Decomposing Beveridge curve dynamics by correlated unobserved components

Transcription

1 Regensbuge DISKUSSIONSBEITRÄGE zu Wishafswissenshaf Univesiy of Regensbug Woing Papes in Business, Eonomis and Managemen Infomaion Sysems Deomposing Beveidge uve dynamis by oelaed unobseved omponens Sabine Klinge *, Enzo Webe ** May 9, 24 N. 48 JEL Classifiaion: C32, E24, E32, J2, J69 Keywods: Beveidge uve, woe flows, ighness, unobseved omponens, Haz efoms * Univesiy of Regensbug, Depamen of Eonomis and Eonomeis, 934 Regensbug, Gemany. sabine.linge@iab.de, and Insiue fo Employmen Reseah (IAB). ** Univesiy of Regensbug, Depamen of Eonomis and Eonomeis, 934 Regensbug, Gemany. enzo.webe@wiwi.uni-egensbug.de, and Insiue fo Employmen Reseah (IAB), IOS Regensbug.

2 Deomposing Beveidge uve dynamis by oelaed unobseved omponens Sabine Klinge a,b, Enzo Webe a,b a) Insiue fo Employmen Reseah, Regensbuge Saße 4, 9478 Nuembeg, Gemany b) Univesiy of Regensbug, Insiue fo Empiial Eonomi Reseah, Univesiässaße 3, 9353 Regensbug, Gemany Absa Beween 979 and 29, he Geman labou mae moved along a Beveidge uve wih hanging slope ha used o shif ouwads bu shifed inwads afe sevee labou mae efoms had ome ino foe. We analyse hese dynamis and fous on he maoeonomi ouome of he efoms. Fo ha pupose, we onsu a new empiial model ha lins equilibium unemploymen heoy o a flexible unobseved omponens model: we disenangle pemanen and ansioy omponens of mahing effiieny and sepaaion ae as well as unemploymen and vaanies. Coinegaion and idenifiaion ae addessed. We find ha mahing effiieny and sepaaion ae eah aoun fo abou half of he inwad shif. Theeby, he inease in end mahing effiieny is exaodinay and esifies o a pemanen impovemen on he labou mae. Is visibiliy, howeve, was eaded by an ovelay wih a suual inease in ighness. Keywods: Beveidge uve, woe flows, ighness, unobseved omponens, Haz efoms JEL: C32, E24, E32, J2, J69 Coesponding auho: D. Sabine Klinge, Insiue fo Employmen Reseah, Fedeal Employmen Ageny, Regensbuge S. 4/We 5b, 9478 Nuembeg, Gemany, sabine.linge@iab.de, phone

3 2 Inoduion Eonomiss used o desibe he Geman labou mae by igidiy, sleosis and hyseesis as labou mae flows wee muh lowe han in he Unied Saes and unemploymen beame pesisen ove ime (Blanhad/Summes 986, Niell 997). Consequenly, he Geman Beveidge uve (BC) he downwad sloping elaionship beween vaanies and unemploymen shifed ouwads. Afe a se of sevee labou mae efoms had ome ino foe in 23 o 25, hings saed o hange. The BC shifed inwads fo he fis ime in deades. Following he sandad inepeaion (see he BC as a ool of maoeonomi poliy analysis in Abaham/Kaz (986) and Blanhad/Diamond (989)), his inwad shif indiaes a suual impovemen of he funioning of he labou mae. By onas, he Gea Reession 28/9 jus aused a limied and seemingly odinay movemen along he uve. We analyse he dynamis of he BC (see also Banihon/Figua 2, 22, Bouve 22, Daly e al. 22) wih speial fous on he maoeonomi ouome of he labou mae efoms. Fo ha pupose, we onsu a new empiial labou mae model. I diely onnes o heoy and allows us o addess impoan issues wih espe o he Geman BC: We will find ou abou he empiial elevane of he heoeial diving foes of BC shifs and movemens along he uve, foemos mahing effiieny, he sepaaion ae and labou mae ighness. Theeby, i is of speial inees also fom a poliy pespeive whehe hese diving foes hanged fo suual o ylial easons, i.e. whehe he funioning of he labou mae impoved pemanenly o jus empoaily. This quesion gains speial impoane as ommon wisdom shifs of he BC efle suual hange wheeas movemens along he uve ae ylial will be hallenged by ou esuls (ompae also Bösh-Supan 99, Kosfeld e al. 28, Fujia/Ramey 29 o Davis e al. 2). This is in siing onas o he developmen of he U.S. labou mae, fo insane, whee unemploymen ose shaply, long-em unemploymen doubled, and he BC shifed ouwads (Benai/Lubi 24, Lubi 23, Daly e al. 22, Sala e al. 23).

4 3 Fuhemoe, we see o unove how diving foes and labou mae vaiables inea and how diffeen pemanen and ylial poesses inefee in he developmen of he BC (Blanhad 997). In ou seup, we ombine he heoeial famewo of he BC and equilibium unemploymen wih he flexibiliy of a oelaed unobseved omponens model (fo he lae, ompae Moley e al. 23). Paiulaly, we inegae a mahing funion ino an unobseved omponens famewo (ompae Dixon e al. 24, Sedláče 24). The model disenangles eah of he ey vaiables (unemploymen, vaanies) and eah of he shifing paamees (mahing effiieny, sepaaion ae, employmen) ino hei unobseved pemanen and ansioy omponens; see King (25) fo anohe appliaion o labou mae flows. The pemanen omponen a ompleely pesisen sohasi end efles suual hange wheeas he ansioy omponen is a mean-eveing end-deviaion. This mehodology is espeially advanageous fo seveal easons: The heoeial BC as a seady sae elaion implies oinegaion beween he seies involved. In ou famewo, we ae able o implemen his ommon end exaly fo he long-un omponens. Theeby, he model an ombine wo feaues: on he heoeial side, we inegae he long-un equilibium while on he empiial side we avoid he usual poblem see e. g. Elsby/Hobijn/Sahin (23) ha obseved unemploymen migh be a bad appoximaion fo equilibium unemploymen. Moeove, he model an epesen omplex ineaions in he labou mae by allowing fo oelaion beween all end and yle shos. Addiionally, we an invesigae whehe he impa of unemploymen and vaanies in he mahing funion diffes wih espe o end o yle. As he main esuls we show ha mahing effiieny and sepaaion ae eah onibued fo abou 5 peen o he inwad shif. While he sepaaion ae has been moe impoan in explaining shifs of he BC ove he whole hoizon, mahing effiieny expeiened an ousanding upun in he afemah of he labou mae efoms. This adds o sudies ha

