MODELLING STRUCTURAL BREAKS IN THE US, UK AND JAPANESE UNEMPLOYMENT RATES. Guglielmo Maria Caporale Brunel University, London

Transcription

1 MODELLING STRUCTURAL BREAKS IN THE US, UK AND JAPANESE UNEMPLOYMENT RATES Guglielmo Maria Caporale Brunel Universiy, London Luis A. Gil-Alana * Universiy of Navarra April 006 Absrac In his paper we use a general procedure o deec srucural breaks a unknown poins in ime which allows for differen orders of inegraion and deerminisic componens in each subsample (see Gil-Alana, 006). Firs, we exend i o he non-linear case, and show by means of Mone Carlo experimens ha he procedure performs well in a non-linear environmen. Second, we apply i o es for breaks in he unemploymen rae in he US, he UK and Japan. Our resuls shed some ligh on he empirical relevance of alernaive unemploymen heories for hese counries. Specifically, a srucuralis inerpreaion appears more appropriae for he US and Japan, whils a hyseresis model accouns beer for he UK experience (and also for he Japanese one in he second subsanple). We inerpre hese findings in erms of differen labour marke feaures. Keywords: Unemploymen, Srucural Breaks, Fracional Inegraion. JEL Classificaion: C3, E3 Corresponding auhor: Professor Guglielmo Maria Caporale, Brunel Business School, Brunel Universiy, Uxbridge, Middlesex UB8 3PH, UK. Tel.: +44 (0) Fax: +44 (0) Guglielmo-Maria.Caporale@brunel.ac.uk * The second auhor graefully acknowledges financial suppor from he Miniserio de Ciencia y Tecnologia (SEC , Spain).

2 . Inroducion In his paper we es for he exisence of breaks a unknown poins in ime in he US, UK and Japanese unemploymen raes by applying a procedure which is an exension of ha inroduced by Bai and Perron (998). Our conribuion is wofold. The firs is of a mehodological naure. As in Bai and Perron (998), our approach is based on he leas square principle. However, i is more general, since i allows for differen (fracional) orders of inegraion as well as differen deerminisic rends in each subsample. Furher, i allows for non-linear srucures. Incorporaing non-lineariies ino a fracional inegraion framework wih breaks a unknown poins in ime has no been aemped before, and represens a mehodological innovaion. We invesigae he properies of our es in he non-linear case by means of Mone Carlo simulaion echniques. The second conribuion is o provide useful empirical evidence o discriminae among differen heories of unemploymen. Noe ha under hyseresis (or persisence see, e.g., Blanchard and Summers, 986, 987 and Cross, 987)) he order of inegraion (denoed by d) should be equal o or close o, whils infrequen breaks would give suppor o he srucuralis view (Phelps, 994). On he oher hand, a value of d close o 0 would favour NAIRU heories (see, e.g., Friedman, 968). We obain empirical resuls using our mehod for esing for breaks, and inerpre he findings in erms of differences in he srucure of he labour markes of he counries we analyse. The layou of he paper is as follows. Secion briefly reviews he recen empirical lieraure esing alernaive heories of unemploymen. Secion 3 describes he economeric approach. Secion 4 repors Mone Carlo evidence on he performance of our es in he non-linear case. Secion 5 presens he empirical resuls. Secion 6 summarises he main findings and offers some concluding remarks.

3 . Tesing unemploymen heories: a brief review of he lieraure Alernaive unemploymen heories have differen implicaions for he ime series properies of unemploymen. For insance, he naural rae heory (see Friedman, 968, and Phelps, 967, 968) implies ha he unemploymen rae should flucuae around a saionary equilibrium level (he naural rae, also known as NAIRU), which is deermined by economic fundamenals. In srucuralis models (see Phelps, 994) he naural rae is endogenised : as in NAIRU models, unemploymen is viewed as having an equilibrium level o which i generally revers when hi by shocks, bu i is also hough o be subjec o infrequen srucural breaks, resuling from changes in economic fundamenals, which affec he equilibrium iself. Hence he unemploymen series should be saionary provided one allows for breaks. However, he adequacy of boh hese heories o accoun for he behaviour of unemploymen has been quesioned in recen decades, owing o he observed high persisence of unemploymen in Europe. Therefore, hyseresis models have been developed (see Blanchard and Summers, 986, 987, and Barro, 998), which characerise unemploymen as a pahdependen variable, wih emporary shocks having permanen or highly persisen effecs. The implicaion is ha he unemploymen rae should be a sochasic process wih long memory, exhibiing a (near) uni roo. Several empirical papers have used ime series and panel echniques o discriminae beween he differen unemploymen heories. Iniially, sandard uni roo ess (such as Augmened Dickey-Fuller (ADF, 979) or Phillips-Perron, 988) were carried ou (see, e.g., Blanchard and Summers, 986, and Alogoskoufis and Manning, 988), he resuls generally being consisen wih he hyseresis hypohesis. Gordon (989) defined full hyseresis as he case of a uni roo and persisence as AR saionariy, and did no find any evidence of full hyseresis in five counries (France, Germany, USA, Japan and he UK) for he ime period Graafland (99) concluded ha, in he 80s, he labour marke in he Neherlands

