Ranking of Job Applicants, On-the-job Search and Persistent Unemployment*

Transcription

1 Rankng of Job Applcans, On-he-job Search and Perssen Unemploymen* by Sefan Erksson and Nls Gofres 7 March 000 We formulae an effcency wage model wh on-he-job search where wages depend on urnover and employers may use nformaon on wheher he searchng worker s employed or unemployed as a hrng creron. We show heorecally ha rankng by employmen saus affecs boh he level and he perssence of unemploymen and numercally ha hese effecs are subsanal. More prevalen rankng n Europe compared o he US because of more rgd wage srucures ec. - could poenally help o explan he hgh and perssen European unemploymen. Keywords: Effcency wage, Turnover, On-he-job search, Perssence, Rankng, Unemploymen, Unons. JEL classfcaon: E4, J64. * We are graeful o Peer Damond, Per-Anders Edn, Peer Fredrksson, Berl Holmlund, Torsen Persson and semnar parcpans a he Insue for Inernaonal Economc Sudes, Sockholm, and Uppsala Unversy for very helpful commens. Fnancal suppor from he Offce of Labor Marke Polcy Evaluaon s graefully acknowledged. Deparmen of Economcs, Uppsala Unversy, Box 513, SE Uppsala, e-mal: Sefan.Erksson@nek.uu.se and Nls.Gofres@nek.uu.se.

2 1. Inroducon When one compares European and US labor markes, several dfferences are apparen. Unemploymen raes are much hgher, urnover s much lower, and he adjusmen back o equlbrum afer a shock appears o be much slower n Europe. Whle hgh unemploymen may plausbly be blamed on unons and labor marke rgdes, and low urnover may be due o culural dfferences, he las observaon s especally nrgung. In several European counres, emporary cyclcal shocks have rased unemploymen and hen has remaned hgh for a long me. Adjusmen coss may be one explanaon for sluggsh employmen adjusmen, bu can hardly be he whole sory. Why s unemploymen so perssen n Europe? 1 In hs paper we ake a new look a hs queson, emphaszng wo aspecs of he labor marke. The frs s ha urnover consderaons are mporan n wage deermnaon. Volunary urnover s subsanal, and when workers qu, frms frm ncur sgnfcan ranng coss o replace hem. Consequenly, frms consder he mplcaons for urnover when hey se wages. The second mporan sarng pon s ha unemployed seem o be a a dsadvanage compared o employed workers when hey compee for jobs. Ths may be because workers lose some of her human capal n unemploymen or because unemploymen s aken as a sgnal of unobserved personal characerscs. If employers perceve unemployed workers o have lower average producvy, hey wll be relucan o hre hem, and hs s especally rue f wage srucures are rgd, prevenng dfferenaon of wages accordng o perceved producvy dfferenals. If urnover s mporan hen he frm s opmal wage should depend on he probably ha a worker lookng for anoher job wll acually fnd one; f hs probably ncreases he frm wll respond by rasng s wage o preven cosly urnover. If, n addon, unemployed workers do no compee for jobs on an equal bass wh employed applcans, hs mus rase he probably for employed workers o ge he jobs hey apply for and hs n urn wll end o rase he wage. In oher words, we should expec an neracon beween he urnover consderaons ha affec wage decsons and he fac 1 We realze ha we are no he frs ones o ask hs queson; we commen below on alernave approaches. By perssence we mean a hgh seral correlaon n unemploymen. 1

3 ha ousders have a dsadvanage compared o nsders when applyng for he same jobs. The bgger hs dsadvanage, he hgher s he chance for employed workers o ge a new job, and he hgher s, ceers parbus, he effcency wage ha s opmal from he frm s pon of vew. To formalze hs nuon, we formulae a model where a fracon of all employed workers apply for new jobs whle mananng her curren jobs. Wheher a person apples for a new job or no depends boh on he relave wage offered by he frm and on a sochasc non-pecunary job sasfacon facor whch affecs he uly gan from swchng jobs. The wage may be se by he frm or n a bargan wh a unon. In eher case, he wage seers ake he effec of he wage on urnover no accoun. We frs consder he case when employers chose whom o hre randomly (no rankng). We show ha even whou rankng unemploymen wll be perssen. Because of he fear of cosly urnover, a permanen negave shock s no fully accommodaed n he nex wage conrac, and hence employmen remans low for some me afer a negave shock. Then we consder a suaon wh rankng,. e. when some employers prefer o hre employed applcans. Rankng ncreases he probably ha an employed worker ges he job he apples for and hs makes opmal for frms o se hgher wages. The resul s boh lower seady sae employmen and a slower adjusmen followng a shock. Smulaons show ha he effecs of a lmed degree of rankng are subsanal for reasonable parameer values. The model s used o nerpre he dfferences beween he US and Europe. As noed above, boh he level and he perssence of unemploymen are much hgher n Europe. There are hree man facors n our model ha mgh explan hese observed dfferences: lower mobly, sronger unons and, perhaps, more rankng n Europe. We fnd ha he lower urnover n he European economes should, by self, lead o lower unemploymen and approxmaely he same amoun of perssence. Snce unemploymen s n fac much hgher n Europe, hs has o be explaned eher by srong unons or by more prevalen rankng. Our smulaons show ha, whn hs model, wage pressure due o srong unons can explan hgh unemploymen, bu no he hgh perssence observed emprcally. Insead, our analyss pons o rankng of job applcans as a poenally mporan explanaon for he perssence of unemploymen observed n mos European labor markes. The noon ha unemployed workers - and especally hose who have been unemployed for a long me - have dffculy compeng for jobs has been around for

