Revista de Métodos Cuantitativos para la Economía y la Empresa E-ISSN: X Universidad Pablo de Olavide España

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1 Revisa de Méodos Cuaniaivos para la Economía y la Empresa E-ISSN: X ed_revmecuan@upo.es Universidad Pablo de Olavide España Glynn, John; Perera, Nelson; Verma, Reeu Uni Roo Tess and Srucural Breaks: A Survey wih Applicaions Revisa de Méodos Cuaniaivos para la Economía y la Empresa, vol. 3, junio, 2007, pp Universidad Pablo de Olavide Sevilla, España Available in: hp:// How o cie Complee issue More informaion abou his aricle Journal's homepage in redalyc.org Scienific Informaion Sysem Nework of Scienific Journals from Lain America, he Caribbean, Spain and Porugal Non-profi academic projec, developed under he open access iniiaive

2 REVISTA DE MÉTODOS CUANTITATIVOS PARA LA ECONOMÍA Y LA EMPRESA (3). Páginas Junio de ISSN: X. D.L: SE URL: hp:// Uni Roo Tess and Srucural Breaks: A Survey wih Applicaions Glynn, John Graduae School of Business Universiy of Wollongong Correo elecrónico: jglynn@uow.edu.au Perera, Nelson Graduae School of Business Universiy of Wollongong Correo elecrónico: nperera@uow.edu.au Verma, Reeu School of Economics Universiy of Wollongong Correo elecrónico: reeu@uow.edu.au ABSTRACT The heme of uni roos in macroeconomic ime series have received a grea amoun of aenion in erms of heoreical and applied research over he las hree decades. Since he seminal work by Nelson and Plosser (1982), esing for he presence of a uni roo in he ime series daa has become a opic of grea concern. This issue gained furher momenum wih Perron s 1989 paper which emphasized he imporance of srucural breaks when esing for uni roo processes. This paper reviews he available lieraure on uni roo ess aking ino accoun possible srucural breaks. An imporan disincion beween esing for breaks when he break dae is known or exogenous and when he break dae is endogenously deermined is explained. We also describe ess for boh single and muliple breaks. Addiionally, he paper provides a survey of he empirical sudies and an applicaion in order for readers o be able o grasp he underlying problems ha ime series wih srucural breaks are currenly facing. Keywords: uni roo, srucural breaks, muliple breaks. JEL classificaion: C12; C MSC: 62P20. Arículo recibido el 28 de mayo de 2007 y acepado el 6 de junio de

3 Conrases de raíces uniarias y cambios esrucurales: un esudio con aplicaciones RESUMEN El ema de las raíces uniarias en series emporales macroeconómicas ha recibido gran aención, ano desde el puno de visa eórico como de invesigación aplicada, en las úlimas res décadas. Desde el rabajo clave de Nelson y Plosser (1982), conrasar la presencia de una raíz en daos emporales ha llegado a ser un asuno de gran inerés. Esa cuesión ganó incluso preponderancia con el arículo de Perron de 1989, que desaca la imporancia de los cambios esrucurales al conrasar procesos de raíces uniarias. Ese rabajo revisa la lieraura disponible sobre conrases de raíces uniarias, eniendo en cuena los posibles cambios esrucurales. Se explica la diferencia enre conrasar cambios cuando la fecha del cambio es conocida (o exógena) y cuando el cambio es deerminado endógenamene. También describimos conrases ano para cambios simples como para cambios múliples. Además,elarículo revisa los esudios empíricos y da una aplicación para que los lecores puedan comprender los problemas subyacenes que se esán afronando en el esudio de las series emporales con cambios esrucurales. Palabras clave: raíces uniarias; cambios esrucurales; cambios múliples. Clasificación JEL: C12; C MSC: 62P20. 64

