Effects of Fiscal Policy on Credit Markets: Evidence in Japan using a Cointegration Analysis

Transcription

1 Global Economy and Finance Journal Vol. 4. No. 2. Sepember 20. Pp Effecs of Fiscal Policy on Credi Markes: Evidence in Japan using a Coinegraion Analysis Abdoul * Using a se of coinegraion and error correcion models wih Threshold Auoregressive (TAR) or Momenum Threshold Auoregressive (MTAR) asymmeric adjusmen, we invesigae wheher he effecs of fiscal policy (i.e. expansionary or conracionary governmen spending shocks) on ineres raes in Japan are asymmeric or no. Fory years (from 969 o 2008) of quarerly series on he price of oil, he Consumer Price Index (CPI) used o compue he real price of oil, governmen spending (nominal value of Federal Governmen spending of goods and services for consumpion and invesmen) and he ineres rae (Three-monh Treasury Bill Rae) obained from he Inernaional Moneary Fund s Inernaional Financial Saisics CD- ROM were used for he differen ess. Empirical resuls show ha he effecs of fiscal policy on ineres raes are asymmeric in Japan. Furhermore, he impulse response funcions indicae ha he resuls are consisen wih a dynamic asymmery in he behavior of fiscal policy movemens. JEL Classificaion Codes: C22, E6, E24. Keywords: Coinegraion, Asymmeric adjusmen, moneary policy, Threshold Auoregressive model, Momenum Threshold Auoregressive model.. Inroducion Recen years have been characerized by a lively debae on he economic role ha governmens should play. In recen years Japan has been plagued by a liquidiy rap and he governmen used fiscal policy o correc he problem. In his paper we will invesigae he impac of Japanese governmen fiscal policy on ineres raes. Afer a brief lieraure review, we inroduce he Threshold and Momenum models of coinegraion. Nex, we presen he resuls of he sudy and some discussions and implicaions of he findings. 2. Lieraure Review Many auhors have invesigaed he effecs of governmen fiscal policy on oupu and several views have sprung. We do no have he preensions of presening all hose views bu raher we will discuss jus a few of hem. Kandil (200), using quarerly daa for he Unied Saes, sudied he asymmery in he effecs of governmen spending shocks. She showed ha while ineres raes increased in he face of expansionary governmen spending shocks, here is no evidence of a reducion in he face of conracionary shocks. Consequenly, he increased governmen * Dr. Abdoul, Deparmen of Finance Economics Enrepreneurship and Markeing Fayeeville Sae Universiy, NC, USA. awane@uncfsu.edu

2 spending crowds ou privae invesmen. Moreover, Kandil (200) showed ha here is evidence of a reducion in privae consumpion as agens anicipae a fuure increase in axes o finance he increased governmen spending. As a resul, oupu growh and price inflaion are decreasing despie expansionary governmen spending shocks, on average, over ime. In view of his evidence, Kandil (200) suggesed ha public finance consideraions ough o dominae aemps o simulae demand using governmen spending when near full-equilibrium capaciy uilizaion in he economy. In conras, conracionary governmen spending shocks are no offse by an increase in privae spending. Hence, demand conracion is pronounced, slowing oupu growh and price inflaion in he face of a reducion in governmen spending. For Kandil (200), he implicaion is ha concerns over he pronounced conracionary effecs of a reducion in governmen spending ough o dominae public finance consideraions near full-equilibrium. Sorensen and Yosha (200) examined he business cycle behavior of sae fiscal policy o deermine wheher policy is asymmeric and, if so, o idenify he causes. They concluded ha sae revenue and expendiure display significan asymmery over he business cycle, wih nearly offseing effecs on he budge surplus. As a resul, sae fiscal policy ends o mue economic booms o roughly he same degree i miigaes slowdowns. The asymmeries in revenue and expendiure appeared o be associaed wih balanced budge rules, alhough heir fundamenal causes canno be clearly idenified. Sorensen and Yosha (200) ried o find ou he poenial causes of asymmeric fiscal policy. They poined ou ha asymmery in fiscal policy may arise for a variey of reasons, including marke consrains, balanced budges rules, lack of budge discipline in upurns, and incumben poliical paries rying o influence voing paerns or forcing he hand of fuure governmens. Sorensen, Wu and Yosha (200) found evidence of poliical business cycle asymmery in he fiscal policy of U.S. sae and local governmens during he period More recenly, using sign resricions on he impulse-response funcions and idenifying he unexpeced variaion in governmen spending by a posiive response of expendiure for up o four quarers afer he shock, Mounford and Uhlig (2005) find a negaive effec in residenial and non-residenial invesmen. In addiion, Afonso (2008c) suggess ha here is some evidence in favor of he exisence of expansionary fiscal consolidaions, for a few budgeary iems (general governmen final consumpion, social ransfers, and axes). Biau and Girard (2005) find a cumulaive muliplier of governmen spending larger han one, and posiive reacions of privae consumpion and privae invesmen in France. De Casro and Hernandez de Cos (2006) use daa for Spain and show ha, while here is a posiive relaionship beween governmen expendiure and oupu in he shor-erm, in he medium and long-erm expansionary spending shocks only lead o higher inflaion and lower oupu. 75

