Dickey Fuller) ess have been used o es for he presence of uni roos in univariae ime series daa. In recen years, a number of invesigaors, noably Levin, Lin and Chu (2002), Hadri (2000), Im, Pesaran and Shin (2003) Maddala and Wu (999) have developed panel-based uni roo ess ha are similar o ess applied o individual series. According o Balagi and Kao (2005), adding he cross secional dimension o uni roo ess can increase he power of he ess due o he informaion in he ime series is enhanced by ha conained in he cross-secion daa. Moreover, in conras o individual uni 9

30 roo ess wih complicaed limiing disribuions, panel uni roo es saisics have normal limiing disribuions 9. Panel uni roo ess developed by Levin e al. (2002), Im e al. (2003), Maddala and Wu (999), and Hadri (2000) can be summarized as follows: Levin e al. (2002) uses Augmened Dickey Fuller (ADF) specificaion by considering he following hree models: Δy i p i = ρ y (7) i, + θilδyi L + α mid m + ε i L= where m =, 2, 3, d m indicaes he vecor of deerminisic variables such as inerceps and ime rends and α mi denoes he corresponding vecor of coefficiens for model m =, 2, 3. In paricular, d = Ø (he empy se), d 2 = {} and d 3 = {, }. Hence, LLC es includes fixed effecs and individual ime rends for each counry and i allows he lag order, p i, be differen for individual cross- secion unis. The null hypohesis of LLC es is ha each individual ime series conains a uni roo agains he alernaive ha each ime series is saionary, i.e., H : ρ 0 and H : ρ 0. 0 = < The major drawback of he LLC es is ha i resrics ρ o be homogeneous across alli. As Maddala (999) poined ou, he null may be fine for esing convergence in growh among counries, bu he alernaive resrics every counry o converge a he same rae. Im e al. (2003) (IPS) allow for heerogeneous coefficien of y i in equaion (7) and propose an alernaive 9 See Balagi and Kao (2005). 20

31 esing procedure based on averaging individual uni roo es saisics. 0 The null hypohesis is ha each series in he panel conains a uni roo, i.e., H : ρ 0 for all i and he alernaive hypohesis allows for some (bu no all) 0 i = of he individual series o have uni roos, i.e., H : ρ < 0 for i =, 2,, N i ρ = 0 for i = N,, N i + where N is he oal number of individual cross-secions unis. IPS differs from LLC because all he series in he alernaive hypohesis are saionary processes in LLC, while in IPS some series can sill be nonsaionary in he alernaive hypohesis. An alernaive approach o panel uni roo ess uses Fisher's (932) resuls o derive ess ha combine he p-values from individual uni roo ess. Maddala and Wu (999) propose a Fisher-ype es which combines he p-values from uni roo ess for each cross-secion i o es for uni roo in panel daa. Maddala and Wu (999) argue ha boh IPS and Fisher es relax he resricive assumpion of he LLC es ha ρ i is he same under alernaive. Tha is o say, he null and he alernaive hypohesis of he Fisher Augmened Dickey Fuller (ADF) uni roo es is he same as for he IPS uni roo es. Boh he IPS and Fisher ess combine informaion based on individual uni roo ess while IPS requires a balanced panel, Fisher ess can be used o es unbalanced panels. 0 Noe ha IPS always conains inerceps only or inerceps and linear rends. Thus in equaion (7) m= is no he case for IPS es. 2

32 Also, he Fisher es can use differen lag lenghs in he individual ADF regressions and can be applied o any oher uni roo ess. All he panel uni roo es menioned above assume ha under he null hypohesis, here is a uni roo. In conras o hese ess, Hadri (2000) derives a residual-based Lagrange muliplier (LM) es where he null hypohesis is ha here is no uni roo in any of he series in he panel agains he alernaive of a uni roo in he panel. This es is also known as a general form of he Kwiakowski-Phillips-Schmid-Shin (KPSS) es from ime series o panel daa. If he presence of a uni roo is deeced in he variables, hen i is necessary o check for he presence of a coinegraing relaionship among he variables. There are wo ypes of panel coinegraion ess in he lieraure. The firs is similar o he Engle and Granger (987) framework which includes esing he saionariy of he residuals from a levels regression. The second panel coinegraion es is based on mulivariae coinegraion echnique proposed by Johansen (988). However, panel echniques may be beer in deecing coinegraion relaionships since a pooled levels regression combines cross-secional and ime series informaion in daa when esimaing coinegraing coefficiens. Pedroni (999, 2004) and Kao (999) exend he Engle-Granger (987) coinegraion es. Kao (999) proposes Dickey Fuller (DF) and Augmened Since EViews6 can only perform homogenous ype of Hadri (2000), his es was no used in he empirical par of he hesis. 22