5 4 onfim he posiive influene of he efoms on mahing effiieny (Fah/Sunde 29, Klinge/Rohe 22, Hewe/Sigis 22). The funioning of he labou mae impoved fo suual easons, indeed: I is he pemanen omponen of mahing effiieny besides he pemanen omponen of he sepaaion ae ha fims up he inwad shif, bu wih delay. The eason fo his delay is a onempoay inease in end ighness: he numbe of he unemployed shan due o highe mahing effiieny and lowe sepaaion ae, and he numbe of vaanies ineased as fims pofied fom highe mae anspaeny, wage modeaion, and wose ouside opions of he employees. This agumen is onfimed by a posiive oelaion beween shos o he end omponens of mahing effiieny and ighness. Thus, he ovelay of seveal labou mae eaions o he efoms leads o wo paallel movemens: he BC shifed inwads and he posiion on he uve moved upwads. Wihin he mahing funion, end and ylial unemploymen ae of simila impoane fo mah fomaion wheeas i is only he ylial omponen of vaanies ha plays a signifian ole. The emainde of he pape is oganized as follows: In he nex seion, we sholy inodue he developmen of he empiial BC in Gemany and desibe why he so alled Haz efoms should have been able o impove he funioning of he labou mae, i. e. indue he BC s inwad shif. Nex, we summaize he heoeial and empiial lieaue on why BC omponens, espeially mahing effiieny and sepaaion ae, should vay pemanenly o/and ansioily. Seion 4 desibes ou model. Afewads, we biefly addess idenifiaion and esimaion saegies and he daa. In seion 7, we inepe he esuls on he unobseved omponens and pesen he exended mahing funion. Finally, we summaize he pape and daw onlusions.

6 ln(vaanies)* 5 2 The Beveidge uve and he Haz Refoms Sleosis and hyseesis used o be emaable haaeisis of he Geman labou mae. Ove deades, unemploymen ose sepwise and beame pesisen. The BC displays his wosening labou mae siuaion by seveal shifs ouwads and movemens downwads along he uve (Figue ). Figue : The Geman Beveidge uve, 979 o ln(unemploymen)* Soue: Fedeal Employmen Ageny, daa manipulaion see ex. Bulles efe o Januay of indiaed yea. In he ealy 98s, he Geman labou mae expeiened a qui and shap deline in vaanies and inease in unemploymen whih maes he impession of a movemen along a BC o is lowe igh edge. Afewads, he BC seepened onsideably. Thus, aleady befoe he Geman eunifiaion, i beame hade o exploi an ineasing numbe of vaanies o edue unemploymen. Reunifiaion iself aused a subsanial igh shif as a high numbe of woes beame unemployed in he ouse of he ansiion of Easen Gemany owads a mae eonomy. (We aleady adjused fo puely saisial effes.) The ouwad shif anno only be aibued o he die effes of he ansiion as i ep on unil 25. Moeove, his shif an be similaly obseved in all fedeal saes of Gemany (Bouve 22) i is no a

7 6 puely Easen Geman phenomenon bu mus be aionalized by suual, e. g. insiuional easons ha pomp unemploymen o pesis. Mass unemploymen wih a high shae of long-em unemploymen aused he govenmen o launh he mos seious labou mae and soial efoms in Geman pos-wa hisoy. The so alled Haz efoms onsised of fou laws and ame ino foe in hee waves beween 23 and 25. I onened many omponens whih an be summaized ino hee main ages (Jaobi/Kluve 27, Klinge/Rohe 22): - Fis, highe effiieny in plaemen sevies ageed on he ineaion of supply and demand. The fome publi employmen sevie was e-oganized wih he aim of poviding mae-onfom plaemen sevies, inease anspaeny abou vaany and woe pofiles and esablish a mae-segmenaion wih speifi suppo. - Seond, ineasing aivaion and pesonal esponsibiliy ageed on labou supply. The efoms ineased he inenives o seah fo a job moe inensively and o be eady o ae onessions. The peiod of enilemen o unemploymen benefis was shoened and means-esed unemploymen assisane fo people wihou laims agains unemploymen insuane was loweed. Fuhe efom omponens in ha aegoy ae a sie definiion of easonable wo, implemening sanions and age ageemens egading seah effo as well as a new ind of sa-up subsidy. - Thid, labou demand was o be boosed by allowing fo highe flexibiliy, fo example wih espe o empoay ageny wo, employmen poeion legislaion and maginal employmen. These feaues ae onsideed o impove he BC posiion (Bouve 22). Moeove, labou demand was simulaed by a modeae wage developmen as he ouside opions of employees wosened hough he efoms (Kebs/Sheffel 23). Saing in lae 26, he BC shifed inwads fo he fis ime in deades.

8 7 The inwad shif ame o an end in lae 28 when he Gea Reession hi he Geman labou mae. Is esponse o a dop of GDP by moe han 5 peen was noedly modeae. Labou demand did no dop as muh as migh have been expeed based on he expeiene fom pevious eessions. This alls fo anohe o a new suual effe ha ould have ovelaid he isis peiod and ha does no show up in a shif of he BC bu in a jus modes movemen along he uve. 3 Tend and yle of Beveidge uve omponens The BC is heoeially deived in he labou mae model populaized by Moensen/Pissaides (994) and suveyed in Pissaides (2). The law of moion of unemploymen and he mahing funion lead o he BC as a downwad sloping seady-sae elaion beween vaanies and unemploymen (see Figue 2). Figue 2: The sylized Beveidge uve v Job eaion (JC) Beveidge uve (BC) u Soue: Pissaides (2), 2. The exa posiion on he BC is maed by he ineseion wih he job eaion uve (JCC). Is oaions ae efleed by hanges in labou mae ighness θ (vaanies ove unemploymen, he angle in Figue 2). An uppe-lef posiion on he uve indiaes a elaively high numbe of vaanies and a elaively low numbe of unemployed. Then, he

9 8 labou mae is igh, and fims may find i diffiul o fill vaanies. The opposie holds in lowe-igh posiions on he BC. Two of he vaiables foming he ineep ae mahing effiieny, i. e. he effiieny omponen of he job finding ae ha inludes seah inensiy as well as publi and pivae job plaemen, and he sepaaion ae (see he model in seion 4). In ou analysis, he hazad aes give he pobabiliies of eihe finding a job ou of unemploymen o losing o quiing one s job and ansiioning ino unemploymen. Thus, one an egad hem as hanes and iss in he labou mae. Changes o hem ause shifs of he Beveidge uve. Following ommon wisdom (e. g. Blanhad/Diamond 989 and he subsequen lieaue), shifs of he BC ae asibed o hanges in labou mae ends aused by hanges in insiuions, ehnology, he seoal omposiion of he eonomy, o demogaphy. These shifs of he BC imply a hange in he pemanen omponen of unemploymen, ofen named suual. On he ohe hand, ylial vaiaion as a onsequene of fluuaing poduiviy oaes he job eaion uve (JCC) suh ha movemens along he BC wee onsideed o be ylial. This adiional view is no beyond doub, howeve. Seveal auhos pu fowad agumens ha issue he ylialiy of mahing effiieny, fo example (Bösh-Supan 99, Kosfeld e al. 28, Fujia/Ramey 29, Davis e al. 2). In line wih hose auhos we ague ha basially all deeminans of Beveidge uve dynamis may vay fo pemanen and ansioy easons. In ohe wods: Shifs ould ou no only fo suual bu also fo ylial easons. Movemens along he uve ould ou no only fo ylial bu also fo suual easons. We give impoan examples in he following. To begin wih, ends in mahing effiieny, sepaaion ae, and ighness ou beause of suual insiuional, demogaphi, ehnologial, seoal hange (ompae Blanhad/Diamond 989, Bösh-Supan 99, Blanhad/Wolfes 2, Davis/Haliwange

