Macroeconomic Effects of Reallocation Shocks: A generalised impulse response function analysis for three European countries.

Transcription

1 Macroeconomic Effecs of Reallocaion Shocks: A generalised impulse response funcion analysis for hree European counries. Theodore Panagioidis a, Gianluigi Pelloni b* and Wolfgang Polasek c a. Deparmen of Economics & Finance, Brunel Universiy, U.K. b. Deparmen of Economics, Ryerson Universiy, Torono,Canada and Faculy of Poliical Sciences, Universiy of Pisa, Pisa, Ialy, address: gpelloni@sp.unipi.i c. Deparmen of Saisics and Economerics, Universiy of Basel, Basel, Swizerland. January 23 Absrac We develop a generalised impulse response funcion (GIRF) approach o explore he differen impacs of aggregae and secoral shocks wihin a VAR-GARCH-M model. Using he oupu of our GIRF analysis, we explore he behaviour of hree European counries (Germany, Spain and he UK). We analyse he aggregae and secoral responses o discriminae among hree differen hypoheses of business cycle flucuaions. Links are esablished and explanaions are provided wihin he sill experimenal characer of our exercise. Keywords: secoral shifs, employmen flucuaions, generalised impulse response funcion, VAR-GARCH models JEL Classificaion Numbers: E3, C, J2. * Corresponding auhor Acknowledgemens: we wish o hank Vincenzo Caponi, Giovanni Gallipoli, Paolo Giordani, Jean Paul Lam, wo anonymous referees and seminar paricipans in he Canadian Economic Associaion 2 Conference and he EEFS-IEFS May 22 Conference in Heraklion-Cree for commens and suggesions. The usual disclaimer applies. Financial suppor from he European Union under he EMASE projec, Conrac no. FAIR 6-CT98-4, and he CNR under he projec Growh, echnological change and labour markes in Europe and seleced OECD counries, Conrac no CT, is graefully acknowledged. Gianluigi Pelloni also graefully acknowledges a Faculy Research Gran from he Inernaional Council for Canadian Sudies.

2 .Inroducion Inersecoral labour reallocaions as a riggering force of aggregae unemploymen flucuaions are he objec of an unsolved puzzle. This puzzle persiss because of he observaional equivalence problem inheren in secoral shifs analysis. A an empirical level, none of he exising approaches aimed a separaing reallocaion unemploymen from unemploymen generaed by aggregae shocks can be deemed as horoughly saisfacory. Earlier analyses could no provide definie evidence. These invesigaions consised mainly of reduced forms equaions measuring he response of aggregae (un)employmen o a dispersion proxy of secoral shifs. Campbell and Kuner (996), CK (996) hereafer, ries o bypass he difficulies embodied in he use of dispersion proxies by modelling secoral shocks direcly using ime series echniques. Pelloni and Polasek (999, 23; hereafer denoed as PP99 and PP3) modifies CK s approach using VAR-GARCH srucures o incorporae he non-lineariy of secoral shifs. These new ime series approaches, hough promising, are in heir early sages and need o be exended and revised. I is he purpose of he presen paper o do so. CK (996) reas secoral shocks symmerically, as if hey were characerised by a posiive-negaive naure like aggregae shocks. PP99 and PP3 poin ou his pifall and esimae a VAR-GARCH-M in sandard form and assess he relaive imporance of secoral shocks by carrying ou a Cholesky decomposiion. In his paper we expand previous sraegies by exploiing he concep of Generalised Impulse Response Funcion (GIRF). We use he GIRF no only as a concepual experimen useful for he analysis of he shocks impacs, bu also as a ool for discriminaing among differen hypoheses. Our paper is srucured as follows. Secion 2 provides he necessary background for our subsequen work. I conains a discussion of mulivariae (G)ARCH models in secoral shifs analysis and describes how GIRF analysis can be used for assessing alernaive hypoheses. In secion 3 we presen he concep of GIRF and is implemenaion wihin our VAR-GARCH-M model, leaving a number of echnical poins for an appendix. We presen he daa of seleced European counries in secion 4. Secion 5 conains he empirical implemenaion of our approach and he discussion of he resuls. The las secion would provide some concluding remarks and presen a furher oulook 2. VAR-ARCH Models of Secoral Reallocaions Lilien (982a) dispersion hypohesis claims ha changes in he composiion of employmen demand would rigger a process of job reallocaion, which would affec aggregae (un)employmen. Earlier represenaions of he hypohesis were provided by reduced form equaions of unemploymen wih he general form: p u = α + α s + α z + u + ε i i 2i i i= i= q ()

