Nonlinear Co-Integration Between Unemployment and Economic Growth in South Africa AndrewPhiri North-WestUniversity,SouthAfrica [email protected] Inthispaper,amomentumthresholdautoregressive(mtar)modelisused toevaluatenonlinearequilibriumreversionbetweenunemploymentand economicgrowthforSouthAfricandatabetweentheperiods2000–2013. Toattainthisobjectiveweestimatethefirst-differenceandthegapmodel variationsofOkun’sspecification.Forthelattermodelvariation,weem- ploythreede-trendingmethodstoobtaintherelevant‘gap’data;namely, theHodrick-Prescott(hp)filter,theBaxter-King(bk)filterandtheButter- worth(bw)digitalfilter.Acommonfindingfromourempiricalanalysisis thatOkun’slawholdsconcretelyforSouthAfricandataregardlessofthe modelspecificationorthede-trendingtechniquethatisused.Moreover, ouranalysisprovesthatunemploymentgrangercauseseconomicgrowth inthelong-run, aresultwhich mayaccount forthejobless-growth phe- nomenonexperiencedbySouthAfricaoverthelastdecadeorso. KeyWords:unemployment,economicgrowth,Okun’slaw,SouthAfrica, mtar model,nonlinearunitroottests,nonlinearco-integration, nonlinearGrangertests,Hodrick-Prescottfilter,Baxter-Kingfilter, Butterworthhigh-passfilter jel Classification: c22, c51, e23, e24 Introduction High economic growth in conjunction with low unemployment under a low inflation environment canbe deemedas the ultimateobjective of macroeconomic policy in South Africa. Over the last decadeor so, two prominentmacroeconomicpolicyframeworkshaveembodiedtheseob- jectives, those being, monetary policy’s ‘inflation-targeting’ regime and fiscal policy’s Acceleratedand Shared Growth Initiative of South Africa (asgisa). Implemented in February 2002 and still in use to date, the inflation-targetpolicyrulespecifiesthattheSouthAfricanReserveBank (sarb) should contain inflation at levels of between 3 and 6 percent, whereasthe asgisa initiativeseekstohalveunemploymentandattaina ManagingGlobalTransitions12(4):303–324 304 AndrewPhiri 6economicgrowthratebytheyear2014.Theassumedcompatibilityof theaforementionedpolicyobjectivesisinevitabledemonstratedasmon- etarypolicyinSouthAfricaisdesignatedtowardsmanipulatingnominal variables like interest rates and inflation as a means of influencing real variablessuchasoutputgrowthandemployment.Ultimately,thesuccess ofdisinflationpolicyisreflectedinitseffectonunemploymentandout- putgrowth.However,up-to-dateSouthAfricahasnotonlytomanaged to achieve arguably the highest economic growth rates in Africa since 1994, but the economy simultaneously boasts one of the highest youth unemploymentratesintheworld.SoeventhoughtheSouthAfricanRe- serveBank(sarb)canbecreditedforcontaininginflationwithinitsset target which has been accompanied with steadily improved economic growth, such acquired growth has been characterized by what is popu- larlyreferredtoasa‘joblessgrowth’syndrome(Hodge2009).Amystery iswarrantedsincethe‘joblessgrowth’phenomenoncontradictstheepic riseofunemploymentcausedbythesharpdeclineofrealoutputexperi- encedworldwideduringthegreatdepression.Therefore,aclassicalchal- lenge for academics and policymakers alike is to provide an adequate account of unemployment-growth correlations in the South African economy. The question regarding the linkage between economic growth and unemployment gained prominence after Okun (1962) depicted the ex- tent to which the unemployment rate is negatively correlated with out- put growth. By analyzing data over the period of 1947 to 1960, Okun (1962)documentedthatunemploymentintheUnitedStatestendstofall by a one percentage point for every 3 percentage point rise in output