10 9 2, King/Moley 27, Boei 2, Banihon/Figua 22, Bouve 22). The mos emaable hange in Geman labou mae insiuions he Haz efoms ha saed a deade ago has been desibed in he pevious seion. Thei effe on mahing effiieny was posiively evaluaed (Fah/Sunde 29, Klinge/Rohe 22, Hewe/Sigis 22). Pemanen effes on he sepaaion ae have no ye been invesigaed diely. As a hin, Rebien/Kene (2) sae ha afe he efoms employees have beome moe willing o mae onessions egading hei woing ondiions. A he same ime, he shae of labou mae ansiions ha happen and ae evesed wihin jus one monh may have ineased (Nodmeie 22) whih eoniles highe insiuional flexibiliy wih shining sepaaion ae in he daa. Mahing effiieny and sepaaion ae ae deeminans of labou mae ighness, IOW of he slope of he job eaion uve (fo a deivaion see Cahu/Zylbebeg 24). Thus, hei pemanen omponens ae aied ove o ha pa of he Beveidge uve dynamis ha used o be desibed as ylial. Fuhemoe, pemanen wage modeaion (and dispesion) may lead o highe pofiabiliy of filled vaanies. The onsequene would be a end inease in ighness whih shows up as a pemanen movemen up he BC. Suh developmens of wages ould sem fom a lowe degee of unionizaion o wosened ouside opions afe he efoms (see Dusmann e al. 24 and Sheffel/Kebs 23 fo elevane in Gemany). On he ohe hand, yles in he sepaaion ae and ighness ae bough in as spilloves of ylial fluuaions of poduiviy. Cyles in mahing effiieny ou beause fims and woes adjus hei seah behaviou o hose poduiviy fluuaions: euiing o seah inensiy is adjused as ompeiion fo (good) woes o fims (Davis e al. 2, Davis 2) and he aveage job finding pobabiliy of he unemployed vay ove he business yle (heeogeneiy hypohesis, see Daby e al. 985, Banihon/Figua 23, Sedláče 24). Fuhemoe, ylial vaiaion in he seah and mahing model has indued a lage amoun of sudies wih egad o he unemploymen volailiy puzzle (e. g. Shime 25, Fujia/Ramey

11 25, Hagedon/Manovsii 28, Pissaides 29). As pa of his basially mioeonomi debae, he ouneylialiy of he sepaaion ae was shown o be subsanial and influenial fo unemploymen dynamis (e. g. Fujia/Ramey 29, Elsby e al. 29, and fo Gemany Nodmeie 22, Hewe/Sigis 22). As a onsequene of he afoemenioned agumens, we employ an empiial saegy o simulaneously idenify poenial ends and yles in all deeminans of BC dynamis. 4 The model In his seion we develop ou labou mae model ha will seve o analyse he BC dynamis, espeially onening he Haz efoms. We follow he seah and mahing lieaue egading heoeial ey feaues (Moensen/Pissaides 994, Pissaides 2, Peongolo/Pissaides 2 on he mahing funion) and inegae hem ino a flexible unobseved omponens speifiaion. Iniially, we fous on he long-un equilibium elaions on he labou mae. In empiial wo, suh heoeial equilibia ae ofen opeaionalised by (linea) elaions beween obseved ime seies alhough hese do no only onain long-un infomaion and, onsequenly, do no appopiaely efle he mae being in equilibium. Elsby/Hobijn/Sahin (23) and Nodmeie (22) ague ha espeially on he Geman labou mae aual unemploymen may be an insuffiien appoximaion of equilibium unemploymen. We will iumven hese poblems by expliily anhoing he seady sae o he (unobseved) pemanen omponens beause i is hei suual ineelaions ha ae unoveed by he eonomi equilibium. Thus, hey fom he oinegaing elaion. Seady sae unemploymen is ahieved in he long-un flow equilibium, i. e. if equilibium mahes and equilibium sepaaions equae. Theeby, following Pissaides (2) and Shime (25), mahes M and sepaaions S ae defined as ansiions beween employmen and unemploymen.

12 () M S All vaiables ae given in logaihms. Eonomeially, expession () implies oinegaion beween sepaaions and mahes if he obseved seies ae I(). Mahes ae fomed by unemployed pesons fom U who leave unemploymen wih a eain pobabiliy, he job finding ae f, whih a leas paly mios labou mae insiuions. Similaly, sepaaions an be efeed o as employees fom E losing o quiing hei job wih a eain pobabiliy, he sepaaion ae s. Changes in he hazad aes efle he eonomi behaviou of agens, e. g. fims deisions on how many people o employ o dismiss. By onas, he flow vaiables ae subje o mee level effes due o hanges in he sos of unemploymen and employmen. We heefoe ewie he flow equilibium () in ems of he long-un omponens of he log-lineaized hazad aes and espeive so vaiables. The long-un omponen of unemploymen U an be seen as some measue of suual unemploymen, in heoy ofen onneed o he onep of he NAIRU. (2) f U s E The model does no assume a onsan labou foe. Alhough ou analysis fousses on ansiions beween unemploymen and employmen, he equilibium elaion (2) does no involve he assumpion ha employmen ae and unemploymen ae fom a die elaionship and add up o, no even wih egad o he given long-un values. These sos may well vay beause of ansiions ino o fom fuhe labou mae saes as well as ou of he labou foe. Moeove, as soon as suh fuhe ansiions indue omposiion effes ha affe mahing effiieny o sepaaion ae, hey will ene ou analysis impliily. Finally, as equaion (2) jus einepes he flow equilibium () and as neihe he sos no he hazad aes ae saionay, all fou fileed end seies shae a oinegaion elaion.

