University of Dundee. A non-perpetual shirking model Chen, Yu-Fu; Zoega, Gylfi. Published in: Economics Letters. DOI: /j.econlet

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1 nvrsy of Dund A non-prpual shrkng modl hn, Yu-Fu; Zoga, Gylf Publshd n: conomcs Lrs DOI: /j.conl Publcaon da: 2015 Documn Vrson Pr rvwd vrson Lnk o publcaon n Dscovry Rsarch Poral aon for publshd vrson (APA: hn, Y-F., & Zoga, G. (2015. A non-prpual shrkng modl. conomcs Lrs, 134, DOI: /j.conl Gnral rghs opyrgh and moral rghs for h publcaons mad accssbl n Dscovry Rsarch Poral ar rand by h auhors and/or ohr copyrgh ownrs and s a condon of accssng publcaons ha usrs rcogns and abd by h lgal rqurmns assocad wh hs rghs. srs may download and prn on copy of any publcaon from Dscovry Rsarch Poral for h purpos of prva sudy or rsarch. You may no furhr dsrbu h maral or us for any prof-makng acvy or commrcal gan. You may frly dsrbu h RL dnfyng h publcaon n h publc poral. ak down polcy If you blv ha hs documn brachs copyrgh plas conac us provdng dals, and w wll rmov accss o h work mmdaly and nvsga your clam. Download da: 19. Nov. 2017

2 Accpd Manuscrp A non-prpual shrkng modl Yu-Fu hn, Gylf Zoga PII: S ( DOI: hp://dx.do.org/ /j.conl Rfrnc: OL 6812 o appar n: conomcs Lrs Rcvd da: 6 March 2015 Rvsd da: 29 Jun 2015 Accpd da: 30 Jun 2015 Plas c hs arcl as: hn, Y.-F., Zoga, G., A non-prpual shrkng modl. conomcs Lrs (2015, hp://dx.do.org/ /j.conl hs s a PDF fl of an undd manuscrp ha has bn accpd for publcaon. As a srvc o our cusomrs w ar provdng hs arly vrson of h manuscrp. h manuscrp wll undrgo copydng, ypsng, and rvw of h rsulng proof bfor s publshd n s fnal form. Plas no ha durng h producon procss rrors may b dscovrd whch could affc h conn, and all lgal dsclamrs ha apply o h journal pran.

3 *Hghlghs (for rvw W drv a fn-horzon vrson of h Shapro-Sglz shrkng modl of unmploymn. Workrs bhavor may chang as hy approach h nd of an mploymn conrac. Our modl prdcs ha wags should b rsng n ag for an unchangd ra of unmploymn.

4 *l Pag A Non-prpual Shrkng Modl Yu-Fu hn a and Gylf Zoga b, c* a conomc Suds, nvrsy of Dund, 3 Prh Road, Dund, K b Dparmn of conomcs, nvrsy of Icland, 101 Rykjavk, Icland c Dparmn of conomcs, Brkbck ollg, Mal Sr, London, K Jun 2015 Absrac W provd a fn-horzon counrpar o h Shapro and Sglz modl of unmploymn o show how workrs ffor falls as hy approach h nd of an mploymn spll. h modl provds a rason for wags rsng mor rapdly han producvy. Kywords: Wags, shrkng, fn horzons, rrmn. JL lassfcaon: J31, J21 * orrspondng auhor: Gylf Zoga, Dparmn of conomcs, nvrsy of Icland, Sæmundargaa, 101 Rykjavk, Icland. mal: gz@h.s; lphon: ; fax: Fnancal suppor from h Iclandc nr for Rsarch and h nvrsy of Icland Rsarch Fund s grafully acknowldgd. W ar graful o an anonymous rfr for commns.

5 *Manuscrp lck hr o vw lnkd Rfrncs 1. Inroducon vry mploymn conrac has a m dmnson. hr ar workrs on mporary conracs; workrs who hav bn gvn an advanc noc of dsmssal know ha hr days on h job ar numbrd; and vn workrs who hav saf prmann jobs ralz ha hy wll vnually rr. In hs papr w xnd and gnralz h wll-known modl of wag sng by Shapro and Sglz (S-S (1984 o show how a workr s propnsy o shrk hs dus vars from h bgnnng o h nd of an mploymn conrac. 2. A non-prpual modl W modl a workr s ffor dcson whn h has fn horzons lavng h nfn horzon cas dscrbd n h S-S papr as a spcal cas. hr ar hr sas of nrmporal uls n h S-S modl for workrs wh ransory probabls o alrnav sas. hs ar h valu of bng mployd, V (whn no shrkng and V S (whn shrkng, and h valu of bng unmployd, V. Workrs rcv h wag w whn mployd and unmploymn bnfs b u whn unmployd. ffor s xrd whn mployd workrs ar no shrkng hr dus whl no ffor s xrd whn workrs shrk. Workrs dscoun fuur uly a ra ρ, fac a consan probably of job rmnaon b durng h conrac prod and h probably q of bng frd f caugh shrkng. W sar wh a rprsnav sa ρ( s, (1 V u s ds wh ransory probably p j of movng o h alrnav sa j V,whr u s s h mmda uly a m s for h sa. W can now nroduc fn horzons by dvdng h nr-mporal ngral V no h prods of m and m whr dnos h m rmanng unl h nd of horzon: ρ( s ρ( s ρ( s + V u s ds u s ds u s ds. (2 0