4 some me (see e. g. Phelps (197), Layard and Nckell (1986)) bu here are few mcrobased models formalzng he dea. The nsder barganng model developed by Blanchard and Summers (1986) and Gofres and Horn (1987) emphaszes he dsncon beween employed and unemployed workers, bu can hardly generae he exreme amoun of perssence found n he daa. Oher relaed papers are Huznga and Schanarell (199) and Gofres and Wesermark (1998), who show ha perssence may arse due o he forward lookng naure of wage decsons, bu whou he neracon beween on-he-job search and rankng ha we emphasze n he presen paper. The paper ha s closes n spr o ours s Blanchard and Damond (1994). They analyze rankng of unemployed workers by duraon n a machng model. The wage s deermned by Nash barganng wh he expeced uly of a recenly lad off worker as hrea pon. Ther man queson s how he wage s affeced f frms rank job applcans accordng o he lengh of unemploymen. The resul s ha rankng has small effecs on he long run wage level, bu subsanal effecs on he wage dynamcs followng a shock. An expeced ncrease n employmen mproves he barganng poson of hose currenly employed - snce hey wll be frs n lne for he new jobs f hey become unemployed - so wages ncrease. Our analyss dffers n several ways. Frs, we focus on on-he-job-search and he advanage of employed job searchers relave o he unemployed raher han he dsncon beween shor-erm and long-erm unemployed. Second, whle Blanchard and Damond ake employmen o be drven by exogenous job creaon and desrucon raes, we are able o solve he model for employmen, calculae perssence, and evaluae he effecs quanavely. Thrd, our resuls dffer qualavely from hose of Blanchard and Damond. In our model, rankng has subsanal effecs no only on he dynamcs, bu also on he long run equlbrum level of wages and employmen. We beleve ha our focus on on-he-job search s he key reason why our resuls dffer n hs respec. 3 In unvarae models of unemploymen, he coeffcen on lagged unemploymen s close o uny for many European counres (see references below). The Blanchard and Summers (1986) verson of he nsder barganng model generaes hyseress, whch s an exreme form of perssence, bu only because hey make very specal assumpons concernng unon preferences ec. - see he dscusson n Blanchard (1991) or Bean (1994). 3 Pssardes (199) consders a relaed model where long-erm unemploymen leads o a loss of skll. There s no rankng n hs model. Insead, frms canno dsngush long-erm and shor-erm unemployed, so all job seekers have he same chance o ge a job. Perssence arses because long erm unemploymen mples a deeroraon of he average qualy of unemployed workers whch makes less profable for frms o hre workers and fewer vacances are creaed. Thus he mechansms are que dfferen from hose consdered here. 3

5 In Secon we formulae he basc model whou rankng, solve for seady sae employmen and show ha unemploymen s perssen even whou rankng. In Secon 3 we nroduce rankng and show ha hs ncreases unemploymen and perssence. Secon 4 exends he model o allow for wage conracs spannng several perods. In Secon 5 we use numercal smulaons o examne wheher he observed dfferences n urnover, unemploymen and perssence beween Europe and he US can be explaned by our model and Secon 6 concludes. On-he-Job Search, Wage Deermnaon and Unemploymen Perssence whou Rankng of Job Applcans The model s nended o capure he fac ha job-o-job flows are subsanal and urnover consderaons are mporan for frms when hey se wages. The mporance of volunary urnover s well documened. Holmlund (1984), Akerlof, Rose and Yellen (1988) repor qu raes around wo percen for he U. S., Sweden and Japan and Boer (1999) fnds ha qus from one job o anoher consue around 50 per cen of all hrng n several European economes. Accordng o Holmlund (1984), abou 8 percen of employed workers n Sweden engaged n job search durng a year and Pssardes and Wadsworh (1994) repor ha around fve per cen of all employed workers n Bran do search for a new job. Lane, Sevens and Burgess (1996) show ha worker reallocaon s wo o hree mes as grea as job reallocaon. Anoher ndcaon of he mporance of qus s he fac ha oal worker urnover s procyclcal reflecng he procyclcaly of qus (Anderson and Meyer (1994)). Also, survey evdence shows ha frms care abou urnover. Fear of ranng/ hrng cos as a resul of qus, as well as fears ha he mos producve workers would qu, deer frms from wage cus (Blnder and Cho (1990), Campbell and Kamlan (1997)). Moreover, as emphaszed by Akerlof, Rose and Yellen (1988), boh wages and non-pecunary facors seem o nfluence qu decsons. We frs consder a case when here s no rankng of job applcans. There are a large number of workers and a large number of dencal frms, bu he number of frms s much smaller han he number of workers. Evens ake place n dscree me and he sequence of evens n each perod s he followng. Near he end of every perod a fracon s of he workers leaves employmen and eners he pool of unemployed. Ths fracon s exogenously gven and represens workers qung or beng lad off for exogenous reasons. Then wages 4

6 are se eher by he frm or n a bargan - and he remanng workers decde wheher o look for a new job or no, consderng he wage offered by he frm, he wage offered elsewhere and a non-pecunary job sasfacon facor. All unemployed workers also search and every searcher subms one applcaon o a randomly chosen frm. 4 Frms recevng he applcaons hen make her choces of whom o hre. We have hree dsnc decsons: frms se wages, workers decde wheher o search and frms decde whom o hre. We now proceed by frs analyzng search and urnover n a specfc frm for a gven wage, hen analyzng he frm s opmal decson abou he wage, and hen we consder he case when he wage s se n a bargan beween he frm and he workers. Fnally we urn o employmen dynamcs n a symmerc general equlbrum and calculae long-run unemploymen and perssence. Search Every worker who remans employed when a new perod begns has o decde wheher o look for a new job or no. We assume ha every employed worker draws a number ν ha deermnes hs job sasfacon from connung o work a hs presen job. The number ν s drawn from a random dsrbuon wh cdf G(ν). Gven ν, hs expeced uly from he curren job s w / ν ; he expeced uly from a randomly chosen new job s w. To keep he model smple, we assume ha every worker makes a new ndependen draw of ν every perod. 5 Furhermore, G(ν) s assumed o be unmodal and have a mean smaller han uny, so f he wage s he same mos workers prefer he job hey have. The employed workers decde wheher o search or no gven he wage offered by he frm, w, he wage expeced elsewhere n he economy w and he parameer ν. Onhe-job search s cosless, so a worker wll sar searchng f fracon of workers searchng n a gven perod s > w / ν. Then he w 4 Wheher workers send n one or more applcaons s less mporan. The mporan assumpon s ha search nensy s aken as gven for all searchers. Ths assumpon s dscussed n he fnal secon. 5 The assumpon ha he gan from swchng jobs s purely emporary s made o smplfy he analyss. In pracce, we would expec hgh seral correlaon n ν. Such a model would be very complcaed, however, snce we would need o keep rack of a dsrbuon of workers wh dfferen levels of job sasfacon. Also, he workers would have o consder effecs on uly n fuure perods when hey consder swchng jobs. 5