13 2 Equaion (2) is he fis sep fo he deivaion of he BC. The seond sep is povided by he mahing funion ha explains job finding pobabiliy depending on unemployed U and vaanies V. We speify a log-linea Cobb-Douglas-ype mahing funion. (3) f m U V m denoes mahing effiieny while α and β ae elasiiies of mahes wih espe o unemploymen and vaanies, espeively. Inegaing (3) ino (2) and eaanging gives he BC as seady sae ombinaions of vaanies and unemploymen. (4) V s E m U Shifs of he BC ae aused by hanges of he ineep. Theefoe, inwad shifs ou if. p. he sepaaion ae o employmen shin and if mahing effiieny o he elasiiy of mahes wih espe o vaanies ise. The slope of he BC is deemined by he wo mah elasiiies. So fa, he deivaion of he BC elied on he long-un omponens of he onsiuing vaiables. In ealiy, howeve, hose long-un omponens ae no obsevable. Insead, empiial BCs onsis of ime seies ha inlude long-un (pesisen) and sho-un (ansioy) omponens. To disenangle hese omponens we develop a oelaed unobseved omponens model. Theeby, eah vaiable is deomposed ino a sohasi end ha apues pemanen effes and a saionay auoegession ha apues ansioy effes (he yle, see equaions 5 o 8). The fous of ou pape is on mahing effiieny and sepaaion ae as hey mio behaviou and insiuions ha (migh) have hanged afe he labou mae efoms. We aim a speifying he ime-vaying popeies of hese paamees.

14 3 As mahing effiieny iself is no obsevable, we inlude he unobseved omponens speifiaion ino an empiial mahing funion (wih he job finding ae f, mahing effiieny m, unemploymen U, vaanies V, he espeive elasiiies α and β, and a whie noise eo em w): f m ( ) U (5) m m m V w The so vaiables ae lagged in ode o ensue ha we appopiaely model he ime paen of he unemployed geing egiseed fis and poenially indue an ouflow afewads. In line wih he speifiaion of mahing effiieny, we also allow fo a sohasi end and a yle in he sepaaion ae; see equaion (6). The same applies o employmen and vaanies. This flexible speifiaion has he advanage ha i les he daa spea when deemining he naue of labou mae poesses. (6) s E V s E V s E V As an impoan feaue of ou model, he seady sae Beveidge elaion (4) summaizes five nonsaionay vaiables ino one equilibium elaion. Theefoe, i implies oinegaion: A mos fou sohasi ends an be independen. Consequenly, we use he Beveidge elaion o speify he pemanen omponen of ou emaining vaiable, unemploymen 2, as a omposie end of employmen, sepaaion ae, mahing effiieny, and vaanies (and besides onol fo a deeminisi end and an ineep); see equaion (7). The speifiaion of a ommon end would no have been possible wih a smoohing file lie HP. Ou appoah ahieves wo impoan goals: Fis, we an appopiaely inegae he esiion semming fom he BC ino ou model. Seond, sine his esiion applies only o he long- 2 Eonomeially, hoosing one of he ohe vaiables would jus imply a linea ansfomaion no aleing he model.

15 4 un omponens, we do no have o ely on he poo appoximaion of equilibium unemploymen by he aual values he yle omponens ae sill unonsained. m s E V U (7) U The inlusion of vaanies as an endogenous vaiable (see equaion 6) loses he model. Wih unemploymen and vaanies eah onsising of a pemanen and a ansioy omponen, fou sepaae elasiiies of mahes wih espe o suual as well as ylial unemploymen and wih espe o pemanen as well as ylial vaanies ould be esimaed fom he mahing funion (5). We efe o his as exended mahing funion and elaboae on his issue in geae deail in seion 7.3. Fuhemoe, he inlusion of vaanies ino he model helps o appoximae a job eaion uve, i. e. a speifiaion fo ighness and he equilibium vaany-unemploymen-elaion. As explained above, we ely on a flexible unobseved omponens speifiaion fo his pupose. One ould also hin abou a moe die anslaion of he job eaion uve semming fom wage uve and labou demand (Cahu/Zylbebeg 24, 53f.). Howeve, his would aise he omplexiy of ou empiial unobseved omponens model beyond he level ha is sill aable. 3 Based on ou geneal vesion, he unobseved omponens of ighness an be dedued fom he infomaion given in he sysem of equaions (5) o (7): V U V m s E (8) V U The suual model fuhe onains he speifiaion of he unobseved omponens. Eah end omponen follows a andom wal wih dif. 3 Empiial job eaion uves have hadly been povided in he lieaue. Daly e al. (22) esimae a longun shape based on a egession of he vaany ae on he naual ae of unemploymen by he U.S. Congessional Budge Offie.

16 5 i i i i (9) fo i = m, s, E, V Eah yle omponen is modeled as a saionay AR(p) poess. () i p j i j i j i fo i = m, s, E, V, U All oos of he lag polynomials i i i p p ( L) L... L in modulus lie ouside he uni ile. Given his mean eveing popey, he yles explain ansioy deviaions fom he end. Besides he mahing sho i w he model inludes fou end shos and five yle shos i. Unlie in onvenional unobseved omponens sudies, hese ae allowed o oelae wih eah ohe aoding o he ovaiane maix in appendix 9.2 (ompae Moley e al. 23). This povides us wih nine oelaions beween measuemen and ansiion shos and 36 fuhe oelaions among he ansiion shos. These oelaions unove how inensely he developmens on he labou mae ovelie and inefee wih eah ohe. This inludes suual and ylial effes as well as shifs of and movemens along he BC. Theeby, end shos lie insiuional hange may affe he yle and vie vesa. A few example hypoheses may undeline he impoane of allowing fo oelaed shos: () The oelaion beween he ends of mahing effiieny and sepaaion ae is supposed o be negaive. As hese paamees ene he ineep of he BC wih diffeen signs, a negaive oelaion of hei end omponens implies ha pemanen shos suh as suual efoms will shif he pemanen pa of he BC hough boh mahing effiieny and sepaaion ae. The effes do no ompensae. (2) Thei ansioy omponens ae also expeed o be negaively oelaed as he pevious lieaue showed ha mahing effiieny is ahe poylial wheeas sepaaion ae is ouneylial. (3) An ovelay of suual and ylial effes would be indiaed by oelaions beween end and yle omponens. Fo example, highe end mahing effiieny afe he efoms as shown by

17 6 Klinge/Rohe (22) may have podued bee mahes suh ha a lowe aio of jobs beomes unpoduive in eessions. In ha ase, i would be negaively oelaed wih he ylial sepaaion ae. (4) A posiive oelaion beween end mahing effiieny and end ighness ould imply ha a suual impovemen of he funioning of he labou mae indues an inease in labou demand shown as ising vaanies suh ha ighness ises, oo. Then, he BC would shif inwads and move up a he same ime. A ommon esul in he unobseved omponens lieaue is a negaive wihin-oelaion, meaning ha he end and he yle omponens of mahing effiieny (o any ohe vaiable) ae negaively oelaed (Moley e al. 23, Sinlai 29). I is inuiive o aionalise his negaive oelaion saing fom he pemanen omponen: If he end ises, he obseved seies aes a while o adjus o he new equilibium pah. The sluggish eaion indues a lag unil full adjusmen, i. e. a negaive yle in he meanime. One pominen example an be found in he eal business yle heoy (Kydland/Peso 982), whee pemanen poduion shos also opeae as dives of business yles. 5 Idenifiaion and esimaion The suual fom of ou oelaed unobseved omponens model onains elasiiies of mahes, dif ems, auoegessive oeffiiens, vaianes and ovaianes of he innovaions as unnowns. Idenifiaion of suh models, espeially of he oelaions, was eaed fo he univaiae ase in Moley e al. (23) and fo he mulivaiae ase by Moley (27) and Sinlai (29). Idenifiaion equies he edued fom of he model o povide enough esimable infomaion o dedue he suual unnowns. The edued fom of a oelaed unobseved omponens model wih ends and yles of AR-ode p is a VARIMA(p,,p) (see appendix 9. fo he exa deivaion). I diely onains he auoegessive yle oeffiiens in is AR pa. The difs an be exaed fom he edued-fom ineep. All ohe paamees ae meged ino he MA pa by means of Gange s Lemma. Hene, he

