University of Pretoria Department of Economics Working Paper Series

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1 Universiy of Preoria Deparmen of Economics Working Paper Series An Economeric Model of he Rand-US Dollar Nominal Exchange Rae Moses M. Sichei, Tewodros G. Gebreselasie and Olusegun A. Akanbi Universiy of Preoria Working Paper: December 2005 Deparmen of Economics Universiy of Preoria 0002, Preoria Souh Africa Tel: Fax: hp://

2 An Economeric Model of he rand-us Dollar Nominal Exchange Rae Moses M. Sichei, Tewodros G. Gebreselasie,& Olusegun A. Akanbi School of Economics, Faculy of Economic and Managemen sciences Universiy of Preoria Absrac Modeling he nominal exchange rae has been one of he mos difficul exercises in economics. This paper aemps o esimae he nominal rand-usd exchange rae under he Dornbusch(1980) and Frankel (1979) overshooing model using he Johansen coinegraion echnique. The overshooing model fis he daa well and ha commodiy prices are sicky in Souh Africa. Thus any moneary policy sraegy o srenghen or weaken he rand by means of raising or cuing ineres rae does he opposie in he shor-run. JEL Classificaion: B23, C22, F31 Key words: Exchange rae, overshooing model, VECM Posgraduae sudens and Lecurer in he School of Economics, a he Universiy of Preoria, Preoria. We are hankful o Prof. Renee van Eyden and Marc Ground for heir consrucive suggesions and commens. Any remaining errors are enirely ours. 1

3 1 Inroducion Souh Africa has adoped various exchange rae managemen policies wih a view o addressing major shocks in he form of significan gold price reducions and poliical crises (Aron e al.1997). Unil 1979, Souh Africa had a fixed exchange rae regime, which was pegged o a paricular currency. Capial conrols were quinessenial in he exchange rae managemen policy. In 1979 he Reserve Bank spli he foreign exchange marke ino wo secions. One marke deal wih forex ransacions relaed o rade in goods and services (commercial rand) while he oher relaed o inernaional capial movemens (financial rand). The financial rand was abolished in 1983 before being re-inroduced in Sepember 1985 o provide some proecion o he domesic economy from he adverse effecs of large capial ouflows a ha ime. The dual exchange rae sysem remained in exisence unil he re-unificaion of he commercial and financial rand in March This led o he curren uniary managed floaing exchange rae in which he Reserve Bank inervenes in he foreign exchange marke mainly o smooh ou undue shor-erm flucuaions in he exchange rae. Afer 1994, Souh Africa followed a gradual approach o eliminaion of exchange conrols raher han a big-bang approach. 2

4 Souh Africa s heighened inegraion ino he rading and financial global marke brough newer challenges o he exchange rae managemen. Indeed, in 2001, he rand depreciaed subsanially and le o he seing up of a commission of inquiry by he governmen o invesigae he causes (Souh Africa, 2002). The commission of inquiry idenified a number of facors which may have been responsible for he depreciaion of he rand; high inflaion differenial, low expor prices, low ineres differenials, porfolio shifs and leads in paymens for impors and lags in expor receips. These developmens call for a need o undersand he deerminans of he nominal rand-dollar exchange rae. Floaing exchange rae models wih fundamens are classified ino wo caegories; moneary exchange rae and porfolio balance models. The moneary exchange rae model is based on eiher flexible prices (Mussa, 1976) or sicky prices (Dornbusch, 1980 and Frankel, 1979). However, exising exchange rae models perform dismally when confroned wih acual daa. Mussa (1979) found four sylised facs abou he exchange rae. Firs, he log of he spo rae is approximaely a random walk. Second, mos changes in he exchange raes are unexpeced. Third, counries wih high inflaion raes end o depreciae a approximaely he inflaion differenial in he long run. Finally, acual exchange rae movemens end o overshoo movemens in smoohly adjusing equilibrium exchange raes. Meese and Rogoff (1983) found ha no exising srucural exchange rae model could reliably ou-predic he naïve alernaive of a random walk a shor- and medium erm horizons. 3