growth.Thereafter,theUnitedStateswasdubbedashavinganestimated ‘Okuncoefficient’of3andaplethoraofsubsequentauthorssoughttoes- timate Okun’s coefficient by either adopting a single-country approach (seeCaraiani2010;Ahmed,Khali,andSaeed2011),panel-dataapproach (seeDixonandShepard2002,1997;Laletal.2010)oramulti-regionalap- proach(seeFreeman2000;Adanu2005;VillaverdeandMaza2009).The appealofOkun’srelationshipisattributedtoitssimplicityanditsexten- siveempiricalsupportqualifiesittobelongatthecoreofmodernmacroe- conomics(JardinandGaetan2011).AsnotedbySilvapulle,Moosa,and Silvapulle(2004),estimatingtheOkuncoefficienthasimportantimplica- tionsforthebusinesscyclesinceitrelatesthelevelofactivityinthelabour markettothelevelofactivityintheproductmarket.WhilstOkun’slaw impliesthatmorelabouristypicallyrequiredforincreasedproductivity ManagingGlobalTransitions NonlinearCo-IntegrationBetweenUnemploymentandEconomicGrowth 305 levels,Okun’scoefficientservesasanindicationofthecostofunemploy- ment in terms of output growth (Noor, Nor, and Ghani 2007). And in consolidationwiththePhillipscurve;Okun’srelationshipassistsmacroe- conomicpolicyindeterminingtheoptimalordesirablegrowthrateasa prescriptionforreducingunemployment(Moosa1997).Overall,Okun’s law is recommended as ‘a rule of thumb’ which provides policymakers withanunderstandingofhowdifferentmarketsadjust,andthusallow- ingforcorrectpoliciestobeselectedwhenfacingshocks(Pereira,Bento inSilva2009). In reality, Okun’s law is more of a statistical relationship rather than a structural feature of the macroeconomy (Knotek 2007). The develop- ment of a pure theoretical foundation for Okun’s relationship has been largely neglected in the academic literature, such that empirically, no functionalform has beendominantly preferredto anyother on the ba- sis of theory (Weber and West 1996). As a consequence, the empirical examination of Okun’s law is typically subject to revisions with the co- movementbetweenoutputgrowthandunemploymentfrequentlybeing analyzedunderdifferentsettings.Sowhilethereisnocontentiononthe importanceofOkun’slaw,debateshaveevolvedontheeconometrictech- niques used to establish this relationship; how the cyclical components are extracted; and whether a dynamic or static specification is adopted (Turturean2007).Recently,thepossibilityofasymmetricbehaviourbe- tweeneconomicgrowthandtheunemploymentratehasaddedanewdi- mensioninthedevelopmentoftheacademicliterature.Takeforinstance JardinandGaetan(2011)whoconsiderasymmetriesinOkun’srelation- ship as being important because asymmetric behaviour can adequately accountforthevaryingeffectivenessofstructuralandstabilizationpoli- cies. Othercommentators,suchasGeldenhuysandMarnikov(2007),con- sidertheimpactofasymmetricbehaviouronpolicyforecastingpractices. In particular, these authors argue that if Okun’s relationship is indeed foundtobeasymmetric,forecastsbasedonlinearestimatesofOkun’sco- efficientcanleadtobiasederrorterms.Andyetanotherclusterofauthors can also be identified, who advocate on the necessity of incorporating asymmetriesinOkun’srelationshipasameansofreinforcingasymmetric behaviourinthePhillipscurve.Therationalebehindthislineofthought is that if Okun’s coefficient changes between regimes, then the sacrifice ratiosshouldalsochangebetweenregimes.Inotherwords,differentde- grees of gradualism in the disinflation process may imply different im- Volume12·Number4·Winter2014 306 AndrewPhiri pacts on unemployment for the same reduction in inflation (Beccarini andGros2008). Our study contributes to the literature by addressing the economic significance of asymmetric behaviour in Okun’s relationship