3 Where u is some measure of unemploymen; s is a dispersion measure () used o proxy he inersecoral dispersion of demand condiions and z is a vecor of aggregae conrol variables. Unemploymen, besides showing a serial correlaion srucure, would be posiively affeced by secoral shifs and posiively or negaively relaed o he aggregae disurbances according o he naure of he specified relaionships. Alhough differen proxies have been employed, an observaional equivalence problem seems o be irrevocably associaed wih he use of dispersion measures (see Lilien, 982b; Abraham and Kaz, 986). Insead of reflecing reallocaion shocks, hese measures could be capuring he effecs of aggregae shocks. To beer undersand his issue we would idenify hree main heoreical approaches: Following Davis (986; 987), we aach he label Normal Business Cycle Hypohesis (NBCH hereafer) o he firs group of models. This group covers hose models where aggregae shocks are he main riggering force of business cycles. The posiive correlaion beween unemploymen and dispersion indices would reflec aggregae disurbances and no labour marke urbulence. Differen income elasiciies of secoral demands would accoun for he dispersion (Abraham and Kaz, 986). Thus an aggregae shock would bring abou secoral responses of differen dimensions and wih differen iming bu all in he same direcion. The Reallocaion Timing Hypohesis (RTH hereafer) is he disinguishing heoreical feaure of he second caegory. According o he RTH (Davis, 986; 987), aggregae disurbances are sill he riggering force of cycles bu recessions will be characerised by labour inersecoral reallocaions. Economic agens would opimally decide o change secor when heir labour marginal produciviy is relaively low (i.e. during a recession). Thus a negaive aggregae shock should come along wih a fairly large amoun of labour inersecoral reallocaions. Again he posiive correlaion beween unemploymen and a secoral dispersion index could emerge as a response o aggregae shocks. The hird group is provided by he Secoral Shifs Hypohesis (SSH, hereafer) where, as discussed above, allocaive shocks would bring abou an aggregae response during a ransiion period required for he ransfer of resources. I is clear ha observaionally equivalen predicions could be generaed by differen approaches o business cycle analysis. Given he problem inheren in dispersion proxies, some researchers have recenly ried o model secoral shocks direcly using mulivariae ime series approaches (c.f. Gallipoli and Pelloni, 2,and references hereafer). CK (996) analyses he relaionship beween U.S. aggregae and secoral employmen hrough a srucural vecor auoregression (SVAR), devoid of cross-indusry dispersion measures. CK develops a bivariae srucure for he growh raes of aggregae employmen and of he manufacuring secoral share over he period 955:2-994:2. The analysis is subsequenly exended o a seven-dimensional VAR. The resuls vary dramaically in accord wih he VAR size and he naure of he resricions. Secoral shocks can accoun for only 6% of he aggregae variance under a shor-run riangular bivariae sysem. Insead, under a long-run resricion for he seven-dimensional VAR, reallocaion disurbances explain 82% of he aggregae variance. CK, hough pahbreaking, has a major drawback: i is characerised by a symmeric response of aggregae employmen growh o secoral shocks (PP99). A negaive (posiive) shock o he manufacuring secor will decrease (increase) aggregae employmen growh. This direcional behaviour is inconsisen wih he SSH (Davis 2