6 h ngral u s ρ( s ds for m prod m can b rwrn as follows ρ( s ρ( ρ( s u s ds u s ds. (3 p ( j hrfor, w nd o dscoun h ngral by h facor f w would lk o rplac wh snc ovr h m prod from o, h ngral dprcas a h ra of p j : quaon (2 can now b rwrn as whr ρ( ρ( s ( ρ+ p j ( ρ( s u s ds u s ds u s ρ( s ds. (4 ρ( s ( ρ+ p j ( ρ( s ( ρ+ p j ( + + V u s ds u s ds V V, (5 ρ( s. Rarrangng gvs V u s ds V 1 V. j p ρ+ (6 quaon (6 shows h rlaonshp bwn h prpual and non-prpual nrmporal ngrals for h sa. On can hn apply quaon (6 o hr sas: V, V S, and V, wh corrspondng ransory probabls: p b, p S b+q, and p a, whr ( V w ds ρ( s s h non-prpual ngral for h valu of bng a non- shrkng mployd workr who facs h probably b of movng o h unmployd sa, ( s s h dsuly of ffor, V w ρ ds s h non-prpual ngral for h valu S of bng a shrkng workr who facs h probably b+q of movng o h unmploymn ( s sa and V b ρ ds s h non-prpual ngral for an unmployd workr who u bcoms mployd wh probably a, whch dnos h probably of fndng jobs. W can drv h followng hr ass prcng quaons by subsung quaon (6 no h Bllman quaons of h prpual cas of h S-S modl; 1

7 ( ρ + b( ( ρ + b( 1 ( ( 1 + ( ρ + a( ρv w b V V 1 ( ρ + b+ q( ( ρ + b+ q( 1 S ( 1 + ( + ( ρ + a( S ρv w b q V V 1 ( ρ + a( ( ρ + a( 1 u ( 1 + ( ρ + b( ρv b a V V 1, (7, (8. (9 sng h no-shrkng condon such ha V V for quaon (8 gvs S ( ρ + b+ q( ( ρ + b+ q( 1 ( 1 + ( + ( ρ + a( ρv w b q V V 1 hr ar hr unknown varabls, V, hr quaons gvs ( ρ ( ρ + b( V 2. (10, w, for (7, (9 and (10. Rarrangng hos ( ρ + b( ( ρ + b( ( b V b V ( a( w ρ + 1 ( ρ ( ρ + b+ q( ( ρ + b+ q(, ( b + q V b + q V 1 0 ( a( w ρ +, (12 1 ( ρ + a( ( ρ + a( + u ( 1 1 a V ( b( ( ρ a V b ρ + 1. (13 Fnally, usng ramr s rul gvs h no-shrkng condon for wags (s Appndx for dals w ( 1 B A a ( b + q bub ( ρ + b + q + ( B A bu ρq + ρ ( a + b + ρ + q ( 1 B A ( ρ + b( ρ + a + aq + ρq ( b( ( 1 ρ + ( b q( ( 1 ρ + + whr A and B. No ha snc A < B w fnd ha (1 B/A s ngav. h numraor of (14 falls fasr han h dnomnaor and h frm nds o pay wags ha rs as h nd of h conrac prod approachs. Bcaus h ffcv dscoun ras for h shrkng sa s ρ + b + q and hghr han h ffcv, (14