4 was characerised by a high and persisen level of unemploymen. Lopez e al. (996) repored ha monhly unemploymen in Spain (976M6-994M0) was consisen wih hyseresis. No (996) did no find evidence of hyseresis in Canada, while Wilkinson (997) did. Subsequen sudies allowed for srucural breaks as well (see, e.g., Michell, 993, Bianchi and Zoega, 998, and Papell e al, 000), using, for insance, he mehod developed by Zivo and Andrews (99). The evidence presened in hese papers mosly gave suppor o srucuralis raher han hyseresis heories, as i suggesed ha unemploymen can be adequaely modelled as a saionary series wih an infrequenly changing equilibrium level. In order o deal wih he well-known problem of he low power of sandard uni roo ess (see Campbell and Perron, 99 and DeJong, 99), more recen sudies have performed panel uni roo ess. Again, some of hese conribuions do no address he issue of possible breaks examples are he papers of Song and Wu (998) and Leon- Ledesma (00), where ess developed by Levin, Lin and Chu (00, LLC hereafer) and Im, Pesaran and Shin (003) respecively are implemened. In mos cases, such sudies conclude ha hyseresis heories are mos appropriae for he European experience, whils NAIRU models appear o work beer for he US. By conras, oher papers ake ino accoun he possibiliy of breaks in a panel conex. Prominen examples are Murray and Papell (000) and Srazicich, Tieslau and Lee (00), applying o OECD daa, respecively, he LLC es and a panel LM -saisic wih up o wo level breaks inroduced by Im, Lee and Tieslau (005). Allowing for breaks is generally found o lead o a rejecion of he hyseresis hypohesis, and o be consisen insead wih srucuralis explanaions of he behaviour of unemploymen. Various heoreical models have been pu forward o endogenise he naural rae of unemploymen. They rely alernaively on produciviy growh (Pissarides, 990), real ineres raes (Blanchard, 999), sock prices (Phelps, 999), insiuional variables (Nickell, 998 and Nickell and Van Ours, 000), or 3

5 he ineracion beween insiuional and macroeconomic variables (Blanchard and Wolfers, 000). Anoher recen srand of he lieraure has exploied new developmens in economerics o sudy unemploymen persisence using fracionally inegraed (ARFIMA) models (see, for insance, Tschernig and Zimmermann, 99; Crao and Rohman, 996; Gil- Alana, 00a, 00; ec.). This approach, unlike earlier ones focusing exclusively on ineger degrees of differeniaion, i.e., d = 0 (saionariy) and d = (nonsaionariy), has he advanage of allowing for fracional degrees of inegraion. The presen sudy falls ino he same caegory, and adops a framework which enables us o invesigae he relevance of he hree ypes of unemploymen heories menioned above; since i allows for fracional orders of inegraion, i is appropriae for boh saionary processes (NAIRU models), and highly persisen/nonsaionary ones (hyseresis hypohesis), and by incorporaing srucural breaks i can also be used o model processes exhibiing regime change (srucuralis heories). For insance, suppose ha i is found ha, as a resul of including a break, he degree of persisence appears o be differen in he wo subsamples, i.e. under one regime shocks have persisen hough no permanen effecs on he unemploymen rae, (i.e., d < ) whils under he oher hose effecs are permanen (d ). This would indicae ha he behaviour of unemploymen is well capured by srucural and hyseresis models respecively in he wo subsamples, shedding ligh on heir empirical relevance. Non-lineariies in he unemploymen rae are also well documened. Specifically, unemploymen has been found o rise faser in recessions han i falls during recoveries (see, e.g., Rohman, 99 for he US case). Possible explanaions are asymmeries in adjusmen coss (Benolilla and Beroli, 990), job desrucion (Caballero and Hammour, 994), and capial desrucion (Bean, 989). Such non-lineariies have been modelled using Markov-swiching models (see, e.g., Bianchi and Zoega), Smooh Transiion 4

6 AuoRegressive (STAR) models (see, e.g., Skalin and Teräsvira, 00), or a non-linear fracional inegraion framework (see Caporale and Gil-Alana, 005). Given heir possible imporance, in he nex secion we exend he esing procedure for breaks used by Gil- Alana (006) in order o allow for non-linear srucures. 3. The economeric approach In his secion we presen a procedure ha enables us o examine he saionariy/nonsaionariy naure of he series of ineres in a very general framework. Firsly, insead of resricing ourselves o he sandard I(0) (saionariy) or I() (nonsaionariy) cases, we consider he possibiliy of fracional orders of inegraion. Assuming ha a sequence {u, = 0, ±, } is I(0), defined as a covariance saionary process wih specral densiy funcion ha is posiive and finie, we define an I(d) process as: d ( L) x = u, =,,..., () where d can be any real number. These processes were iniially inroduced by Robinson (978), Granger (980, 98) and Hosking (98), and hey have been widely employed in recen years o describe he dynamic behaviour of economic and financial daa. (Diebold and Rudebusch, 989; Baillie, 996; Gil-Alana and Robinson, 997). Secondly, our framework also allows for he inclusion of deerminisic erms, like inerceps, linear rends or even non-linear srucures of he Threshold AuoRegressive (TAR) or Momenum Threshold AuoRegressive (MTAR)-form (see, e.g. Enders and Granger, 998; Enders and Siklos, 00). Finally, he possibiliy of srucural breaks a unknown poins in ime is also aken ino accoun. Gil-Alana (006) proposes a very simple procedure for esimaing fracional orders of inegraion wih deerminisic linear rends and a single break a an unknown dae. 5

7 Following ha approach, we assume ha y is he observed ime series, generaed by he model d α x ; ( L) + + x = u, =,... Tb () y = β, y d b + T = α + β + x ; ( L) x = u, = T,...,, (3) where he α's and he β's are he coefficiens corresponding respecively o he inercep and he linear rend; d and d may be real values, u is I(0) and T b is he ime of he break ha is assumed o be unknown. Noe ha he model in equaions () and (3) can also be wrien as: d ~ ( L ) y ( ) ~ = α d + β ( d) + u, =,..., Tb, (4) d ~ ( L) y ( ) ~ = α d + β ( d) + u, = Tb +,..., T, (5) ~ i d where ( di ) = ( L), ~ d and ( d ) ( L) i i =, i =,. This approach is based on he leas square principle proposed by Bai and Perron (998). Firs, we choose a grid for he values of he fracionally differencing parameers d and d, for example, d io = 0, 0.0, 0.0,,, i =,. Then, for a given pariion {T b } and given d, d -values, squared residuals, (d ( j) o, d ( j) o ), we esimae he α's and he β's by minimising he sum of T ( j) ( j) b d ~ ~ T o ( j) ( j) d min ( L) y (d ) (d ) ( L) o α o β o + y = = Tb + w.r..{ α, α, β, β } ~ ( j) ~ ( j) α (do ) β (d ) o () () Le ˆ( α Tb ; d o, do ) and ˆ () ( β ( Tb ; d, ) o do ) denoe he resuling esimaes for () () pariion {Tb} and iniial values d o and d o. Subsiuing hese esimaed values in he () () objecive funcion, we obain RSS(Tb; d o, d o ), and minimising his expression for all 6