4 986). In fac he macroeconomic effecs of reallocaion shocks should emerge from he unfavourable impac of labour marke urbulence on he exising allocaion of resources. The acual volume of reallocaions will bring abou a corresponding oscillaion in aggregae (un)employmen. To capure he pervasive non-lineariy of secoral shifs, PP99 inroduces a five dimensional VAR model wih a GARCH-M componen. The laer should capure he non-linear naure of he SSH. The model s variables are he aggregae employmen growh and he growh raes of secoral employmen shares. The measured secoral variances are inerpreed as proxies of employmen reallocaions. The model allows for boh shocks wih a ime-varying (condiional) variance and volailiy clusering. The general specificaion of he PP s models is given by an M-dimensional VAR (k) - GARCH (p,q) - M(r) process: y = k r µ + ε = β + i y i + ψ ih i + ε i= i= p B (2) vechh vech ivech( = α + A i H i + Θ ε iε i ) (3) i= where y is a (M ) vecor of variables, H is a (M M) diagonal condiional variancecovariance marix, vech H is a {[ M (M + ) / 2 ] } vecor, h is an M-dimensional vecor of condiional variances, ε is an M-dimensional process of muually and serially uncorrelaed random errors and so vech ( ε ε ) is an [ M (M + ) / 2 ]- dimensional vecor, α and β are respecively {[ M (M + ) / 2 ] } and (M ) vecors of ime invarian inercep coefficiens, B, y, A and Q are coefficien marices, he firs wo are of dimension (M M) whereas he oher wo have dimension {[ M (M + ) / 2 ] [ M (M + ) / 2 ] }. The vech symbol denoes he column-sacking operaor for he elemens of a symmeric marix lying on and below he main diagonal. (2) The crucial feaure of his specificaion is ha he condiional means are funcions of he conemporaneous and lagged values of he condiional variances. In his way we can verify wheher he informaion conen of he condiional variances is relevan in deermining he esimaes of he condiional mean values. The SSH is capured by imposing he dependence of he aggregae employmen growh raes on he esimaed j secoral variances. For secor j a ime, he esimaed variance, h, would be he squared disance beween he value of he random variable "secor j's employmen share" and is mean. The esimaed variances are inerpreed as measures of labour reallocaions. PP99 esimaes a five-dimensional VAR for he US economy wihin a Bayesian se up. The variance decomposiion analysis provides srong suppor for secoral reallocaions. The GARCH srucure seems o capure imporan feaures of he sysem s dynamics, hus srenghening he role of he secoral componens. However, he variance decomposiion analyses in PP99 and PP3 employ a Cholesky decomposiion. Though boh papers use an ordering of he variables which is unfavourable o he SSH, heir resuls canno be invarian o he chosen ordering. In his paper we exend PP s analyses by applying he concep of GIRF which is a suiable ool for mulivariae non-linear q i= 3

5 models (Koop, Pesaran and Poer, 996; KPP hereafer). The GIRF can single ou a specific shock wihou resoring o ad hoc idenifying resricions. A he same ime i generaes unique responses. We can use he GIRF as a ool for discriminaing among he NBCH, he RTH and he SSH. In fac we can observe if he responses o a specific shock mirror he characerisic paerns of one of he compeing heories. In his manner we should be able o corroborae one of he hree hypoheses by inspecion of he variables pahs. Since we have VAR-GARCH-M model, we can also define he GIRF for he condiional variances. If secoral urbulence is deeced hen he NBCH would have o be rejeced. Table summarises he sylised facs generaed by he differen ypes of shocks. Le us assume a posiive aggregae shock: If we observe posiive changes in all he secoral shares hen he NBCH is corroboraed. In such a case, secoral responses could be differen in size bu should die ou quie rapidly. If insead no all shares are moving in he same direcion hen he evidence favours he RTH. In his case he secoral responses should persis for a longer span. The SSH insead requires secoral shocks and is borne ou when such shocks are accompanied by a large aggregae response associaed o large secoral reallocaions. The changes in he secoral shares should persis as hey represen changes in demand composiion. TABLE THEORY CHARACTERISTICS IMPULSE RESPONSE FUNCTION-MEAN Normal Cycle Hypohesis NBCH Reallocaion Timing Hypohesis RTM Business Secoral Shifs Hypohesis SSH Triggering Force: Aggregae Shocks. Triggering Force: Aggregae Shocks. Large reallocaions (when economy in recession). Triggering Force: Secoral Shifs. Change in composiion of demand. Secoral Componens move o he same direcion as a resul of an aggregae shock. Large Reallocaions when economy is in recession. No (or lile) reallocaion oherwise. Large reallocaions and aggregae response o secoral shocks. IMPULSE RESPONSE FUNCTION-VARIANCES Small variance responses as a signal of small inersecoral reallocaions. Large variance responses as a signal of large acual reallocaion. Large variance responses as a signal of large acual reallocaion. 3. The Generalised Impulse Response Funcion As KPP poins ou: The radiional impulse response funcion is designed o provide an answer o he quesion: Wha is he effec of a shock of size δ hiing he sysem a ime on he sae of he sysem a ime +n, given ha no oher shocks hi he sysem?. The IRF analysis is used in dynamic models such as a VAR o describe he impac of an exogenous shock (innovaion) in one variable on he oher variables of he sysem. A uni (one sandard deviaion) increase in he j h variable innovaion (residual) is inroduced a 4

