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1 Universiy of Wollongong Research Online Faculy of Commerce - Papers (Archive) Faculy of Business 2005 Tesing for Srucural Breaks in Ausralia's Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models Mosayeb Pahlavani Universiy of Sisan & Baluchisan, Iran, mp60@uow.edu.au A. Valadkhani Universiy of Wollongong, abbas@uow.edu.au A. C. Worhingon Universiy of Wollongong, a.worhingon@griffih.edu.au Publicaion Deails This aricle was originally published as Pahlavani, M, Valadkhani, A and Worhingon, AC, Tesing for Srucural Breaks in Ausralia's Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models, Universiy of Wollongong, Discipline of Economics Working Paper Series, No. WP05-02, Research Online is he open access insiuional reposiory for he Universiy of Wollongong. For furher informaion conac he UOW Library: research-pubs@uow.edu.au

2 Tesing for Srucural Breaks in Ausralia's Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models Absrac This paper employs all quarerly ime series currenly available o endogenously deermine he iming of srucural breaks for various moneary aggregaes and ineres raes in Ausralia over he las hiry years. The Innovaional Oulier model (IO) and he Addiive Oulier model (AO) are hen used o es for nonsaionariy. Afer accouning for he single mos significan srucural break, he resuls from boh models clearly indicae ha he null of a leas one uni roo canno be rejeced for almos all series examined. The srucural breaks found coincide wih imporan policy changes during he period of financial deregulaion saring in he 1980s. Disciplines Business Social and Behavioral Sciences Publicaion Deails This aricle was originally published as Pahlavani, M, Valadkhani, A and Worhingon, AC, Tesing for Srucural Breaks in Ausralia's Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models, Universiy of Wollongong, Discipline of Economics Working Paper Series, No. WP05-02, This journal aricle is available a Research Online: hp://ro.uow.edu.au/commpapers/204

3 Universiy of Wollongong Economics Working Paper Series 2005 hp:// Tesing for Srucural Breaks in Ausralia s Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models Mosayeb Pahlavani Abbas Valadkhani and Andrew Worhingon WP March 2005

4 Tesing for Srucural Breaks in Ausralia s Moneary Aggregaes and Ineres Raes: An Applicaion of he Innovaional Oulier and Addiive Oulier Models By Mosayeb Pahlavani Abbas Valadkhani * School of Economics and Informaion Sysems and Andrew Worhingon School of Accouning and Finance Faculy of Commerce Universiy of Wollongong Wollongong, NSW Ausralia 2522 Fax: * : abbas@uow.edu.au Absrac This paper employs all quarerly ime series currenly available o endogenously deermine he iming of srucural breaks for various moneary aggregaes and ineres raes in Ausralia over he las hiry years. The Innovaional Oulier model (IO) and he Addiive Oulier model (AO) are hen used o es for nonsaionariy. Afer accouning for he single mos significan srucural break, he resuls from boh models clearly indicae ha he null of a leas one uni roo canno be rejeced for almos all series examined. The srucural breaks found coincide wih imporan policy changes during he period of financial deregulaion saring in he 1980s.