8 values of d o and d o in he grid we obain: RSS(Tb ) = arg min{i, j} (i) ( j) RSS(Tb ;do,do ). Then, he esimaed break dae, Tˆ k, is such ha ˆ = arg min RSS ( T ), T k i =,..., m i where he minimisaion is over all pariions T, T,, T m, such ha T i - T i- εt. The regression parameer esimaes are he associaed leas-squares esimaes of he esimaed k-pariion, i.e., ˆ α i = ˆ β i = ˆ α ({ ˆ i Tk }), ˆ β ({ ˆ i Tk }), and heir corresponding differencing parameers, d ˆ i = dˆ ({ ˆ i Tk }), for i = and. In Gil-Alana (006) i is shown ha he raes of convergence of he esimaes are similar o hose in Bai and Perron (998), since he values are chosen in such a way as o minimise he residual sum of squares and, under he appropriae specificaion, u should follow an I(0) process. Moreover, several Mone Carlo experimens conduced in ha sudy show ha he procedure performs exremely well even in relaively small samples. In his paper we exend he above procedure o allow for non-lineariies. Tha is, we consider for each subsample a model of he form y = f ( z ; θ ) + x, =,,... (6) where f may be of a non-linear naure, z is a vecor of (weakly) exogenous variables, θ represens he unknown coefficiens, and x is driven by (). The main problem wih his equaion lies in he ineracion beween he fracional polynomial d ( L) and he possibly 7

9 non-linear funcion f, and he esimaion of he parameers involved in such a relaionship. For he purpose of he presen sudy, le us assume ha f(z ; θ) = θ g(z ), where g is of a non-linear naure. In such a case, () and (6) become: d ( L) y = θ ' w + u, =,,..., (7) where w = d ( L) g(z ), and hence, he "non-lineariy" is no in erms of he parameers, bu in erms of a non-linear funcion of he variables z. We can obain he OLS esimae of θ and residuals: uˆ d T T = ( L) y ˆ' θ w, ˆ = d θ w w ' w ( L) y, = = and he same ype of analysis as in Gil-Alana (006) can be conduced here. This procedure can easily be exended o he case of muliple breaks (see again Gil-Alana, 006). In he presen sudy, hough, we do no consider his case, bu focus insead on a single break o explain he sochasic naure of unemploymen. The reason is he following. Srucuralis heories imply infrequen breaks in he unemploymen series. Therefore, here could be more han a single break. However, for he validiy of he ype of long-memory (fracional inegraion) model we use for unemploymen i is necessary ha he daa span a sufficienly long period of ime o deec he dependence across ime of he observaions; given he sample size of he series employed here, he inclusion of wo or more breaks would resul in relaively shor subsamples, hereby invalidaing he analysis based on fracional inegraion. Moreover, oher recen empirical sudies on unemploymen in he US and UK come o he conclusion ha a single break is sufficien o describe he behaviour of hese series (e.g. Anderon, 998). 4. Mone Carlo resuls In his secion we examine by means of Mone Carlo simulaions he performance of he 8

10 procedure described in Secion 3 in he case of non-linear srucures. We assume ha he Daa Generaing Process (DGP) is he following: d = 0.5I(y > 0) + 0.I(y 0) + x ; ( L) x = u,,..., Tb (8) y = y d = + I(y > 0) + 0.5I(y 0) + x ; ( L) x = u, = Tb,..., T, (9) where I(x) sands for he indicaor funcion, and u is a whie noise process. We generae Gaussian series using he rouines GASDEV and RAN3 of Press, Flannery, Teukolsky and Veerling (986). [Inser Figure abou here] Figure conains plos of simple realisaions of he model given by (8) and (9) wih T = 300, T b = 50, and (d, d ) = (0, 0), (0.5, 0.5), (0.5, 0.5), (0.5, 0.75), (0.75, 0.5) and (, ). I can be seen ha, when he possibiliy of fracional inegraion is no considered (i.e., d = d = 0), visual inspecion of he series does no clearly reveal he occurrence of a srucural break. By conras, when d = d = 0.5 or 0.5, he break is clearly noiceable, and even more so for higher orders of inegraion (e.g., d = d = ). I can also be clearly deeced when he orders of inegraion are differen for each subsample. Tables 3 repor he probabiliies of correcly deermining he iming of he break and he fracional differencing parameers in he model given by (8) and (9). In Table i is assumed ha in he rue DGP, T b = T/, d = 0. and d = 0.4. Thus, he wo subsamples are covariance saionary, hough wih a componen of long-memory behaviour. In Table, T b is sill equal o T/, d = 0.7 and d = 0.3. Finally, in Table 3, he break is assumed o ake place a T/4, wih d = 0.6 and d = 0.8, and hence he wo subsamples are now nonsaionary. In all cases, we perform he procedure described in 9