6 dae and hen i is reurned o zero hereafer. In general he pah followed by he variable y m, in response o a one ime change in y j,, holding he oher variables consan a all imes, is called he IRF. This is he prevalen form of IRF used in empirical work, however in our paper we follow KPP, and call i he radiional IRF, TIRF, and define i formally as TIRF ( n, δ, ϖ = E[ y + n ε ) = = δ, ε + =,..., ε + n =, ϖ ] E[ y + n ε =, ε + =,..., ε + n =, ϖ ] (4) where y is a random vecor, ε + i is a random shock, ϖ a specific realisaion of he informaion se Ω and n is he forecas horizon. Thus we have a realisaion of y +n generaed by he sysem when i is hi by a shock of size δ for i = while all shocks are equal o zero for i =,2,,n, and a realisaion of y +n when ε + i = for all i =,,n (he benchmark represenaion). The difference beween hese wo realisaions provides a general definiion of he TIRF. KPP argues ha in he case of mulivariae non-linear models, (a VAR-GARCH model for example), he applicaion of he TIRF can be affeced by problems of composiion, hisory and shock dependence and propose a unified approach valid boh for linear and non-linear models. They call his form of IRF he generalised IRF (GIRF) and define i as GIRF n, ε, ω ) E[ y ε, ω ] E[ y ϖ ] (5) ( = + n j, + n The GIRF is a random variable given by he difference beween wo condiional expecaions which are hemselves random variables (3). In fac he GIRF is made up of wo componens. The firs par is he expecaion of y +n condiional on hisory ( ϖ Ω ) and he chosen shock ε j,. Thus all oher conemporaneous and fuure shocks are inegraed ou. The second componen is he base-line profile (i.e. he condiional expecaion of y +n given he observed hisory). The impulse responses emerging from he GIRF are unique and invarian o he ordering of he variable of he sysem (KPP; Pesaran and Shin, 998). These properies (coping wih he problems of composiion dependence, hisory dependence and shock dependence) of mulivariae nonlinear sysems make he GIRF an appropriae ool o carry ou our experimen. We confine he echnical deails of our implemenaion of he GIRF o he appendix. 4.Daa We esimae and es agains alernaive specificaions (VAR, VAR-GARCH, VAR- GARCH-M) he model given by (2)-(3) using daa from seleced European counries. The counries of ineres are Germany, Spain and he UK. The relevan variables for our analysis are he aggregae employmen growh rae and he growh raes of employmen shares of he relevan secors. The uilized secoral daa are presened in Table 2. Alongside he counries, he sample periods and he daa frequency, we also lis he feasible secoral decomposiions for each counry (see Daa Appendix). The choice of he secors was deermined by boh pracical (daa availabiliy) and heoreical reasons. 5