33 Dickey Duller (ADF)-ype uni roo ess. The DF ype es from Kao follows he following model: y = α + βx + e (8) i i i i y = y + u (9) i i i x = + ε (20) i x i i where i =, N and =,.T. As boh y i and x i are random walks, i follows ha under he null hypohesis of no coinegraion, he residual series, e i, should be nonsaionary. The model has varying inerceps across he crosssecion observaions, he fixed effecs specificaion, and common slopes across i. Wih his model, he DF es can be calculaed from he esimaed residuals as: e = ρ e + v (2) i i i where e i is he esimaed residual of equaion (8) The ADF ype es from Kao is based on he esimaed residuals of he following equaion: p i + γ j j= e i = ρ e Δ ei j + vip (22) where e i is he esimaed residual of equaion (8) and p denoes number of he lags in ADF specificaion. To es wheher x i and y i are coinegraed based on DF or ADF es saisics, he null and he alernaive hypoheses can be wrien as H : ρ and H : ρ, respecively. 0 = < 23

34 Pedroni (999, 2004) propose several ess for he null hypohesis of coinegraion in panel daa model ha allows for considerable heerogeneiy. Pedroni es differs from Kao es in he sense ha i incorporaes heerogeneous inerceps and rend coefficiens across cross-secions o equaion (8) and i assumes ρ o be heerogeneous across cross-secions in equaion (2). Pedroni es consrucs four panel saisics and hree group panel saisics o es he null hypohesis of no coinegraion agains he alernaive hypohesis of coinegraion. In he case of panel saisics, ρ is assumed o be he same across all he cross secions, hus he null and alernaive hypoheses are H : ρ for 0 i = all i and H : = ρ, respecively. In he case of group panel saisics ρ is ρ i < allowed o vary over he cross secions, hus he null and alernaive hypoheses are H : ρ for all i and H : ρ for a leas onei. 0 i = i < Maddala and Wu (999) use Fisher-ype es o propose an alernaive approach o esing for coinegraion in panel daa by combining ess from individual cross-secions o obain a es saisic for he full panel. Based on he resuls of Maddala and Wu (999), his hesis applies o Johansen Fisher Panel Coinegraion es combining individual Johansen's coinegraion race ess and maximum eigenvalue ess. In Johansen s mulivariae coinegraion echnique, Trace Saisic ess for a mos r coinegraing vecors among a sysem of N>r ime series, and he Maximal Eigenvalue Saisic ess for exacly r coinegraing vecors agains he alernaive hypohesis of r+ coinegraing vecors. 24

35 Johansen s mulivariae coinegraion echnique in a panel framework consiss of wo seps. The firs one is he esimaion of a panel Vecor Auoregresssion (VAR) model and he second one is he deerminaion of wheher an inercep and/or a rend ener coinegraion analysis. In general, five disinc models can be considered alhough he firs and he fifh model are no likely o happen and are also implausible in erms of economic heory. 2 Therefore, he problem reduces o a choice of one of he hree remaining models (Model 2, 3, 4) 3. Johansen (992) suggess applying he Panula principle in order o decide which model should be used. The Panula principle involves he esimaion of all hree models and he presenaion of he resuls from he mos resricive hypohesis (i.e. r = number of coinegraing relaions = 0 and model 2) hrough he leas resricive hypohesis (i.e. r = number of variables enering he VAR-= n- and model 4). The model selecion procedure hen includes moving from he mos resricive model, a each sage comparing he race saisic o is criical value, sopping only when i is concluded for he firs ime ha he null hypohesis can no be rejeced. 4 2 Model : No inercep or rend in CE or VAR, Model 2: Inercep (no rend) in CE, no inercep or rend in VAR, Model 3: Inercep in CE and VAR, no rends in CE and VAR, Model 4: Inercep in CE and VAR, linear rend in CE, no rend in VAR, Model 5: Inercep and quadraic rend in he CE inercep and linear rend in VAR. 3 See Aseriou and Hall (2007). 4 For more deail see Aseriou and Hall (2007). 25