7 S ( w / w ) = 1 G( w / w ), (1) where S s decreasng and our assumpons abou he dsrbuon mply ha S (1) > 0. All searchng workers apply for one job each perod and subm her applcaons randomly. The fracon of prevously employed workers qung o ake anoher job s hen ( 1 s ) S( w / w ) a, where a s he probably ha an employed searcher fnds a job (o be deermned laer). Wage seng In hs secon we assume ha he wage can be changed every perod. 6 When seng he wage, he frm akes accoun of he fac ha labor urnover s cosly. For every worker he frm hres, ncurs a hrng cos equal o c mes he average wage w. The producon funcon s θ ( F l ), where θ may be nerpreed as producvy, prce, or produc demand. If wages are se n nomnal erms, θ wll be a compose varable ncludng boh real and moneary facors. 7 To smplfy, we assume ha volunary qus are suffcenly large ha all employmen adjusmen can be made by varaons n hrng, 8 and subjecve cerany; he frm opmzes as f he fuure was known wh cerany. 9 The frm solves he followng maxmzaon problem: 6 In Secon 4 we generalze hs o he case when he wage s se for N perods 7 If, for example, each frm faces a demand curve of he form η q = ( p / p) m / p, where p s he frm s prce, p s he prce level and m s money supply, and produces under consan reurns o scale wh producvy θ, revenue of he frm can be wren θ 1 1/ η 1/ η 1 1/ η ( / p) ( ) m l. Wh predeermned prces, an unexpeced moneary shock clearly affecs employmen. Wh predeermned nomnal wages bu fully flexble prces, he suaon s more complcaed. Prces are se wh a fxed markup on margnal cos, whch s w plus he hrng cos mnus he hrng cos ha s saved nex perod, all dvded by θ. Sll, fxed nomnal wages mply ha prces adjus less han fully o moneary shocks. As we wll see below, only unexpeced changes n θ affec employmen. 8 Ths assumpon smplfes, bu s no crucal for he presen analyss. I s mporan for he opmaly of nomnal wage conracs, however see Gofres (198). Noe ha we could nclude some random (exogenous) closure and brh of some frms creang mcroeconomc job desrucon whou changng he macroeconomc analyss. 9 Hence he dynamc analyss below refers o he adjusmen of employmen afer an unexpeced once and for all shock o θ. 6

8 ( θ F( l ) w l cw ( l (1 s (1 S( w / w ) a ) l )) j max β + j + j + j + j + j + j + j + j + j + j 1 w + j, l + j j= 0 () The frs order condons are l ' ( / )(1 cs w w s) a l = 1 0 (3) θ F ( l ) w cw + βcw (1 S ( w / w ) a 0. (4) ' = Equaon (4) defnes he labor demand funcon l l w, w, θ, a, w, w ). Inserng = ( hs no (3) we ge he followng equaon, whch mplcly deermnes he frm s opmal wage, he effcency wage, w : e e e e l( w, w,, a+ 1, w + 1, w) = (1 s) cs '( w / w) al 1 θ. (5) The opmal wage s such ha he drec cos of a margnal wage ncrease equals he reducon n urnover coss assocaed wh a wage ncrease. The opmal wage depends posvely on he average wage level, he hrng cos, and he probably ha a searcher ges a job. Unons and Barganng In mos European labor markes, and some pars of he US labor marke, he wage s se n negoaons beween employers and a unon. Even f here s no formal unon organzaon, workers may have barganng power because hey could poenally ake collecve acon agans he frm. The negoaon process s modeled as n Gofres and Wesermark (1998). The frm and he unon make alernae offers. Afer a bd s rejeced, may urn ou ha workers are unable o connue he srke, and f hs suaon occurs, he frm ses s opmal wage, w, defned above. Oherwse, barganng connues unl e one pary acceps a bd made by he oher pary. Ths wage seng mechansm generaes a wage ha s approxmaely equal o a unon markup facor µ mes he wage ha he frm would se f was free o se he wage: w = µ w. (6) e 7

9 The sze of he markup depends on he workers ably o las a conflc, he mpaence of he pares ec. (see Appendx 1). Subsung no (5) we ge he followng equaon whch deermnes he wage when workers have barganng power: l( w /, w, θ, a+ 1, w + 1 / µ, w) = c(1 s) S '( w / µ w) al 1 µ. (7) The Level and Perssence of Unemploymen Snce we are neresed n aggregae employmen, we consder a symmerc general equlbrum where all frms se he same wage. Ths s he naural suaon snce all frms and workers are assumed o be dencal and herefore solve he same problem. 10 Then we have from equaon (7): l = Ω( 1 s) al 1, (8) where Ω = -c S (1/µ). The parameer Ω s a measure of wage pressure arsng from he combned effecs of he effcency wage mechansm and unon barganng power; boh facors end o rase wages n a compleely symmerc way n our model. The fnal sep s o deermne a, he probably o ge a job for an employed searcher. In a symmerc equlbrum, he number of people hred per frm s: h = l ( 1 l 1 + (1 S(1) al 1. (9) Ths equaon smply says ha hrng s equal o he number of workers he frm wshes o employ hs perod mnus he workers who reman from las perod, akng no accoun exogenous and endogenous separaons. There are many more workers han frms and we assume ha each frm ges a leas as many applcans as has job openngs. In hs secon we consder he case whou rankng where he frm has no preferences beween employed and unemployed workers bu smply draws he desred number of workers randomly from he ple of applcaons. Then he probably o ge a job s he same for all searchers and s deermned by: 10 We assume ha all frms se he wage a he same me so we do no have overlappng conracs. Obvously, overlappng conracs of he Taylor varey may generae perssence, bu we wan o examne how much perssence we ge n he model whou hs addonal source of perssence. 8