7 Secors like public adminisraion and agriculure were avoided, since he firs one is largely no sensiive o shocks and he behaviour of he second is mainly deermined by facors exraneous o our ineress. Wihin he limi impose by he daa we have ried o make he secors as homogenous as possible across he differen counries. The Res secor in Germany includes employees ha are no included in agriculure, producion indusries, rade, ranspor and communicaions. TABLE 2: DATA SUMMARY COUNTRY FREQUENCY FROM TO SECTORS UK Quarerly 978:2 998:2, Finance,, Trade Germany Quarerly 962: 998: Communicaions,, Res Spain Quarerly 987: 999:4,, Services Using Bayes facor esing, all he univariae series emerge as being I(), while heir firs differences are saionary (c.f. PP99, for a deailed discussion of Bayesian saionary ess). As we originally considered he naural logarihms of he relevan variables, we esimae our model for he growh raes of aggregae employmen and he growh raes of employmen secoral shares (All of hem were found o be I(). Resuls available from he auhors). For a more deailed discussion on he daa see Panagioidis, Pelloni and Polasek (2). 5.Empirical resuls We esimae and es model (2)-(3) and carry ou he GIRF analysis for he mean and he variance wihin a Bayesian framework (cf. PP99 and PP2, for deails). The model has been esimaed using a Gibbs-Meropolis algorihm, which provides an exac small sample soluion. Model and order selecion is carried ou using Bayes facor esing (PP99 for deails). Bayes facors are calculaed according o he marginal likelihood concep illusraed by Chib and Jeliazkov (999) which is based on Chib (995). In each insance he VAR-GARCH-M model has been preferred o alernaive specificaions. In paricular we seleced a VAR(2)-GARCH(2,2)-M(2) for Germany and he UK, and a VAR()-GARCH(,2)-M() for Spain. The GIRF analysis is carried ou wihin he seleced VAR-GARCH-M model. We wish o sress ha our resuls should be seen as preliminary. The emphasis of our experimen is more on is mehodological poenial han on he acual oucomes. The empirical resuls emerge from a specific experimenal framework which, o be able o provide final evidence, may need furher exensions. As we have already poined ou, he GIRF analysis can be viewed as he oucome of a concepual experimen. The generaed oupu depends on he naure of he esimaed model and he srucure of he shocks. Once a model has been seleced, hrough appropriae esing, he configuraion of he chosen shocks will become crucial for generaing he pahs of he relevan variables. In our experimen we would resric ourselves o explore he implicaions of emporary posiive shocks. Of course, we could have inroduced a differen and more complex design of he shocks. Probably a more ariculaed framework is needed o disenangle he hree 6

8 examined hypoheses. However, given ha our ineres is in he mehodological poenial of our approach, we resric our exercise o he simples scenario. Even wihin he boundaries of his experimen we can exrac enough informaion o evaluae he poenial usefulness of our approach. Our oupu is presened in Figures o 6. Figures -3 provide he GIRF plos for he means (GIRF) while Figures 4-6 display he GIRF plos for he volailiies (GIRF-V). If we look a he mean responses for Germany (Figure 2) and Spain (Figure 3), we can see ha hey presen similar profiles. When a emporary aggregae shock is inroduced, all secoral componens move in he same direcion and here is no much difference in he size of heir responses. The effecs of an aggregae shock end o die ou quickly and afer four quarers hey are almos compleely reabsorbed. These sor of emporal profiles seem o reflec wha we would expec under he NBCH. A similar oulook is displayed when a secoral componen is shocked. However here we are facing one of he above-menioned difficulies in implemening our approach. A single posiive shock o an individual secor may no be a proper represenaion of a reallocaion shock. Allocaive disurbances are composiional and no direcional and could bring abou permanen changes in secoral shares. Thus he shock we are inroducing eiher i is par of a more complex srucure (4) or i capures a secoral shock which, by varying he level of demand a indusry level, can vary he level of aggregae demand. Be ha as i may, he generaed informaion is a leas sufficien o discriminae beween NBCH and RTH. The emerging profiles sugges ha he NBCH has o be preferred. The similariy beween he wo counries is confirmed by he plos of he GIRF-V. Given he naure of he VAR-GARCH-M model, we view he GIRF-V as a ool which can correcly capure he effecs of reallocaion shocks. When we shock he secoral variances of manufacuring (Germany) and consrucion (Spain), we can see he aggregae componen ends o respond quie srongly. In boh counries a secoral shock brings abou a cerain amoun of secoral variabiliy in he oher secors. These responses end o die ou afer 5 quarers on average. The GIRF-V oupu seems o sugges ha reallocaions are aking place and ha a volailiy shock would resul in urbulence in mos of he cases. This secoral response is slighly sronger in Germany han in Spain. For Germany we can draw a picure where he SSH could be working alongside he NBCH. In he case of Spain, he evidence in suppor of he SSH is slighly weaker while he GIRF profiles cerainly corroborae he NBCH. A differen profile emerges for he UK (Figure ). As far as he mean equaions are concerned, an aggregae shock brings abou a sizable response only in he consrucion secor (5). Insead secoral shock can generae appreciable, hough shor lived, movemens in aggregae employmen. A he same ime readjusmens of differen size and direcion ake place in mos of he secors. A shock o manufacuring has no effecs on rade and finance, bu generaes a change in oal employmen which does no die ou afer 8 periods. The financial secor, one of he mos dynamics secors of he UK economy, seems o creae he mos significan responses. If we look a he GIRF-V (Figure 4) he aggregae response o secoral shocks is always noiceable, while all he secoral componens reac quie sensibly. This evidence can be inerpreed as a signal of subsanial reallocaions. The UK oupu does no bear ou he NBCH. Insead i is 7