5 1 I. INTRODUCTION I goes wihou saying ha srucural change is of considerable imporance in he analysis of macroeconomic ime series. Srucural change occurs in many ime series for any number of reasons, including economic crises, changes in insiuional arrangemens, policy changes and regime shifs. An associaed problem is esing of he null hypohesis of srucural sabiliy agains he alernaive of a one-ime srucural break. If such srucural changes are presen in he daa generaing process, bu no allowed for in he specificaion of an economeric model, resuls may be biased owards he erroneous non-rejecion of he non-saionariy hypohesis (Perron 1989; Perron 1997; Leybourne and Newbold; 2003). Convenionally, daing of he poenial break is assumed known a priori in accordance wih he underlying asympoic disribuion heory. Tes saisics are hen consruced by adding dummy variables represening differen inerceps and slopes, hereby exending he sandard Dickey-Fuller procedure (Perron 1989). However, his sandard approach has been criicized, mos noably by Chrisiano (1992), who argued ha daa-based procedures are ypically used o deermine he mos likely locaion of a break: evidence of an endogeneiy or sample selecion problem. This invalidaes he disribuion heory underlying convenional esing. In response, a number of sudies have developed differen mehodologies for endogenising daes, including Zivo and Andrews (1992), Perron (1997), Lumsdaine and Papell (1998) and Bai and Perron (2003). These have shown ha by endogenously deermining he ime of srucural breaks, bias in he usual uni roo ess can be reduced. Perron and Vogelsang (1992), has proposed a class of es saisics which allows for wo differen forms of a srucural break: namely, he Addiive Oulier (AO) model, which is more relevan for series exhibiing a sudden change in he mean (he crash model), and he Innovaional Oulier (IO) model, which capures changes in a more gradual manner hrough ime. The purpose of his paper is o employ he IO and AO models o examine srucural breaks in money aggregaes and ineres raes associaed wih Ausralian financial deregulaion from he 1980s. The deecion of srucural breaks wihin hese ime series will presen clear and novel evidence of he impac of his imporan period of insiuional and regulaory change. Perron (1997: 356), for example, argues ha if one can sill rejec he uni-roo hypohesis under such a scenario i mus be he case i would be rejeced under a less sringen assumpion. The moneary aggregaes and ineres rae series examined are he naural logs of quarerly observaions for he longes period available. The moneary

6 2 measures are he moneary base (MB), M1, M3, and broad money (BM), measured in AUD billions and expressed in consan prices using he consumer price index (1989/90 = 100). The ineres rae variables are RS (a shor-erm ineres rae proxied by he yield on 90-day bank acceped bills and RL (a long-erm rae proxied by he yield on 10-year Treasury bonds). The remainder of he paper is as follows. Secions II and III briefly discuss he heoreical underpinnings of he IO and AO models, respecively. Secion IV presens he empirical resuls and comparison is made beween convenional uni roo ess and hose obained wih he IO and AO models. Secion V provides some concluding remarks. II. INNOVATIONAL OUTLIER MODELS The IO1 model allows for gradual changes in he inercep and he IO2 model accommodaes gradual changes in boh he inercep and he slope of he rend funcion, such ha: K IO1: x = µ + θdu + β+ δdt ( b) + αx 1 + ci x i + e (1) i= 1 IO2: x = µ + θdu + β+ γdt + δdt ( b) + αx 1 + ci x i + e (2) K i= 1 where T b denoes he ime of break (1<T b <T) which is unknown, DU =1 if > T b and zero oherwise, DT = T if > T b and zero elsewhere, DT ( ) =1 if =Tb+1 and zero oherwise, x is any general ARMA process and e is he residual erm assumed whie noise. The null hypohesis of a uni roo is rejeced if he absolue value of he -saisic for esing α=1 is greaer han he corresponding criical value. Perron (1997) suggess ha T b (he ime of srucural break) can be deermined by wo mehods. In he firs approach, equaions (1) or (2) are sequenially esimaed assuming differen T b wih T b chosen o minimize he -raio for α =1. In he second approach, T b is chosen from among all oher possible break poin values o minimize he -raio on he esimaed slope coefficien (γ) The runcaion lag parameer or k is deermined using he daa-dependen mehod proposed by Perron (1997). In his he choice of k depends upon wheher he -raio on he coefficien associaed wih he las lag in he esimaed auoregression is significan. The opimum k (or k * ) is seleced such ha he coefficien on he las lag in an auoregression of order k* is significan and ha he las coefficien in an auoregression of order greaer han k* is insignifican, up o a maximum order k (Perron, 1997). Wih quarerly daa, k max = 8 b