10 l (1 l + (1 Sa l 1 1 a =, (10) n (1 l 1 + (1 Sl 1 where we smplfy noaon by wrng S(1)=S. Ths equaon says ha he probably o ge a job for a searcher s he number of hrngs (gven by (9)) dvded by he oal number of searchng workers conssng of boh unemployed workers, n ( 1 s) l 1, and employed workers searchng on-he-job ( 1 s ) Sl 1. Solvng equaon (10) for a we ge he followng expresson: l (1 l 1 a =, (11) n (1 l 1 whch s smply hrng dvded he number of unemployed job seekers. The chance o ge a job does no depend on he number of employed workers lookng for jobs. The nuon s ha every worker who changes jobs leaves one job and akes one job, so he number of jobs avalable for he remanng searchers remans he same. Combnng (11) wh equaon (8) gves us: l (1 l 1 l = Ω(1 l 1. (1) n (1 l 1 Ths equaon mplcly deermnes employmen as a funcon of employmen n he prevous perod. Evaluaon of (1) n an equlbrum wh consan employmen, l l, allows us o deermne he seady sae employmen rae = 1 l ss 1 =. (13) n (1 (1 + sω) The model has he naural rae propery; producvy does no affec employmen n he long run. Hgher wage pressure Ω due o hgh urnover coss or srong unons resuls n lower employmen, an ncreased flow from employmen o unemploymen (s) has an ambguous effec on he naural rae, bu for plausble parameer values rases unemploymen. 9

11 Dfferenng (1) wh respec o l 1 and evaluang n seady sae we ge an expresson for he monhly perssence of employmen whch, for laer reference, we denoe ρ ; m ρ m l l 1 l= l ss (1 u = (1 ( u ss ss s + sl l ss ss ), (14) where u denoes unemploymen. I can be shown ha hs expresson s posve for reasonable values for he parameers. To undersand why employmen depends posvely on employmen n he prevous perod, magne ha we are nally n seady sae. Then θ falls unexpecedly and permanenly. Ths happens afer he wage has been fxed, so frms respond by cung employmen. Employmen says a hs lower level unl he end of he perod. In he nex perod frms cu her wages, bu no so much ha employmen mmedaely reurns o s seady sae value. If wages would mmedaely fall o he new seady sae level, here would be a large ncrease n employmen, many vacances open o workers searchng on he job, and frms would suffer from excessve urnover. Foreseeng hs, each ndvdual frm would hen have an ncenve o devae by rasng s wage so as o reduce urnover. Therefore he equlbrum soluon mus be ha frms reduce wages less and employmen remans low for some perods afer a negave shock. 11 Numercal analyss of he model We have jus shown ha employmen wll reman low for some me afer a negave shock even whou rankng of job applcans. In he nex secon we wll show ha hs mechansm s renforced when frms rank job applcans. Bu before urnng o he effecs of rankng, s nformave o pu some numbers no he model o see how perssen unemploymen wll be whou rankng. Effecvely, here are hree free parameers n he model: he flow from employmen no unemploymen, s, he fracon of employed workers searchng on he job, S, and, he combned "wage pressure" effec resulng from urnover coss and srong unons, Ω. Whle s can be measured wh reasonable precson, here are few esmaes of 11 Huznga and Schanarell (199) and Gofres and Wesermark (1998) make a smlar argumen, bu hose papers dd no consder on-he-job search. 10

12 S avalable, and no drec measures of Ω. We do, however, have measures of he average job-o-job flow, whch n our model corresponds o S mes a, and he unemploymen rae, u/n. We herefore se S and Ω n such a way ha he equlbrum job-o-job flow and unemploymen correspond o he values observed emprcally. In Table 1 we repor emprcal esmaes ha we use for s, Sa and u/n and he mpled values for S and Ω. 1 The perod s aken o be one monh. The las wo rows show he mpled seady sae probably o ge a job for a job applcan and he resulng yearly perssence of 1 unemploymen generaed by he model, defned as ρ =. ρ m Table 1 Observed socks and flows and mpled parameer values and (yearly) perssence for dfferen economes. Parameer US Germany France s Sa u/n S Ω a ρ We see ha, wh parameer values conssen wh he socks and flows observed n he US and European labor markes, unemploymen becomes que perssen n Germany and France bu no n he U. S. The perssence found n he model s much smaller han emprcal esmaes, however. Blanchard and Summers (1986) and Alogoskoufs and Mannng (1988) esmaed smple auoregressve models for unemploymen and found ha he coeffcen for lagged unemploymen s close o uny for mos European counres, bu only around.4 for he US (wh yearly daa). 13 Our basc model herefore seems o generae oo lle perssence See Secon 5 for furher dscusson of hs approach and Appendx 3 for dealed dscusson of hese numbers. 13 Hgh seral correlaon n unemploymen may be due o wo concepually dfferen mechansms. One s ha cyclcal (aggregae demand) shocks affec unemploymen and hen he adjusmen back o equlbrum akes a long me. Anoher possbly s ha shocks o he naural rae (e. g. changes n unon barganng power) hemselves are hghly perssen (and frequen). The presen model s of he frs ype. Jaeger and 11

13 3. Rankng of Job Applcans Havng formulaed he basc model we are now ready o analyze he effec of rankng. There s evdence ha employers prefer o hre already employed workers. Blau and Robns (1990) showed ha n he U. S. employed job searchers receve almos wce as many job offers as unemployed searchers wh he same search effor. Wner-Ebmer (1991) found ha employmen saus s used as a screenng devce for producvy n Ausra. Agell and Lundborg (1999), n a survey of Swedsh frms, found ha employers do vew unemploymen as a sgnal of lower producvy. How wll rankng affec he basc decsons made by he agens n our model? How wll rankng affec he seady sae level of employmen and he degree of perssence? How bg are he effecs quanavely? These are he quesons o whch we now urn. Before we ncorporae rankng n he model s mporan o be clear abou wha we mean by rankng. In hs model, rankng means ha employers somemes, when choosng beween applcans for a parcular job, prefer o employ someone who has a job o an unemployed worker. Formally, we assume ha frms rank applcans n hs way for a fracon r of he jobs. Snce here are many applcans of each caegory per job, only employed applcans are hred o hose jobs. Ths defnon of rankng rases an mporan queson. Why do frms chose o rank her applcans? Whn he conex of our formal model we can smply defend our assumpon by ponng ou ha workers are dencal, so frms are ndfferen beween rankng and no rankng and may as well rank applcans. Bu he model would be more convncng f frms had a reason o rank workers. A naural argumen s ha he perceved producvy of an employed worker s hgher han ha of an unemployed worker. In fac, s enough ha unemployed workers are perceved o be an nfnesmal amoun less producve, on average, o jusfy rankng, provded ha he wage s he same. Such an argumen could be crczed, however, by Parknson (1994) use an unobserved componens echnque o ry o dsngush hese wo sources of perssence. They fnd ha effecs of cyclcal shocks on unemploymen are subsanally more perssen n Europe han n he US. Smlar resuls wh Swedsh daa are obaned n Assarsson and Jansson (1998) 14 In addon, he obaned values of S and Ω appear mplausble. Low urnover n Europe s no a all explaned by a lower wllngness o change jobs, bu enrely by an exremely low probably o fnd a new job. 1