9 favouring hypoheses which envisage an inerplay beween aggregae movemens and secoral reallocaions. Thus he available evidence provides suppor for eiher he RTH or he SSH. I is worhwhile o noe how our resuls only parially corroborae PP3. The evidence emerging from PP3 suggess ha inersecoral labour reallocaions have a significan and subsanial impac boh for he UK and Germany. This resul is surprising since previous empirical work has always assigned a limied role o secoral shifs in hose counries. Even more saggering is ha he size of he aggregae effecs of secoral reallocaions are a leas as big for Germany as for he UK. However, i would have been reasonable o expec ha secoral shifs were more effecive in he UK han in Germany. Tha because, while he UK has been characerized by an increasingly flexible labour marke, Germany has epiomized he ypical welfare srucure of coninenal Europe. Therefore PP3 suggess ha he differen insiuional arrangemens in Germany and UK do no affec he macroeconomic effecs of secoral reallocaions. Our resuls confirm he imporance of secoral shifs for he UK, bu reappraise heir relevance for Germany. Secoral shifs seem o be presen and o maer, bu heir imporance is somehow scaled down. Changes in reallocaion (un)employmen could be dependen on he differen degrees of labour marke flexibiliy. 6.Conclusions and Furher Oulook A GIRF (Generalised Impulse Response Funcion) approach has been developed o explore he differen impacs of aggregae and secoral shocks wihin a VAR-GARCH-M model. The goal of our experimen is o provide a new and beer undersanding of he dynamics and he ineracions characerising aggregae employmen and secoral reallocaions. The noion of he GIRF, viewed as he resul of a concepual experimen, has been applied o his aim. We have aken ino accoun he hree main heoreical frameworks of (un)employmen flucuaions: namely he normal business cycle hypohesis (NBCH), he reallocaion iming hypohesis (RTH) and he secoral shifs hypohesis (SSH). We explored he behaviour of hree European counries (Germany, Spain and he UK), using he oupu of a GIRF analysis. We could esablish links and provide explanaions Thus, hough our approach is sill in an experimenal sage, useful conclusions were drawn and policy implicaions could be considered. For insance, our evidence suggess ha he NBCH could provide a saisfacory framework for Spain while he SSH could be operaional in he UK and o a lesser degree in Germany. Appropriae macroeconomic policies could be appropriae for Spain bu hey should no effecive in he UK. Germany may insead provide he example of a more complex policy mix. We wish o sress once more he innovaive naure of our approach. Our resuls should be seen sricly in he mehodological perspecive of our experimen. Definiive resuls should be expeced once more complex modelling sraegies of he relevan shocks will be inroduced. The main obsacle is o design a srucure which could accommodae he composiional naure of secoral disurbances alongside he inrinsic asymmeries of RTH and SSH. The exploiaion of he GIRF properies seems a promising perspecive in his direcion. 8