4 1. Inroducion During he las hree decades, he mehods of esimaion of economic relaionships and modeling flucuaions in economic aciviy have been subjeced o fundamenal changes. The mehod of esimaion of he sandard regression model, Ordinary Leas Square (OLS) mehod, is based on he assumpion ha he means and variances of hese variables being esed are consan over he ime. Variables whose means and variances change over ime are known as non-saionary or uni roo variables. Therefore, incorporaing non-saionary or uni roo variables in esimaing he regression equaions using OLS mehod give misleading inferences. Insead, if variables are non-saionary, he esimaion of long-run relaionship beween hose variables should be based on he coinegraion mehod. Since he esing of he uni roos of a series is a precondiion o he exisence of coinegraion relaionship, originally, he Augmened Dickey-Fuller (1979) es was widely used o es for saionariy. However, Perron (1989) showed ha failure o allow for an exising break 1 leads o a bias ha reduces he abiliy o rejec a false uni roo null hypohesis. To overcome his, Perron proposed allowing for a known or exogenous srucural break in he Augmened Dickey-Fuller (ADF) ess. Following his developmen, many auhors including, Zivo and Andrews (1992) and Perron (1997) proposed deermining he break poin endogenously from he daa. Lumsdaine and Papell (1997) exended he Zivo and Andrews (1992) model o accommodae wo srucural breaks. However, hese endogenous ess were criicized for heir reamen of breaks under he null hypohesis. Given he breaks were absen under he null hypohesis of uni roo here may be endency for hese ess o sugges evidence of saionariy wih breaks (Lee and Srazicich, 2003). Lee and Srazicich (2003) propose a wo break minimum Lagrange Muliplier (LM) uni roo es in which he alernaive hypohesis unambiguously implies he series is rend saionary. The objecive of he paper is o survey he recen developmen of uni roo hypoheses in he presence of srucural change a he unknown ime of he break. The salien feaure of he paper is o propose a reamen of his imporan opic in a non echnical way. The srucure for he res of paper is as follows. Secion 2 discusses he convenional uni roos ess, which do no ake ino accoun srucural breaks. Secion 1 This may be he change in he series as a resul some unique economic evens.

5 3 explains he uni roo esing ha akes ino accoun one srucural break. Uni roo esing ha akes ino accoun muliple srucural breaks are presened in Secion 4. In secion 5, he auhors review some empirical sudies and demonsrae he applicaion of he echniques presened in he previous secions. Finally, in secion 6, he auhors presen some concluding remarks. 2. Tradiional Uni Roo Tess Nelson and Plosser (1982) argue ha almos all macroeconomic ime series one ypically uses have a uni roo. The presence or absence of uni roos helps o idenify some feaures of he underlying daa generaing process of a series. In he absence of uni roo (saionary), he series flucuaes around a consan long-run mean and implies ha he series has a finie variance which does no depend on ime. On he oher hand, non-saionary series have no endency o reurn o long-run deerminisic pah and he variance of he series is ime dependen. Non-saionary series suffer permanen effecs from random shocks and hus he series follow a random walk. If he series is non-saionary and he firs difference of he series is saionary, he series conains a uni roo. The commonly used mehods o es for he presence of uni roos are he Augmened Dickey-Fuller (ADF) ess (Dickey and Fuller, 1979 and 1981). The main hrus of he uni roo lieraure concenraes on wheher ime series are affeced by ransiory or permanen shocks. This can be esed by he ADF model, which is primarily concerned wih he esimae ofα. In he following equaion, we es he null hypohesis of α = 0 agains he alernaive hypohesis of α < 0: y = u + β + αy + c y + ε k 1 i 1 (1) i= 1 where denoes he firs difference, y is he ime series being esed, is he ime rend variable, and k is he number of lags which are added o he model o ensure ha he residuals, ε are whie noise 2. Schwarz Bayesian Crierion (SBC) and Akaike Informaion Crierion (AIC) are used o deermine he opimal lag lengh or k. Nonrejecion of he null hypohesis implies ha he series is non-saionary; whereas he rejecion of he null indicaes he ime series is saionary. 2 This means ε has zero mean and consan variance ha is uncorrelaed wih ε s for s.

