Mean Reversion of Balance of Payments GEvidence from Sequential Trend Break Unit Root Tests. Abstract

Transcription

1 Mean Reversion of Balance of Paymens GEvidence from Sequenial Trend Brea Uni Roo Tess Mei-Yin Lin Deparmen of Economics, Shih Hsin Universiy Jue-Shyan Wang Deparmen of Public Finance, Naional Chengchi Universiy Absrac We analyze he G7 counries daa se of real balance of paymens series. The uni roo ess wih an endogenously deermined brea dae in he rend funcion proposed by Zivo and Andrews (992) is employed o characerize he balance of paymens series. The empirical resuls show ha allowing for a brea in he rend funcion could aler he oucome of he sandard uni roo ess for some series. We are graeful o he associae edior Professor Mar Wynne of his journal for his valuable suggesions. Ciaion: Lin, Mei-Yin and Jue-Shyan Wang, (28) "Mean Reversion of Balance of Paymens GEvidence from Sequenial Trend Brea Uni Roo Tess." Economics Bullein, Vol. 6, No. 4 pp. - Submied: January 3, 28. Acceped: January 3, 28. URL: hp://economicsbullein.vanderbil.edu/28/volume6/eb-8f45a.pdf

2 . Inroducion The analyical model inroduced by he famous papers of Mundell (962, 963) and Fleming (962), which gave rise o he erm Mundell-Fleming model, is a very popular approach o examining he impac of various polices in an open economy. One of he ey assumpions of Mundell-Fleming model is ha he balance of paymens (BOP) is zero in equilibrium; ha is, he rade balance equals he ne capial ouflow. However, here is very lile aenion on he characerisic of BOP ime series. If BOP is mean revering, i follows ha he BOP will reurn o is rend pah over ime and he assumpion of Mundell-Fleming model is reasonable. On he oher hand, if BOP follows a random wal process, any shoc or innovaion has a susained effec. Thus he fuure BOP canno be prediced based on is hisorical movemens and he analyical approach of Mundell-Fleming model mus be modified. This paper will invesigae he issue ha wheher he BOP is bes characerized by following a random wal or mean revering process. We employ he uni roo ess wih one srucural brea in he rend funcion proposed by Zivo and Andrews (992) o examine he random wal hypohesis for he BOP of G7 counries. The resuls of he uni roo ess wihou srucural brea show ha he BOP follows a random wal process for Germany, Ialy, Japan and Unied Saes. However, mos of he G7 counries, he BOP series will suppor he mean reversion hypohesis when he uni roo ess are allowing for one srucural brea in he rend funcion. This paper proceeds as follows. Secion 2 covers a descripion of daa and economeric mehods used in his paper. The empirical resuls are presened in Secion 3. And finally he las secion offers a conclusion. 2. The daa and he empirical mehodology 2.. The daa The daa se, obained from he Inernaional Moneary Fund s Inernaional Financial Saisics (IFS), comprises quarerly observaions for G7 counries, including Canada (CAN), France (FRA), Germany (GER), Ialy (ITA), Japan (JPN), Unied Kingdom (UK) and Unied Saes (USA). The sample period is from 98: o 26:3. Two indexes are employed o measure he equilibrium of BOP. One, denoed by BOP, is defined as summing up he ne balance in curren accoun, capial accoun and financial accoun. Allowing for he saisical discrepancy, we define he oher index, BOP 2, as overall balance which adds he ne errors and omissions o he previous Inernaional Moneary Fund has reorganized he iems in BOP and newly esablished financial accoun in 997. See Balance of Paymens Manual published by IMF and compare he difference beween he 4 h ediion and he 5 h ediion. Because he financial accoun in he 5 h ediion is roughly equivalen o he capial accoun in he 4 h ediion, BOP before 997 is calculaed by summing up he ne balance of curren accoun and capial accoun.