5 Given he curren managed floaing exchange rae suppored by exchange conrols in Souh Africa, he sicky price moneary model is he mos appropriae. The sickyprice and overshooing model of exchange rae allow shor-erm overshooing of he nominal and real exchange raes above heir long-run equilibrium levels. This emanaes from he ineracion of sluggishly adjusing goods markes and hyperacive asse markes. There is a dearh of sudies ha es he validiy of eiher he Dornbusch s or Frankel s approach in Souh Africa. Brink and Koekemoer (2000) esimaed he Dornbusch s version of he moneary model for Souh Africa using he hree-sep Engle and Yoo coinegraion procedure. Their model employed nominal money supply, real GDP, and inflaion rae of Souh Africa relaive o hose of he US. The long run coefficiens are consisen wih he Dornbusch s sicky price heory and saisically significan. This paper herefore is an aemp o exen he work of Brink and Koekemoer (2000) by applying Johansen mulivariae coinegraion approach. The res of he paper is srucured as follows. Secion 2 aemps o shed some ligh on he general framework and idenify he similariies and differences ha exis beween he Dornbusch sicky-price overshooing heoreical model and he one developed laer by Frankel (1980). Secion 3 deals wih he esimaion mehodology and he daa. Secion 4 discusses he esimaion resuls while secion 5 presens he conclusions. 2 4

6 Model specificaion The moneary exchange rae model is predicaed on he fac ha since he exchange rae is he relaive price of foreign and domesic money, i should be deermined by he relaive supply and demand of hese moneys. The Dornbusch(1980) and Frankel (1979) models begin by expressing he funcion of real money demand in logarihmic noaion. Home counry: p = m β y + δi (1) Foreign counry: p = m β y + δi (2) Combining Equaions 1 and 2 and assuming ha he purchasing power pariy condiion holds in he long run generaes; e = p p = ( m m ) β ( y y ) + δ ( i i ) (3) The model esimaed by Frankel (1979) is differen o some exen from Equaion 3 because of inroducing wo addiional assumpions. The firs assumpion is ha ineres rae pariy is associaed wih efficien markes in which he bonds of differen counries are perfec subsiues; d i i = (4) The second fundamenal assumpion is ha he expeced rae of depreciaion is a funcion of he gap beween he curren spo rae and an equilibrium rae, and of he expeced long-run inflaion differenial beween he domesic and foreign counries: d = θ ( e e) + π π (5) 5

7 Where e is he log of he spo rae; π and π are he curren raes of expeced long-run inflaion a home and abroad, respecively. Combining Equaions 4 and 5 yields; 1 e e = [( i π ) ( i π )] (6) θ Frankel (1979) argues ha he expression in brackes can be described as he real ineres differenial. Using bars o denoe equilibrium values, Frankel (1979) furher argues ha when follows. e = e, i i = π π in he long run and expressed Equaion 3 as e = p p = m m β ( y y ) + δ ( π π ) (7) Furhermore, subsiuing Equaion 7 ino Equaion 6 and assuming ha he curren equilibrium money supply and income levels are given by heir curren acual levels, a complee equaion of spo rae deerminaion given below. 1 1 e = m m β ( y y ) ( i i ) + ( + δ )( π π ) (8) θ θ Equaion 8 can be expressed wih an error erm as follows. e = m m β ( y y ) + α( i i ) + ϕ( π π ) + u (9) Where α (=-1/θ) is hypohesized negaive and φ (=1/θ + δ) is hypohesized posiive and greaer han α in absolue value. The innovaion ha was inroduced by Frankel (1979) aims a combining he Keynesian assumpion of sicky price wih he Chicago 6