3 Heppke-Falk e al. (2006) use cash daa for Germany, and find ha a posiive shock in governmen spending increases oupu and privae consumpion, alhough he effec is relaively small. Giordano e al. (2007) show ha, in Ialy, governmen expendiure has posiive and persisen effecs on oupu and on privae consumpion. Afonso and Sousa (2009) worked on a paper ha provides a deailed evaluaion of he effecs of fiscal policy on he composiion of GDP, namely, by esimaing he impac of governmen spending and governmen revenue shocks on privae consumpion and privae invesmens as in Gali e al. (2007). Second, Afonso and Sousa (2008) asked how asse markes (via sock prices and housing prices) are affeced by fiscal policy shocks. Third, Afonso and Sousa (2009) looked a he impac of fiscal policy on he exernal secor hrough he effecs on exchange rae in line wih Monacelli and Peroi (2006). Fourh, Afonso and Sousa (2009) analyzed he effecs of fiscal policy shocks on he growh rae of moneary aggregaes, herefore assessing he poenial ineracion beween fiscal policy and moneary policy in he spiri of Davig and Leeper (2005), Chung e al. (2007), and Gali and Monacelli (2008). Fifh, Afonso and Sousa (2009) looked a he impac of fiscal policy on he labor marke, namely, by assessing is impac on wages and produciviy. In addiion an imporan conribuion of Afonso and Sousa s paper is he use of quarerly fiscal daa, which allowed hem o idenify precisely he effecs of fiscal policies. They analyzed empirical evidence from he U.S., U.K., Germany and Ialy, respecively for he periods 970:3-2007:4, 964:2-2007:4, 980:3-2006:4, and 986:2-2004:4. The mos relevan findings of Afonso and Sousa s paper can be summarized as follows. Governmen spending shocks (i) have, in general, a small effec on GDP; (ii) do no impac significanly on privae consumpion; (iii) have a negaive impac on privae invesmen; (iv) have a varied effec on housing prices ha ranges from a posiive and persisen effec o a negaive effec and gradual recovery according o he counry under consideraion, a paern ha depends on he effec on (long-erm) ineres raes; (v) lead o a quick fall in sock prices; (vi) do no impac significanly on he price level and he average cos of refinancing he deb; (vii) have a small and posiive effec on he growh rae of moneary aggregaes; (viii) lead o a depreciaion of he real effecive exchange rae; and (ix) have a posiive and persisen impac on produciviy. On he oher hand, governmen revenue shocks: (i) have posiive (alhough lagged) effecs on GDP and privae invesmen, as a resul of he fiscal consolidaion; (ii) a posiive effec on boh housing prices and sock prices ha laer mean revers, bu he exac impac depends on he effecs on (long-erm) ineres raes; (iii) in general, do no 76