7 3 (Lumsdaine and Papell 1998). The IO2 model allowing for a change in boh he inercep and slope is also specified. III. ADDITIVE OUTLIER MODEL In conras o he gradual change in he IO model, he AO model assumes srucural changes ake place insananeously. Tesing for a uni roo in he AO framework is hen given by a wo-sep procedure (Perron, 1994). To sar wih, he rend is removed from he series: y = µ + β+ γdt * + y (3) where ỹ is he derended series. Since equaion (3) assumes ha a srucural break only impacs on he slope coefficien, he following is hen esimaed o es for a change in he slope coefficien: K = α 1 + i i + i= 1 y y c y e (4) Similarly o he IO mehodology, hese equaions are esimaed sequenially for all possible values of T b (T b = k + 2,..,T-1) where T is he oal number of observaions so as o minimise he -saisic for α =1. The lag lengh is daa-deermined using he general o specific, and he break dae is assumed o be unknown and endogenously deermined by he daa. The null hypohesis is rejeced if he -saisic for α is larger in absolue value han he corresponding criical value. An alernaive, which is more widely used is o selec T b as he value, over all possible break daes, ha minimizes (or maximizes) he value of he -saisic on γ=0 (Harris and Sollis 2003). This approach has been used in his sudy. IV. EMPIRICAL RESULTS Table 1 presens he daa definiions and sources of he moneary measures and ineres raes examined. The resuls of convenional ADF ess (wih consan and rend) up o a maximum of 5 runcaion lags are also presened. As shown, all variables are non-saionary (conain a leas one uni roo) for he sample period under invesigaion. However, and as discussed earlier, applying he ADF uni roo es may be biased owards non-rejecion of he uni roo hypohesis. Tha said, here is lile evidence as o which of he wo models specified above is mos appropriae o capure he effec of an endogenous srucural break on he hypohesis ess. If a series ruly exhibis a rend, hen esimaing a model (such as IO1) ha does no have a

8 4 rend variable may fail o capure some imporan characerisics of he daa. On he oher hand, if here is no upward or downward rend in he daa, he es power o rejec he nobreak null hypohesis is reduced as he criical values increase wih he inclusion of a rend variable (Ben David and Papell, 1997). Since visual inspecion of he ime series indicae upward or downward rends (see Figure 1), he IO2 model and he AO model (allowing for a change in slope) are used. Noneheless, since γˆ is highly significan in all esimaes, he inclusion of a change (break) in slope is also jusified ex pos. In order o decide which paricular IO model is mos relevan, he following model selecion procedure is adoped. Firs, he leas resricive model (IO2) is esimaed and if γˆ is significan a he 5 percen level or beer, hen he resuls are repored in Table 2. If γˆ is no saisically significan, hen he resuls of an IO1 model are presened. Since γˆ for all esimaed equaions are highly significan, only he resuls of he IO2 model are abled. In order o deermine he sudden effec of an unknown srucural break, he AO model is also esimaed and he resuls presened in Table 3. Based on he resuls in Tables 2 and 3, he primary resuls of he analysis are as follows. Firs, he AO model saisics indicae ha all series under invesigaion are non-saionary. This is consisen wih he resuls of he ADF ess in Table 1. I hen appears ha capuring he mos imporan srucural break by he AO model has no challenged any inferences abou ime series propery of he daa garnered by convenional ADF ess. Similar resuls are obained using he IO2 procedure, suggesing all variables are non-saionary wih he excepion of MB. Second, he iming of any srucural break (T b, year and quarer) for each series using boh he IO and AO approaches are shown in Tables 2 and 3, respecively. Possible causes of he srucural breaks found in each series are presened in he las column of each able. The IO2 model shows ha hese daes closely approximae major policy changes occurring during financial deregulaion in he 1980s. The iming of he srucural changes based on he IO2 model (impacing on boh he inercep and he slope of each series) are represened by a solid line in Figure 1, wih a doed line for he AO model. Depending on he series in quesion here are beween 113 and 181 quarerly observaions covering he las hree o five decades in Ausralian economic hisory.