11 Secion 3 for a grid of d, d values = 0, 0., 0.4,,, and values for he break T * = (T b T/5), (), (T b + T/5), where T b is he correc ime of he break. The number of replicaion is equal o 0,000 in each case. I is apparen from hese ables ha he adoped procedure deermines accuraely he break dae in virually all cases. We find zero-probabiliies for all values of d and d if T* is smaller han T b - or higher han T b +. Thus, we repor in he ables only he probabiliies corresponding o T * = T b, T b, T b, T b +, and T b +. In Tables and he break is assumed o ake place a T/. Firs, we consider he case of d = 0. and d = 0.4 (Table ). I can be seen ha, if T = 00, he procedure yields he correc specificaion of he model in 37.45% of he cases. The oher wo cases wih a large percenage correspond boh o T * = T b, wih d = d = 0. (3.07%), and d = 0. and d = 0.6 (.35%). For his sample size, he sum of he probabiliies of correcly deecing he break-ime is 93.9%. Increasing he sample size appears o increase he probabiliy of correcly specifying he model: his is equal o 57.9% wih T = 00; 70.5% wih T = 300, and 84.45% wih T = 500. In his las case, he probabiliy of accuraely deermining he break poin is equal o 95.68%. [Inser Tables 3 abou here] In Table we assume nonsaionariy for he firs subsample (d = 0.7) and saionariy for he second one (d = 0.3), sill wih a break a T/. Here he highes probabiliies are in all cases hose corresponding o he rue model, followed closely by hose for he local deparures (d = 0.7 wih d = 0. and 0.5), wih T * = T/. In Table 3 i is assumed ha he break akes place a T/4, and ha he wo subsamples are nonsaionary (d = 0.6 and d = 0.8). Here, he probabiliies corresponding o he rue model are slighly Of course, we could also have considered he case wih d, d equal o 0, 0.,,, or even used a grid of 0.0 incremens, bu in such cases he probabiliy of correcly deermining he break would be subsanially reduced by his refinemen in he procedure, leading o higher probabiliies for he parameer values close o he rue one. 0

12 smaller han in he previous cases, hough sill sufficienly high o deec he rue DGP, especially if he sample size is large enough. On he whole, he evidence presened in his secion seems o sugges ha our procedure for fracional inegraion wih a srucural break and non-linear srucures performs well in finie samples. 5. Empirical resuls All hree unemploymen raes are seasonally adjused. The US series is quarerly, and covers he period 960Q-004Q4; he source is he IMF s Inernaional Financial Saisics. The UK series is monhly, for he ime period 970M 005M9, and is obained from he Labour Force Survey (hp://www. saisics.gov.uk). In he case of Japan, he sample period is 973Q-004Q, and he daa source is he OECD saisics. In Tables 4-6 we display he models seleced on he basis of he procedure described in Secion 3, for five differen specificaions. Firs, we consider he case wihou deerminisic erms (model ). Then, we assume a consan, and a consan and a linear rend, for each subsample (models and 3); finally, we also consider non-linear TAR (model 4) and M-TAR (model 5) srucures. More precisely, we esimae he following models: di. y = x, ( L) x = u, = T +,,..., T. di bi bi. y = α + x, ( L) x = u, = T +,,..., T. i bi bi 3. y = α + β + x, ( L) x = u, = T +,,..., T. i i di bi bi i i di + bi 4. y = γ I( y > 0) + γ I( y < 0) + x, ( L) x = u, = T,,..., T Noe ha higher daa frequencies (wih more observaions) are preferable for he purpose of fracional inegraion analysis, bu monhly daa were available only in he case of he UK; herefore, quarerly series have been used for he US and Japan.

13 i i di + bi 5. y = δ I( y > y) + δ I ( y < y) + x, ( L) x = u, = T,,..., T, where y in models 4 and 5 refers o he sample mean, and T b0 = ; T b = T b and T b = T. In each case we assume ha he I(0) disurbances u follow firs a whie noise and hen an AR() process of form: u = α i u - + ε, i =,. Higher AR srucures were also considered, and he resuls were no significanly differen from hose presened here. [Inser Table 4 abou here] For he U.S. series, he main resuls are he following (see Table 4). The break dae is almos he same in all models, ranging from 7Q o 75Q (i is 75Q in 4 ou of he 0 models presened). I clearly corresponds o he firs oil price shock. The values of d and d (he order of inegraion of he firs and second subsample respecively) are in mos cases beween 0 and, providing evidence of fracional inegraion and persisence. The esimaes of he parameer d range beween 0.66 and.0, and hose of d beween 0.80 and.. In general, we observe higher orders of inegraion in he second subsample, implying ha he degree of persisence is higher afer he break. The whie noise and AR() specificaions yield raher similar resuls. When a linear ime rend is included in he model (model 3), he slope coefficiens are saisically insignifican in boh subsamples. Therefore, model 3 can be discarded in favour of model (wih an inercep). As for he non-linear srucures, he coefficiens of model 4 are significan for he firs subsample ( γ and γ ), while in model 5 hey are significan for he second subsample only ( δ and δ ). The similariies beween he coefficiens of he non-linear models in he wo subsamples seem o indicae ha he adjusmen process is symmeric in he case of US unemploymen. Noe, for example, ha in model 4 he significan coefficiens are 5.34 and 5.49 for he firs subsample. In model 5, he values are.973 and 3.3 for he case of whie noise u, and.485 and.50 wih auocorrelaed disurbances.

14 [Inser Table 5 abou here] The resuls for U.K. are repored in Table 5. As can be seen, in mos cases he break occurs in he early 80s, namely a decade laer han in he US (only in hree of he esimaed models here is an earlier break, more precisely in 973). Furher, unlike in he US case, virually all he fracional parameers are esimaed o be higher han, implying permanen deviaions from equilibrium and a much higher degree of persisence in he UK unemploymen rae. 3 Specifically, he values of d are found o range beween 0.99 and.83, and hose of d beween.07 and.5. The range of values becomes narrower if he hree cases corresponding o a break occurring in he 70s are excluded, being now equal o [ ] and [ ] for d and d respecively. This is in line wih previous papers on UK unemploymen, finding orders of inegraion sricly above (Gil-Alana, 00b, c). As in he US case, here is no evidence of asymmeries when esimaing nonlinear TAR and M-TAR models. For example, in model 5, he significan coefficiens in he wo subsamples are , 4.03 and , 4.04, respecively in he case of whie noise disurbances, and -3.58,.974 and ,.966 wih AR() disurbances. [Inser Table 6 abou here] Table 6 repors he resuls for Japan. I can be seen ha in his case all he esimaed break poins are beween 99Q and 993Q. In fac, in four ou of he en models considered, he break akes places in he firs quarer in 993, namely one decade laer han in he UK, and almos wo decades laer han in he US. I can be argued ha his migh be a consequence of he sample period considered, which sars in 973Q. Therefore, as a robusness check, we also applied our procedure o annual daa, which are available from 960, and he break was again found o occur in The orders of 3 Anderon (998) also finds persisence in he UK unemploymen, hough in his sudy he break occurs slighly earlier, namely in Anderon (998) repors ha a break ook place in 974, wih an increase in unemploymen persisence. Our resuls are more mixed. 3