36 CHAPTER V EMPIRICAL ANALYSIS 5. Daa The quarerly daa covering he period of 980: : 04 for 4 indusrialized counries is used for he empirical analysis. The counries consis of Ausralia, Belgium, Canada, Denmark, France, Germany, Ialy, Japan, Neherlands, Spain, Sweden, Swizerland, Unied Kingdom and Unied Saes. The composiion of he sample is resriced due o unavailabiliy of daa and he necessiy for a balanced panel. The variables include money supply, income, ineres raes, price levels, and nominal exchange raes. As a measure of money supply, M3 expressed in millions of naional currency is used for all counries excep Swizerland and Unied Kingdom. Money supply is money plus quasi money for Swizerland and Unied Kingdom due o unavailabiliy of M3 daa for hese counries. 5 Seasonally adjused 5 See Mark and Sul (200), Engel and Wes (2005) and Engel, Mark and Wes (2007) for he usage of differen measures of he money supply across counries. As in Mark and Sul (200), he money supply daa are seasonally adjused by aking he average of he curren and hree previous quarers. 26

37 indusrial producion index (2000=00) is uilized as a proxy of income. Threemonh deposi raes consiue a measure for shor-erm ineres raes. Price levels are measured using consumer price index (CPI) wih base year of Finally, nominal exchange raes expressed in unis of home currency per dollar for 3 indusrialized counries are included o he model. M3, money plus quasi money, indusrial producion index, and consumer price index daa for all counries excep Belgium, Ialy, Neherlands and Spain are aken from he web sie of IMF s Inernaional Financial Saisics (IFS). M3 daa for Belgium, Ialy, Neherlands and Spain and hree-monh deposi raes daa for all counries are aken from Global Financial Daabase. Nominal exchange rae daa expressed in unis of home currency per dollar for 3 indusrialized counries are aken from he web sie of Organizaion of Economic Co-operaion and Developmen (OECD). Wih he excepion of ineres raes all variables are expressed in logarihms Panel Uni Roo Tess This hesis uilizes IPS and Fisher ADF Chi-square panel uni roo saisics in order o examine inegraion properies of he exchange raes, relaive income levels, relaive money supplies, relaive ineres raes, and relaive price levels across counries. Since LLC and homogeneous ype of Hadri es saisics are resricive in he sense ha all cross-secions have or do no have a uni roo, focusing on less resricive IPS and Fisher ADF Chi-square es saisics can lead o more accurae resuls abou inegraion properies of he variables. IPS 27

38 and Fisher ADF Chi-square es resuls in levels and firs differences are presened in Table 5.2. and Table 5.2.2, respecively. Table 5.2.: IPS Panel Uni Roo Tess for Saionariy Variables Wihou Trend Wih Trend Conclusion s I() m-m I() y-y.7.88 I() i-i I() p-p. -.5 I() Δs I(0) Δ(m-m) I(0) Δ(y-y) I(0) Δ(i-i) I(0) Δ(p-p) I(0) Noes: The symbols s, m-m, y-y, i-i, and p-p denoe nominal exchange rae, money supply differences, indusrial producion index differences, deposi raes differences, and consumer price index differences of individual counries and US, respecively. Similarly, Δs, Δ(m-m), Δ(y-y), Δ(i-i), and Δ(p-p) sand for firs differences of nominal exchange rae, money supply differences, indusrial producion index differences, deposi raes differences, and consumer price index differences of individual counries and US, respecively. All variables are expressed in logarihms excep ineres raes. IPS es saisics includes an individual inercep and boh an individual rend and inercep. Lag lenghs are chosen by Akaike Informaion Crierion (AIC)., and sand for he level of significance a 5 %, and %, respecively. 28

39 Table 5.2.2: ADF-Fisher Chi-square Panel Uni Roo Tess for Saionariy Variables Wihou Trend Wih Trend Conclusion s I() m-m I() y-y I() i-i I() p-p I() Δs I(0) Δ(m-m) I(0) Δ(y-y) I(0) Δ(i-i) I(0) Δ(p-p) I(0) Noes: The symbols s, m-m, y-y, i-i, and p-p denoe nominal exchange rae, money supply differences, indusrial producion index differences, deposi raes differences, and consumer price index differences of individual counries and US, respecively. Similarly, Δs, Δ(m-m), Δ(y-y), Δ(i-i), and Δ(p-p) sand for firs differences of nominal exchange rae, money supply differences, indusrial producion index differences, deposi raes differences, and consumer price index differences of individual counries and US, respecively. All variables are expressed in logarihms excep ineres raes.adf Fisher Chisquare es saisics includes an individual inercep and boh an individual rend and inercep. Lag lenghs are chosen by Akaike Informaion Crierion (AIC)., and sand for he level of significance a 5 %, and %, respecively. According o IPS es resuls, all variables wih individual inerceps and rends are nonsaionary in levels a % and 5 % significance levels. IPS es resuls also indicae ha all variables wih individual inerceps are nonsaionary in 29