14 argung ha he frm could offer dfferen wages for he dfferen groups, each wage correspondng o he producvy of he group. Thus here mus be some rgdy of he wage srucure ha prevens frms from dfferenang wages accordng o perceved producvy dfferences. In he followng we assume ha here s such a rgdy. Wh rankng, he search and wage seng decsons are made as before, bu employed workers are more lkely o ge hred han unemployed workers are. We assume ha workers do no know for whch jobs rankng s appled bu send n her applcaons a random. Usng a o denoe he probably for an employed searcher o ge a job we have: a l = r (1 l 1 (1 Sl + (1 Sa l 1 1 l (1 l + (1 r) n (1 l (1 Sa l + (1 Sl 1 1. (15) Wh probably r he worker apples for a job where employed searchers are preferred and n hs case he probably o ge a job s hrng per frm dvded by he number of employed searchers per frm. Wh probably (1-r) he worker apples for a job where he employer does no have any preference for a parcular ype of worker and n hs case he probably o ge a job s hrng dvded by he oal number of searchers per frm. Solvng (15) for a gves us: ( l (1 l )( rn r(1 l + (1 Sl a =. (16) ( n (1 l 1)(1 S (1 r) l 1 ) Conrary o he case whou rankng he fracon of employed workers lookng for jobs, S, affecs a drecly. If more workers search on-he-job, her chance o ge a job decreases for a gven level of employmen. Lookng back a equaon (15) we see ha an ncrease n S has wo couneracng effecs on he probably for employed workers o ge a job. More on-he-job search means ha more workers leave her jobs and hs ncreases he number of job openngs, bu here are also more applcans for jobs, especally for hose jobs whch are predesned for employed applcans. Inspecng he rgh hand sde of (15) we see ha he laer effec domnaes: he more workers ha do on-he-job search he smaller s her chance o ge a job. Combnng (16) wh (8), fnally, gves us: 13

15 l ( l = Ω(1 (1 l 1 )( rn r(1 l ( n (1 l (1 Sl )(1 S(1 r) 1 ). (17) As before, hs equaon mplcly deermnes employmen as a funcon of employmen n he prevous perod. Evaluang (17) n seady sae we ge l ss n (1 S(1 r) s(1 Ωr =. (18) sω(1 r + sω(1 S + (1 S(1 r) For he seady sae level of employmen l ss o be posve he followng condon mus be fulflled: 1 r r > sω. (19) S Equaon (19) can be nerpreed as gvng a lm o how much rankng our model can ake. If r ges very hgh we ge a suaon where equlbrum employmen s equal o zero. Tha r canno be oo large s mos evden f we consder he exreme case when employers hre almos only employed workers. Then unemployed workers have a very small chance o be hred. Snce every perod a share s leaves employmen bu very few unemployed workers ge hred employmen s only sable a zero. In he followng we assume ha condon (19) s sasfed. One may suspec employmen o be lower he more rankng here s snce rankng mples a less well funconng labor marke. In Appendx we dfferenae (18) and show ha hs s n fac he case: ( l ss / n) < 0 r. (0) Ths resul can be explaned as follows. In our model he flow from employmen o unemploymen s a consan fracon of employmen. The flow from unemploymen o employmen on he oher hand s depends on he probably for an unemployed worker o ge a job. If more frms rank by employmen saus hs probably s reduced, ceers parbus, and he only way hs can be reconcled wh he seady sae condon ha nflow equals ouflow s ha he level of unemploymen s hgher. 14

16 Anoher neresng queson s how rankng affecs he perssence of unemploymen. Dfferenang (17) wh respec o l 1 and evaluang n seady sae we ge an expresson for ρ and dfferenang once more wh respec o r we can show ha rankng ncreases perssence (see Appendx ): r ρ m l = / l 1 > 0. r l= l ss (1) The nuon behnd equaon (1) can be undersood by exendng he dscusson n he non-rankng case. Afer a negave shock o producvy, he wage wll no fall mmedaely o he new seady sae level because, f dd, employmen would recover very rapdly and here would be many vacances and excessve urnover. Thus wages adjus slowly alhough he level of unemploymen s hgh. Ths mechansm s renforced by rankng, snce when employed workers have prory for some jobs, her chance o ge a new job depends less on he sock of unemploymen and more on he number of vacances. Quanave Effecs of Rankng Havng showed analycally ha rankng reduces he level of employmen and rases he perssence of unemploymen we now ask wheher hese effecs are quanavely mporan. To answer hs queson we ake he values for he US economy n Table 1 and examne wha happens o seady sae employmen and perssence as we ncrease he fracon of jobs for whch workers are ranked from zero o 40 percen The numbers n Table are calculaed keepng s, S and Ω consan a he values from Table 1. Our purpose here s no o descrbe any real world economy bu o examne he poenal quanave effecs of rankng, keepng he oher fundamenal parameers consan a some reasonable values. 15

17 Table Equlbrum values wh dfferen degrees of rankng. u/n ρ r= r= r= r= r= From Table we can conclude ha rankng has large effecs on boh he level and he perssence of unemploymen. If rankng s appled for one ffh of he new jobs, unemploymen almos doubles and becomes much more perssen. Comparng our resuls o hose of Blanchard and Damond (1994) who found subsanal effecs on wage dynamcs, bu only small effecs on he seady sae, one mgh wonder why we also ge long run effecs. Our nerpreaon s he followng. In Blanchard and Damond he wage s se accordng o he Nash barganng soluon and he sae of he labor marke affecs wage seng va he hrea pon, whch hey ake o be he suaon f he employed worker was o become unemployed. 15 Ths means ha rankng has wo compeng effecs on he wage. If an employed worker were o become unemployed, hs chance o fnd a new job soon would be much beer snce he would be frs n lne for new jobs. Bu on he oher hand he does run a small rsk of becomng long-erm unemployed hmself. As urns ou n he smulaons made by Blanchard and Damond, he ne effec on he wage s small unless he oally gnores he fuure,.e. has a very hgh dscoun rae. In our model he worker can connue o work a hs old job f he does no ge he one he apples for. Snce employed job-searchers do no rsk becomng long-erm unemployed he second effec does no appear. Therefore, rankng has an unambguous and srong effec on wages and employmen n he long run. 15 See Gofres and Wesermark (1998) for a crcsm of hs way of modelng wage barganng. 16