for South Africandata.Tothisend,ourstudymakesuseofthemomentumthresh- old(mtar)autoregressiveframeworkofEndersandGranger(1998).The logicbehindthechoiceofouradoptedapproachcanbedescribedasfol- lows.EngleandGranger(1987)arguethatevidenceofunitrootsbetween apairoftimeseriesvariablesnecessitatestheuseofco-integrationanaly- sispriortotheestimationofanyregressionformedbythevariables.Ac- cordingtotheauthors,thepresenceofco-integrationwouldthenimply thatthevariablesfollowacommonlong-runtrendandthe ols estima- tionofthetimeserieswillnotyieldspuriousresults.Thisisanimportant implicationforourcasestudysincepreviousempiricalworkshavecau- tionedofunitroot I(1)behaviourinoutputgrowthandunemployment variablesforSouthAfricandata(seeHodge2006;BurgerandMarnikov 2006;GuptaandUliwingiye2010).Andyetitshouldalsobenotedthat these conclusions are based on studies which assume a linear data gen- eratingprocess(dgp)amongtheseries.Ofrecent,ithasbecomewidely acceptedthatstandardunitroottests,sufferfromlowpowerwhenalin- earapproximationofanotherwisenonlineartimeseriesisusedtoevalu- atetheintegrationpropertiesofatimeseries(EndersandGranger1998). A similar contention has risen for co-integration analysis, in which re- searchers like Enders and Dibooglu (2001) prove that the implicit as- sumption ofsymmetricadjustmentisproblematiciftheadjustmentto- wardslong-runequilibriumisnotlinear.Inparticular,theauthorsargue thatthepresenceofnonlinearitiesbetweenapairoftimeseriessignifiesa highprobabilityofnonlinearadjustmentprocessestowardsthelong-run equilibrium for the data. With this in mind, our paper probes into the possibilityofasymmetricbehaviourbetweentheunemploymentrateand outputgrowthusingthe mtar model.Wechoosethismodelbecauseit representsasimpleyetflexibleframeworkthatcansimultaneouslyfacili- tatefor(1)nonlinearunitroottests,(2)nonlinearco-integrationanalysis; and(3)nonlinearcausalityanalysis. Therefore,againstthisbackdrop,wepresenttheremainderofthepa- perasfollows.Thefollowingsectionofthepaperpresentstheempirical frameworkof the study whereas section four presents the empirical re- sults of the study. The paper is concluded in section five by providing policyrecommendationsandsuggestingavenuesforfutureresearch. ManagingGlobalTransitions NonlinearCo-IntegrationBetweenUnemploymentandEconomicGrowth 307 EmpiricalFramework OurpaperusestwoclassesofOkun’slawspecifications;namely,thefirst differences model and the gap model. To ensure that we obtain a bal- anced,robustviewontheestimationresults,wespecifytheOkun’sspec- ifications on both the direct and the reverse regressions of unemploy- mentonoutputgrowth.Forinstance,inspecifyingthe‘firstdifferences’ versionofOkun’slaw,thelinkbetweentheunemploymentrate(ur)and economicgrowth(gdp)isrepresentedas: ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎜⎜⎜⎜⎜⎜⎝Δgdpt⎟⎟⎟⎟⎟⎟⎠ = ⎜⎜⎜⎜⎜⎜⎝β1 0 ⎟⎟⎟⎟⎟⎟⎠⎜⎜⎜⎜⎜⎜⎝ Δurt ⎟⎟⎟⎟⎟⎟⎠+⎜⎜⎜⎜⎜⎜⎝ξt1⎟⎟⎟⎟⎟⎟⎠, (1) Δurt 0 β2 Δgdpt ξt2 whereΔisthefirstdifferenceoperatorsuchthatΔgdpt = gdpt −gdpt−1 and Δurt = urt − urt−1. On the other hand, the ‘gap model’ measures thesevariables in termsoftheir deviations fromlong-run trendsandis specifiedas: ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎜⎜⎜⎜⎜⎜⎝gdpct⎟⎟⎟⎟⎟⎟⎠ = ⎜⎜⎜⎜⎜⎜⎝β1 0 ⎟⎟⎟⎟⎟⎟⎠⎜⎜⎜⎜⎜⎜⎝ urtc ⎟⎟⎟⎟⎟⎟⎠+⎜⎜⎜⎜⎜⎜⎝ξt1⎟⎟⎟⎟⎟⎟⎠, (2) urtc 0 β2 gdpct ξt2 where urtc ≡ urt − urt* and gdpct ≡ gdpt − gdp*t are representative of the cyclical components of the unemployment rate and real output, re- spectively;withgdp*denotingameasureofpotentialoutputgapandur* t t theunemploymentgapvariable.Havingspecifiedourbaselinetheoreti- calmodels,wecanproceedtointroduceco-integrationanalysisamongst