8 dscoun ra for h non-shrkng sa ρ + b, shrkng s lss harmful o workrs whos conrac wll xpr soon. For h prpual cas, w hav AB. hus h no-shrkng condon bcoms bu ρq + ρ a + b + ρ + q w bu + + ( a + b + ρ, (15 ρq q whch s h orgnal no-shrkng condon of Shapro and Sglz. Now dno h numbr of mployd workrs of ag by L. In sady sa, h ouflow from mploymn o unmploymn quals bl and should qual o nflow of workrs from unmploymn o mploymn a(n -L whr N s h numbr of workrs of ag n h labor forc. bl a( N L. ( a + b bl N L + b bn N L bn N L b u and w g hus 1 a b u u. Subsung back no (14 gvs h no-shrkng condon n qulbrum as a rlaonshp bwn wags and unmploymn. w ( 1 B A b( ( 1 u u ( b + q bub ( ρ + b + q ( 1 ( + ( + (( 1 + (( 1 + ( B A bu ρq + ρ ( b u + ρ + q + ( 1 (( 1 ( 1 B A ρ b ρ b u u b u u q ρq. B A ρ + b ( ρ + b u u + b ( u u q + ρq (17 I follows ha ach cohor of workrs has a dsnc wag curv or no-shrkng consran dscrbd by quaon (17. h non-shrkng consran s drawn n Fgur 1 blow as an upward-slopng nonshrkng consran for dffrn ag groups wh bnchmark valus blow h fgur. hr ar only small dffrncs bwn young and mddl-agd workrs. Bu h wag curvs for oldr workrs ar subsanally hghr. I follows ha h wag or unmploymn ndd o prvn a 40-yar old workr from shrkng hs dus s no much hghr han ha ndd o prvn a 20 yar old workr from dong so bu a sgnfcanly hghr wag s ndd o prvn a 50 yar old workr from shrkng han s h cas of h 40 yar old on. 3

9 As shown n Fgur 2 w fnd ha h wag rqurd o prvn shrkng rss rapdly n h yars ag group whn unmploymn s 10%, n h yars ag group whn unmploymn s 20% and n h group whn unmploymn s a saggrng 40%. 3. Dscusson Our modl prdcs ha wags nd o ncras as a workr approachs h nd of a conrac whn s dffcul o monor ffor and unmploymn s hld consan. I follows ha wags ar ncrasng n ag for a gvn unmploymn ra. h modl dscrbs wag sng n labor marks whr hr s subsanal asymmrc nformaon abou workrs ffor and monorng s dffcul, such as h mark for profssonals, managrs, ducad workrs and also n larg frms. In such marks oldr workrs wll hr fac a hghr unmploymn ra, whch rducs h cos of mployng hm, b mor producv du o xprnc or pushd no rrmn. W ar no h frs o propos an xplanaon for wags rsng fasr han producvy wh ag. Lazar (1979, 1981 drvd a modl whr wags ar s blow producvy for young workrs and hn abov producvy for workrs approachng rrmn for ncnv rasons, hnc also provdng a jusfcaon for mandaory rrmn. Anohr xplanaon for rsng wag profls s ha of Frank and Huchns (1993 who assum ha sasfacon dpnds on h ra of chang of consumpon. Rsng wag profls may b dsrd by workrs who fnd dffcul o pospon consumpon hrough volunary savngs. Whl rsng wag profls may provd ncnvs and b dsrd by h workforc our modl provds addonal nsghs no h rlaonshp bwn m unl rrmn and producvy. hr s vdnc ha h bhavor of workrs may chang as hy approach h nd of nur. Fglo (1995 found ha h dcson o rr from polcs rsuls n polcal shrkng manng lss pary dscpln usng a mul-yar panl daa s. n (2001 also found ha volunarly rrng mmbrs of ongrss shrkd by falng o rprsn h nrss of hr consuns. Parkr and Powrs (2002 found ha spndng on forgn ravl s hghr among mmbrs of ongrss who ar abou o lav offc. DBackr (2012 dcs shrkng by snaors n hr las rm 4

10 ha s lmd by polcal pars ha consran h polcan dpndng on hs pos- Sna carr chocs. In spors, Kraumann and Solow (2009 xamnd ncnvs n basball conracs and found ha playrs who ar lss lkly o sgn a subsqun conrac showd wors prformanc. hr ar mprcal suds ha suppor h prdcons of our modl. Mdoff and Abraham (1981 fnd an assocaon bwn xprnc and rlav arnng bu no assocaon bwn xprnc and rlav prformanc for managrs and profssonals n wo larg.s. compans. Dos (2006 us anadan daa and fnds ha producvy s lowr han wags for oldr workrs who hav a las an undrgradua dgr alhough h vdnc on h drc ffc of ag on producvy s mxd. Lallmand and Ryck (2009 arbu low mploymn ras among oldr workrs n Blgum o oldr workrs bng mor cosly o mploy and lss producv han prm ag workrs. Sudyng producvy daa from larg Blgan frms hy fnd ha a hghr shar of oldr workrs lowrs avrag producvy. In conras, Börsch-Supan and Wss (2008 sudy producvy n a Grman car manufacurng company and fnd ha xprnc kps h producvy of oldr workrs from fallng by gvng hm an ably o avod makng srous rrors. 4. onclusons By xndng h modl of Shapro and Sglz (1984 w hav found ha workrs ndncy o shrk hr dus ncrass as hy approach h nd of nur. Morovr, h hra of unmploymn has a smallr ffc on hs workrs rqurng frms o ras hr wags or mak hm rdundan. 5