3 BOP. All he accouns in BOP are measured in billions of US dollars. The indexes employed in his paper, BOP and BOP 2, are deflaed by he consumer price index of each counry and hen seasonally adjused by moving average mehod. 2 Time series plos of seasonally adjused BOP and BOP 2 for each counry are shown in Figure. The descripive saisics are presened in Table. BOP Table : Descripive saisics, 98:-26:3 Canada France Germany Ialy Japan UK USA Mean Maximum Minimum Sandard deviaion Sewness Kurosis BOP 2 Mean Maximum Minimum Sandard deviaion Sewness Kurosis The oher mehod o measure he BOP may be he raio of he BOP o GDP. However, his paper is he es for he uni roo of he BOP ime series for each counry separaely. The rend has been included in he regression. We hin i is no necessary o move he scale effec by dividing he GDP when he uni roo is irrelevan o he comparisons among counries. 2

4 CANBOP CANBOP2 FRABOP FRABOP GERBOP GERBOP2 ITABOP ITABOP JPNBOP JPNBOP2 UKBOP UKBOP USABOP USABOP2 Figure : Plos of BOP ime series 3

5 2.2. The economeric mehodology The prevalen approach o examining he random wal hypohesis is uni roo ess. To provide a benchmar, we sar by he Augmened Dicey-Fuller (ADF) uni roo ess. The ADF regressions are: j j j= µ α β j j ε j= y = µ + α y + c y + ε () y = + y + + c y + (2) where y refers o he BOP or BOP 2 ime series in each counry, y is he lagged firs difference, =,2,, T is an index of ime. Equaion and 2 have α = as he null hypohesis of a uni roo in y, and α < as he alernaive hypohesis. If he null hypohesis is rejeced, Equaion means ha y is a mean saionary series and Equaion 2 indicaes ha y is rend saionary. The sufficien lags of are included in ADF uni roo ess o yield y approximaely whie noise residual. There are wo daa-dependen mehods o selec he lag parameer. The firs one originally implemened by Perron (989) is a general o specific recursive procedure based on he value of he -saisic on he coefficien of he las lag. I sars wih a predeermined upper bound. If he las included lag is significan, max is seleced. However, if max is insignifican, he number of lags is reduced by one unil he las lag in he esimaed auoregression is max significan. Hayashi (2, p594) suggesed he formula.25 max in(2( T /) ) = as lag selecion rules of upper bound. In his paper, we use he approximae % asympoic criical value of.6 o assess he significance of he las lags and max = 2 is se according o Hayashi s formula. I mus be noed ha he oher mehod o selec he lag order is he minimum of Aaie Informaion Crierion or Schwarz Bayesian Crierion. Ng and Perron (993) indicaed ha he informaion-based crieria end o selec very parsimonious models leading o ess wih serious size disorions. For he reason, we use general o specific approach of Perron (989) o selec he lag parameer. Perron (989) showed ha he sandard uni roo ess are biased owards non-rejecion of he uni roo hypohesis if he daa are characerized by he saionary processes wih one brea in he rend funcion. Perron (989) also developed procedures ha es for a uni roo allowing for a one-ime srucural change in he rend. However, he brea daes repored in Perron (989) were chosen ex-ane and no modified ex-pos. Some papers have focused on his issue and proposed es procedures ha relax he exogeneiy assumpion abou he deerminaion of he brea dae. Zivo and Andrews (992) exended Perron s (989) model by endogenizing he 4

6 choice of brea dae from he daa. We will apply he versions of Zivo and Andrews (992) o invesigae he uni roo hypohesis for BOP series. We firs assume ha he one-ime change in he srucure occurring a ime TB(< TB< T ). In he noaion of Perron (989), Model A has he following represenaions: j j j= y = µ + α y + β + θ DU + c y + ε (3) Model B is depiced as: j j j= y = µ + α y + β + γ DT + c y + ε (4) And Model C can be wrien in he form as: y = µ + α y + β + θ DU + γ DT + c y + ε (5) j j j= DU is an indicaor dummy variable for mean shif occurring a ime TB, and is he corresponding rend shif variable where if > TB DU = oherwise TB if > TB DT = oherwise Model A ( he crash model) allows for a one-ime change in he inercep of he rend funcion. Model B ( he changing growh model) specifies a change in he slope of he rend funcion. Model C combines he changes in he inercep and slope of he rend funcion. The null hypohesis for a uni roo in y imposes he resricion on he coefficien ha α = in each model. Under he null hypohesis of a saionary flucuaion around he rend funcion, we have he following specificaion: α <. Zivo and Andrews (992) suggesed he region (.5T and.85t ) as he searching inerval for he brea dae in order o exclude he beginning or he end poins of he sample. The brea dae mus be chosen o give he leas favorable resul for he null hypohesis. Therefore we selec he brea dae recursively by choosing he value of TB ha minimizes he -saisic for esing for α = in he appropriae auoregression. DT 3. Empirical resuls The resuls for he uni roo ess wihou srucural brea, Equaion and 2, are repored in Table 2. The BOP series may follow a random wal process for he cases of Germany and Ialy wih rend, Germany and Japan wihou rend. The BOP2 series is saionary excep in he case of Unied Saes wih rend. 5