thevariables.We,therefore,takeheedofEndersandGranger(1998)and modelasymmetricadjustmentbetweentheunemploymentandrealout- put growth variables by allowing the residual deviations (i.e. ξti) from the long-run equilibrium of regressions (1) and (2) to behave as a tar process.Formally,theseresidualsaremodelledasfollows: (cid:8)p δξti = Itρ1ξt−1+(1−It)ρ2ξt−1+ βiΔξt−1+εt. (3) i=1 Inourpaper,weidentifyfourtypesofco-integrationrelationswhich govern the asymmetric dynamics within Okun’s law, namely; tar with a zero threshold; consistent tar with a nonzero threshold; mtar with azerothreshold;andconsistent mtar withanonzerothreshold.Inthe tar modelwithazerothreshold,theindicatorfunction,It,issetaccord- ingto: Volume12·Number4·Winter2014 308 AndrewPhiri ⎧ It = ⎪⎪⎪⎨⎪⎪⎪⎩01,,iiff\ξξtt−−11 <≥00 . (4) Underthe tar modelwithanonzerothreshold,wesetIt,as: ⎧ It = ⎪⎪⎪⎨⎪⎪⎪⎩01,,iiff\ξξtt−−11 <≥ττ , (5) whereτisthevalueofthethresholdvariable.EndersandGranger(1998) suggest the use of a grid search procedure, as demonstrated in Hansen (1997), to derive a consistent estimate of the threshold i.e. the thresh- oldestimateyieldingthelowest rss isconsideredthetruethresholdes- timate. The tar models are designed to capture potential asymmetric deepmovementsintheresidualsif,forexample,positivedeviationsare more prolonged than negative deviations (Enders and Dibooglu 2001). Enders and Granger (1998) and Caner and Hansen (2001) suggest that bypermittingtheHeavisideindicatorfunction,It,torelyonthefirstdif- ferencesof the residuals, Δξt−1, a mtar version of equation (11) can be developed.Theimplicationofthe mtar modelisthatcorrectionmech- anismdynamicsincebyusingΔξt−1,itispossibletoaccessifthemomen- tumoftheseriesislargerinagivendirectionrelativetothedirectionin thealternativedirection.Inotherwords,the mtar modelcaneffectively capture large and smooth changes in a series whereas the tar model showsthe‘depth’oftheswingsinequilibriumrelationship.Inmodelling mtar thresholdco-integrationwithazerothreshold,theindicatorfunc- tionMt,issetas: ⎧ Mt = ⎪⎪⎪⎨⎪⎪⎪⎩01,,iiff\ξξtt−−11 <≥00 . (6) Whileinthe mtar modelwithanonzerothreshold,Mt,issetas: ⎧ It = ⎪⎪⎪⎨⎪⎪⎪⎩01,,iiff\ξξtt−−11 <≥ττ . (7) Forboth tar and mtar specifications,EndersandSilkos(1998)de- monstratethatasufficientconditionforstationaryofξt−1 isthatρ1,ρ2 < 0.Ifξt−1isfoundtobestationary,theleastsquaresestimatesofρ1andρ2 haveanasymptoticmultivariatenormaldistributionforanygivenvalue ofaconsistentlyestimatedthreshold.Moreover,thenullhypothesisofno ManagingGlobalTransitions NonlinearCo-IntegrationBetweenUnemploymentandEconomicGrowth 309 co-integration(i.e.h : ρ = ρ = 0)canbeformallytestedusingastan- 01 1 2 dard F-statistic for both tar and mtar models. If the null hypothesis ofnoco-integrationisrejected,itispossibletotestforthenullhypoth- esis of symmetric adjustment (i.e. h : ρ = ρ ) against the alternative 02 1 2 ofasymmetricadjustment(i.e.h : ρ (cid:2) ρ )usingasimilarF-test.The 12 1 2 empiricalF-distributionforthenullhypothesis;ρ = ρ = 0istabulated 1 2 inEndersandDibooglu(2001)whereasEndersandSiklos(2001)report criticalvaluesfortestingthenullhypothesisofρ (cid:2) ρ .Ifbothnullhy- 1 2 pothesesofnoco-integrationandnoasymmetricco-integrationcanbe simultaneously rejected, the granger representation theorem is satisfied and thus an associated error correction model can be estimated for the pair of time series variables. Thus in validating the presence of thresh- old co-integration, the error correction model can be modified to take intoaccountasymmetriesasinBlakeandFomby(1997).Inourstudywe augmenteachofourthresholdco-integrationregressionswiththresholds