6 3. Uni Roo Tess in he presence of Srucural Break The debae on uni roo hypohesis underwen renewed ineres following he imporan findings of Nelson and Plosser (1982). The radiional view of he uni roo hypohesis was ha he curren shocks only have a emporary effec and he long-run movemen in he series is unalered by such shocks. The mos imporan implicaion under he uni roo hypohesis sparked by Nelson and Plosser (1982) is ha he random shocks have permanen effecs on he long-run level of macroeconomics; ha is he flucuaions are no ransiory. These findings were challenged by Perron (1989), who argues ha in he presence of a srucural break, he sandard ADF ess are biased owards he nonrejecion of he null hypohesis. Perron argues ha mos macroeconomic series are no characerized by a uni roo bu raher ha persisence arises only from large and infrequen shocks, and ha he economy reurns o deerminisic rend afer small and frequen shocks. According o Perron, Mos macroeconomic ime series are no characerized by he presence of a uni roo. Flucuaions are indeed saionary around a deerminisic rend funcion. The only shocks which have had persisen effecs are he 1929 crash and he 1973 oil price shock (1989, pp.1361). Perron s (1989) procedure is characerized by a single exogenous (known) break in accordance wih he underlying asympoic disribuion heory. Perron uses a modified Dickey-Fuller (DF) uni roo ess ha includes dummy variables o accoun for one known, or exogenous srucural break. The break poin of he rend funcion is fixed (exogenous) and chosen independenly of he daa. Perron s (1989) uni roo ess allows for a break under boh he null and alernaive hypohesis. These ess have less power han he sandard DF ype es when here is no break. However, Perron (2005) poins ou ha hey have a correc size asympoically and is consisen wheher here is a break or no. Moreover, hey are invarian o he break parameers and hus heir performance does no depend on he magniude of he break. Based on Perron (1989), he following hree equaions are esimaed o es for he uni roo. The equaions ake ino accoun he exisence of hree kinds of srucural breaks: a crash model (2) which allows for a break in he level (or inercep) of series; a changing growh model (3), which allows for a break in he slope (or he

7 rae of growh); and lasly one ha allows boh effecs o occur simulaneously, i.e one ime change in boh he level and he slope of he series (4). p = 0 + α1du + d( DTB) + β + ρx 1 + φi x 1 i= 1 x α + e (2) p = 0 + γdt * + β + ρx 1 + φi x 1 i= 1 x α + e (3) p = 0 + α1du + d( DTB) + γdt + β + ρx 1 + φi x 1 i= 1 x α + e (4) Where he inercep dummy DU represens a change in he level; DU =1 if ( > TB) and zero oherwise; he slope dummy DT (also DT *) represens a change in he slope of he rend funcion; DT* = -TB (or DT *= if > TB) and zero oherwise; he crash dummy (DTB) = 1 if = TB +1, and zero oherwise; and TB is he break dae. Each of he hree models has a uni roo wih a break under he null hypohesis, as he dummy variables are incorporaed in he regression under he null. The alernaive hypohesis is a broken rend saionary process. However, Perron s known assumpion of he break dae was criicized, mos noably by Chrisiano (1992) as daa mining. Chrisiano argues ha he daa based procedures are ypically used o deermine he mos likely locaion of he break and his approach invalidaes he disribuion heory underlying convenional esing. Since hen, several sudies have developed using differen mehodologies for endogenously deermining he break dae. Some of hese include Banerjee, Lumisdaine and Sock (1992), Zivo and Andrews (1992), Perron and Vogelsang (1992), Perron (1997) and Lumsdaine and Papell (1998). These sudies have shown ha bias in he usual uni roo ess can be reduced by endogenously deermining he ime of srucural breaks. Zivo and Andrews (1992) endogenous srucural break es is a sequenial es which uilizes he full sample and uses a differen dummy variable for each possible break dae. The break dae is seleced where he -saisic from he ADF es of uni roo is a a minimum (mos negaive). Consequenly a break dae will be chosen where he evidence is leas favorable for he uni roo null. The criical values in Zivo and Andrews (1992) are differen o he criical values in Perron (1989). The difference is due o ha he selecing of he ime of he break is reaed as he oucome of an esimaion procedure, raher han predeermined exogenously.

