Severance Payments, Judicial Mistakes and Unemployment

Transcription

1 Svranc Paymnts, Judicial Mistaks and Unmploymnt Nikolai Stählr Univrsity of Mainz May 4, 2005 First Draft Abstract In th discussion about mploymnt protction, littl attntion has bn givn to judicial mistaks. Only in th cas of dismissals du to conomic rasons, th mploy is ntitld to a svranc paymnt. This givs incntiv for firms and workrs to not rport th tru rason for th dismissal. Givn judicial mistaks whn dciding on th tru rason of dismissals, this papr highlights th importanc and implications of thos mistaks. It is shown that rducing judicial mistaks may hav positiv ffcts on mploymnt. Still, an ovrall bttr judicial systm concrning mploymnt protction dos not ncssarily imply lowr unmploymnt rats. Furthrmor, this papr shows that in prsnc of judicial rrors, unmploymnt can unambiguously incras whn incrasing mploymnt protction. Thm: Labour Markt Policy Kywords: mploymnt protction, svranc paymnt, judicial mistaks, matching modls, shirking, unmploymnt JEL-Cod: J 41, J 64, J 65, J 68 Addrss corrspondnc to: Nikolai Stählr, Univrsity of Mainz, Dpartmnt of Economics (FB03/LS Gork), Jakob-Wldr-Wg 5, Mainz, Grmany. stahl@uni-mainz.d. I would lik to thank Florian Baumann, Salvator Barbaro and Laszlo Gork for hlpful commnts. 1

2 1 Introduction Employmnt protction, including svranc paymnts, is a favourd topic to discuss about among labour conomists, politicians and vn privat prsons. Employmnt protction laws tnd to b mor svr in Europ than in th USA. In th Europan contxt, spcially Grmany is known for its strict mploymnt protction lgislation. Not only in Grmany, but also in many othr OECD countris, dismissals can only b justifid through prsonal, disciplinary or oprational rasons (OECD 2004). Th mploy is ntitld to insist on a judicial rviw of his dismissal (s Kittnr 2000). Judgs or juris possibly mak mistaks in such a rviw. Usually, oprational dismissals involv som kind of svranc paymnt, whil prsonal and disciplinary ons (in this modl shirking) do not. That givs incntiv for firms to labl thir layoffs as disciplinary ons, whil workrs want to labl thir dismissal as oprational to obtain th svranc paymnt. This disput is usually sttld in court. Th judicial rviw of th dismissal can crat two typs of mistaks. First, mistaknly allowing a shirkr to rciv svranc paymnts, typ I. Scond, not allowing a non-shirkr to rciv th svranc paymnts, typ II. In thir study, Ichino t al. (2003) find that in Italy, 22% of all dismissals ar takn to court and aftr all, 17% of th dismissals ar ovrruld by court. Furthrmor, thy find in an mpirical and (gam) thortical approach that judgs might b biasd by th labour markt situation whn sttling th dismissal disput. For th firm thy analyz in thir papr 1, thy find out that a bad labour markt situation can influnc judgs dcision in favor of th workr. This at last allows th assumption that a judicial rviw allows for som intrprtation and rrors dfintly do occur (ithr by mistak or vn dlibratly). In this analysis I am not intrstd in th origin of judicial mistaks, but in th ffct thos mistaks hav on th labour markt outcom and th unmploymnt rat and thrfor, tak thm as givn. Still, Ichino t al. (2003) giv a lot of justification for such an assumption. In th scintific discussion about mploymnt protction and svranc paymnts, th implications of judicial mistaks for th unmploymnt rat hav hardly bn tackld - vn though Galdón-Sánchs and Güll (2000) and Ichino t al. (2003) hav adumbratd thir xistnc. Litratur on mploymnt protction usually dos not considr th possibility of thos mistaks. Th main rsult of th rsarch can b summarizd by saying that thr ar ambiguous ffcts on unmploymnt du to mploymnt protction (s Brtola 1990, 1999, Garibaldi 1998 or Mortnsn and Pissarids 2001). Considring ths mistaks allows to driv a condition to rsolv this ambiguity. Galdón-Sánchs and Güll (2003) tak into account th xistnc of judicial mistaks in a modifid fficincy wag modl of Shapiro and Stiglitz (1984). In thir modl, th dismissal is an xognous vnt. Firms hav to pay svranc paymnts du to typ I and typ II mistak with th sam probability. 2 Galdón-Sánchs and Güll (2003) claim that this dos not hav 1 Ichino t al. (2003) us firm lvl data of a spcific firm which thy do not nam. 2 In th following modl stup, this implis m = z. 2