8 assumpion ha here are secular raes of inflaion. Unlike he original hypohesis concerning he relaionship beween he exchange rae and he nominal ineres rae differenial, i urns ou ha he exchange rae is negaively relaed o he nominal ineres differenial, bu posiively relaed o he expeced long run-inflaion differenial. The main difference beween he models of Dornbusch and Frankel lie in he hypohesised sign of he coefficien of he nominal ineres rae in heir equaions. Unlike he hypohesized negaive sign in he Frankel model, Dornbusch argues ha relaively higher domesic ineres raes reduce he demand for real balances, raise prices, and herefore bring abou an exchange depreciaion, i.e., posiive coefficien of he ineres rae. The esimable model is specified in equaion 10. The expeced sign of he coefficiens are as hypohesized by Dornbusch (1980) and Frankel (1979). ln e = ( + ) m f ln m ( ) y,ln y π (10) / + + ( i i ) ( π ),, ln e is he logarihm of nominal rand-us dollar exchange rae(rand/us dollar). m ln is he difference beween Souh Africa s nominal money supply (M3) o m US money supply(m3). y ln y is he difference beween Souh African real GDP 7

9 and US real GDP in differen currencies. (i i ) is he difference beween nominal Treasury bill rae of Souh Africa and he US. beween Souh Africa and he US. ( π π ) is he inflaion differenial In he sandard moneary model, he coefficiens have srucural inerpreaions, which vary wih underlying assumpions. The money supply coefficien is resriced o be uniy since an increase in he relaive money supply a home is hypohesized o lead o an equi-proporionae depreciaion (Dornbusch, 1980 and Frankel, 1979). Consisen wih he moneary approach, he coefficien for he real GDP differenial is expeced o be negaive. A negaive sign is expeced on he difference of nominal ineres rae differenial under he Frankel (1979) bu a posiive relaionship under he Dornbusch (1980) model. Inflaion differenial is expeced o have a posiive sign. 3 Esimaion mehodology In accordance wih Johansen (1988), Equaion 10 is re-specified as a reduced-form vecor auoregression (VAR); X = β 0 + β1x β j X j + ε (11) Where X is a vecor of variables; X y = ln y m,ln m ( π ),( i i ), π, ln e 8

10 The ordering of he variables is dicaed by he need o have meaningful impulseresponse funcions from he VECM. Cholesky decomposiion is uilised for orhogonalisaion, which implies ha he Cholesky facor is lower riangular. Thus he firs variable is no affeced conemporaneously by any oher variable in he VAR. The las variable (exchange rae) is conemporaneously affeced by all he oher variables. Along wih he long-erm relaionship ha is capured by he Dornbusch model specified in Equaion 3, a VECM (Vecor Error Correcion Model) of he following form is esimaed o see he shor run exchange rae dynamics. X p π i X i + i= 1 = π X ε (12) The esimaion procedure is as follows. Firs, reduced-form VAR in Equaion 11 is esimaed and diagnosic ess performed. Second, Johansen coinegraion es is performed. The coinegraing vecors and loading marices are idenified. Third, a VECM in Equaion 12 is esimaed and diagnosic ess performed. Finally, innovaion accouning (impulse-responses and variance-decomposiion analyses) is performed. In view of he exensive naure of he esimaion procedure only seleced resuls are presened in he main body and he appendix. 9

11 4 Esimaion resuls The appropriae model is seleced on he basis of he naure of he DGP of all he five variables, he original Dornbusch (1980) model and he resuls of he race and maximum eigenvalue ess are presened in Table 1. On he basis of applying he Panula principle o esing which version of he deerminisic componen should be used, he race es idenified wo coinegraing vecors while he maximum eigenvalue es found no coinegraion for a model wih rend bu no inercep in he coinegraing equaion (CE). Table 1: Coinegraion es resuls Trace Tes Maximum Eigenvalue Tess H 0 H 1 λ-trace Sa. 5% CV H 0 H 1 λ-max 5% CV r = 0 r r = 0 r = r 1 r r = 1 r = r 2 r r = 2 r = r 3 r r = 3 r = r 4 r r = 4 r = Equaion 13 shows he long-run par of he VECM in Equaion 12. The firs long-run equaion is he nominal exchange rae. The coefficien of he relaive money supply is normalized o one in accordance wih he original model of Dornbusch (1980). 10