18 7 sysem of equaions semming fom he nonzeo auoovaianes of he MA pa mus be ih enough o deive his infomaion. Theeby, he numbe of nonzeo auoovaianes is given by he lag ode of he MA pa whih in un depends on he lag ode of he unobseved auoegessive yles (see appendix 9.). Beyond he AR oeffiiens and dif ems, he numbe of unnowns in he suual fom wih =4 ends and =5 yles amouns o 59: 4 mah elasiiies (see seion 7.3) + (++) vaianes + ( )/2 ovaianes. Compaing his numbe of unnowns o he piees of infomaion given by he auoovaianes leads o he onlusion ha in ou seup 3 nonzeo auoovaiane maies hus a lag lengh of 2 ae neessay. The lag lengh was hosen by empiial invesigaion. We ondued esidual analyses on univaiae auxiliay egessions. The null of no esidual auooelaion in LM ess ould no be ejeed fo lag lenghs of a leas 3. Moeove, infomaion ieia onfimed a easonable fi o he daa, even hough he hoie was no always unifom. In any ase, wih an empiial lag lengh of 3, he model is idenified. This hoie balanes he need fo pasimony in a omplex model and suffiienly ih dynamis of he given vaiables. Fo esimaion puposes, he suual model is as in sae-spae epesenaion (see appendix 9.2). Maximum lielihood is applied o esimae he paamees of he mahing funion and all vaianes and ovaianes. Theeby, he lielihood funion is onsued using he pediion eo deomposiion fom he Kalman file. 6 Daa To alulae he hazad aes, we use a 2 peen andom sample of he Inegaed Employmen Biogaphies (IEB, Vesion 9.), whih is povided by he Insiue fo Employmen Reseah (IAB) and allows o aggegae individual labou mae saes and ansiions in beween. The IEB oves all individuals in Gemany who eihe have been employed subje o soial seuiy, have eeived unemploymen benefis, have paiipaed

19 8 in pogams of aive labou mae poliies (fom 2 on), o have offiially been egiseed as job-seees a he Geman Fedeal Employmen Ageny (fom 2 on); fo daa epos on ealie vesions see Jaobebbinghaus/Seh 27, Obeshahsie e al. 29. Fo evey peson in ou daase aged beween 5 and 65 yeas we define he main employmen saus a he h of eah monh fom Januay 979 o Deembe 29. If he employmen saus hanges fom one monh o he nex, we oun his ansiion as an exi fom one saus and an eny ino anohe saus. To model suh hanges, a non-ineseing daa se is equied fo eah peson. In he ase of paallel spells, only he mos impoan sae is examined. The dominan saus is seleed using a pioiy lis. Ou aning ieia ae appoined by logial easons ombined wih he pioiy fo highe daa qualiy. As a esul, saes assoiaed wih employmen geneally dominae unemploymen and non-employmen. Howeve, maginal employmen ans behind unemploymen sine i may only be used o add inome o unemploymen benefi wihin he legal esiions. This ule ensues ha unemploymen spells ae no ineuped by jus maginal employmen. Saes elaed o he seond labou mae (job eaion shemes in he publi o quasi-publi seo) and fuhe aining o qualifiaion have highe pioiy han unemploymen spells. Fuhemoe, sho gaps beween spells have o be filled off hand. We inepolae up o 4 days if he saus befoe and afe a gap was idenial o if a gap up o 4 days peedes o follows an unemploymen spell. The job finding ae is alulaed as aio of ansiions fom unemploymen ino employmen (subje o soial seuiy, seond labou mae e.g. job eaion shemes, maginal employmen) and unemploymen in he peeding monh. Similaly, he sepaaion ae gives he elaion of he evese ansiions o employmen in he peeding monh.

20 9 Daa on he so vaiables in ou model ae povided by he offiial saisis of he Geman Fedeal Saisial Offie (employmen subje o unemploymen insuane) and he Fedeal Employmen Ageny (egiseed unemploymen and vaanies). 4 We adjus all seies fo seasonaliy by X2-ARIMA. In he few ases when he seasonal paen was no appopiaely apued by he sandad poedue, we esimae hese seasonal oulie effes in auxiliay egessions and adjus fo hem. Similaly, he suual beas due o Geman eunifiaion wee eliminaed. Augmened Diey Fulle ess wih suual beas (level shifs due o eunifiaion) as well as KPSS ess on he eunifiaion adjused seies wee ondued o he (non)saionaiy (Table ). Table : Uni oo ess seies es value of es saisi 5 peen iial value lags bea dae deeminisis job finding ae sepaaion ae ADF m3 2 KPSS none onsan ADF m2 3 KPSS none onsan employmen vaanies unemploymen ADF m 5 KPSS.88.5 none ADF m6 6 KPSS.28.5 none ADF m6 KPSS.2.5 none onsan, end onsan, end onsan, end Noe: ADF iial values aoding o Lanne e al. (22), KPSS iial values aoding o Kwiaowsi e al. (992), KPSS es on eunifiaion adjused seies. KPSS ejes he null of saionaiy fo all seies, and ADF does no eje he null of nonsaionaiy bu fo vaanies. We will allow fo sohasi ends in all vaiables. Vaanies migh be a bodeline ase, bu hee he esimae of he end vaiane ould sill beome zeo in ou unobseved omponens famewo. 4 In onas o many ohe ounies hee ae offiial monhly ime seies fo he so of volunaily epoed vaanies in Gemany. This is he bes appoximaion we an use. The seies of oal vaanies fom he epesenaive Geman job vaany suvey (Kene e al. 2) is oo sho and of oo low fequeny. Coeions suh as he elaion of inflows of egiseed vaanies o all hies (Fanz 26, p. 6) do no onside suual o business yle speialies of he vaany epoing ae.