15 inegraion are clearly differen in he wo subsamples, before and afer he break. Specifically, before 993, mos of he esimaed values are sricly smaller han, while afer ha dae hey are equal o or higher han. If u follows an AR() process, he esimaed values of d are very close o 0 in hree ou of he five models, being equal o 0.04, 0.03 and 0.4 for model, 3, and 5 respecively. In hese cases, however, i is clear ha he low order of inegraion found in he firs subsample is associaed wih large AR coefficiens describing he ime dependence across he observaions, hese coefficiens being equal o 0.969, and 0.95 for models, 3 and 5 respecively. Nex, we selec for each counry he bes model on saisical grounds. In he case of he US, a ime rend appears no o be required, since he slope coefficiens are no significanly differen from zero. Moreover, he esimaed coefficiens for he wo nonlinear models are raher similar in he wo subsamples, and herefore hese models can be ruled ou. In he model wih an inercep (model ), he esimaed order of inegraion is slighly above in he second subsample for he case wih AR() disurbances, and he AR coefficiens are close o zero in he wo subsamples. Therefore, he following specificaion is chosen for he US: 0.68 y = x ; ( L) x = ε, =,,..., Tb = 75Q, 0.83 y = x ; ( L) x = ε, = Tb +,..., T. Moving on o he UK, again i appears ha he non-linear models can be discarded because of he insignifican coefficiens (in model 4) and he similariies beween he coefficiens in he wo subsamples (in model 5). Model 3 can also be discarded on he grounds of he insignificance of he slope coefficiens. Thus, we focus on model (wih an inercep): in boh cases (whie noise and AR() u ) he coefficiens for he orders of inegraion are higher han, and also higher in he firs subsample. We choose he specificaion wih auocorrelaed disurbances because of he significan coefficiens. 4

16 Therefore, he seleced model is he following:.8 y = x ; ( L) x = u ; u = 0.53u + ε, =,,..., Tb = 8M 4,.5 y = x ; ( L) x = u ; u = 0.7u + ε, = Tb +, Finally, in he case of Japan, using he same ype of argumens as before, we focus on he model wih an inercep (model ). When u is specified as a whie noise he orders of inegraion are 0.93 and.4 respecively for he wo subsamples, whils, if u is modelled as an AR() process, he corresponding values are 0.04 and.4. (As previously menioned, he low order of inegraion in case of he firs subsample is due o he compeiion wih he AR coefficien in describing he dependence across he observaions). Thus, for his counry we choose he following model: 0.93 y =.7 + x ; ( L) x = ε, =,,..., Tb = 93Q,.4 y =.39 + x ; ( L) x = ε, = Tb +, [Inser Figure abou here] Figure shows he impulse responses o a uni shock compued for he firs 5 periods for each counry and each subsample, based on he seleced models. I can be seen ha in he US (and also in Japan in he second subsample) he size of he response increases a firs and hen sars decreasing very slowly. Also, in he US he convergence process is slower during he second subsample. By conras, in he remaining cases (he wo subsamples in UK and he second one in Japan) he process is explosive and no mean-revering even in he long run, consisenly wih he earlier findings on persisence. To sum up, he empirical resuls indicae ha here is a single significan break occurring in all hree cases (hough he daing is differen: he early 70s in he UK, a decade laer in he US, and wo decades laer in Japan). This could be seen as prima facie evidence ha a srucuralis model migh be appropriae o describe unemploymen..., T...., T. 5

17 behaviour in hese counries. However, a closer look a he order of inegraion of he series suggess ha his migh no be he case for all hree economies. Specifically, he fac ha he esimaed fracional parameers are consisenly higher han in he UK means ha in his counry he economic environmen is such ha shocks o unemploymen (and hence macroeconomic policy) have permanen effecs, hereby giving suppor o a hyseresis model. An order of inegraion higher han is also found in he case of Japan in he second subsample, indicaing a change in he labour marke ha has resuled in hyseresis. By conras, in he firs subsample, and in boh periods in he case of he US, he esimaed degree of persisence implies ha, alhough he speed of adjusmen owards equilibrium is slow, 5 unemploymen exhibis mean reversion, consisenly wih he naural rae hypohesis, appearing o be a near-uni roo process, wih shocks having long-lasing bu no permanen effecs. This finding, combined wih he evidence of a break, gives suppor o a srucuralis view of unemploymen behaviour. Hence i appears ha differen models (hyseresis and srucuralis) are appropriae o accoun for he unemploymen experience of he differen counries and periods under invesigaion. The impulse response analysis also confirms he earlier findings. Overall, our resuls, and he persisence ranking, are in line wih earlier sudies (e.g., Alogoskoufis and Manning, 988), also reporing ha Japan and he US ypically display lower degrees of unemploymen persisence han European counries. The mixed evidence on wheher persisence has decreased or increased in he UK since he early 980s 6 migh a firs seem surprising in view of he labour marke reforms (aimed a eliminaing rigidiies) implemened by he Conservaive governmen led a he ime by Mrs. Thacher. However, oher auhors, such as Blanchflower and Freeman (994), have 5 In Anderon (998), he unemploymen persisence parameer is esimaed o be highes in he UK, and bigger in Japan han in he US, as in he presen paper. 6 We find ha he esimaed fracional parameers are higher in he firs subsample for he seleced model and in mos, bu no all cases. (See Table 5). 6