9 6 Table 1. Daa descripion, sources and ADF es resuls Descripion of series Variable Source Daa available ADF -saisic Opimal lag lengh 4 Inference Moneary base MB 1975: : Non-saionary Currency CUR 1959: : Non-saionary Reserve Bank of Ausralia Bullein M1 M1 (2005), Monhly Money and Credi 1975: : Non-saionary Saisics. M3 M3 1965: : Non-saionary Broad money BM 1976: : Non-saionary Consumer price index P Ausralian Bureau of Saisics (2005) Consumer Price Index, Ca. No : : Non-saionary 90-day bank acceped bills 10-year Treasury bonds RS Ausralian Bureau of Saisics 1955: : Non-saionary (2005) Modellers' Daabase, Ca. RL No : : Non-saionary Noes: Akaike Informaion Crierion (AIC) used o deermine he opimal lag lengh in he ADF equaion (log form). Trend and inercep included.

10 7 Table 2. IO model wih a change in boh inercep and slope Variable Lag ê βˆ θˆ γˆ αˆ αˆ Inference Break T b Possible causes Ln(MB) Saionary 1996q1 Ln(M1) Non-saionary 1982q4 Ln(RS) Non-saionary 1980q3 Ln(RL) Non-saionary 1979q4 Ln(M3) Non-saionary 1980q3 1996: Wallis Inquiry ino financial sysem esablished 1982: Removal of quaniaive conrol on bank lending Treasury bonds ender sysem inroduced Minimum erms on many oher fixed deposis removed End of quaniaive lending guidance 1980: Ineres rae ceiling on bank deposi raes lifed 1979: Esablishmen of he Campbell Commiee Treasury noes are offered a ender for he firs ime 1980: Ineres rae ceiling on bank deposi raes lifed Ln(BM) Non-saionary 1992q2 1992: 1991/92 Recession Review of credi risk managemen sysem conduced Noes: Where he number of observaions is more han 100 (infinie sample), he criical values a he 1% and 5% are and -5.05, respecively (Perron, 1997).

11 8 Table 3. AO model wih a change in slope only Variable K γ ˆ γ ˆ αˆ αˆ Ln(MB) Ln(M1) Ln(RS) Ln(RL) Ln(M3) Ln(BM) Inference Nonsaionary Nonsaionary Nonsaionary Nonsaionary Nonsaionary Nonsaionary Break T b 1982q3 1986q2 1986q3 1986q4 1984q1 1995q3 Possible causes 1982: End of quaniaive lending guidance The removal of minimum erms on many oher fixed deposis Treasury bonds ender sysem inroduced 1986: Ineres rae ceiling on new housing loans removed Sauory reserve deposis phased ou Non-bank financial insiuions permied o issue paymen orders 1984: Sock exchange deregulaed Saving banks offer cheque accouns Non-bank financial insiuions admied as foreign exchange dealers Bank deposi rae and mauriy resricions removed 1995: Banks allowed limied equiy in small/medium businesses Noes: Where he number of observaions is more han 100 (infinie sample), he criical values a he 1% and 5% are and -5.05, respecively (Perron, 1997).

12 9 Figure 1. Plos of he series and esimaed iming of srucural breaks Tb=1982q3 Tb=1996q Tb=1982q4 Tb=1986q Ln(MB/P) Ln(M1/P) Tb=1980q3 Tb=1986q Tb=1979q4 Tb=1986q Ln(RS) Ln(LR) Tb=1980q3 Tb=1984q Tb=1992q2 Tb=1995q Ln(M3/P) Ln(BM/P) Noe: The ime (T b ) of srucural breaks based on: (a) he IO2 model (impacing on boh he inercep and he slope of each series) is shown by a solid line (b) he AO model (impacing on he slope only) is indicaed by he doed line.