21 2 7 Resuls 7. Saes, innovaions, and Beveidge uve dynamis Coelaed unobseved omponens models povide a vey flexible famewo wihou any a pioi esiions. Thus, hey allow fo a wide ange of esuls ha ould no even heoeially be ahieved by moe esiive poedues. Wihin ha ange of esuls, wo ae fequenly onfimed by he daa: () a high negaive oelaion beween end and yle of he deomposed seies and (2) a end omponen ha is moe volaile han he obseved seies iself (e. g. Moley e al. 23, Sinlai 29). This seond feaue is found fo he unobseved omponens of mahing effiieny, sepaaion ae, and ighness (Figues 3 o 5). 5 I efles he muliude of shos ha ause pesisen effes on he labou mae. Also, i sands in onas o he smooh ends esuling fom sandad bu also esiive files lie HP. Ou esuls will lead us o a new pespeive on he naue of movemens along and shifs of he BC. Summaizing he o- o ounemovemen of he ends and yles, we an onlude on pemanen o ansioy dynamis of he Geman BC, espeially afe he Haz efoms. Figue 3 displays he job finding ae as well as end and yle of mahing effiieny as esimaed wihin he exended mahing funion. 6 In he afemah of he Haz efoms, saing in 23 and even moe emaably fom 25 on, he job finding ae ineased onsideably. The main eason fo his impovemen is an inease in mahing effiieny whih songly suppos empiial sudies ha sae suh a posiive impa of he labou mae efoms (Fah/Sunde 29, Klinge/Rohe 22, Sala e al. 23, Hewe/Sigis 22). Ou analysis moeove eveals ha he inease oo plae in he pemanen 5 Fuhe esuls on vaiables no disussed in his seion bu inluded in he omplee model speifiaion ae available fom he auhos on eques. 6 Noe ha he end onsanly lies below he obseved seies due o he addiional ems U and V on he igh hand side of he mahing funion in equaion (5).

22 979M 98M 983M 985M 987M 989M 99M 993M 995M 997M 999M 2M 23M 25M 27M 29M logaihm logaihm 2 omponen, in ohe wods: labou mae impovemen afe he efoms via mahing effiieny was suual, indeed. A simila inease has neve been obseved befoe in he pas 3 yeas. This is onay o he eonomi upswing aound he un of he millennium, when he inease in he job finding ae was only empoay as he ylial omponen ose while he end sayed fla. Fuhemoe, he Gea Reession a he un of he yeas 28/29 did no lead o a shap ylial eaion bu seems o ma he fading ou of pevious suual effes on mahing effiieny. Figue 3: Job finding ae and mahing effiieny: obsevaions, end and yle eession job finding ae end_m yle_m (igh sale) Soue: Insiue fo Employmen Reseah and own esimaion. Business yle daing by ECRI. The sepaaion ae plays a omplemenay ole in explaining he BC s inwad shif afe he labou mae efoms. Is developmen is subsanially diven by he end (Figue 4); ineases duing GDP eessions and deeases duing GDP expansions wee ofen aused by pemanen shos. Afe he labou mae efoms, boh end and yle aused he sepaaion ae o deease, wih he end playing he majo ole. Howeve, ompaed o hisoial developmens, ha end deease was no as ousanding as he jump in end mahing effiieny.

23 979M 98M 983M 985M 987M 989M 99M 993M 995M 997M 999M 2M 23M 25M 27M 29M logaihm 22 Figue 4: Sepaaion ae: obsevaions, end and yle eession sepaaion ae end_s yle_s Soue: Insiue fo Employmen Reseah and own esimaion. Business yle daing by ECRI. Mahing effiieny and sepaaion ae deemine he ineep of he BC wih diffeen signs. In piniple, hey ould ompensae eah ohe. Bu if hey develop in opposie dieions, as in he afemah of he efoms, hey senghen eah ohe s effe on he shif of he BC. In summay, he only inwad shif of he Geman BC in he pas 3 yeas oo plae mosly beause he sepaaion ae shan and mahing effiieny ineased ousandingly, boh fo pemanen easons. Even hough ou analysis does no allow fo a ausal inepeaion, his finding is a song indiao fo he effeiveness of he labou mae efoms ageing exaly seah effo and demand inenives. Eonomially, end unemploymen (ompae equaion (7)) shan by.4 peen pe monh beween is highes value in Mah 25 and is lowes value in Novembe 28. The inease of end mahing effiieny and he deease in end sepaaion ae eah aoun fo abou half of ha eduion (aveage gowh onibuion -.72 and -.76 peenage poins), wheeas he influenes of employmen and vaanies wee negligible a ha ime. Fuhemoe, we alulae aveage monhly hanges fo eonomi expansion yeas 999/2 and when he emaable BC inwad shif oo plae. In he fis phase, log end unemploymen shan by.7 pe monh on

24 2 m 2 s E2 23 aveage, in he seond phase he monhly eduion was.2. The ole of end mahing effiieny hanges in hese eduions ineased fom 3.8 peen in he fis phase o 56.3 peen in he seond phase while he impoane of end sepaaion ae hanges deeased fom 94. o 58.8 peen. Consideing he whole ime span, he sepaaion ae expeiened moe volailiy and highe ampliudes han mahing effiieny. Afe he ealy 98s, BC shifs o he igh wee mainly aused by fuhe ineases in he suual sepaaion ae wheeas mahing effiieny expeiened ahe limied hanges. This onnes o he sudies by Fujia/Ramey (29) o Hewe/Sigis (22) ha sess he impoane of he sepaaion ae fo unemploymen dynamis. This is poved by he vaianes of he shos o end and yle sepaaion ae ha ae muh lage han hose of he mahing effiieny shos (Table 2). Fuhemoe, he end sho and he yle sho of mahing effiieny have simila vaianes wheeas fo he sepaaion ae, he yle sho vaiane is hee imes as lage as he end sho vaiane. Table 2: Tend and yle sho vaianes of mahing effiieny and sepaaion ae i end vaiane peen of oal VAR(i) yle peen of oal VAR(i) mahing effiieny sepaaion ae Noe: vaiane popoions of ighness lage han beause of negaive ovaiane beween end and yle. I migh appea puzzling ha he shif of he BC beame visible only in lae 26 alhough he shifing paamees aleady saed o hange in 25. A simila seeming onadiion ous in he ealy 98s when he developmen of he BC may well be misinepeed as movemen along he uve alhough sepaaion ae and mahing effiieny hanged emendously. We an dissolve he onfli when onsideing he ovelay of shifs on he one hand and movemens along he uve aused by pemanen o ansioy oaions of he job eaion

25 979M 98M 983M 985M 987M 989M 99M 993M 995M 997M 999M 2M 23M 25M 27M 29M logaihm 24 uve on he ohe. Noably, oaions of he job eaion uve ae efleed by hanges in labou mae ighness (ompae Figue 2 in seion 2). As Figue 5 shows, he end of ighness is moe volaile han he seies alulaed fom he aual daa. I also has a highe vaiane han he yle. Consequenly, oaions of he JCC ou mosly fo pemanen easons. This is in line wih business yles diven by pemanen poduiviy shos (Moley e al. 23, Webe 2) and wih he fa ha suual hange (seos, ehnology) may ome along wih business yle fluuaions (e. g. Caballeo/Hammou 994). The seies of ighness adjuss sluggishly o end shos. This paen eaes a yle wih opposie sign duing he ime of adjusmen (Moley e al. 23) and implies a negaive oelaion beween end and yle of ighness (see 7.2). Figue 5: Tighness: obsevaions, end and yle eession ighness end_ighness yle_ighness Soue: Fedeal Employmen Ageny and own esimaion. Business yle daing by ECRI. Taing he developmen of end mahing effiieny, end sepaaion ae and end ighness ogehe, i beomes obvious ha he seep inease in ighness afe 25 eaded he appeaane of he BC inwad shif unil ighness had eahed is new pesisen plaeau. Tighness ose so shaply beause vaanies eaed quily o he hange in eonomi