18 repored a slower ransiion from unemploymen o employmen in he Thacher years. These resuls can be explained in erms of labour marke and insiuional differences. I is usually argued ha he poorer unemploymen performance of he European economies compared o he US is due o imperfecions in he labour marke (see, e.g., Layard e al, 99). Feaures such as decenralised wage deerminaion (see Calmfors and Driffill, 988), low social securiy and rade union densiy, and minimum employmen proecion are ofen hough o accoun for he beer labour marke oucomes in he US. 7 Bu in he period Japan ouperformed even he US in erms of unemploymen. In he Layard e al. (99) sudy, wage flexibiliy in he small business secor and he fac ha female workers exi he labour marke during recessions were highlighed as imporan facors accouning for he absence of hyseresis in Japan. An OECD sudy (994) aribued insead he successful Japanese experience o some oher key feaures of he Japanese labour marke, in paricular long-erm employmen relaionships, high invesmen in raining and worker loyaly. As for he higher degree of persisence since he early 90s, his migh be due o inensive on-he-job raining and he resuling firmspecific skills leading o high coss of hiring and firing: in response o possibly emporary negaive shocks, firms migh be relucan o fire employees wih highly specialised skills, who would have o be replaced in he upurn by new workers requiring cosly addiional raining. This reduces boh job creaion and desrucion, and hence increases unemploymen persisence. 8 7 Noe, however, ha he neoclassical paradigm (wih he associaed deregulaion policies) has been criicised as exhibiing some heoreical weaknesses, such as second bes problems, exernaliies ec. (see, e.g., Greg and Manning, 997). Also, i has been poined ou ha, in addiion o he degree of cenralisaion, oher feaures of he bargaining process, such as he degree of unionisaion and coordinaion, as well as he coverage of bargaining, are imporan (see OECD, 997). 8 For a more exensive discussion of he Japanese case, see Brunello (990). 7

19 6. Conclusions In his paper we have made a wofold conribuion. Firs, we have exended o he nonlinear case a general procedure o deec srucural breaks a unknown poins in ime which allows for differen orders of inegraion and deerminisic componens in each subsample (see Gil-Alana, 006). The suggesed procedure has been shown by means of Mone Carlo experimens o be able o deermine accuraely he iming of he break in a non-linear, fracionally inegraed framework. Second, we have applied i o es for breaks in he US, UK and Japanese unemploymen raes, and assessed he empirical relevance of alernaive unemploymen heories in each case. Our empirical findings sugges ha unemploymen is subjec o infrequen breaks (more specifically, a single break has been idenified in he hree counries under sudy), and ha non-lineariies do no play a very imporan role. Moreover, unemploymen appears o exhibi a higher degree of persisence in he UK compared o he US and Japan (alhough in he case of he US persisence has risen since he beginning of he 80s, and in Japan hyseresis is found in he period saring in 993). Overall, i seems ha a srucuralis inerpreaion (see Phelps, 994) is more appropriae for he US and Japan, whils a hyseresis model (see Blanchard and Summers, 986, 987, and Barro, 998) accouns beer for he UK experience (and also for he Japanese one in he second subsample). The persisence ranking and he resuls in general can be inerpreed in erms of he differen characerisics of he labour marke in he counries being analysed. In paricular, imperfecions and rigidiies prevening or slowing down labour marke adjusmen and clearing (despie he Thacher reforms) migh be responsible for he inferior unemploymen performance of he UK compared o he US and Japan. The beer labour marke oucomes achieved in he wo laer counries could be aribued o higher flexibiliy and deregulaion in he case of he US, whils long-erm employmen 8

20 relaionships and oher relaed facors migh play a role in he case of Japan (see Layard e al, 99). Our analysis could be exended by esimaing a mulivariae fracional model, including regressors such as real oil prices and real ineres raes, which migh accoun for he observed behaviour of he unemploymen rae, and also allowing for possible crosscounry linkages. This could be paricularly informaive when analysing he impulse response of unemploymen o various ypes of shocks (e.g. price shocks), including shocks affecing unemploymen in oher counries in he firs insance. However, his is beyond he scope of he presen sudy, and is lef for fuure research. 9

21 References Alogoskoufis, G.S. and A. Manning, 988, On he persisence of unemploymen, Economic Policy, 7, Anderon, R., 998, "Policy regimes and he persisence of wage inflaion and unemploymen", The Mancheser School, 66, Bai, J. and J. Perron, 998, Esimaing and esing linear models wih muliple srucural changes, Economerica, 66, Baillie, R.T., 996, Long memory processes and fracional inegraion in economerics, Journal of Economerics, 73, Barro, R., 988, The naural rae heory reconsidered: he persisence of unemploymen, American Economic Review, Papers and Proceedings, 78, Bean, C.R. (989), Capial shorage, Economic Policy, 8, -53. Benolilla, S. and G. Berola (990), Firing coss and labour demand: how bad is eurosclerosis?, Review of Economic Sudies, 57, Bianchi, M. and G. Zoega, 998, Unemploymen persisence: does he size of he shock maer?, Journal of Applied Economerics, 3, Blanchard, O.J., 999, Wage dynamics: reconciling heory and evidence, American Economic Review, Papers and Proceedings, 89,, Blanchard, O.J. and L.H. Summers, 986, Hyseresis and he European unemploymen problem, NBER Working Paper Series no Blanchard, O.J. and L.H. Summers, 986, Hyseresis in unemploymen, European Economic Review, 3, Blanchard, O.J. and J. Wolfers, 000, The role of shocks and insiuions in he rise of European unemploymen: he aggregae evidence, Economic Journal, 0, C-C33. Blanchflower, D. and R. Freeman (994), Did he Thacher reforms change Briish labour marke performance? in R. Barrell (ed.), The UK Labour Marke, Cambridge, Cambridge Universiy Press. Brunello, G. (990), Hyseresis and "The Japanese Unemploymen Problem": A Preliminary Invesigaion, Oxford Economic Papers, 4, 3, Caballero, R.J. and M.L. Hammour (994), The cleansing effec of recessions, American Economic Review, 84, Calmfors, L. and J. Driffill (988), Bargaining srucure, corporaism and macroeconomie performance, Economic Policy, 3, 6 (April 988),