errorcorrectionspecifications.Inparticular,the tar-tec modelcanbe expressedas: ⎛ ⎞ ⎜⎜⎜⎜⎜⎜⎝Δgdpt⎟⎟⎟⎟⎟⎟⎠ = λ11Itξt−1+λ12(1−It)ξt−1 Δurt (cid:8)p (cid:8)p + α1iΔgdpt−1+ β1iΔurt−1. (8) i=1 i=1 Whereasthe mtar-tec modelisspecifiedas: ⎛ ⎞ ⎜⎜⎜⎜⎜⎜⎝Δgdpt⎟⎟⎟⎟⎟⎟⎠ = λ21Mtξt−1+λ22(1−Mt)ξt−1 Δurt (cid:8)p (cid:8)p + α2iΔgdpt−1+ β2iΔurt−1, (9) i=1 i=1 where the indicator functions for the tar and mtar model specifica- tions are represented by It and Mt respectively. Through the above de- scribedsystemsoferrorcorrectionmodels,twotypesofjointhypotheses canbetested.Firstly,thepresenceofasymmetriesbetweenthevariables couldinitiallybeexaminedbyexaminingthesignsonthecoefficientsof the error correction terms. This involves testing the null hypothesis of h03: λi1ξt−1 = λi2ξt−1 against the alternative h13: λi1ξt−1 (cid:2) λi2ξt−1. The secondtypeofhypothesistestedisthatofgrangercausalityeffectswhich Volume12·Number4·Winter2014 310 AndrewPhiri relatively examines whether all Δgdpt−k and Δurt−k are statistically dif- ferentfromzero. Grangertests areused toexaminewhetherthe lagged values of one variable do not improve on the explanation or ‘granger- cause’ another variable. In particular, the null hypothesis that urt does notleadtogdptcanbedenotedas:h04:αi = 0,i = 1,...,k;whereasthe nullhypothesisthatgdpt doesnotleadtourt is:h05:βi = 0,i = 1,...,k. AllaforementionedhypothesesarebasedonastandardF-test.Further- more,threetypesofjointhypothesescanbeformedfromthe tec model. Firstly,grangercausalitytestscanbeimplementedbytestingwhetherall Δgdpt−k andΔurt−k arestatisticallydifferentfromzerobasedonastan- dardF-testandiftheλcoefficientsoftheerrorcorrectionarealsosignif- icant. EmpiricalAnalysis empirical data The data used in the empirical analysis consists of the annual percent- age change in the real gross domestic product which is gathered from theSouthAfricanReserveBank(sarb)onlinedatabasewhereastheun- employment rate for all persons aged above 15 years of age is collected fromvariousissuesofthequarterlylabourforcesurveys(qlfs)ascom- plied by Statistics South Africa (statssa). Our empirical analysis uses quarterlyadjusteddataobtainedfortheperiodsextendingfrom2000to 2014.Thechoiceofoursampleperiodandperiodicityreflectsthelimi- tations in the availability of the time-series data on unemployment and economicgrowthforSouthAfrica.Althoughitwouldbedesirabletoem- ploy a longer span of data, the available data provides the advantage of avoidingtheissueofpotentialstructuralbreaksrelatedtoSouthAfrica’s politicalandstructuralreformssuchasthoseexperiencedin1994.More- over, we take note that while our data is relatively short, it is, however, up-to-dateandfurthereliminatestheproblemofdataunreliabilityasso- ciatedwiththeSouthAfricanunemploymentseriesbefore2000.Further giventhatgrossdomesticproductisavailableonaquarterlybasisandthe unemploymentrateislimitedtohalf-yearlydata,weusecubicsplinein- terpolationtoconvertthehalf-yearlyunemploymentdataintoquarterly dataoverthesametimeperiod.Wefavourtheuseofcubicsplineinterpo- lationoverothertimeseriesdataconversiontechniquesduetoitscom- putationalaccuracyandstabilityofcomputation.Moreover,cubicspline interpolationssatisfythefurtherconditionattheendpoint. Asapartofourdataconstruction,weintroducethede-trendingmeth- ManagingGlobalTransitions NonlinearCo-IntegrationBetweenUnemploymentandEconomicGrowth 311 ods used to extractthe ‘potential output’ and ‘unemploymentgap’ vari- ables necessary to estimate the gap version of Okun’s specification. The constructionofthese‘gapvariables’isnecessarysincethereexistsnoob- servabledataonthetrendcomponentsoftheunemploymentandoutput