26 25 ondiions wheeas i oo unemploymen some ime o adjus o he new insiuional famewo. Besides his, deegulaion in some segmens led o an inease in demand fo highly flexible labou suh as sho-em, fixed-em, pa-ime o empoay ageny wo. An inease in hese inds of jobs may inflae vaanies by a high unove bu no equivalenly edue unemploymen. The slow adjusmen of unemploymen is onfimed by a negaive oelaion beween is end and yle. By he same oen, he fla downwad slope of he BC in he ealy 98s aually efles pemanen shifs o he igh and movemens down he uve a he same ime Coelaions and labou mae impliaions The omplex ineaions on he labou mae ae eluidaed by he seveal end and yle shos oelaions. Beause of sluggish adjusmen of ime seies o pemanen shos, mos unobseved omponens sudies esimae a negaive oelaion beween end and yle of one and he same vaiable. In ou appliaion, his is only ue fo ighness wheeas mahing effiieny and sepaaion ae show up wih hadly any oelaion beween hei end and yle shos (Table 3). This aouns eihe fo a vey qui adjusmen of he shifing paamees o hanges in hei ends o whih is moe plausible wih egad o he muliple soues of oelaions in ou mulivaiae model fo ompensaoy effes. Table 3: Coelaions beween he shos of he main unobseved saes 7 Similaly, Fujia (2) agues ha ineases in unemploymen and dops in vaanies (movemens along he uve, a fis glane) ome along wih hanges in sepaaion ae and job finding ae deeminans of he ineep as well as a hump-shaped vaany developmen.

27 26 end_m end_s end_θ yle_m yle_s yle_θ end_m end_s end_θ yle_m yle_s.8 yle_θ Mahing effiieny and sepaaion ae ae negaively oelaed in ends (-.4) as well as in yles (-.). Wih egad o he pemanen omponens his oelaion eveals ha insiuional and suual hange (o pemanen poduiviy shos) wo hough boh hannels in a simila way: he BC eloaes hough boh shifing paamees ino he same dieion; he effes usually do no ompensae eah ohe, as would have been he ase wih posiive oelaion. Moeove, he wo paamees follow an opposie ylial paen. Tend sepaaion ae and ylial mahing effiieny ae oelaed a.5 whih suggess a ime-onsuming suual adjusmen poess on he labou mae ha is ansioily hidden by ylial paens. Fo example, when end sepaaions shan in he afemah of he efoms beause labou demand ineased and fims ep moe of hei saff, he pool of he unemployed does no ge filled wih jus ame-in unemployed ha have good hanes o leave quily. As a esul, mahing effiieny shins, oo, bu only empoaily. In he long-un, insead, highe labou demand and he highe value of vaanies uges fims o seah moe inensively and hie people, whih in he end aises pemanen mahing effiieny (see negaive oelaion above). The oelaions beween he shifing paamees and ighness emphasize he ovelay of shifs and movemens along he uve, whih was aved ou in he pevious subseion. The oelaions beween end ighness and end mahing effiieny a.6 as well as end sepaaion ae a -.5 imply a pemanen inwad shif being aompanied by a pemanen movemen up he uve o vie vesa. Exaly his was obseved afe he efoms.

28 27 Eonomially, his an be explained by a ommon dependene of sepaaions, vaanies, and unemploymen on pemanen hanges of labou mae insiuions and poduiviy. Labou mae insiuions ha hange end mahing effiieny oespondingly hange ighness as hey influene vaanies via seah oss and benefis of ompanies and unemploymen via is duaion. 7.3 The mahing funion As announed in seion 4, ou model onains an exended mahing funion ha may unfold diffeen elasiiies of mahes wih espe o he ends o yles of unemploymen and vaanies, an issue no onsideed in he lieaue so fa. This seion pesens he exended funion, paamee esimaes and inepeaion. Equaion () epeas he mahing funion wih speial egad o he unobseved omponens of unemploymen and vaanies. f m m U () Paamee esimaes ae given in Table 4. U V V w Table 4: Esimaion esuls fo he mahing funion oeffiien sandad eo signifiane elasiiy of mahes wih espe o end unemploymen α *** ylial unemploymen α *** end vaanies β.9.22 ylial vaanies β ** Signifiane levels: *** peen, ** 5 peen. Regading unemploymen, he genealizaion does no eveal diffeen onlusions. The elasiiies of mahes wih espe o boh end and ylial unemploymen ae esimaed a nealy whih is high ompaed o he summaies by Peongolo/Pissaides (2) o Boesma/van Ous (999). Howeve, sine we allowed fo ime-vaying mahing effiieny in ou funion, esuls ae no diely ompaable. Eonomially, an elasiiy subsanially

29 28 smalle han implies a dispopoionaely smalle eduion in mahes when unemploymen shins. This may no be plausible as a eduion in unemploymen ypially eeps meely bad iss wihin he pool. Mahing funion esimaes fo he goup of he long-em unemployed by Klinge/Rohe (22) ame up wih a vey obus elasiiy beween.9 and, oo. In onas o unemploymen, he impa of vaanies in he exended mahing funion diffes onsideably beween end and yle: end vaanies ae no signifian; i is only he elasiiy of mahes wih espe o ylial vaanies ha shows up wih a signifian oeffiien of.3. 8 This esul esembles esimaes of aggegae so-flow mahing funions ha wee aionalized by a sysemai elemen in seah (Coles/Smih 998, Gegg/Peongolo 25, Fah/Sunde 29): unemployed aleady now he exising so of vaanies bu did no mah. In he nex ound of appliaions, hey will fous on newly inoming vaanies. Even hough some people ha jus eneed unemploymen may mah wih old vaanies, his effe is no lage enough o eae a signifian onibuion of he so of vaanies in he mahing funion. 9 As hese vaanies do no mege ino mahes, hey beome pesisen and fom a leas pa of he pemanen omponen. Insead, inflows ino vaanies have a signifian impa wih an elasiiy usually esimaed beween.3 and.4. Those new vaanies ae filled moe easily, aise mahes and, onsequenly, disappea hey ae ansioy. Given ha suh a poedue does no only efe o inflows bu also holds fo a popoion of ou so vaiable, his popoion of vey sho-em vaanies is liely o be pa of ou ylial omponen. 8 In sum, ou mahing funion hen eveals slighly ineasing euns o sale. Peongolo/Pissaides (2) also summaize sudies ha eje he null of onsan euns. They ague as heoeial disadvanage, howeve, ha ineasing euns o sale ae ompaible wih moe han one equilibium, one wih high and one wih low seah aiviy. 9 Inidenally, his implies an elasiiy of fo he so of unemploymen in onsan euns o sale speifiaions as in Gegg/Peongolo (25).