4 have an impac on he price level; and (iv) lead o an appreciaion of he real exchange rae. The objecive of his paper is o invesigae he asymmeric effecs of governmen spending shocks (i.e. fiscal policy) on variables in he credi marke (such as ineres rae and he price level). Specifically, we will examine wheher expansionary and conracionary governmen spending shocks have he same effecs on he variables menioned above. Employing newly developed echniques, he analysis will provide evidence on asymmery in he effecs of policy shocks. 3. Daa and Mehodology We will modify and improve Kandil s (200) mehodology which is very similar o ha of Cover (992). We will use new and more appropriae esimaion echniques such as uni-roo and coinegraion ess wih possibiliy of error correcion. Since Kandil (200) used daa conaining over 30 years of observaions, i is possible, perhaps likely, ha he daa are non-saionary. Therefore, esimaion of equaions based on such daa would subjec he resuls o spurious concerns raised by Granger and Newbold (974). Anoher concern peraining o ime-series consideraions as poined ou by Hendry (986), Granger (998) and Hakkio and Rusch (989), is ha esimaing economic relaionships such as produciviy, unemploymen and wage o he exclusion of he long-run associaion beween he variables may creae biases. This is paricularly he case if he variables are coinegraed. Therefore, a beer way of proceeding is o invesigae wheher here exiss a long-run relaionship beween he variables. Building upon Kandil s (200) empirical models, several models will be used o es he asymmeric effecs of governmen spending shocks. To es he asymmeric effecs of governmen spending shocks in he credi marke, he following model will be esimaed: r g o u 0 2 () Where r is he log value of he nominal ineres rae; g is he log value of governmen spending; o is he log value of energy price; u is he disurbance erms. In erms of Equaion (), if he oupu, he governmen spending, and he energy price are all I () and he linear combinaion r 0 g 2o u is saionary, hen he variables are coinegraed of order (.). The vecor x is ( r,,, ) g o and he coinegraing vecor γ is ). According o Enders (995), he sysem is in (

5 long-run equilibrium when γx = 0. The deviaion from long-run equilibrium-called he equilibrium error- is u so ha u = γx. The equaions menioned above will be esimaed for long-run relaionship and for coinegraion allowing for TAR and MTAR adjusmen following Engle and Granger s (987) mehodology. The esing procedure is described in he following secion. 3. Threshold and Momenum Models of Coinegraion The Engle and Granger (987) mehodology as applied o he fiscal policy model begins by posiing a long-run equilibrium relaionship of he forms given for example in equaion (). The nex sep in he Engle and Granger procedure focuses on he OLS esimae of in he following regression equaion: (2) Where he esimaed regression residuals from () are used o esimae (2). Rejecing he null hypohesis of no coinegraion (i.e., acceping he alernaive hypohesis 2 << 0) implies ha he residuals in (2) are saionary wih mean zero. As such, equaion (2) is an aracor such ha is pull is sricly proporional o he absolue value of -. The change in equals muliplied by - regardless of wheher - is posiive or negaive. The implici assumpion of symmeric adjusmen is problemaic if he money-supply shock adjusmen is asymmeric. A formal way o inroduce asymmeric adjusmen is o le he deviaions from he long-run equilibrium in equaion () behave as a Threshold Auoregressive (TAR) process. Thus, i is possible o replace (2) wih: I I 3 2 Where I is he Heaviside indicaor such ha: if I 0 if Asymmeric adjusmen is implied by differen values of and 2 ; when - is posiive, he adjusmen is -, and if - is negaive, he adjusmen is 2 -. A sufficien condiion for saionariy of { } is for: -2 < (, 2 ) < 0. Moreover, if he { } sequence is saionary, he leas squares of esimaes of and 2 have an asympoic mulivariae normal disribuion if he value of he hreshold is known (or consisenly esimaed). Thus, if he null hypohesis = 2 = 0 is rejeced, i is possible o es for symmeric adjusmen (i.e., = 2 ) using a sandard F-es. Since adjusmen is symmeric if = 2, he Engle-Granger es for coinegraion is a special case of (3). 78