40 levels a % significance level excep ineres rae differences. According o ADF Fisher Chi-square es resuls, all variables wih and wihou rends are nonsaionary a % significance level. Boh IPS and Fisher Chi-square es saisics indicae ha all variables wih and wihou rends in firs differences are saionary a 5 % significance level. Overall, all variables are found o be inegraed of order one, I (), meaning ha a prerequisie for he panel coinegraion analysis is provided. Based on panel uni roo saisics resuls one can proceed o panel coinegraion analysis in order o examine long-run relaionship beween exchange raes and moneary fundamenals or exchange raes and Taylor rule fundamenals Panel Coinegraion Analysis This hesis employs Johansen Fisher panel coinegraion es in order o provide evidence for he exisence of a long run relaionship beween exchange raes and moneary fundamenals or Taylor-rule fundamenals across counries. Johansen Fisher panel coinegraion es is applied for he panel version of (9) and (6). Pedroni and Kao panel coinegraion ess are based on Engle-Granger (987) mehodology which is quie resricive when analyzing he coinegraing properies of an n-dimensional vecor of I() variables where several coinegraion relaionships may arise. Since his hesis esimaes a rivariae sysem including nominal exchange raes, price levels and ineres raes, i is possible o obain more han one coinegraing relaionship formed by hese variables. Johansen Fisher Panel Coinegraion echnique has an advanage over 30

41 he Pedroni and Kao panel coinegraion ess in he sense ha i relaxes he assumpion of a unique coinegraing vecor among he variables. Before applying Johansen Fisher Panel Coinegraion es, an opimal lag lengh for wo differen panel-based VAR models should be deermined; he firs one consiss of nominal exchange raes, money supply differences and income level differences and he second one includes nominal exchange raes, ineres raes differences and price level differences. Afer choosing opimal lag lengh based on Schwarz informaion crieria, he Panula principle is used for boh models in order o deermine he appropriae model regarding he deerminisic componens. Table 5.3. and Table show Panula principle resuls for moneary model including nominal exchange raes, relaive money supplies and relaive income levels and Taylor-rule model including nominal exchange raes, relaive ineres raes and relaive price levels, respecively. Table 5.3.: The Panula Principle Resuls using s, (m-m), (y-y) r n-r Model 2 Model 3 Model s : Nominal exchange rae expressed in unis of home currency per dollar m-m : Difference of money supply beween individual counries and US y-y : Difference of indusrial producion index beween individual counries and US r : Number of coinegraing relaions 3

42 n : Number of variables enering he Vecor Auoregression (VAR) Model 2: Inercep (no rend) in CE, no inercep or rend in VAR Model 3: Inercep in CE and VAR, no rends in CE and VAR Model 4: Inercep in CE and VAR, linear rend in CE, no rend in VAR indicaes he firs ime ha he null can no be rejeced a 5 % significance level according o probabiliies compued using Chi-square disribuion. Lag lengh is chosen as six based on Schwarz informaion crieria. Table 5.3.2: The Panula Principle Resuls using s, (i-i), (p-p) r n-r Model 2 Model 3 Model s : Nominal exchange rae expressed in unis of home currency per dollar i-i : Difference of deposi raes beween individual counries and US p-p : Difference of consumer price index beween individual counries and US r : Number of coinegraing relaions n : Number of variables enering he Vecor Auoregression (VAR) Model 2 : Inercep (no rend) in CE, no inercep or rend in VAR Model 3 : Inercep in CE and VAR, no rends in CE and VAR Model 4 : Inercep in CE and VAR, linear rend in CE, no rend in VAR indicaes he firs ime ha he null can no be rejeced a 5 % significance level according o probabiliies compued using Chi-square disribuion. Lag lengh is chosen as six based on Schwarz informaion crieria. Saring wih he smaller number of coinegraing vecors r = 0, he model selecion procedure is based on checking wheher he race saisic for model 2 rejecs he null, if yes proceeding o he righ, checking wheher hird model rejecs he null, and so on. The resuls in Table 5.3. indicae ha he appropriae model for he panel coinegraion analysis of he exchange rae wih 32