growthvariables.Alsotakingintoconsiderationthatamajorityofthese de-trendingtechniquesarenotwithoutscepticism,itisstandardpractice toapplyavariety/differentde-trendingtechniquestoensurerobustness in the regressions analysis. Therefore in following along this course of reasoning,ourstudyconsidersthreealternativede-trendingtechniques, namelytheHodrick-Prescott(hp)filter;theBaxter-King(bk)filterand theButterworth(bw)digitalfilterasrespectivelyintroducedbyHodrick andPrescott(1997),BaxterandKing(1999);andPollock(2000).Thepur- pose of using these three de-trending techniques is to enable a robust analysisconcerningthesensitivityoftheestimatedOkun’scoefficientto thedifferentchoicesofourgapvariableestimates. unit root tests Intestingforunitroots,webeginonthesimplepremiseofsubjectinga univariatetimeseries,yt,tothefollowinggeneralizedautoregression: Yt = ϕyt−1+εt, εt ∼ N(0,σ2ε). (10) Heuristically,onecantestthenullhypothesisofaunitrootash :ϕ = 1 0 againstthealternativehypothesisofanotherwisestationaryseries.How- ever,aspreviouslydiscussed,thereexistsaproblemoflowpowerassoci- atedwithtraditionalunitroottestswhentheunderlyingdatagenerating processoftimeseriesisproventobeasymmetric.Therefore,inorderto accommodateasymmetricbehaviourintheunitroottestingprocedure, were-formulateregression(10)intermsoffirstdifferences.Thisenables ustofollowinpursuitofEndersandGranger(1998)andspecifytheunit root testing regressions for the tar model with a zero threshold and a consistentthresholdestimate,respectively,as: Δyt = εt(εt−1 < 0)+εt(εt−1 ≥ 0)+υt, (11) Δyt = εt(εt−1 < τ)+εt(εt−1 ≥ τ)+υt, (12) Whereas the mtar version of the unit root test regression with a zero thresholdandaconsistentthresholdestimatethresholdare,respectively, specifiedas: Δyt = εt(Δεt−1 < 0)+εt(Δεt−1 ≥ 0)+υt, (13) Volume12·Number4·Winter2014 312 AndrewPhiri table1 NonlinearUnitRootTests Variable Model Lag Asymmetrytest Unitroottest Decision (i.e.ρ =ρ ) (i.e.ρ =ρ =0) 1 2 1 2 gdp tar  . .*** LinearI(0) (.)* (.)*** NonlinearI(0) c-tar  .* .*** NonlinearI(0) (.)* (.)*** NonlinearI(0) mtar  . .*** LinearI(0) (.)** (.)*** NonlinearI(0) c-mtar  .* .*** NonlinearI(0) (.)* (.)*** NonlinearI(0) ur tar  . .* LinearI(0) (.)* (.)** NonlinearI(0) c-tar  . .* LinearI(0) (.)* (.)** NonlinearI(0) mtar  . .* LinearI(0) (.)* (.)** NonlinearI(0) c-mtar  . .* LinearI(0) (.)* (.)** NonlinearI(0) notes Significancelevelcodes:***,**and*denotethe,andsignificance levelsrespectively.Testsstatisticsforthefirstdifferencesofthevariables,i.e.Δgdptand Δurtaregiveninparenthesis. Δyt = εt(Δεt−1 < τ)+εt(Δεt−1 ≥ τ)+υt. (14) Thereafter,twohypothesescanbeformedfromregressions(11)–(14). Thefirsthypothesistestsforasymmetrieswithinthetimeseries.Tothis end,wetestthenullhypothesisofnoasymmetriceffectsash : ρ = ρ 00 1 2 againstthealternativehypothesisofanasymmetricdatageneratingpro- cess(i.e.h : ρ (cid:2) ρ ).Subsequenttotestingforasymmetriceffects,we 01 1 2 thenproceedtotestforunitrootbehaviourwithinthetimeseries.Prag- matically,thenullhypothesisofaunitrootistestedash :ρ = ρ = 0 10 1 2 against the alternative hypothesis of an otherwise stationary asymmet- ric process (i.e. h :ρ (cid:2) ρ (cid:2) 0). The aforementioned tests of asym- 10 1 2 metry and unit root behaviour are performed on time series variables of economic growth and the unemployment rate. The lag length of the thresholdmodelswhichfacilitatethesetestsaredeterminedbythe aic informationcriterion. As is evident from table 1, the empirical test results obtained for the time series in their levels are quite mixed. For instance, in scanning ManagingGlobalTransitions