11 Rfrncs Börsch-Supan, Axl H. and Mahas Wss (2008, Producvy and h Ag omposon of Work ams: vdnc from h Assmbly Ln, MA Dscusson Papr No Avalabl a SSRN: hp://ssrn.com/absrac or hp://dx.do.org/ /ssrn DBackr, Jason (2012, Polcal Pars and Polcal Shrkng, Publc hoc, 150 (3-4, Dos, B. (2006, Wags, Producvy and Agng, D conoms, 159, Fglo, Davd N. (1995, h ffc of Rrmn On Polcal Shrkng: vdnc From ongrssonal Vong, Publc Fnanc Rvw, 23 (2, Frank, Robr H. and Robr M. Huchns (1993, Wags, Snory, and h Dmand for Rsng onsumpon Profls, Journal of conomc Bhavor & Organzaon, 21 (3, Kraumann, Anhony. and John L. Solowhp://js.sagpub.com/conn/10/1/6.shor - aff-2 (2009, h Dynamcs of Prformanc Ovr h Duraon of Major Lagu Basball Long-rm onracs, Journal of Spors conomcs, 10 (1, Lallmand,. and F. Ryck (2009, Ar Oldr Workrs Harmful for Frm Producvy?, D conoms, 157, pp Lazar, dward P. (1979, Why Is hr Mandaory Rrmn? h Journal of Polcal conomy, 87 (6, Lazar, dward P. (1981, Agncy, arnngs Profls, Producvy, and Hours Rsrcons, Amrcan conomc Rvw, 71, Mdoff, Jams L. and Kaharn G. Abraham (1980, xprnc, Prformanc, and arnngs, h Quarrly Journal of conomcs, 95 (4, Parkr, Glnn R. and Sphn. Powrs (2002, Sarchng for Sympoms of Polcal Shrkng: ongrssonal Forgn ravl, Publc hoc, 110 (1-2, Shapro, arl and Josph. Sglz (1984, qulbrum nmploymn as a Workr Dscpln Dvc, Amrcan conomc Rvw, 74 (3, n, harls (2001, Rprsnaon, Volunary Rrmn, and Shrkng n h Las rm, Publc hoc, 106 (1-2,

12 Appndx quaons (11-(13 can b wrn as follows: A ρ + b V b V Aw A, (A1 B ρ + b + q V b + q V Bw, (A2 0 a V + a V bu, A (A3 ( ρ whr ( b( ( 1 ρ + b q A, B 1 ρ + + a, and 1 ρ +. ramr s rul gvs h soluons for no-shrkng condons wags A + b b A B b q b q 0 ( ρ ( ρ + + ( + (A4 w a A ( ρ + a b + b A b A + b + q b + q B B a A ( ρ + a 0 ( ρ ( ρ u. xpandng h drmnans gvs (A5 ( ρ + ( + + ( ρ + + ( ρ + ( + u ( ρ + + A( ρ + b + q( ρ + a + Bab Ba ( b + q B ( ρ + b( ρ + a Bbu b b q A b q a Ba b q Abb b q w quaon (A5 can furhr b smplfd as follows,. (A6 w ( B A bub ( ρ + b + q + Bbu ρq + ( A B a ( b + q + A ρ ( a + b + ρ + q ( A B ( ρ + b( ρ + a + aq + Aρq ( A B a ( b + q bub ( ρ + b + q + Bbu ρq + A ρ ( a + b + ρ + q ( A B ( ρ + b( ρ + a + aq + Aρq ( 1 B A a ( b + q bub ( ρ + b + q + ( B A bu ρq + ρ ( a + b + ρ + q. ( 1 B A ( ρ + b( ρ + a + aq + ρq 7

13 Fgur 1. Ag-dpndn wag curvs 10 Wags of NS ag60 ag55 ag50 ag40 ag mploymn Paramr valus: ρ 0.1, b 0.1, q 0.3, 1.0, b u 1, N No ha 45 mpls ha ag 20; and 5 mans ha ag 60, f w assum ha ag 65 s h ag a whch workrs ar no longr wllng o work. Fgur 2. h non-shrkng wag and ag Paramr valus: Sam as n Fgur 1. 8