6 Since he exac naure of he non-lineariy may no be known, i is also possible o allow he adjusmen o depend on he change in - (i.e. - ) insead of he level of -. In his case, he Heaviside indicaor of (4) becomes: I if 0 0 if 0 Even hough Hansen (997) shows ha seing a Heaviside indicaor using - can perform beer han he specificaion using pure TAR adjusmen, Enders and Granger (998) and Enders and Siklos (200) show ha he series exhibis more momenum in one direcion han he oher. They call his model Momenum-Threshold Auoregressive (M-TAR) model. Respecively, he F-saisics for he null hypohesis = 2 = 0 using he TAR specificaion of (4) and he M-TAR specificaion of (5) are called and. As here is generally no presumpion as o wheher o use (4) or (5), he recommendaion is o selec he adjusmen mechanism by a model selecion crierion such as he AIC. If he errors in equaion (3) are serially correlaed, i is possible o use an augmened hreshold model for he residuals. In his circumsance, equaion (3) is replaced by: The disribuions of I and p 2 i i i 5 I 6 depend on he number of observaions, he number of lags in equaion (3) and he number of variables in he coinegraing relaionship. Enders and Siklos (200) repor criical values using coinegraing vecors conaining up o hree variables. Since he model used in his sudy conains four variables in he coinegraing relaionship, we develop firs he criical values for he four-variable case. 3.2 Daa The Inernaional Moneary Fund s Inernaional Financial Saisics provides he core daa for Japan. To es he effecs of fiscal policy on he credi marke, fory years of quarerly series (from 969 o 2008) on he price of oil, he Consumer Price Index (CPI) used o compue he real price of oil, governmen spending (nominal value of Federal Governmen spending of goods and services for consumpion and invesmen) and he ineres rae (Three-monh Treasury Bill Rae) are colleced. 3.3 Impulse Response Funcions According o Enders (995), he shape of he impulse response funcions and he resuls of he variance decomposiions can indicae wheher he dynamic responses of he variables conform o heory. We shall examine differen responses of oupu o governmen spending shocks, ax revenues shocks and real price of oil shocks. 79

7 4. Empirical Resuls 4. Resuls for he Tes of Saionariy Since by definiion coinegraion necessiaes ha he variables be inegraed of he same order, we preesed he variables for heir order of inegraion. The Dickey-Fuller (DF) es and he Augmened Dickey-Fuller (ADF) es are used o infer he number of uni roos (if any) in he oupu, money supply, price of oil and ineres rae series for each counry. Lag 8, which is deermined by he Akaike Informaion Crierion (AIC), is used in he ADF es. Table provides he summary of he findings. Boh he DF and ADF ess fail o rejec he null hypohesis (all he -saisics are less han he DF criical values) of any of he variables. These findings sugges ha he series are all I (). As a resul, he series are non-saionary and we proceed by aking firs differences of he series and es for coinegraion. Table : Uni Roo Tes Resuls DF Tes ADF Tes Lag Lag AIC Japan R Po Gx The Dickey Fuller (DF) criical values for T = 00 are 3.5, -2.89, -2.58, a %, 5% and 0% levels respecively. r = ineres rae; po = price of oil; gx = Governmen Expendiures. 4.2 Resuls of he Long Run Relaionships in he Credi Marke We use OLS o esimae he long run relaionships of he variables ineres rae, governmen spending (or governmen expendiures) and price of oil as implied by Equaion () above. The long run coinegraing equaions for Japan are as follow (he - saisics are in parenheses): r g 0.840o (5.) ( 3.69) (4.59) (7) Where r is he log value of he nominal ineres rae; g is he log value of governmen spending; o is he log value of energy price. Economic heory predics ha he coefficiens on he governmen spending (g ) should be posiive and less han one. I predics also ha he coefficien on he price of oil 80

8 should be posiive and less han one. As anicipaed, all he coinegraing parameers in he above equaions urn ou o be consisen wih he economic heory excep for he coinegraing parameer of he governmen spending variable. The coinegraing parameers of he variables are all saisically significan a convenional saisical significance levels. The residuals found in he above equaions (7) are used o proceed wih he coinegraion and asymmeric adjusmen ess. 4.3 Coinegraion and Asymmeric Tess wih Possibiliy of TAR or MTAR Adjusmen in he Credi Marke To es for coinegraion and asymmery, we saved he residuals of he long-run relaion equaions (7) in he sequence. For each ype of asymmery, we se he indicaor funcion I according o Equaion (4) or Equaion (5) and esimaed an equaion in he form of Equaion (6). The AIC was used o selec he mos appropriae lag lengh p and adjusmen mechanism (i.e. TAR versus MTAR adjusmen). The sample value of he F-saisic for he null hypohesis 2 0 was compared wih he appropriae criical value repored in Table 2 and/or 3. If he alernaive hypohesis is acceped (i.e., he null hypohesis of no coinegraion is rejeced), we hen used Chan s (993) mehodology o find he consisen esimae of he hreshold. Afer all, here is no reason o presume ha he hreshold is idenically equal o zero. Once he hreshold is properly esimaed, we es for symmeric versus asymmeric adjusmen (i.e., we es he null hypohesis ) using he usual F-saisic. 2 8

9 Table 2: Disribuion for he F-Saisic for he Null Hypohesis 2 in he 4-variable case LAGGED CHANGES LAG 2 LAGS 3 LAGS 4 LAGS 90% 95% 99% 90% 95% 99% 90% 95% 99% 90% 95% 99% THE TAR MODEL: THE MTAR MODEL:

10 Table 3: Disribuion for he F-Saisic for he Null Hypohesis 2 in he 4- variable case LAGGED CHANGES 5 LAGS 6 LAGS 7 LAGS 8 LAGS 90% 95% 99% 90% 95% 99% 90% 95% 99% 90% 95% 99% THE TAR MODEL: 50 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A THE MTAR MODEL: 50 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Noe: NA indicaes no available. We do no provide he criical values for he model wih more han 5 lags using only 50 observaions. Table 4 repors he esimaed values for he i and he sample F-saisics for he null hypohesis 2 0 as well as he F-saisics for he null hypohesis 2 using he lag lengh and adjusmen mechanism seleced by he AIC. The lag lengh is seleced such ha he Akaike Informaion Crierion (AIC) is minimized. As such AIC selecs 8 lags for Japan. Table 4: The Esimaed Adjusmen Equaions (ineres raes) Counries 2 a b 2 Lags c AIC Flag Japan ** 3.43 ** MTAR (.02) (-.63) a Enries are he sample values of or for he adjusmen process shown in column 8.,, indicae significance levels of 0%, 5% and % respecively. -saisics are in parenheses. 83

11 b Enries in his column are he values for he sample F-saisic for he Null Hypohesis ha he adjusmen equaions are equal. c Enries in his column are he number of lags of seleced by AIC. The esimaed for he null hypohesis 2 0 is 8.97 in Japan. The criical value repored in Table 3 a he 5% significance level wih 50 observaions and 8 lags is As such, we rejec he null hypohesis of a uni roo in favor of saionariy wih asymmeric adjusmen. The poin esimaes of he i sugges ha negaive deviaions from he long-run equilibrium are eliminaed much faser han posiive deviaions. Specifically in Japan, 7.9% of a negaive deviaion is eliminaed wihin a quarer while 5% of a posiive deviaion is eliminaed during he same ime frame. The F-saisic for asymmeric adjusmen ( 2 ) is given in Table 4. For he Japan, he F-saisic (3.43) rejecs symmeric adjusmen a he 5% significance level in favor of asymmeric MTAR adjusmen. According o Lukepohl (994) he coefficiens of coinegraion relaions canno be inerpreed as elasiciies. This is because he ceeris paribus canno be meaningful. The error correcion specificaions can be more informaive. 4.4 The Error-Correcion Represenaion: TAR or MTAR Asymmeric Adjusmen in he Credi Marke (Ineres Rae) Having found evidence supporing asymmeric adjusmen in Japan and using he long relaion implied in Equaion (7), he esimaed error-correcion equaions assuming Momenum Threshold Auoregressive (MTAR) adjusmen (wih -saisics in parenheses) are: o A L) o A ( L) g A ( L) r 0.72z 0.85z (8) Where: z z g r A A ( (3.24) ( 0.26) ( L) o A22( L) g A23( L) r 0.052z 0.074z ( 2.83) (0.68) ( L) o A32( L) g A33( L) r z 0.07z ( 0.79) ( 0.58) r g 0.840o, I 5 I r g 0.840o, I = Threshold Heaviside Indicaor Funcion, A ij (L) is a polynomial in he lag operaor L, and he lag lengh is seleced using he mulivariae version of AIC, which seleced 8 lags (9) (0) 84