12 y ln α 11 α12 y 1 α 21 α 22 m β11 1 β 31 β 41 1 ln π X 1 = αβ X 1 = α 31 α 32 m (13) β 32 1 β 52 ( ) α 41 α π π 42 1 ( ) α 51 α 52 i i 1 ln e 1 The second coinegraing vecor idenifies he ineres rae differenial equaion. I relaes ineres rae differenial wih inflaion differenials and he exchange rae. The esimaed nominal exchange rae equaion is presened in equaion 14 wih - values in parenheses; ( π ) 0.72 ( i i ) 0.06 y m ln e = ln 1ln ( 3.05) y + π (14) m (5.09) ( 18.74) (3.19) All he coefficiens are saisically significan and consisen wih wha was hypohesized by Dornbusch-Frankel model (Equaion 10). Income elasiciy of demand is consisen wih Dornbusch model and implies ha an increase in income differenial would lead o an appreciaion of he rand-dollar exchange rae. The coefficien for he money supply differenial is resriced o uniy. The coefficien on he inflaion differenial is consisen wih he Dornbusch-Frankel moneary model. I is posiive and greaer han he coefficien for ineres differenial in absolue erms. Thus an increase in Souh Africa s inflaion relaive o he US leads o a depreciaion of he rand in he long-run. The value of he ineres semi-elasiciy of money demand is consisen wih he Frankel(1979) model and no Dorbusch(1980) model. This means ha relaively 11

13 higher ineres raes in Souh Africa reduce prices and herefore bring abou nominal appreciaion of he rand. The magniude of his parameer is posiively relaed o price sickiness. The more rapid price adjusmen is he smaller his coefficien is in absolue erms. The coefficien of 0.72 shows ha goods marke prices in Souh Africa adjus sluggishly while he asse marke is hyperacive. The posiive ime rend means ha he nominal exchange rae generally depreciaed during he period 1994o The esimaed second coinegraing vecor is an equaion for ineres differenial. ( i i ) = ( π ) 1.45 ln e (5.12) π (15) ( 7.92) (3.56) Firs, an increase in inflaion differenial leads o an increase in ineres rae differenial. This may be raionalized by he fac ha Souh Africa would increase ineres raes o conain he inflaion pressures. Second, a depreciaion of he rand would lead o a reducion in ineres rae differenial. Since Souh Africa s ineres raes are generally above hose of he US (Figure 4 in he appendix), depreciaion of he rand is consisen wih high ineres raes in he US i.e reduced nominal ineres rae differenial. Third, here is a general rend of he ineres differenial o increase as shown by he posiive ime rend. Table 2 presens adjusmen coefficiens (α-values or loading marices) ha play significan role in bringing back he sysem o equilibrium in case of discrepancy from he long run relaionship. Firs, he α-values are all wihin 0 o 2 range as expeced. 12

14 Second hose variables wih 0 loading facors (speed of adjusmen) mean ha he coinegraing vecor does no ener ino he shor-run deerminaion for ha variable. This means ha hose variables are weakly exogenous. For insance, income differenial is weakly exogenous in he exchange rae and ineres rae differenial equaions. Thus, if here is a shock ha pushes exchange rae away from he equilibrium in Equaion 14, income differenial would no adjus immediaely o correc he discrepancy. This is expeced given he fac ha real GDP akes ime o adjus as opposed o financial variables. Table 2: Esimaed Loading Marices and Weak Exogeneiy Tess Variables ln e equaion ( i i ) equaion y ln y m ln (4.81) (-4.71) m ( π π ) (4.50) i i ( ) ln e (-1.42) 0.15 (1.59) Noes: -saisics are given in square brackes. : The likelihood raio es for binding resricions is LR = ( ). The probabiliy of commiing Type I error in he parenhesis. This es refer o boh long-run and he above loading marix resricions. Third, he fac ha some loading facors are posiive in he exchange rae equaion implies ha hey end o push he sysem away from equilibrium. The nominal exchange rae, alhough negaive, is insignifican implying ha i does no play a pivoal role in reurning he exchange rae (Equaion 14) back o equilibrium. 13