3 any ffct on th rsults. Thy find out that in prsnc of judicial mistaks, unmploymnt unambiguously incrass whn incrasing th lvl of svranc paymnts. That is du to th fact that in prsnc of judicial mistaks, th paymnt of svranc paymnts is not nutralizd through an accordant dcras of wags in complt and prfct markts by anticipating ths paymnts as it is in Lazar (1990). In th prsnt modl, th dismissal rason is xplicitly modld. Disciplinary dismissals tak plac whn firms find a workr shirking and oprational layoffs ar ndognously dtrmind. Job cration according to individual firm s optimization is also xplicitly modld. I allow, in contrast to Galdón-Sánchs and Güll (2003), th probabilitis of having to pay th svranc paymnt to diffr. 3 I find out that an incras of th lvl of svranc paymnts dos not hav th clar cut sign on th ffct on unmploymnt as in th modl of Galdón-Sánchs and Güll (2003) - vn whn modling th mistaks alik - which rsults from th fact that job cration is xplicitly modld. 4 Th problm is analyzd in a matching modl a la Pissarids (2000) to b abl to xplicitly modl ndognous oprational dismissals and, mayb vn mor important, th firm s dcision of job cration ndognously. To b abl to hav tru disciplinary dismissals, th matching modl is augmntd by th possibility of shirking a la Shapiro and Stiglitz (1984). I will show that rducing th typ I mistaks unambiguously dcrass unmploymnt, whil th ffct of a rduction of typ II mistaks is ambiguous. Furthrmor, I can show that undr crtain conditions concrning ths two typs of mistaks, unmploymnt can unambiguously incras whn th lvl of svranc paymnts is incrasd, but this is not compulsory to happn. As it is oftn claimd in th political dbat that a bttr judicial systm improvs job cration and lowrs unmploymnt, I am also abl to show that this dos not hav to hold. Th ffcts at work can brifly xplaind as follows. Rducing th typ I mistaks dcrass th rsrvation wag that firms hav to pay to prvnt shirking. That incrass th valu of nwly cratd jobs and thrfor, th offr of vacancis. Additionally, it dcrass th rsrvation productivity (bcaus labour costs dcras), which lads to fwr dismissals. Fwr dismissals and mor vacancis unambiguously dcras unmploymnt. Rducing th typ II mistaks dcrass th rsrvation wag, bcaus th highr probability of rciving th svranc paymnt whn not shirking givs incntiv for th workr to shirk lss. On th on hand, lowr wags incras th valu of nwly cratd jobs. On th othr hand, th highr xpctd dismissal costs dcras th valu of nwly cratd jobs. Th lattr ffct dominats th first ffct which dcrass markt tightnss. Dcrasing rsrvation productivity and markt tightnss hav ambiguous ffct on th unmploymnt rat. Th ffct of incrasing th lvl of svranc paymnt dpnds on th rlation of th two mistaks. On th on hand, incrasing svranc paymnt incrass th rsrvation wag not 3 Which in th following modl implis m z. 4 Not that in th prsnt modl, th sign is ambiguous. For som condition, th rsults agr with ach othr. But from a thortical point of viw, this condition must not ncssarily hold. 3

4 to shirk through typ I mistak. On th othr hand, it dcrass through typ II mistak. Thrfor, rsrvation productivity might ithr fall or ris. Furthrmor, highr svranc paymnts yild highr xpctd costs of dismissals and thrfor dcrass job cration. For th typ I mistak bing high nough rlativ to th typ II mistak, rsrvation productivity incrass, which thn unambiguously incrass unmploymnt whn mploymnt protction is incrasd. A bttr judicial systm, maning dcrasing typ I and typ II mistaks, is oftn blamd to hav ngativ ffct on unmploymnt by politicians and officials. I can show that an improv of th judicial systm dos unambiguously dcras th numbr of dismissals through th wag ffct. Th improvmnt assurs no-shirkrs to rciv svranc paymnts whn bing dismissd du to oprational rasons whil it maks it hardr for shirkrs to rciv thos paymnts whn bing caught shirking. Thrfor, th incntiv to shirk dcrass which maks it possibl to lowr wags. But th indicatd positiv ffct on job cration cannot b found from a thortical point of viw. On th on hand, th incntiv to crat nw jobs incrass through th wag ffct. On th othr hand, it dcrass bcaus th xpctd costs of dismissals incras. Thrfor, th ffct on job cration and unmploymnt stays ambiguous. A condition for job cration to incras (which thn dcrass unmploymnt) can b drivd - but again, from a thortical point of viw, it is not clar why this condition should hold. Th rst of th papr is organizd as follows. First, in sction 2, I am going to introduc th modl. Scond, in sction 3, a comparativ static analysis is don. Third, in sction 4, th ffcts of an improv of th judicial systm ar analyzd. Last, in sction 5, th main findings ar summarizd. For important calculations, a mathmatical appndix is addd. 2 Th Modl 2.1 Basic Structur Considr an conomy with a continuum of infinitly livd homognous workrs which is normalizd to on. Firms ar also masurd in an continuum whil fr markt ntry condition dtrmins thir numbr. Th discount rat of workrs and firms is r. Workrs instantanous utility function is givn by V (w, ) = w, whr w is th wag incom and charactrizs th cost of ffort whn working. Following Pissarids (2000), all firms ar idntical and hav on vacancy to offr. Th labour markt is charactrizd by sarch frictions. Unmploymnt u and vacancis v xist at th sam tim. Th production flow of a firm-workr match is dscribd in a valu function and shall latr on b calld job. Th matching procss is dscribd by a linar homognous and concav matching function m(v, u). Th ratio θ = v/u is calld markt tightnss. It is dtrmind ndognously. Th rat at which vacancis ar filld is givn by q(θ) = m(1/θ, 1), whr q (θ) < 0. Unmployd workrs find a job at rat θq(θ) = m(θ, 1), whr [θq(θ)] > 0. 4