18 4 Wage Conracs So far, we have absraced from medum erm wage conracs. We assumed ha wages could be changed as ofen as workers decde wheher o search or no. Bu here s ample evdence ha wages are changed nfrequenly. Unon conracs ypcally specfy wages for one o hree years, and less formal mplc wage conracs n non-unon secors probably also exend for some me. Snce medum or long-erm wage conracs hemselves conrbue o perssence, s mporan o allow for such conracs n numercal smulaons. 16 We now assume ha wages are fxed for N perods; o be concree, hnk of he case when he perod s one monh and wages are changed n January each year (N=1). To avod some echncal complcaons n hs case, we assume ha he frm has o choose one employmen level for he whole year afer has observed he wage. Turnover sll occurs hroughou he year. Ths mples ha (unless here s a shock) employmen wll only change n January; n he oher monhs, only replacemen hrng akes place. The effcency wage condon correspondng o (5) s herefore: Nl T e = 1 s) cs'( w / w )[ a l + ( N 1) a l )], () ( T T 1T T 1 T T where T s a me ndex for years, a 1T s he probably o ge a job n he frs perod of he wage conrac (n January) and a T s he (consan) probably n he remanng perods (February-December). 17 Consderng a symmerc general equlbrum, defnng Ω as before and usng (16) we now ge: 16 Also, he mporance of unexpeced shocks s much greaer when wages are fxed for subsanal perods. 17 If he wage s se for a year, bu he frm s allowed o change employmen every monh, here wll be complcaed whn-year employmen dynamcs. When hrng, frms ake accoun of he probably ha a hred worker qus n he nex perod, n whch case hey do no save hrng coss n ha perod. Such whn-year dynamcs appear perpheral relave o our purpose and we avod by assumng ha employmen changes once each year. 17

19 N lt (1 lt 1( rn r(1 lt 1 + (1 Sl = Ω( 1 ( n (1 lt 1 )(1 S(1 r) lt T 1 ) + s( rn r(1 lt + (1 SlT ) ( N 1) ( n (1 l )(1 S(1 r) T. (3) As before, hs equaon mplcly deermnes employmen as a funcon of employmen n he prevous perod. Long run equlbrum employmen s he same as before ndependen of he lengh of wage conracs bu perssence ncreases (for more deals see Appendx ). Ths s llusraed n Table 3 where we agan se s, S and Ω as n Table 1 and show values of ρ for wage conracs of dfferen lengh and dfferen levels of rankng. Table 3. Perssence (ρ) wh one-monh, one-year and wo-year wage conracs. N=1 N=1 N=4 r= r= r= r= r= As expeced, long erm wage conracs conrbue o perssence bu he effec s farly modes compared o he effec of rankng. For example ncreasng he lengh of he wage conracs from one o welve monhs leads ncreases ρ o.7 whle ncreasng he fracon of jobs wh rankng o 30 % rases perssence o.7. Noe also ha wh much rankng, he speed of adjusmen of employmen s so low n any case ha medum erm wage conracs add very lle o perssence We consder wage conracs ha fx one wage for he whole conrac perod. In pracce, unon conracs ha exend beyond one year ypcally specfy one wage for each year and hence hey are less rgd han he 4 monh wage conrac consdered here. The one-year wage conrac seems mos relevan. 18

20 5. Undersandng he Dfference beween Europe and he US. Compared o he US, unemploymen s hgher n Europe, urnover s lower, and flucuaons n unemploymen are much more perssen. An neresng queson s wheher he mechansms dscussed above could poenally explan hs dramac dfference. Can plausble dfferences n he fundamenal parameers generae he subsanal dfferences n labor marke oucomes ha we observe emprcally? 19 There are four fundamenal parameers n he model: he fracon of he employed workers leavng o unemploymen n each perod, s, he fracon of employed workers ha apply for a new job each perod, S, wage pressure, Ω, and he fracon of jobs for whch frms rank applcans, r. Whle s can be measured reasonably well we lack drec measures of he oher parameers. However, we do have esmaes of he followng hree emprcal magnudes: he flow from employmen o employmen, S mes a, he fracons of he workforce ha s unemployed, u/n, and he perssence of unemploymen, ρ. We may hus ask he followng queson: Are here plausble values of he fundamenal parameers S, Ω, and r such ha Sa, u/n and ρ ake values conssen wh emprcal esmaes? 0 Snce we have hree free parameers and hree observable magnudes, he parameers are jus denfed, meanng ha we can deduce he values of he fundamenal parameers usng he seady sae equaons n our model - provded ha a soluon exss. Bu a pror, s no obvous ha a soluon exss, and even f a soluon exss, he resulng parameer values may be mplausble. The emprcal esmaes of s, Sa, u/n and ρ for he US, Germany and France are repored n he frs four rows of Table 4. 1 These esmaes have been colleced from varous sources and he measuremen of he dfferen flows and socks s dscussed n Appendx 3. We noe ha urnover raes are much lower n he European counres; boh qus no unemploymen and urnover beween jobs are beween one quarer and half he raes 19 Our purpose s no o es he model, bu o ask wheher he mechansms dscussed here mgh explan he observed dfferences beween labor markes 0 In prncple, one could examne how well he model explans oher observaons. Wh comparable me seres daa on labor marke flows one could examne wheher he model s conssen wh cyclcal flucuaons of hese flows n dfferen counres. Also, one could examne he relaon beween employmen and wages, bu hs requres a more explc modelng of he shocks (real and nomnal). These opcs are lef for fuure research. 1 We hnk of Germany and France as examples of European economes wh hgh and perssen unemploymen. We chose no o look a he Scandnavan counres snce cenralzed wage seng dffers n fundamenal ways. 19