15 Figure 1 shows he graphs of he esimaed coinegraing relaions in Equaions 14 and 15 from he VECM. Since he graphs rever o he equilibrium (zero), he coinegraing relaions are appropriae. Figure 1: Coinegraing relaions from VECM Coinegraing relaion for nominal exchange rae equaion Coinegraing relaion for nominal ineres rae differenial equaion Period Period Impulse-response funcions A shock o he i-h variable no only direcly affecs he i-h variable bu is also ransmied o all of he oher endogenous variables hrough he dynamic (lag) srucure of he VAR. An impulse response funcion races he effec of a one-ime shock o one of he innovaions on curren and fuure values of he endogenous variables. The impulse responses are derived from he VECM, which is ohorgonalised using Cholesky (lower riangular) decomposiion. Figure 2 shows he impulse-responses. 14

16 Figure 2:Response o one sandard deviaion shock over 30-quarer horizon Response of nominal ineres rae differenial o shocks from nominal money supply(m3) differenial Deviaion from equilibrium Appreciaion < >Depreciaion Response of nominal exchange rae o shocks from real GDP differenial Quarers Quarers Appreciaion < >Depreciaion Appreciaion < >Depreciaion Response of nominal exchange rae o shocks from nominal money supply (M3) differenial Quarers Response of nominal exchange rae o shocks from nominal ineres rae diferenial Appreciaion < >Depreciaion Appreciaion < >Depreciaion Response of nominal exchange rae o shocks from inflaion differenial Quarers Response of nominam exchange rae o is own shocks Quarers Quarers Firs, he expecaion is ha he expansion in money supply lowers ineres raes. This can be seen in he impulse-response graph (row 1-column 1 of Figure 2). A one sandard deviaion Cholesky posiive innovaion of nominal money supply differenial 15

17 causes a revision downwards of he forecas of ineres rae differenial over he 30 - quarers period. Second, once he public observe he increase in he money supply hey would form an immediae raional expecaion ha ulimaely he rand will depreciae proporionaely. There will be poenial fligh of capial ou of Souh Africa, which pus pressure on he rand o depreciae. The poenial capial fligh from Souh Africa, ln e would only cease when he rand overshoos is long-run level i.e. ln m ln m ( ) This can be seen in he impulse-response (row 2-firs column 1 of Figure 2). > 0. Third, a one sandard deviaion posiive innovaion in nominal ineres rae differenial leads o a depreciaion of he rand in he firs 8 quarers and appreciaion hereafer (row 3-column 1 in Figure 2). This means ha he resuls are consisen wih Dornbusch(1980) only in he firs 8 quarers bu in line wih Frankel(1979) model hereafer. This is quie imporan for he Moneary Policy Commiee (MPC) of he Reserve Bank. A relaively higher nominal ineres raes in Souh Africa leads o a depreciaion of he rand in he firs 8 quarers and only deliver he inended resuls hereafer. Fourh, one sandard deviaion posiive shock from real GDP differenial causes nominal exchange rae o appreciae over he 30 quarers horizon (row 1-column 2 of Figure 2). This is in line wih he Dornbusch-Frankel sicky prices model. 16