22 Campbell, J.Y. and P. Perron, 99, Pifalls and opporuniies: Wha macroeconomiss should know abou uni roos, NBER Macroeconomics Annual, 4-0. Caporale, G.M. and L.A. Gil-Alana (005), Non-lineariies and fracional inegraion in he US unemploymen rae, WP no. 05-7, Deparmen of Economics and Finance, Brunel Business School, Brunel Universiy, London; also, DP no. 05-3, Cenre for Inernaional Capial Markes, London Meropolian Universiy, London. Crao, N. and P. Rohman, 996, Measuring hyseresis in unemploymen raes wih long memory models, Working Paper, Eas Carolina Universiy, Deparmen of Economics. Cross, R., 987, Hyseresis and insabiliy in he naural rae of unemploymen, Scandinavian Journal of Economics, 89,, De Jong, D.N., J. Nankervis, N.E. Savin and C.H. Whieman, 99, The power problems of uni roo ess in ime series wih auoregressive errors, Journal of Economerics, 53, Dickey, D. and W. Fuller, 979, Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion, 74, Diebold, F.X. and G.D. Rudebusch, 989, Long memory and persisence in aggregae oupu, Journal of Moneary Economics, 4, Friedman, M., 968, The role of moneary policy, American Economic Review, 58, - 7. Enders, W. and C.W.J. Granger, 998, Uni-roo ess abd asymmeric adjusmen wih an example using he erm srucure of ineres raes, Journal of he American Saisical Associaion, 6, 3, Enders, W. and P. Siklos, 00, Coinegraion and hreshold adjusmen, Journal of Business and Economic Saisics, 9,, Gil-Alana, L.A., 00a, The persisence of unemploymen in he USA and Europe in erms of Fracionally ARIMA Models, Applied Economics, 33 (0), Gil-Alana, L.A., 00b, Esimaion of fracional ARIMA models for he UK unemploymen, Annales d'economie e de Saisique, 6, Gil-Alana, L.A, 00c, A fracionally inegraed exponenial specral model for he UK unemploymen, Journal of Forecasing, 0, Gil-Alana, L.A., 00, Modelling he Persisence of Unemploymen in Canada, Inernaional Review of Applied Economics, 6, Gil-Alana, L.A., 006, Fracional inegraion and srucural breaks a unknown periods of ime, mimeo, Universiy of Navarra. Gil-Alana, L.A. and P.M. Robinson, 997, Tesing of uni roos and oher nonsaionary

23 hypoheses in macroeconomic ime series, Journal of Economerics, 80, Gordon, R.J., 989. Hyseresis in hisory. Was here ever a Phillips curve? American Economic Review, Papers and Proceedings, 79, 0-5. Graafland, J.J., 99, On he causes of hyseresis in long erm unemploymen in he Neherlands, Oxford Bullein of Economics and Saisics, 53,, Granger, C.W.J., 980, Long memory relaionships and he aggregaion of dynamic models, Journal of Economerics, 4, Granger, C.W.J., 98, Some properies of ime series daa and heir use in economeric model specificaion, Journal of Economerics, 6, -30. Gregg, P. and A. Manning (997), Labour marke regulaion and unemploymen, in D. Snower and G. de la Dehesa (eds.), Unemploymen Policy: Governmen Opions for he Labour Marke, Cambridge Universiy Press, Cambridge, Hosking, J.R.M., 98, Fracional differencing, Biomerika 68, Im, K.-S., M.H. Pesaran and Y. Shin, 003, Tesing for uni roos in heerogeneous panels, Journal of Economerics, 5, Im, K.-S., J. Lee and M. Tieslau, 005, Panel LM uni roo ess wih level shifs, Oxford Bullein of Economics and Saisics, 67, Layard, R., Nickell, S. and R. Jackman (99), Unemploymen: Macroeconomic Performance and he Labour Marke, Oxford Universiy Press, Oxford. Leon-Ledesma, M., 00, Unemploymen hyseresis in he US saes and he EU: A panel approach, Bullein of Economic Research, 54, Levin, A., C.-F. Lin and C.-S. Chu, 00, Uni roo ess in panel daa: asympoic and finie-sample properies, Journal of Economerics, 08, -4. Lopez, H., E. Orega and A. Ubide, 996. Explaining he dynamics of Spanish unemploymen, Working Paper in Economics, no.96/4, European Universiy Insiue. Michell, W.F., 993, Tesing for uni roos and persisence in OECD unemploymen raes, Applied Economics, 5, Murray, C.J. and D.H. Papell, 000, Tesing for uni roos in panels in he presence of srucural change wih an applicaion o OECD unemploymen, in Nonsaionary Panels, Panel Coinegraion, and Dynamic Panels (Advances in Economerics, 5), ed. by B.H. Balagi, JAI Press, Nickell, S., 998, Unemploymen: quesions and some answers, Economic Journal, 08, Nickell, s. and J. Van Ours, 000, The Neherlands and he Unied Kingdom: a European