43 moneary fundamenals is he one wih he inercep (no rend) in CE, no inercep or rend in VAR, namely model 2. The resuls in Table also show he appropriae model for he panel coinegraion analysis of he exchange rae wih Taylor-rule fundamenals is he one wih inercep in CE and VAR, linear rend in CE, no rend in VAR, namely model 4. Hence, based on hese findings, Johansen Fisher panel coinegraion resuls of he exchange rae wih moneary fundamenals and he exchange rae wih Taylor-rule fundamenals are given in Table and Table 5.3.4, respecively. Table 5.3.3: Johansen Fisher Panel Coinegraion Resuls using s, (mm), (y-y) Number of Coinegraing Vecors Fisher Sa. from Trace Tes Prob. Fisher Sa. from Max- Eigen Tes Prob. r r r s : Nominal exchange rae expressed in unis of home currency per dollar m-m : Difference of money supply beween individual counries and US y-y : Difference of indusrial producion index beween individual counries and US r : Number of coinegraing vecors denoes saisical significance a he % level. EViews6 compues probabiliies using asympoic Chi-square disribuion. Lag lengh is equal o six. 33

44 Table 5.3.4: Johansen Fisher Panel Coinegraion Resuls using s, (i-i), (p-p) Number of Coinegraing Vecors Fisher Sa.from Trace Tes Prob. Fisher Sa. from Max- Eigen Tes Prob. r r r s : Nominal exchange rae expressed in unis of home currency per dollar i-i : Difference of deposi raes beween individual counries and US p-p : Difference of consumer price index beween individual counries and US r : Number of coinegraing vecors denoes saisical significance a he % level. EViews6 compues probabiliies using asympoic Chi-square disribuion. Lag lengh is equal o six. Table indicaes ha here exis a unique coinegraing vecor among nominal exchange raes, relaive money supplies, and relaive income levels a % significance level. Similarly, Table shows ha exisence of one coinegraing vecor among nominal exchange rae, relaive ineres raes, and relaive price levels a % significance level. The conclusion ha here is one coinegraing vecor, however, does no necessarily imply suppor for he moneary model or Taylor rule model in deermining he exchange raes. For ha o be presen, he relaionship among he variables mus be reasonably consisen wih hose implied by he moneary and he Taylor rule exchange rae equaions. 34

45 On he basis of hese resuls, wo long-run exchange rae equaions can be esimaed in order o assess he impac of moneary and Taylor-rule fundamenals on nominal exchange raes Esimaion and Resuls In he coinegraed panels, using ordinary leas square (OLS) mehod o esimae he long-run equaion leads o biased and inconsisen esimaor of he parameers. OLS esimaes suffer from asympoic bias unless he regressors are sricly exogenous, so ha he OLS sandard errors can no generally be used for valid inference. Pedroni (2000) proposes fully modified ordinary leas square (FMOLS) esimaion while Kao and Chiang (2000) and Mark and Sul (200) recommend he dynamic ordinary leas squares (DOLS) as he alernaive mehods of panel coinegraion esimaion. FMOLS esimaion correcs for endogeneiy and serial correlaion o he ordinary leas square (OLS) esimaor. To correc for endogeneiy bias and o obain an unbiased esimaor of he long-run parameers, DOLS uses a parameric adjusmen o he errors by augmening he saic regression wih leads, lags, and conemporaneous values of he regressors in firs differences. Boh FMOLS and DOLS provide consisen esimaes of sandard errors ha can be used for inference. According o Kao and Chiang (2000) FMOLS and DOLS esimaors have normal limiing properies, even hough DOLS esimaor ouperforms FMOLS esimaor in empirical analysis. On he basis of he earlier findings in 35

46 favor of panel DOLS esimaion, DOLS mehod is employed o esimae longrun exchange rae equaion which relaes nominal exchange raes wih moneary and Taylor-rule fundamenals. Then, he following exchange rae equaion based on panel DOLS mehod is esimaed: s i ' = α + θ + x β + i i q ij j= q c Δx i+ j + v i (23) where i =, N and =,.T, { s i } are x, β is a 2x vecor of slope parameers, { α } are he inerceps indicaing individual fixed effecs, i { θ } sand for common ime effecs, { v i } are he error erms, { x i } are 2x where x = ( m m ) and x = ( y y ) for he moneary model, x i i 2i i = ( i i ) and x = ( p p ) for he Taylor-rule model and q sands for i i 2i i number of leads and lags of he firs differenced regressors. Table 5.4. and Table denoe panel DOLS resuls for moneary model and Taylor-rule model, respecively. Table 5.4.: Panel Dynamic OLS Esimaes of Moneary Model FE FE-T β 0.8 (0.023) (0.08) 2 β (0.046) 0.63 (0.063) 36