13 10 I is ineresing o observe ha he resuls of boh he IO2 and AO models indicae ha endogenously deermined srucural changes coincide wih he exensive program of financial deregulaion. Consider he example of he IO model (Table 2) and he M1 moneary measure. As indicaed, he mos major srucural break in his series (indicaing a significan change in boh he inercep and he slope) over he period occurred in 1982q4. This paricular break may be aribued o he gradual effecs of several policy changes during his ime, including: (i) he relaxaion of he mauriy resricions on cerificae of deposis; (ii) removal of some resricions on Ausralian overseas invesmens; (iii) removal of quaniaive conrols on bank lending; and (iv) inroducion of he new Treasury bonds ender sysem. In addiion, a sudden change in he slope of M1 as derived from he AO model occurred in 1986q2. One argumen is ha his paricular srucural break corresponds wih several policy changes in 1986 including: (i) he removal of ceiling raes on new home loans: (ii) he aboliion of sauory reserve deposis; and (c) regulaory permission for non-bank financial insiuions o issue paymen orders (Juner and Hawrey, 1997). As anoher example consider he M3 moneary measure. From he mid-1970s unil 1985, moneary policy was conduced in Ausralia by argeing he annual growh of M3. However, his policy was hen abandoned because deregulaion of he financial sysem had made M3 a misleading indicaor of he sance of moneary policy (Grenville, 1990). Table 3 and Figure 1 indicae ha his policy change caused a significan srucural break in M3 in 1984q1. I is also worh noing ha none of he subsequen policy changes resuled in such an obvious change in he slope of M3. A change in boh in he inercep and he slope of his series in 1980q3 is also deeced wih he IO model in Table 2. V. CONCLUSION This paper uses all available quarerly daa o ime endogenously he mos imporan srucural breaks in four moneary aggregaes and wo ineres rae series in he Ausralian economy. Boh he Innovaional Oulier (IO) (assuming gradual changes in inercep and/or slope) and he Addiive Oulier (AO) (assuming insananeous changes in inercep) models are used. The resuls indicae ha he mos significan srucural breaks deeced over he more han hiry year sample period correspond o policy changes associaed wih financial deregulaion in he 1980s.

14 11 Tha is, while here are oher evens ha may have affeced hese ime series over he sample period, major srucural change is concenraed in he period of financial deregulaion. This provides complemenary evidence o models employing exogenously imposed srucural breaks in he Ausralian macroeconomy. The empirical resuls based on hese models do no provide much evidence agains he null hypoheses of uni roos in hese series. In oher words, despie considering srucural breaks in all series, almos all moneary aggregaes and financial variables examined are found o be I(1). This is consisen wih he resuls obained by convenional ADF esing. However, while Perron s (1997) approach is he mos advanced mehod o endogenously deec he single mos significan srucural break, hese models are unable o idenify muliple srucural breaks. Since nonsaionariy esing wih muliple srucural breaks may yield conflicing resuls o convenional ADF ess, fuure work could concenrae on such clear refinemens.

15 12 REFERENCES Bai, J. and Perron, P.2 (2003) Criical values for muliple srucural change ess, Economerics Journal, 6(1), Ben David, and Papell, D.H, (1998) Slowdowns and Meldowns: poswar growh evidence from 74 counries, Review of Economics and Saisics, 28(2), Harris, R. Sollis, R. (2003) Applied Time Series Modelling and Forecasing, John Wiley, New York Juner, D.J. and Hawrey, K.M. (1997) Financial Markes Money and Risk, Fourh ediion, Addison Wesley Longman, Melbourne. Leybourne, S.J and Newbold, P. (2003) Spurious rejecions by coinegraion ess induced by srucural breaks, Applied Economics, 35(9), Lumsdaine, R. L., and Papell, D.H. (1997) Muliple rend breaks and he uni roo hypohesis, Review of Economics and Saisics, 79(2), Perron, P. (1989) The grea crash, he oil price shock, and he uni roo hypohesis, Economerica, 57(6), Perron, P. (1994) Uni roo and srucural change in macroeconomic ime series, In Rao. B. (ed.) Coinegraion for he Applied Economis, Macmillan, London. Perron, P. (1997) Furher evidence on breaking rend funcions in macroeconomic variables, Journal of Economerics, 80(2), Perron, P. and Vogelsang, T. (1992) Nonsaionariy and level shifs wih a applicaion o purchasing power pariy, Journal of Business and Economic Saisics 10, Zivo, E., and Andrews, D. (1992) Furher evidence on he grea crash, he oil price shock, and he uni roo hypohesis, Journal of Business and Economic Saisics 10(3),