7 BOP Table 2: Augmened Dicey-Fuller (ADF) uni roo ess Canada France Germany Ialy Japan UK USA ADF (wih rend) ** * * * * P value Lag order ( ) ADF (wihou rend) * * ** * * P value Lag order ( ) BOP 2 ADF (wih rend) * ** * ** ** * P value Lag order ( ) ADF (wihou rend) * * * -3.77* * * *** P value Lag order ( ) The symbols *, ** and *** indicae significance a %, 5% and % saisical level. 2. Criical values are from MacKinnon (99). To consider he possible srucural brea in he rend funcion, we implemen Zivo and Andrews sequenial brea uni roo ess. The resuls for Model A, B, C are shown in Table 3, 4, 5 respecively. The criical values provided by Zivo and Andrews (992) depend on he relaive locaion of he brea dae in he sample (denoed by λ = TB/ T). However, here is no much variaion in he criical values. Therefore we only repor he criical values for α corresponding o a brea dae a mid-sample ( λ =.5 ). In Table 3 and 5, he resuls show ha he null hypohesis is rejeced in BOP and BOP 2 for Model A and C. In Table 4, for Model B, he null hypohesis is rejeced excep BOP of Germany. γ = Zivo and Andrews didn provide he criical values for esing for θ = or. We es he significance of θ or γ by sandard -saisic. The change in he inercep of rend funcion (θ ) is significan for mos of he BOP series. However, he change in he slope of he rend funcion ( γ ) is no so obvious. We conclude ha he BOP follows a saionary process for mos of he G7 counries. Comparing he difference in he resuls beween he sandard ADF uni roo ess and Zivo and Andrews sequenial brea uni roo ess, we find ha allowing for a brea in he rend funcion may aler he oucome of he sandard uni roo ess for some series. 6

8 BOP Table 3: Zivo and Andrews (992) es for uni roo: Model A Canada France Germany Ialy Japan UK USA TB 997:2 992:2 99: 998: 22:4 984:2 996: λ α -2.57* * -2.9* -.687* -2.72* -.283* -.635* (-4.56) θ 3.66** (2.2822) (-5.759) *** (-.8525) ( ) * (3.643) (-4.537) ** (-2.527) (-6.87) * (4.745) (-3.58) ** (-2.52) BOP 2 (-5.878) * (3.73) TB 995:4 994:2 989:4 99:2 22:4 993:3 995:4 λ α * * -.498* * * -.927* -.659** (-5.648) θ.4922*** (.834) (-5.759) *** (-.8525) (-.32) (.63) ( ) * ( ) ( )) 3.279* (3.847) (-5.48) * (-3.753) The -saisics are given in parenheses. 2. The %, 5% and % criical values for α corresponding are -4.32, and The symbols *, ** and *** indicae significance a %, 5% and % saisical level. (-4.97) * (3.2999) BOP Table 4: Zivo and Andrews (992) es for uni roo: Model B Canada France Germany Ialy Japan UK USA TB 995: 993:3 995:4 996:2 2:4 986:4 22:4 λ α -.842** -3.52* ** * * ** (-4.53) γ.79 (.323) (-5.874).28*** (.7982) ( ) -.686** ( ) (-4.97) (-.284) ( ) 3.73* (3.8797) ( ).6653* (2.9552) BOP 2 ( ) (-.647) TB 999:4 984:3 992:3 992:3 2: 994:4 993:3 λ α -.988* * * -.767*** * ** -.874** ( ) ( ) (-9.983) ( ) ( ) (-4.358) ( ) γ * ** 7