21 observed for he US. Unemploymen s hgher n Europe bu he dfference wh respec o perssence s even more srkng. Can we fnd plausble values of he unobserved parameers ha explan hese dfferences? As urns ou, a soluon exss and he mpled values for S, Ω and r are presened n Table 4. We also repor he mpled values for employed and unemployed job-searchers o ge a job n seady sae. Table 4 Observable magnudes and mpled values for he parameers. Parameer US Germany France s Sa u/n ρ S Ω r a a u How should we nerpre hese resuls? I seems ha n order o explan he observed smaller worker flows, hgher unemploymen raes and much hgher perssence n Europe whn hs model, we mus assume ha here s much less on-he-job search, a b lower wage pressure and much more rankng n Europe han n he US. In he followng we frs ry o explan why we ge hese resuls n he model and how robus he resuls are. Then we urn o he queson wheher hey are plausble. Effecs of ndvdual parameers To undersand why we ge hese resuls s nsrucve o examne he effec of each ndvdual parameer on unemploymen and perssence. In Table 5 we repor he effec on unemploymen and perssence as we vary one parameer a he me, sarng from a The resul ha here s lower wage pressure n Europe does no appear o be very robus o changes n npu daa bu he oher resuls are que robus (see below). 0

22 baselne case consruced by akng he averages of he parameer values for he US and France. Table 5 Effecs of changes n ndvdual parameers on unemploymen and perssence. s S Ω r Unemploymen (u/n) Perssence (ρ) Baselne case s ncreases S ncreases Ω ncreases r ncreases In order o explan hese resuls nuvely, noe ha frms are always on her labor demand curves, so f employmen falls, wages mus ncrease and conversely. Thus we can nfer wha happens o employmen by examnng how wages are affeced by he parameer change for a gven level of employmen. Noe also ha wages adjus slowly afer a shock and perssence depends on how quckly wages adjus afer a shock o employmen. A hgher exogenous flow from employmen o unemploymen (s) mples ha for a gven level of employmen here wll be more job openngs, wll be easer for searchers o ge a job and frms herefore have an ncenve o rase wages, so employmen mus go down (compare (7)). Also, here s an ncrease n perssence. An ncrease n on-he-job search (S) mples ha here are more people applyng for jobs, less chance o ge a job and hence frms wll reduce wages. Thus employmen ncreases and here s less perssence. An ncrease n wage pressure (Ω) obvously rases wages and leads o hgher unemploymen and also slows down wage adjusmen afer a shock so we ge more perssence. As dscussed n he prevous secon, rankng (r) has he same qualave effec, bu from Table 5 we see ha rankng has a relavely sronger effec on perssence. Havng clarfed he effec of each of he fundamenal parameers on employmen and perssence, consder wha happens o employmen and perssence f we le he 1

23 urnover parameers, s and S, go from he hgher US values o he lower French values, keepng Ω and r a he US values. Ths s done n Table 6. Table 6 Unemploymen and perssence when movng from he US values owards he French values ¼ of he dsance a a me (remember ha hese approxmaons ge less and less accurae when we move far away from he calbraed values). s S u (ss) ρ When we decrease he urnover raes, sarng from values fed o he US economy, we ge lower unemploymen and hgher perssence. From hs s clear ha he reducon n unemploymen comng from lower s domnaes he effec n he oppose drecon from lower S. When comes o perssence he oppose s rue; he effec from lower S domnaes. From hs exercse we can conclude ha he lower urnover raes characerzng European labor markes by hemselves should gve somewha hgher perssence bu also lower unemploymen compared o he US economy. We have o fnd he explanaon for he hgh and perssen unemploymen n Europe among he oher wo facors. Wage pressure and rankng have smlar effecs n he model: boh end o rase he equlbrum rae of unemploymen and make he effecs of shocks o employmen more perssen. Thus, he hgher level of unemploymen and hgher perssence n Europe could poenally be explaned eher by hgher wage pressure due o srong unons or by more prevalen rankng, or by some combnaon of hese facors. Bu as we have seen above, rankng has a relavely sronger effec on perssence. 3 Ths s why he smulaon pons o more prevalen rankng as a poenal explanaon of he much hgh degree of perssence observed n Europe. 3 Pu dfferenly, f we ncrease wage pressure only unl unemploymen reaches he level observed for France, we ge less perssence han wha we observe emprcally.

24 Robusness As dscussed above, here s some uncerany concernng several of he numbers used o descrbe he dfferen economes. How sensve are our conclusons? To check hs, we change he npu daa one a a me holdng he oher parameers consan. As can be seen from Table 7, our concluson ha rankng s more prevalen n Europe seems o be que robus o changes n npu daa. We can ncrease or decrease every flow parameer by a leas around 50 per cen whou changng our qualave conclusons. Table 7 The nervals for whch our resul ha European economes have a hgher degree of rankng han he US holds when one npu s changed a a me. Inpu France Germany s Sa ρ Are he Resuls Plausble? The resul ha here s less on-he-job search n Europe s hardly surprsng gven he lower urnover raes. European workers appear o be less moble and hs may be due o culural dfferences, poorly funconng housng markes ec. The smulaons sugges ha rankng could poenally be an mporan cause of hgh unemploymen and, especally, hgh perssence n Europe. In our vew, hs s also n lne wh wha we would expec a pror. As dscussed n Secon 3, frms wll raonally prefer o hre already employed workers f wo condons are fulflled: ) hey expec unemployed workers o have lower average producvy and ) wages canno be adjused o make up for he dfference n producvy. If wages were compleely flexble, he loss of human capal due o unemploymen would affec he fuure wage, bu would no necessarly affec he reemploymen prospecs of he unemployed worker. The loss of human capal n unemploymen should be smlar n dfferen economes, bu here are srong ndcaons ha wages are more rgd n Europe. Unons ypcally end o compress wage dsrbuons, especally whn groups wh smlar jobs and qualfcaons and nss on wage dfferenals beng based on objecve and verfable crera equal pay for equal work. Thus seems lkely ha employers n Europe fnd 3