30 29 8 Conlusions The piue of he Geman BC beween 979 and 29 shows movemens along he uve wih hanging slope as well as many ouwad and one inwad shif. As a edued-fom elaionship, i eveals no insighs ino he dives of hese dynamis. Suual onen is added o hese desipions by means of an unobseved omponens analysis, fuhe onsideing oinegaion beween labou mae vaiables. I disenangles eah of he BC onsiuens ino a pemanen and a ansioy seies and allows analysing he ime-vaying popeies of mahing effiieny, sepaaion ae, and ighness. Theeby, we gahe infomaion on he deeminans of shifs of he BC, movemens along he uve, and hei ineaion. This is espeially valuable as he BC shifed inwads fo he fis ime in deades afe sevee labou mae efoms had ome ino foe beween 23 and 25. Thus, ou analysis onibues o he mao-evaluaion of ha efom. The inspeion evealed he following main esuls: Fis, alhough he sepaaion ae used o be he moe ponouned fao in explaining BC dynamis ove he whole ime span, boh sepaaion ae and mahing effiieny almos equally led o he inwad shif afe he efoms. Seond, he funioning of he labou mae impoved pemanenly, ha is fo suual easons. The end-yle deomposiion eveals an exaodinaily song inease in end mahing effiieny whih is in line wih he aim of he Haz efom o aise inenives fo moe inense job seah as well as highe labou demand. The end inease ame o an end a he onse of he Gea Reession. Thid, shifs as well as movemens along he uve ou fo pemanen and ansioy easons, usually a he same ime. Thus, a shap inease in end ighness eaded he inwad shif of he BC despie labou mae funioning saed o impove ealie.

31 3 In summay, he oelaed unobseved omponens model is able o eveal pemanen and ansioy soues of BC dynamis. Poliy eommendaions should ae hese diffeen movemens and hei soues ino aoun. Clealy, appopiae design and hoie of poliy measues depends on obseved labou mae developmen being of eihe suual o ylial naue and on he onee insiuional o eonomi diving foes. Thus, ou famewo offes a pomising dieion of fuue eseah, poviding valuable landmas fo appopiae poliy design. One fuhe sep ino his dieion an be given by digging deepe ino he oe of he oelaions beween ends and yles; one mehodology o do so has been povided by Webe (2). 9 Appendix 9. Idenifiaion Using maix epesenaion, he fis pa of he suual model given in equaions (5) o (7) eads as follows. Theeby, is he numbe of endogenous vaiables and he numbe of independen sohasi ends. The veo of endogenous vaiables, y, inludes job finding ae f, sepaaion ae s, employmen E, vaanies V, and unemploymen U (all in logs):,,,, w A A T y w I y y To deive he edued fom we fis ae fis diffeenes ha lead o saionay seies. L is he lag opeao: w L I L I L A I L I AL T y ) ( ) )( ( ) )( ( Tend veo and yle veo ae given in he suual fom as mulivaiae andom wal and mulivaiae auoegession, espeively (see equaions (9) and ()):

32 3,, L I i L L L wih L L L p i p i i L,...,,... ) ( ) ( ) ( ) ( ) ( Inseing ino he diffeened equaion and eaanging gives he edued fom: w L I L L I L A I AL T L A T y L ) )( ( ) )( ( ) )( ( ) ()( ) ( A omplee desipion of he daa geneaing poess inludes he oinegaion elaion beween he model vaiables; see Moley (27) fo a simila example. In ou seup, oinegaion is ahieved by he long-un flow equilibium in equaion (2) by he fixed oinegaing veo [ - -]. As hee ae no fee paamees o be idenified fom his equilibium elaion, we sip his pa of he edued fom fo beviy. Aoding o Gange s Lemma (Gange/Mois 976), he hee igh-hand-side MA expessions add up o a new MA poess whose ode is deemined by he highes lag lengh of he oiginal poesses : ) ( ~ p MA. Hene, he edued fom is a VARIMA(p,,p+) poess. Theeby, he only ow ha lag lengh p+ applies o is he mahing funion, all ohe elemens of ae MA(p). The yle oeffiiens ae diely idenified fom he AR oeffiiens of he VARIMA. The dif ems ae deemined fom he edued-fom ineep one we now abou he maies T and A ha inlude he suues of he esied end and he mahing funion. The lag ode of he new MA poess would deline if he oiginal poesses shaed ommon oos.

33 Infomaion on T and A as well as infomaion on he vaianes and ovaianes of he suual shos mus be idenified fom he auoovaianes of he newly fomed MA 32 poess : ( j) ( j) E j fo fo j p j p The fis auoovaiane maix () povides infomaion on vaianes and ((-))/2 ovaianes. The following auoovaiane maies () o ( p) eah povide 2 piees of infomaion as he elemens below and above he main diagonal ae no longe idenial. The las non-zeo auoovaiane maix ( p ), howeve, povides only piees of infomaion as he veo p onains only one non-zeo elemen. In sum, he auoovaianes of he MA em of he edued fom delive 3 p 2 2 equaions onaining he paamees of 2 T, A, A w, as well as COV. e The numbe of unnowns in he suual fom beyond he AR oeffiiens and dif ems is given by: 4 paamees and a vaiane of he mahing funion, end sho vaianes, yle sho vaianes and he elaed ovaianes beween all of hem (see w COV in e appendix 8.2). They add up o 5 The neessay ondiion fo idenifiaion equies he numbe of unnowns being no lage han he numbe of auoovaiane equaions. The ompaison unoves ha his ondiion is fulfilled fo lag lenghs p 2.

34 Sae spae epesenaion In he sae-spae model, boh ends and yles ae eaed as unobseved saes. The measuemen equaion onnes hem o he obseved seies (as abbeviaes he oal numbe of auoegessive oeffiiens p ): ) ( ) (2 ) 2 ( ) ( as as w z G y wih he veos of endogenous vaiables U V E s f y and unobseved saes V E s m U p m U V E s m U V E s m V E s m z 2 The onneion o he obsevables is given in he paamee maix G. ) ( 2 as G The esidual veo onains only he innovaion of he mahing funion: w w The ansiion equaion desibes he evoluion of he unobseved saes: ) (2 ) (2 ) 2 (2 ) (2 ) 2 ( as as as as as as e z H d z The ansiion maix H speifies he andom wals of he ends and he auoegessions of he yles. Fuhe elemens (zeos and ones) ae needed o aoun fo lagged saes. Eah maix i onains he AR oeffiiens of he i-h lag on he main diagonal and zeos on he seonday diagonals.