5 According to Shapiro and Stiglitz (1984), firms nd th workr to work at an ffort lvl = to b productiv. If th ffort falls blow this ffort lvl, th firm closs down. Effort is a binary choic. Workrs can ithr work (at th ffort ) or shirk (whr th ffort is = 0). Inspctions occur according to a Poisson procss with arrival rat p and ar costlss. If a workr is caught shirking, th firm-workr match will b rsolvd. Furthrmor, ach job has an idiosyncratic productivity ɛ [ɛ l, ɛ u ], which is distributd according to th cumulativ distribution function G(ɛ), with g(ɛ) bing th corrsponding dnsity function. Productivity shocks occur to vry singl job at th Poisson rat λ. In cas of a shock, a nw idiosyncratic productivity is drawn from th distribution G(ɛ). If th productivity falls blow som ndognously dtrmind thrshold valu (which is calld rsrvation productivity), th job is dstroyd. Workrs ar ntitld to rciv a svranc paymnt T as long as thy ar dismissd du to oprational rasons. If dismissd du to disciplinary rasons (shirking), workrs miss out. This givs th incntiv for firms to claim th dismissal has takn plac du to shirking, vn though it has bn du to a productivity shock. Workrs hav th incntiv to claim that th dismissal has takn plac du to oprational rasons vn though it was du to disciplinary rasons. This conflict can b takn to court (s Kittnr 2000). 5 Judgs might mak mistaks du to information dficits. Thrfor, following Güll (1999), with probability m, tru disciplinary dismissals ar mistaknly judgd to b oprational layoffs. With probability (1 z), rdundancis ar mistaknly judgd to b disciplinary dismissals Th Valu Functions Workrs Th valu function for an mployd workr, dnotd by W (ɛ), satisfis th following Bllman quation rw (ɛ) = (1) { [ ɛu ] } w(ɛ) + λ W (x)dg(x) + G( )(U + zt ) W (ɛ) + pl() [U + mt W (ɛ)], max =0or= whr w(ɛ) is th wag th workr arns dpnding on idiosyncratic productivity. l() is a function of th ffort which quals unity in cas of = 0 and quals zro in cas of =. 5 Not that in th blow dscribd modl, all disputs ar sttld in court, bcaus no costs occur from taking th disput thr. Sinc I am intrstd in th isolatd ffcts of judicial mistaks, this simplifying assumption dos not harm th following analysis. For a first, simpl approach of introducing costs associatd with going to court, s Galdón-Sánchs and Güll (2003). Evn thr, vrybody gos to court as long as th xpctd bnfit from going to court is highr than th punishmnt whn caught lying in court, s also sction 5. 6 Th rstriction that th two mistaks ar indpndnt will b abolishd in sction 4. But for now, th isolatd ffct of thos mistaks ar of intrst. 5