9 (-.7837) (-.7748) (-.739) (.245) (2.934) (.5648) (2.4286) The -saisics are given in parenheses. 2. The %, 5% and % criical values for α corresponding are -4.55, and The symbols *, ** and *** indicae significance a %, 5% and % saisical level. BOP Table 5: Zivo and Andrews (992) es for uni roo: Model C Canada France Germany Ialy Japan UK USA TB 22:3 994:3 99: 994:3 998:4 989:4 22:2 λ α -.358* * * -.783** * * -.864* (-8.93) ( ) ( ) (-4.569) (-5.58) ( ) ( ) θ *** 8.233* 4.86*** * * 5.98* γ.4223** ( ) (.6742) (3.993) (.8598) (-3.75) (3.953) (3.47) (2.7).274*** (.886) -.44 (-.6483) -.44 (-.2489) 3.779* (4.2667).94* (3.6793) BOP * (-3.287) TB 988:4 994:2 992:4 99: 997:3 993:3 995:4 λ α -.286* -.278* -.57* ** -.94** -.963* -.45** ( ) ( ) (-.2225) (-4.899) (-4.644) ( ) ( ) θ -.897** 3.789*** *** * * * γ (-2.738) (.9328) (-.757) ( ) (-.746) (-3.42) (3.5549) (-.586).82 (.53) -.45 (-.258) -.27 (-.5583).226* (2.6968) -.8 (-.24) The -saisics are given in parenheses. 2. The %, 5% and % criical values for α corresponding are -4.9, and The symbols *, ** and *** indicae significance a %, 5% and % saisical level..45** (2.264) 4. Conclusion This paper inends o characerize he BOP ime series. The sandard ADF uni roo ess show he BOP may follow a random wal process in some series. However, for mos of he G7 counries, he BOP is rend saionary when he uni roo ess are allowing for one srucural brea in he rend funcion. This implies ha he assumpion of Mundell-Fleming model abou he equilibrium of BOP is appropriae. 8

10 The crucial feaure of his paper is ha we use he recursive -saisic on he las lag o choose he order of he esimaed auoregression. This mehod is urgenly recommended by Perron. Besides we employ he Zivo and Andrews sequenial brea uni roo ess o endogenize he choice of brea dae. We have no aemp o show wha happens in he brea dae. The purpose of his paper is o sugges ha allowing for a brea in he rend funcion could aler he oucome of he sandard uni roo ess. Reference Fleming, M. J. (962), Domesic Financial Policies Under Fixed and Under Floaing Exchange Raes, Inernaional Moneary Fund Saff Papers, 9, Hayashi, F. (2), Economerics, Princeon Universiy Press, Princeon, NJ. MacKinnon, J. (99), Criical Values for Coinegraion Tess, in Long-run Economic Relaionship: Readings in Coinegraion (Eds) R. F. Engle and C. W. Granger, Oxford Universiy Press, Oxford, Mundell, R. A. (962), The Appropriae Use of Moneary and Fiscal Policy Under Fixed Exchange Raes, Inernaional Moneary Fund Saff Papers, 9, Mundell, R. A. (963), Capial Mobiliy and Sabilizaion Policy under Fixed and Flexible Exchange Ras, Canadian Journal of Economics and Poliical Science, 29, Ng, S. and Perron, P. (995), Uni Roo Tess in ARMA Models wih Daa Dependen Mehods for he Selecion of he Truncaion Lag, Journal of he American Saisical Associaion, 9, Perron, P. (989), The Grea Crash, he Oil Price Shoc and he Uni Roo Hypohesis, Economeica, 57, Zivo, E. and Andrews, D. (992), Furher Evidence of he Grea Crash, he Oil-price Shoc and he Uni-roo Hypohesis, Journal of Business and Economic Saisics,,