8 Even hough Banerjee, Lumisdaine and Sock (1992) use endogenous srucural break es, he ess are rolling and recursive ess. The numbers of breaks are deermined by non-sequenial ess which use sub-samples. This can be viewed as no having used he full informaion se, which may have implicaions for he power of hese ess. This work was exended by Perron and Vogelsang (1992) and Perron (1997) who proposed a class of es saisics ha allows for wo differen forms of srucural break. These are he Addiive Oulier (AO) and Innovaional Oulier (IO) models. The AO model allows for a sudden change in mean (crash model) while he IO model allows for more gradual changes. Perron and Vogelsang (1992, pp.303) argue ha hese ess are based on he minimal value of saisics on he sum of he auoregressive coefficiens over all possible breakpoins in he appropriae auoregression. While Perron (1997, pp. 356), 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 under a less sringen assumpion". Perron and Vogelsang (1992) applied hese wo models for non-rending daa (raw daa), while Perron (1997) modified hem for use wih rending daa. Applying he procedure for esing he uni roo hypohesis, which allows for he possible presence of he srucural break, has a leas wo advanages. Firs, i prevens yielding a es resul which is biased owards non-rejecion, as suspeced by Perron (1989). Second, since his procedure can idenify when he possible presence of srucural break occurred, hen i would provide valuable informaion for analyzing wheher a srucural break on a cerain variable is associaed wih a paricular governmen policy, economic crises, war, regime shifs or oher facors. However, wo imporan issues need o be raised here. Firsly, he power of hese ess has been quesioned by Perron himself and ohers. The issue has been raised by some auhors o he rade-off beween he power of he es and he amoun of informaion incorporaed wih respec o he choice of break poin (Perron 1997, pp.378). Secondly, hese ess only capure he single mos significan break in each variable, raising he quesion: wha if here are muliple breaks in each individual variable? We now urn our discussion o muliple breaks in a ime series.

9 4. Muliple Srucural Breaks Several sudies 3 argue ha only considering one endogenous break is insufficien and leads o a loss of informaion when acually more han one break exiss (Lumsdaine and Papell (1997). Lumsdaine and Papell (1997) inroduce a procedure o capure wo srucural breaks and argue ha uni roos ess ha accoun for wo significan srucural breaks are more powerful ha hose ha allow for a single break. Lumsdaine and Papell exend he Zivo and Andrews (1992) model allowing for wo srucural breaks under he alernaive hypohesis of he uni roo es and addiionally allow for breaks in level and rend. Ohers who have considered muliple breaks are Clemene, Monañés and Reyes (1998) who base heir approach on Perron and Vogelsang (1992) bu allow for wo breaks. Ohara (1999) uilizes an approach based on sequenial -ess of Zivo and Andrews o examine he case on m breaks wih unknown break daes. He provides evidence ha uni roo ess wih muliple rend breaks are necessary for boh asympoic heory and empirical applicaions. Papell and Prodan (2003) propose a es based on resriced srucural change, which explicily allows for wo offseing srucural changes. These endogenous break ess ha allow for he possibiliy of one or muliple breaks; Zivo and Andrews, Banerjee e al., Perron (1997), Lumsdaine and Papell (1997) and Ohara (1999) do no allow for break(s) under he null hypohesis of uni roo and hus derive heir criical values accordingly 4. This may poenially bias hese ess. Nunes e al (1997) show ha his assumpion leads o size disorions in he presence of a uni roo wih a break and Perron (2005, pp.55) suggess ha here may be some loss of power. Furhermore, Lee and Srazicich (2003) demonsrae ha when uilizing hese endogenous break uni roo ess, researchers migh conclude ha he ime series is rend saionary when in fac he series is non-saionary wih break(s). 3 Ben-David e al (2003) argue ha failure o allow for muliple breaks can cause he non-rejecion of he uni roo null by hese ess which incorporae only one break. Lumsdaine and Papell (1997) argue ha consideraion of only one endogenous break may be no sufficien and under such circumsances i could lead o loss of informaion. Maddala and Kim (2003) believe ha allowing for he possibiliy of wo endogenous break poins provides furher evidence agains he uni roo hypohesis. 4 This hypohesis differs from Perron s (1989) exogenous break uni roo ess, which allows for he possibiliy of a break under boh he null and he alernaive hypohesis.