18 Fifh, one sandard deviaion posiive shock from inflaion differenial leads o a depreciaion of he rand in he firs 5 quarers (row 2-column2 in Figure 2). Thereafer, he rand appreciaes. This means ha he response is in accordance o wih he moneary model of he exchange rae in he firs 5 quarers only. Finally, exchange rae depreciaing shocks ha originae ouside he VECM cause he rand o depreciae over he 30-quarer horizon. Figure 3 shows he forecas error variance decomposiion (FEVD) of he nominal exchange rae. The FEVD provides informaion abou he relaive imporance of each random innovaion in affecing he nominal exchange rae over he 30-quarer period. Since VECM is orhogonalised using he Cholesky (lower riangular) decomposiion, he nominal exchange rae (ordered las in he VAR) is affeced by all he oher variables in he VECM. In he beginning, much of he errors made in forecasing exchange rae are aribued o is own shocks. Thereafer he errors are increasingly aribued o shocks from ineres rae differenial, real GDP differenial and inflaion differenial. The nominal money supply differenial plays limied role in explaining he forecas errors in nominal exchange rae. Thus he variables included in he VECM are imporan in explaining he movemen of nominal exchange rae. 17

19 Figure 3: Forecas Error Variance Decomposiion of Nominal Exchange Rae 60 Percenage conribuion o forecas error of nominal exchange rae Due o shocks from real GDP differenial Due o shocks from nominal money supply differenial Due o shocks from inflaion differenial Due o shocks from ineres rae differenial Due o is own own shocks 5 Conclusion The Dornbusch-Frankel sicky-price overshooing moneary model appears o underlie he movemen of he nominal rand-usd exchange rae in he period 1994 o Nowihsanding he convenional wisdom concerning he fuiliy of srucural exchange rae modeling aribued o Meese and Rogoff (1983), he model has some lessons for he MPC in he shor-run and long-run. Firs, prices in Souh Africa are sicky as shown by he high-income elasiciy of demand. Second, increasing ineres 18

20 raes wih a view o srenghening he rand does he opposie in he shor-run i.e. depreciae he rand in he firs 8 quarers. References ARON J., ELBADAWI I. & KAHN B.( 1997) Deerminans of Real Exchange Rae in Souh Africa, Cenre for Sudies of African Economies, Universiy of Oxford, Working Paper Series WPS/ APPLEYARD, D.R. & A.J.FIELD (1992) Inernaional economics. Boson: Richard D. Irwin Inc. BRINK, S. & R.KOEKEMOER (2000) The Economics of Exchange Raes: A Souh African Model, Souh African Journal of Economic and Managemen Sciences, Vol. 3, No.1: DICKEY,D. and W.A.FULLER (1981) Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica, 49: DORNBUSCH, R. (1980) Exchange Rae Economics: Where Do We Sand?, Brookings Papers on Economic Aciviy, 1980(1): FRANKEL, J.A. (1979) On he Mark: A Theory of Floaing Exchange Raes Based On Real Ineres Differenials, American Economic Review, 69(4): JOHANSEN, S. (1988) Saisical Analysis of Coinegraion Vecors, Journal of Economic Dynamics and Conrol, 12: MEESE R. & ROGOFF K.(1983), Empirical Exchange Rae Models of he Sevenies: Do hey Fi Ou of Sample?, Journal of Inernaional Economics, 14,