24 unemploymen miracle?, Economic Policy, 30, No, L., 996. Hyseresis in he Canadian labour marke. Evidence from he 990s, Research Repor No. 9605, Deparmen of Economics, Universiy of Wesern Onario. OECD (994), Jobs Sudy, OECD, Paris. OECD (997), Employmen Oulook, OECD, Paris. Papell, D.H., C.J. Murray and H. Ghiblawi, 000, The srucure of unemploymen, Review of Economics and Saisics, 8, Phelps, E.S., 967, Phillips curve, expecaions of inflaion and opimal unemploymen, Economica, 34, Phelps, E.S., 968, Money-wage dynamics and labor-marke equilibrium, Journal of Poliical Economy, 76, Phelps, E.S., 994, Srucural Slumps: The Modern Equilibrium Theory of Unemploymen, Ineres, and Asses, Cambridge, MA, Harvard Universiy Press. Phelps, E.S., 999, Behind his srucural boom: he role of asse valuaions, American Economic Review, Papers and Proceedings, 89,, Phillips, P.C.B. and P. Perron, 988, Tesing for a uni roo in a ime series regression, Biomerika, 75, Pissarides, C., 990, Equilibrium Unemploymen Theory, Oxford, Basil Blackwell. Press, W.H., B.P. Flannery, S.A. Teukolsky and W.T. Weerling, 986, Numerical recipes: The ar of scienific compuing, Cambridge Universiy Press, Cambridge. Robinson, P.M., 978, Saisical inference for a random coefficien auoregressive model, Scandinavian Journal of Saisics, 5, Skalin, J. and T. Teräsvira (00), Modelling asymmeries and moving equilibria in unemploymen raes, Macroeconomic Dynamics 6, 0-4. Song, F.M. and Y. Wu, 998, Hyseresis in unemploymen? Evidence from OECD counries, Quarerly Review of Economics and Finance, 38, 8-9. Srazicich, M.C., M. Tieslau and J. Lee, 00, Hyseresis in unemploymen? Evidence from panel uni roo ess wih srucural change, mimeo. Tschernig, R. and K.F. Zimmermann, 99. Illusive persience in German unemploymen, Recherches Economiques du Lovaine, 58, Wilkinson, G., 997. A micro approach o he issue of hyseresis in unemploymen; evidence from he labour marke aciviy survey, Bank of Canada, Working Papers

25 Zivo, E. and D.W.K. Andrews, 99, Furher evidence on he Grea Crash, he oil-price shock and he uni roo hypohesis, Journal of Business and Economic Saisics, 0,

26 FIGURE Examples of simple realisaions wih non-linear erms, fracional inegraion and srucural breaks y d yr = = d ( 0) 0.5 ( 0) ; ( ) r = I y > + I y + x L x = u, = Tb +,..., T ( = 0.5I( y 0) 0. ( 0) ; ( ) > + I y + x L x = u, =,..., Tb ( T d = 0 and d = 0 d = 0.5 and d = 0.75 / ) 300) d = 0.5 and d = 0.5 d = 0.75 and d = d = 0.5 and d = 0.5 d = and d =

27 y TABLE Probabiliies of deecing he rue model wih a break a T/ and d = 0. and d = I( y 0. > 0) + 0.I( y 0) + x ; ( L) x = u, =,..., Tb ( T / ) 0.4 > 0) + 0.5I( y 0) + x ; ( L) x = u, = Tb,..., T, r = = y I( y r = + T * d d T = 00 T = 00 T = 300 T = 500 T b T b T b T b T b In bold, he probabiliies corresponding o he rue model. 6

28 y TABLE Probabiliies of deecing he rue model wih a break a T/ and d = 0.7 and d = I( y 0.7 > 0) + 0.I( y 0) + x ; ( L) x = u, =,..., Tb ( T / ) 0.3 > 0) + 0.5I( y 0) + x ; ( L) x = u, = Tb,..., T, r = = y I( y r = + T * d d T = 00 T = 00 T = 300 T = T b T b T b T b T b In bold, he probabiliies corresponding o he rue model. 7

29 y TABLE 3 Probabiliies of deecing he rue model wih a break a T/4 and d = 0.6 and d = I( y 0.6 > 0) + 0.I( y 0) + x ; ( L) x = u, =,..., Tb ( T / 4) 0.8 > 0) + 0.5I( y 0) + x ; ( L) x = u, = Tb,..., T, r = = y I( y r = + T * d d T = 00 T = 00 T = 300 T = T b T b T b T b T b In bold, he probabiliies corresponding o he rue model. 8

30 TABLE 4 Resuls for he UNITED STATES Model Model Model 3 Model 4 Model 5 W. N. AR() W. N. AR() W. N. AR() W. N. AR() W. N. AR() T b 73Q4 75Q 75Q 74Q4 75Q 75Q 7Q 74Q3 74Q4 74Q3 d d α (0.48) (4.36) (0.6) (3.36) α (5.4) (8.3) (6.86) (.8) β (-0.7) (0.6) β (-.3) (-0.68) γ (8.93) (.03) γ (.8) (.47) γ (9.30) (.7) γ (.09) (.5) δ (-.07) (-0.43) δ δ δ τ τ.973 (5.7) (-0.56) 3.3 (5.9).485 (5.6) (-0.9).50 (5.0) values in parenheses. In bold, significan coefficiens a he 95% significance level. 9

31 TABLE 5 Resuls for he UNITED KINGDOM Model Model Model 3 Model 4 Model 5 W. N. AR() W. N. AR() W. N. AR() W. N. AR() W. N. AR() T b 73m 73m 83m 8m4 83m 8m 73m9 80m3 8m 8m3 d d α (70.4) (38.) (65.34) (8.8) α (5.7) (46.34).76 (.94) (.30) β (.38) (0.66) β (-0.34) (-.8) γ (.04) (-0.56) γ (0.0) 0.05 (.) γ (-0.0) (-0.03) γ (.38) (0.55) δ ( (-33.43) δ δ δ τ τ 4.03 (3.) (-63.76) 4.04 (3.).974 (9.9) (-3.76).966 (9.77) values in parenheses. In bold, significan coefficiens a he 95% significance level. 30