10 In his regard spurious rejecions may occur. Thus, as poined ou by Lee and Srazicich (2003), a careful inerpreaion of resuls in empirical work is required. The minimum Lagrange Muliplier (LM) uni roo es proposed by Lee and Srazicich (2003) 5 no only endogenously deermines srucural breaks bu also avoids he above problems of bias and spurious rejecions. Furhermore, he Lee and Srazicich (2003) procedure corresponds o Perron s (1989) exogenous srucural break (Model C) wih change in he level and he rend. Lee and Srazicich s (2003) 6 model allows for wo endogenous breaks boh under he null and he alernaive hypohesis. They show ha he wo-break LM uni roo es saisic which is esimaed by he regression according o he LM principle will no spuriously rejec he null hypohesis of a uni roo. 5. Empirical Sudies In his secion, we, firsly, review he work of many auhors based on he daa se used by Nelson and Plosser (1982). Secondly, we review he sudies by some auhors on differen daa ses from various counies. Finally, we apply he ess discussed in he previous secions o Indian economic daa. Nelson and Plosser Daa Using annual daa for 14 macroeconomic variables from he Unies Saes of America over he period 1909 o 1970, Nelson and Plosser (1982) could no rejec he uni roo hypohesis wih he sandard ADF es for 13 of hem including Gross Naional Produc (GNP). They conclude ha hese series behave more like a random walk han like ransiory deviaions from seadily growing rend. This led many researchers o believe ha ime series are influenced by he number of permanen shocks. Subsequen empirical findings such as Sulz and Wasserfallen (1985) and Wasserfallen (1986) suppored he uni roo hypohesis in he sense ha mos of he US macroeconomic variables are no saionary a level. Perron (1989) using he Nelson and Plosser daa se allows for a known single break dae mehodology o es for he presence of uni roo. He chooses he sock 5 Iniially, Amsler and Lee (1995) designed heir invarian Lagrange Muliplier (LM) uni roo es wih one exogenous break. 6 If only one break is significan, Srazicich e al. (2004) recommend running he one-break LM uni roo es proposed by Lee and Srazicich (2004).

11 marke crash of 1929 as a break poin ha permanenly changed he level of series. Peron s resul challenged mos of Nelson and Plosser s conclusions. He rejecs he uni roo null for 11 series ha Nelson and Plosser found o be non-saionary. The resuls confirmed he view ha where here is a srucural break, he ADF ess are biased owards he non-rejecion of he uni roo. He proposes ha such a series are beer described as saionary around a rend wih a srucural break in Perron also applies he same es using quarerly poswar real GNP series for he US economy from1947:1 o 1986: III. He includes a one-ime change in he slope of he deerminisic rend in 1973 due o he oil price shock. The quarerly GNP series is also found o be saionary. Zivo and Andrews (1992) who es for a single endogenous break dae find less evidence agains he uni roo hypohesis han Perron (1989) does. Zivo and Andrews provide evidence ha confirmed Nelson and Plosser s findings, in he sense ha he resuls are mosly in favour of he inegraed model. Zivo and Andrews (1992) rejec he uni roo a he five percen significance level for only hree ou of 13 variables using he Nelson and Plosser daa. However, he resuls for nominal GNP, real GNP and indusrial producion are consisen wih Perron s as hese variables are rejeced even afer he break was endogenously deermined. Lumsdaine and Papell (1997) re-examine he Nelson and Plosser daa for wo endogenous breaks, finding more evidence agains uni roos han Zivo and Andrews bu less han Perron (1989). Using finie-sample criical values, hey rejec he uni roo null for five series a he five percen significance level, he hree series found by Zivo and Andrews plus employmen and capia real GNP. As suggesed by various auhors, hese endogenous ess have some size problems as he break(s) are considered only under he alernaive hypohesis. Lee and Srazicich (2003) also applied heir wo-break minimum LM uni roo es o Nelson and Plosser s (1982) daa and compared i wih he wo-break Lumsdaine and Papell es. They find sronger rejecions of he null using he Lumsdaine and Papell es han he LM es. A he five percen significance level, hey rejec he null for six series wih he Lumsdaine and Papell es and four series wih he LM es. Only he uni roo null of indusrial producion and he unemploymen rae are rejeced by boh he Lumsdaine and Papell and LM ess. Furhermore, Lee and Srazicich poin ou ha he null is rejeced a he five percen