21 MUSSA, M.(1976) The Exchange Rae, he Balance of Paymens, and Moneary and Fiscal Policy Under a Regime of Conrolled Floaing, Scandinavian Journal of Economics, 78, MUSSA, M.(1979) Empirical Regulariies in he Behaviour of Exchange Raes and Theories of he Exchange Rae Marke in: Brunner,K.& Melzer, A.H.(ed.) Policies for Employmen, Prices and Exchange Raes. Norh-Holland, New York,9-57. PARUOLO, P. (1997) Asympoic Inference on he Moving Average Impac Marix in Coinegraed I(1) VAR sysems, Economic Theory, 13: ROGOFF, K. (1999) Moneray models of Dollr/Yen/Euro nominal exchange raes: Dead or undead? The Economic Journal, 109: F655 F659. ROGOFF, K. (2002) Dornbusch s Overshooing Model Afer Tweny-Five Years Second Annual Research Conference, Inernaional Moneary Fund, Mundell-Fleming Lecure, (Revised January 22, 2002). SOUTH AFRICA. Deparmen of Jusice and Consiuional Developmen Final Repor of he Commission of Inquiry ino he Rapid Depreciaion of he Exchange Rae of he Rand and Relaed Maers.[Online] Available from hp:// [Accessed: ]. TAYLOR, M.P. (1995) The Economics of Exchange Raes, Journal of Economic Lieraure, 33:

22 Appendix Daa Quarerly daa are colleced for all he variables from IMF s inernaional financial saisics, he Souh African Reserve Bank, and Bureau of Economic Analysis of he U.S. Deparmen of Commerce. Daa is seasonally adjused daa on all he variables. The sudy is limied o he period covering 1994Q1 o 2004Q4 since variabiliy in he exchange rae of he Rand was resriced via he dual exchange rae regime. Figure 4: Graphical Represenaion of all he Variables 1.20E E E E+13 Rands 8.00E E E E E E+12 US dollars 2.00E E E S o uh A frica rea l G D P in rands US real GDP in dollars 0.00E+00 21

23 1.0E E+13 Rands 8.0E E E E+12 US dollars 4.0E E E E E S ouh A frica nom inal m one y supply(m 3) in rands US nom inal m oney supp ly(m 3) in dollars 0.0E Percenage inflaion Souh Africa inflaion rae US inflaion rae 22

24 Percenage ineres rae S ouh A frica nom inal ineres rae U s n o m in a l in e re s ra e Rand/US dollar Nom inal exchange rae Tess for uni roo All he variables included in he model are esed for uni roo. The Augmened Dickey Fuller es of uni roo is performed on each of he variables using an ieraive procedure highlighed in Enders (2004:213). All he variables are found o be I(1). 23

25 Table 3: The ADF es for uni roo Variable Model specificaion ADFsaisic e Join es (Fsaisic) Inercep & Trend (random Φ 3= walk wih drif and ime rend) Inercep (random walk wih drif) Φ 1= None (pure random walk) I(1) m m Inercep & Trend (random walk wih drif and ime rend Inercep (random walk wih drif) Φ 3= Φ 1= I(1) y y Inercep & Trend (random walk wih drif and ime Φ 3= rend) Inercep (random walk wih drif) Φ 1= None (pure random walk) I(1) i i Inercep & Trend (random walk wih drif and ime Φ 3= rend) Inercep (random walk wih drif) Φ 1= None (pure random walk) I(1) p p Inercep & Trend (random walk wih drif and ime Φ 3= rend) Inercep (random walk wih drif) Φ 1= None (pure random walk) I(1) Noes : ( )[ ] Significan a 10 (5), [1] percen level Criical values for he Φ 3, and Φ 1 are from Dickey and Fuller (1981) General o specific model ieraive procedure in Enders (2004:213) is used Conclusion Reduced-Form VAR Diagnosic Tess All he roos have modulus less han one and lie inside he uni circle. Oher diagnosics ess for he VAR are presened in Table 4. he error erm is whie noise despie he lack of normaliy of he disribuion of he error erms. However, he resuls of he Johansen (1988) ess will no be affeced because of he lack of normaliy as long as he skewness of he disribuion of he error erms is fine (Paruolo, 1997). 24

26 Table 4: Diagnosics on he reduced-form VAR H 0 Tes Saisic Prob. Serial correlaion No serial correlaion LM-Tes χ 2 (lag. 3) Normaliy Normally disribued JB Join error erms Kurosis Join Skewness Join Heroschedasiciy No heroschedasiciy χ