12 In Equaion (0), he ineres rae in Japan seems o adjus faser when here is a posiive discrepancy from he long-run equilibrium han when here is a negaive discrepancy. Specifically, he poin esimaes imply ha he ineres rae adjuss by 3% of a posiive deviaion from long-run equilibrium, bu by only.7% of a negaive gap. The -saisics imply ha neiher of he coefficiens on he error-correcion erms is significan a convenional significance levels. In equaions (8) and (9), only he coefficiens of he posiive error-correcion erms (i.e. z ) are significan a convenional significance levels. These resuls indicae ha adjusmens owards he long-run equilibrium are accomplished via changes in he governmen spending and he real price of oil. 5. Conclusion and Policy Implicaions This sudy invesigaes he asymmeric effecs of fiscal policy (i.e. governmen spending) on ineres raes (proxying credi marke condiions) in Japan. Fory years of quarerly series on he price of oil, he Consumer Price Index, governmen revenues, governmen spending and he ineres rae for Japan are obained from he Inernaional Moneary Fund s Inernaional Financial Saisics CD-ROM. We use a coinegraion analysis developed by Engle and Granger o es he effecs of fiscal policy shocks on oupu. The Engle-Granger coinegraion analysis finds ha he variables in he credi marke are coinegraed which is an indicaion of he exisence of long-erm equilibrium relaionships beween he ineres rae, governmen spending and he he price of oil in boh counries. The coinegraing parameers in he credi marke urn ou o be consisen wih economic heory predicions excep for he coinegraing parameer of he governmen spending variable. The asymmeric adjusmen ess conclusively indicae ha he effecs of fiscal policy on ineres raes are asymmeric. The impulse response funcion indicaes ha he resuls are consisen wih a dynamic asymmery in he behavior of he governmen spending movemens. Specifically, a negaive governmen spending shock produces a significanly larger response in ineres raes as compared o is posiive counerpar. Furhermore, he error-correcion represenaion reveals ha he effecs of posiive governmen spending movemens dwindle raher quickly in Japan. The resuls for a negaive governmen spending change, however, do no dwindle ha quickly. These resuls show evidence ha he ineres rae decreases in he face of conracionary governmen spending shocks in Japan. Furhermore, here is no evidence ha he ineres rae significanly increases in he face of expansionary governmen spending shocks. The resuls found in Japan are no consisen wih he findings of he sudies of previous auhors such as Kandil (200). 85

13 Overall he resuls found in his sudy and described above will have ineresing policy implicaions. In Japan, expansionary governmen spending shocks do no have posiive effecs on he ineres rae. The ineres rae is no responsive o governmen spending and oupu growh. Perhaps one explanaion why ineres raes are no responsive o governmen spending is ha Japan has been plagued by a liquidiy rap and a subborn deflaion for quie some ime. As such, public finance consideraions ough o dominae aemps o simulae he economy using governmen spending during recessions because chances are ha he increase in governmen spending will no crowd ou privae spending. Furhermore, a vigorous fiscal policy in Japan may help figh agains he subborn price deflaion because he price level is very responsive o expansionary governmen spending shocks. On he oher hand, here is evidence ha conracionary governmen spending shocks in Japan will reduce ineres raes and oupu, bu no he price level. Therefore, because of exremely low prices and ineres raes, conracionary governmen spending would be an inadequae policy in Japan as i migh depress prices and ineres raes furher. References Afonso, A & Sousa, RM 2009, The Macroeconomic Effecs of Fiscal Policy, ECB working paper series, forhcoming. Afonso, A 2008c, Expansionary fiscal consolidaions in Europe: new evidence, Applied Economic Leers, forhcoming. Afonso, A & Sousa, RM 2008, Fiscal Policy, housing and sock prices, ECB working paper, forhcoming. Biau, O & Girard, E2005, Poliique budgéaire e dynamique économique en France: l approche VAR srucurel., EconomieePrévision,pp. 69-7, -24. Chan, KS 993, Consisency and limiing disribuion of he leas squares esimaor of a hreshold auoregressive model, The Annals of Saisics, Vol. 2, pp Chung, H, Davig, T & Leeper, EM 2007, Moneary and Fiscal swiching,journal of Money, Credi and Banking, Vol. 39, No. 4, pp Cover, JP 992, Asymmeric effecs of posiive and negaive money-supply shocks, Quarerly Journal of Economics, Vol.07, pp Davig, T & Leeper, EM, Flucuaing macro policies and he fiscal heory,nber Working Paper #22. De Casro Fernandez, F&Hernandez De Cos, P2006, The Economic effecs of exogenous fiscal shocks in Spain: a SVAR approach,ecb working paper #647. Enders, W 995, Applied Economeric Time Series, John Wiley and Sons, Inc, New York, s ediion. Enders, W & Granger, CWJ 998, Uni-Roo Tess and Asymmeric Adjusmen Wih and Example Using he Term Srucure of Ineres Raes,Journal of Business and Economic Saisics,Vol.6, pp Enders,W and Siklos, P200, Coinegraion and Threshold Adjusmen, Journal of Business and Economic Saisics, Vol.9, pp Engle, RF and Granger, CWJ 987, Coinegraion and Error Correcion: Represenaion, Esimaion and Tesing,Economerica,Vol. 55,pp

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