25 much more dffcul o dfferenae wages accordng o perceved producvy dfferenals compared o he US where unons are nonexsen n mos secors. 4 Conssen wh hs vew, here s evdence ha workers who are lad off n Europe ge a smaller wage reducon compared o he prevous job han n he US - f hey ge a new job. 5 Of course, her chance o ge a new job s much smaller. Wage pressure s found o be of he same order of magnude n our hree economes and n fac s found o somewha lower n he European economes han n he US. 6 A frs sgh, hs resul appears counernuve gven he srengh of European labor unons. Recall, however, ha wage pressure n our model has wo dfferen sources: effcency wage/urnover consderaons and unons wh srong barganng power. The dramacally hgher mobly of he US workforce suggess ha he frs facor should be more mporan n he US whle he laer s clearly more mporan for European labor markes. In erms of he model, f US workers search on he job more ofen (hgher S) we would also expec her job search o be more responsve o wage changes (hgher S (x) for a gven value of x). 7 On he oher hand, unon barganng power (µ) s surely sronger n Europe, so he ne effec on wage pressure (- c S (1/µ)) s no obvous a pror. To llusrae hs pon, consder he case when he dsrbuon G(ν) s exponenal: λν ˆ G( ν ) = 1 e ; ν 0. (4) Suppose furher ha workers face a movng cos whch reduces he uly from a new job by a fracon 1-φ. Then he fracon dong on-he-job search s 4 Furhermore, employmen proecon s ypcally more srngen n European counres. If producvy of ndvdual workers s mperfecly observed, an employer has o use sgnals such as employmen saus o nfer he producvy of an ndvdual worker. In such a suaon, laws ha make hard and/or expensve o fre a worker ha urns ou o have low producvy wll make frms relucan o hre workers who may urn ou o have low producvy. If, n addon he wage canno be dfferenaed accordng o hese sgnals hs lemons problem may lead o src dscrmnaon of groups where here are many lemons. 5 Gbbons and Kaz (1991), Jacobson, Lalonde, and Sullvan (1993). Burda and Merens (1999) revew he evdence and repor evdence for Germany. See also Grund (1999). 6 Ths concluson s no very robus wh respec o changes n npu daa. 7 Ths s no a necessary connecon. I could be ha hgher mcroeconomc volaly and larger wage dsperson n he US rase urnover, bu sll he effec of he wage on urnover s he same as n France. 4

26 S(w /w) = 1- G(w / φw) = e λ w / w (5) where λ = λ ˆ / φ. Thus -λ S(1) = e,. e. λ = -ln(s(1)). Usng he daa on S(1) n Table 4 we fnd ha λ equals 3.17 for he US, 4.61 for Germany and 4.4 for France. Hgher values of λ ndcae hgher movng coss for European workers. To fnd ou he mplcaons for he unon markup, le us compare he US and France. Usng he facs 1/ µ ha Ω = - c S (1/µ) and S' (1/ µ ) = λs(1) we can wre Ω Ω FR US λ = λ FR US S S FR US (1) (1) 1/ µ FR 1/ µ US. (6) Usng he numbers from Table 4 we fnd ha he unon markup mus be hgher n France han n he US. The equaon does no allow us o deermne he level of he markup, bu o ge some dea of he magnude of he dfference, suppose ha here s no markup (µ = 1) n he US. Then he unon markup facor for France mus be equal o Pu dfferenly, he negoaed wage n a parcular frm/secor n France s 8 percen hgher due o unons for gven labor marke condons. Alhough hs example bulds on very specfc assumpons shows ha our smulaons are fully conssen wh he observaon ha unons are sronger n Europe. 6. Concludng Dscusson When an economy recovers from a recesson here are many job openngs. To avod excessve urnover, frms rase wages and, as a resul, he reurn o equlbrum s slowed down. Ths mechansm can, by self, lead o a sgnfcan amoun of perssence, bu canno alone explan all he perssence (seral correlaon) of unemploymen found n he daa. If some employers rank applcans by employmen saus when hey hre, hs rases boh he equlbrum level of unemploymen and s seral correlaon (perssence). Wh rankng, employed workers who look for new jobs have a hgher probably, ceers parbus, o ge he jobs hey apply for. Frms herefore offer hgher wages o preven urnover and equlbrum unemploymen ncreases. Perssence also ncreases snce, afer an ncrease n unemploymen, here s less ncenve o cu wages because unemployed workers compee less effcenly for he jobs. We show quanavely ha hese effecs 5

27 are subsanal for reasonable parameer values. We also show ha more frequen rankng of job applcans n Europe compared o he US could poenally explan he exreme perssence of European unemploymen. An neresng aspec of our model s ha unemploymen benefs do no maer. Unemploymen benefs do no affec employed workers consderng a change of job and qus no unemploymen are aken as exogenous n he model. Implcly, we assume ha workers who wan o look for anoher job need no qu her curren job o do so, and ha hose who qu no unemploymen do hs for oher reasons. Ths assumpon s n lne wh evdence ha unemployed workers spend a raher small fracon of her me on job search, so n mos cases s possble ofen even advanageous - o reman employed whle searchng for a new job. 8 If some workers have o qu her job n order o look for a new job, hs mples a role for unemploymen benefs (provded ha quers can poenally become elgble for unemploymen benef) and makes qus more procyclcal, bu also complcaes he dynamc analyss consderably. 9 Our model s a varaon of he demand sde explanaons of unemploymen, conanng elemens from nsder-ousder, barganng and effcency-wage heores of unemploymen. Parallel o hese demand orened heores here s he supply sde explanaon: unemploymen arses because hgh unemploymen benefs make unemployed workers search less nensely, unwllng o ake he jobs hey could ge, ec. Ljungqvs and Sargen (1998) have recenly developed a model along hose lnes. Whle her man purpose s o explan he secular ncrease n European unemploymen somehng we do no aemp o explan hey also show ha her model can generae perssence. Bu alhough hey assume ha workers lose on average 40 percen of her human capal when hey become unemployed, and ha he replacemen rao s as hgh as 70 percen, hey ge a very modes amoun of perssence: abou 1/8 of he shock remans afer wo years. 30 These smulaons llusrae a pon made by Pssardes (199) and also dscussed by Bean (1994). Whle s rue ha unemploymen persss f some of hose lad off due o a negave shock are slow o reurn o employmen, hs ype of effec becomes progressvely less mporan as hose who were unemployed a he me of he shock fnd jobs. I sops o operae enrely once hey have lef he unemploymen pool, so hs ype of model canno 8 For a revew of such evdence, see Chaper 8 n Layard, Nckell and Jackman (1991). 9 A person qung no unemploymen has o consder he possbly ha he remans unemployed for a long me, so dynamc programmng mehods mus be employed o solve he model. Ljungqvs and Sargen (1995) consder a model wh endogenous qus. 30 See Table 4 and Fgure 8 n Ljungqvs and Sargen (1998). 6