10 NOTES () Lilien (982a) originally proposed a dispersion index based on he weighed sandard deviaion of he secoral shares growh raes σ ˆ N = i= N i, ( ln N i, ln N ) 2.5 where N is aggregae employmen, N i, is employmen in secor i, i =,2,,K. Lilien s index has been widely used as a measure of inersecoral labour reallocaion. Oher alernaive dispersion measures have been proposed in he lieraure. However, heir implemenaions were equally unsuccessful in separaing he movemens in he proxies generaed by secoral shocks from hose brough abou by allocaive disurbances (for a survey c.f. Gallipoli and Pelloni, 2). (2) For a deailed discussion of he model, he esimaion echnique and he model selecion procedure see PP99 and PP2. (3) The GIRF is based on he concep of generalised ransfer funcion (Priesley, 988). C.f Poer (2), for a deailed discussion on he GIRF and is heoreical foundaions. (4) A more complex srucure, reflecing he composiional naure of inersecoral reallocaions, would involve secoral shocks compensaing each oher so as o leave he level of aggregae demand unaffeced. (5) This migh be due o he differen income elasiciies of secoral demands as well. (6) An explanaion migh perhaps be aemped along he lines of Beach and Kaliski, (985). DATA APPENDIX Sources of he daa: UK: Naional Saisics, hp:// Germany: Federal Saisical Office, hp:// Spain: Naional Saisics Insiue, hp:// 9

11 APPENDIX A. Generalised Impulse Response Funcion Impulse response funcions are used in VAR sysems o describe he dynamic behaviours of he whole sysem wih respec o uni shocks in he residuals of he ime series. For non-linear ime series sysems, like mulivariae GARCH models, he concep has o be exended o generalised impulse response funcions. In exension of he approach of Hamilon (994, p.38) and KPP we define he generalised impulse response funcion o be he derivaive: y + n / ε = M n, s =,2, (A.) for he VAR-GARCH-M model; where n is he forecas horizon span and Mn is he lag n marix of he MA represenaion of y. Each column of M n is defined as he numerical derivaive in direcion yˆ + n + + n + + n Ω ( ε ) = n [ E( y ε, Ω ] E[ y ], s =,2, (A.2) where Ω is he informaion se up o ime, ε + varies over all uniy vecors and y ˆ + n is he predicive disribuion. The expecaion is aken as he mean of he predicive disribuion and is esimaed by he average over he simulaed fuure pahs calculaed from he MCMC oupu. The difference beween he prediced value of he vecor y ˆ + n a ime +n in (A.2) corresponds o he j h column of he marix M n. By doing a separae simulaion for impulses o each componen of he innovaion vecor ( j =,,M), all of he columns of M n can be calculaed, i.e. M n [ + n + n M = yˆ ( e ),..., yˆ ( e )], (A.3) where e,, e M are he M uniy vecors of order M. Noe ha he impulse response funcion of a non-linear sysem is no ime invarian, i depends on he ime, he forecas origin. Deails of he approach are found in Polasek and Ren (2). Also, we calculae he impulse response funcion for he condiional variances of he VAR-GARCH-M model using he following formula: ˆ H = n [ E ( Hˆ ε, Ω ] E [ Hˆ ], s =,2, (A.4) + n + n + + n Ω