12 significance level for real GNP, nominal GNP, per-capia real GNP and employmen using he Lumsdaine and Papell es, bu he null for hese variables is only rejeced a he higher significance level wih he LM es. A summary of he uni roo ess using he Nelson and Plosser daa se is given below in Table 1. Table 1: Uni Roo Tess wih he Nelson and Plosser s Daa (1982) Se Empirical Sudies by: Nelson and Plosser (1982) Perron (1989)** Model Uni Roo (wih possible breaks) Saionary (wih possible breaks) ADF es wih no break 13 1 Exogenous wih one break Zivo and Andrews Endogenous wih one (1992)* break Lumsdaine and Papell Endogenous wih wo (1997)* breaks Lee and Srazicich Endogenous wih wo (2003)** breaks * Assume no break(s) under he null hypohesis of uni roo. ** Assume break(s) under boh he null and he alernaive hypohesis Oher sudies There have been a number of oher sudies ha es for an endogenous one break model in boh he inercep and slope. These include Raj (1992) who ess for per capia real Gross Domesic Produc (GDP) for nine counries; Perron (1994) ess for real GDP for 11 counries; and Ben-David and Papell (1995) ess for boh aggregae and per capia real GDP for 16 counries. These sudies rejec he null of uni roo for half he counries. In comparison, Ben-David, Lumsdaine and Papell (2003) apply he Lumsdaine and Papell (1997) approach for wo srucural breaks o an inernaional daase for 16 counries. They rejec he uni roo hypohesis for hreequarers; 24 ou of 32 cases. This is fify percen more rejecions han in models ha allow for a single break. Banerjee, Lumsdaine, and Sock (1992) using poswar daa for seven OECD counries, were no able o rejec he uni roo hypohesis for five counries (France, Germany, Ialy, Unied Kingdom, and US). However for Canada and Japan, he uni roo is rejeced agains he alernaive of a saionary broken rend.

13 Ghaak (1997) ess he uni roo hypohesis under srucural breaks for 12 macro-economic ime series daa for India for he period He finds ha he convenional ADF ess allowing for no srucural breaks canno rejec he uni roo hypohesis for any of he series supporing Nelson and Plosser (1982). Allowing for exogenous breaks in he level and rae of growh, Ghaak finds ha Perron s (1989) ess rejec he uni roo hypohesis for hree series. The Zivo and Andrews ess (1992) for endogenous breaks for India confirm he Perron s es and lead o he rejecion of he uni roo null hypohesis for hree more series. Srazicich e al (2004) apply he endogenous wo-break LM uni roo es for annual daa on per capia GDP for 15 OECD counries for he period o deermine if per capia incomes are sochasically converging. They find ha 10 of he 15 log relaive income series rejec he null of uni roo a he en percen significance level, concluding ha significan suppor for income convergence among OECD counries. Srazicich e al (2004) find sronger suppor for convergence han previous sudies which are conduced wihou srucural breaks. Applicaion o Indian Daa In his secion, we use Indian daa from 1950 o 2005 o illusrae he esing of uni roo hypohesis wih srucural breaks. The daa includes annual Gross Domesic Savings (GDS), Gross Domesic Invesmen (GDI) and Goss Domesic Produc (GDP). The firs sage ess for uni roo wihou allowing for any srucural breaks. The empirical evidence repored in Table 2 indicaes ha he ADF es for GDS and GDI are saionary while he uni roo null for GDP canno be rejeced a he five percen significance level. However, he criicism of he convenional ADF mehod was ha he failure o allow for exising breaks leads o a bias ha reduces he abiliy o rejec a false uni roo null hypohesis. Therefore, in he nex sage, we es wheher he uni roo ess for he variables were biased because possible breaks in he series were ignored. We consider wo cases: (1) one-break endogenous model (Perron 1997); and (2) wobreak endogenous model (Lee and Srazicich 2003). We rejec he uni roo null for GDP wih boh one and wo-break models a he five percen significance level. Thus, he GDP daa for India suppors Perron s (1989) findings ha failure o allow for an