12 REFERENCES Abraham, K. and L. Kaz, (986), Cyclical Unemploymen: Secoral shifs on aggregae disurbances, Journal of Poliical Economy, 94, Beach, C. and S. Kaliski, (985), The Impac of Secoral Shifs, Demographic Changes and Deficien Demand on Unemploymen in Canada, Queen s Discussion Paper no. 624, Aug. Campbell, J.R. and K.N. Kuner, (996), Macroeconomic effecs of employmen reallocaion, Carnegie-Rocheser Conference Series on Public Policy, 44, Chib, S. and I. Jeliazkov, (999), Marginal Likelihood from he Meropolis-Hasings Oupu, Washingon Universiy Discussion Paper. Chib, S., (995), Marginal Likelihood from he Gibbs Oupu, Journal of he American Saisical Associaion, 9, Davis, S.J., (986), Allocaive Disurbances and Temporal Asymmery in Labor Marke Flucuaions, WP 86-38, Graduae School of Business, Universiy of Chicago. Davis, S.J., (987), Allocaive Disurbances and Specific Capial in Real Business Cycle Theories, American Economic Review, 77, Gallipoli, G. and G. Pelloni, (2), Macroeconomic effecs of employmen reallocaion: a review and an appraisal from an economeric perspecive, Discussion Paper 2-, Deparmen of Economics, Universiy of Sheffield, UK Hamilon, J., (994), Time Series Analysis, Princeon Universiy Press. Koop, G., H. Pesaran and S.M. Poer, (996), Impulse Response Analysis in non-linear Mulivariae Models, Journal of Economerics, 74, Lilien, D., (982a), Secoral Shifs and Cyclical unemploymen, Journal of Poliical Economy, 9, Lilien, D., (982b), A secoral model of he business cycle, MRG Working Paper no. 823, Universiy of Souhern California. Panagioidis, T., G. Pelloni, and W. Polasek, (2), Macroeconomic Effecs of Reallocaion shocks, EMASE - Repor No. I3A WP ask 3. Pelloni, G. and W. Polasek, (999), Inersecoral Labour Reallocaion and Employmen Volailiy: A Bayesian analysis using a VAR-GARCH-M model, Discussion Paper no. 99/4, Universiy of York, York, UK

13 Pelloni, G. and W. Polasek, (23), Macroeconomic effecs of secoral shocks in U.S., U.K. and Germany: a BVAR-GARCH-M approach, Compuaional Economics forhcoming, February. Pesaran, H.H. and Y. Shin, (997), Generalized impulse response analysis in linear mulivariae models, Economics Leers, 58, Polasek, W. and L. Ren, (2), Generalized Impulse Response Funcions for VAR- GARCH-M Models, mimeo, Insiue of Saisics and Economerics, Universiy of Basel, March. Poer, S.M., (2), Nonlinear Impulse Response Funcions, Journal of Economic Dynamics and Conrol, 24, Priesley, M.B., (988), Non-Linear and Non-Saionary Time Series, Academic Press, New York. 2

14 FIGURE Individual impulse response plos of employmen (for he mean) in UK from 978 Q o 998 Q2 for he VAR(2)-GARCH(2,2)-M(2) model. UK Finance Trade UK Finance Trade 3

15 UK Finance Trade - UK Finance Finance Trade UK Trade Finance Trade - 4

16 FIGURE 2 Individual impulse response plos of German employmen (for he mean) from 97 Q o 998 Q for he VAR(2)-GARCH(2,2)-M(2) model. Germany Communicaion Res Germany Communicaion Res

17 Germany Communicaion Communicaion Res Germany Res Communicaion Res 6

18 FIGURE 3 Individual impulse response plos of employmen (for he mean) in Spain from 987 Q o 999 Q4 for he VAR()-GARCH(,2)-M() model. Spain Services Spain Services

19 Spain Services Spain Services Services 8

20 FIGURE 4 Individual impulse response plos of employmen (for he volailiy) in he Unied Kingdom from 978 Q o 998 Q2 for he VAR(2)-GARCH(,)-M(2) model. UK Employmen (Volailiy) Finance Trade UK (Volailiy) Finance Trade

21 UK (Volailiy) Finance Trade UK Finance (Volailiy) Finance Trade UK Trade (Volailiy) Finance Trade 2

22 FIGURE 5 Individual impulse response plos of German employmen (for he volailiy) from 97 Q o 998 Q for he VAR(2)-GARCH(,)-M(2) model. Germany Employmen (Volailiy) Communicaion Res Germany (Volailiy) Communicaion Res 2

23 Germany Communicaion (Volailiy) Communicaion Res Germany Res (Volailiy) Communicaion Res

24 FIGURE 6 Individual impulse response plos of employmen (for he volailiy) in Spain from 987 Q o 999 Q4 for he VAR(2)-GARCH(,)-M() model. Spain Employmen (Volailiy) Services Spain (Volailiy) Services 23

25 Spain (Volailiy) Services Spain Services (Volailiy) Services 24