14 exising break leads o a bias ha reduces he abiliy o rejec a false uni roo null hypohesis. Table 2: Uni Roo Tess wih Indian Daa Variables ADF Tess Perron (97) Perron (97) Lee and Sraizich IO Model* AO Model* (2003) ** LGDS Saionary Saionary Saionary Saionary wih wo wih one break wih one break breaks LGDI Saionary Saionary Saionary Saionary wih wo wih one break wih one break breaks LGDP Uni roo Saionary Saionary Saionary wih wo wih one break wih one break breaks * Assume no break under he null hypohesis of uni roo. In he IO model (Innovaional Oulier model), changes are assumed o ake place gradually, allowing for a break in boh he inercep and slope and in he AO model (Addiive Oulier), changes are assumed o ake place rapidly, allowing for a break in he slope. ** Assume breaks under boh he null and he alernaive hypohesis. 6. Concluding Remarks The main objecive of he paper has been o review he recen developmens in esing of he uni roo hypoheses in he presence of srucural change. This survey reveals ha here is a significan amoun of lieraure ha has focused on he uni roo hypohesis in he presence of srucural change. The original, Augmened Dickey- Fuller ess was criicized on he basis of a failure o allow for an exising break leading o a bias ha reduces he abiliy o rejec a false uni roo null hypohesis. To overcome his, Perron (1989) iniially proposed a one known or exogenous srucural break in he Augmened Dickey-Fuller ess. As a resul of he personal judgmen involved in deermining he breaks, Zivo and Andrews (1992) and Perron (1997) proposed deermining he break poin endogenously from he daa. Lumsdaine and Papell (1997) exended he Zivo and Andrews (1992) model o allow for wo srucural breaks. Unlike Perron s (1989) null hypohesis, hese endogenous ess assume no breaks under he uni roo null. Given he breaks are absen under he null hypohesis of uni roo here may be endency for hese ess o sugges evidence of saionariy wih breaks (Lee and Srazicich, 2003). The wo-break Lee and Srazicich (2003) procedure no only allows for he breaks o be deermined endogenously from he daa bu breaks are allowed under boh he null and he alernaive hypohesis.

15 The secondary objecive of he paper was o review empirical sudies based on he Nelson and Plosser (1982) daa and oher sudies. Nelson and Plosser (1982) canno rejec he uni roo hypohesis wih he sandard ADF es for 13 of hem including GNP. Perron (1989) using he Nelson and Plosser daa se allows for a known single break dae as he sock marke crash of 1929 rejecs he uni roo null for 11 series ha Nelson and Plosser found o be non-saionary. Zivo and Andrews (1992) who es for a single endogenous break dae find evidence ha confirmed Nelson and Plosser s findings, in he sense ha he resuls are mosly in favour of he inegraed model. Zivo and Andrews (1992) rejec he uni roo a he five percen significance level for only hree ou of 13 variables using he Nelson and Plosser daa. Lumsdaine and Papell (1997) re-examine he Nelson and Plosser daa for wo endogenous breaks, finding more evidence agains uni roos han Zivo and Andrews bu less han Perron (1989). Lee and Srazicich (2003) also applied heir wo-break minimum LM uni roo es o Nelson and Plosser s (1982) daa and compared i wih he wo-break Lumsdaine and Papell es. They find sronger rejecions of he null using he Lumsdaine and Papell es han he LM es. The empirical evidence based on he Indian daa shows ha savings and invesmen series are saionary wih a break. This is consisen wih he resuls obained by he convenional ADF uni roo es wihou a break. However, GDP is found o be non- saionary using he convenional ADF es, bu saionary wih breaks a he five percen level wih boh Perron s (1997) one break model and Lee and Srazicich (2003) wo break model. We conclude ha here is no consensus on he mos appropriae mehodology o perform uni roo ess or no consensus abou he empirical resuls of uni roo ess has emerged from his survey. An imporan poin o noe here is ha esing for srucural breaks when he series is oherwise non-saionary will affec wheher here is evidence of a srucural break. 7 The developmen of esing for uni roos wih srucural breaks in he univariae framework raises a quesion of incorporaion of breaks in he coinegraion framework. The basic quesion here is how we can incorporae breaks of each ime series ino he coinegraion framework. The developmen in his area is very limied 7 See Perron (2005).

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