6 Thrfor, th asst pricing function for an mployd workr is influncd by th wag minus th ffort, th option valu in cas of a productivity shock and th option valu in cas a shirking workr is dismissd. If productivity falls blow th rsrvation productivity, th match is rsolvd and th workr bcoms unmployd. In this cas, th workr obtains th utility of an unmployd U and a rdundancy paymnt T with probability z. In cas th workr is fird du to disciplinary rasons, th workr also rcivs th utility of unmploymnt and a rdundancy paymnt T with probability m. Analogously, th Bllman quation for a nwly cratd match can b writtn as rw 0 = (2) { [ ɛu ] max w 0 + λ W (x)dg(x) + G( )(U + zt ) W 0 + pl() [ U + mt W 0]}. =0or= Th asst pricing function of unmploymnt can b statd as ru = θq(θ) [ W 0 U ]. (3) For simplicity I assum that workrs do not rciv unmploymnt bnfits. Thrfor, th utility flow of unmploymnt quals th option valu of finding a job. To prvnt shirking, th workr must gt a high nough rnt from working so that shirking dos not pay. That yilds W (ɛ) = W (ɛ) =0 [W 0 = W 0 =0 rspctivly]. This givs th no-shirking-condition, furthr on NSC, (calculations ar in analogy to Rochtau (2002, Appndix A1)) W 0 U + mt, (4) p and W (ɛ) U + mt. (5) p Equations (4) and (5) stat that a shirkr savs th work disutility, but bars a capital loss W 0 U [W (ɛ) U rspctivly] if h is fird bcaus bing caught shirking. That vnt occurs with probability p. Whn bing fird, th shirkr additionally rcivs a rdundancy pay T with probability m. As long as th NSC is fulfilld, no workr shirks in quilibrium. If it is not, all workrs shirk. Using quation (1) in combination with quation (5), and (2) with (4) rspctivly, th no-shirking wag can b calculatd as [ ] w 0, w(ɛ) (r + λ) p + mt + λg( )zt + [r + λ(1 G ))] U λ ɛu W (x)dg(x). (6) 6

7 Equation (6) is th no-shirking (minimum) wag that th firm must pay to prvnt a workr from shirking. As can asily b sn in quation (6), th wag is indpndnt of th idiosyncratic componnt ɛ of a firm-workr match. Thrfor, this no-shirking wag is qual for all idiosyncratic productivitis. Using quation (3) to liminat U, on obtains [ ] w 0 = w(ɛ) = [(r + λ) + (r + λ(1 G( ))θq(θ)] p + mt + λg( )zt λ ɛu W (x)dg(x). (7) For furthr analysis, this wag, quation (7), is assumd to b paid by firms. 7 Firms Analogously to th abov, th firm s Bllman quation can b writtn as [ ɛu ] rj(ɛ) = ɛ w(ɛ) + λ J(x)dG(x) G( )zt J(ɛ). (8) Th firms s asst pricing function consists of th ndd ffort multiplid with th idiosyncratic productivity minus th wags plus th option valu of a shock. In cas th productivity falls short of th rsrvation productivity, th firm has to pay a svranc paymnt T with probability z. As th firms know that thy hav to pay at last th noshirking wag (quation (7)) to prvnt workrs from shirking, for all wags w(ɛ) blow th no-shirking wag, all jobs will b closd. 8 Thrfor, th no-shirking wag crats a natural lowr boundary for th rsrvation productivity, which will b xplaind in mor dtail latr on. For nwly cratd jobs, th Bllman quation rads [ ɛu ] rj 0 = ɛ u w 0 + λ J(x)dG(x) G( )zt J 0, (9) whr nwly cratd jobs ar ndowd with th highst possibl productivity ɛ u (s Pissarids 2000). 7 Wag bargaining is usually modld as a Nash bargaining procdur with th workr s outsid option bing unmploymnt and th firm s outsid option bing th ngativ dismissal taxs. Following Muthoo (1999), in this stting, bargaining has to b modld with an insid option. Firms know that thy hav to pay at last th no-shirking wag, bcaus othrwis, thy will not b productiv. If th workr s productivity is too low and firms cannot afford th no-shirking wag, jobs will b dstroyd and thrfor, th wag gnrats a lowr boundary for rsrvation productivity. Workr s insid option is thir utility whn bing paid th no-shirking wag. Th wag rsulting from bargaining with insid options turns out to b th no-shirking wag. Furthrmor, vn whn using bargaining with outsid options, th bargaining has to b mad subjct to quation (7). According to Rochtau (2002), th rsulting wag whn th rstriction is binding, is th no-shirking wag. This is th intrsting cas w ar focusing our attntion on. 8 If firms did not pay th no-shirking wag, thy would not b productiv (s quations (8) and (9)). Thrfor, firms must pay at last th minimum wag to prvnt shirking. 7

8 Analogously, I driv th Bllman quation for a vacancy V. Rcruitmnt costs ar givn by c pr priod. rv = c + q(θ) [ J 0 V ]. (10) Fr markt nrty for firms implis that vacancis will b cratd as long as thir prsnt valu is gratr zro. Accordingly, in quilibrium V = 0 has to hold, yilding J 0 = c q(θ). (11) 2.3 Job Dstruction, Job Cration, and Unmploymnt For givn policy paramtrs, th markt quilibrium is spcifid by th two ndognous variabls markt tightnss θ and rsrvation productivity, govrning th procsss of job cration and job dstruction. Th rsrvation productivity is dtrmind by th job dstruction condition that th workr will b dismissd, if firm valu falls blow th ngativ xpctd dismissal costs. Thrfor, J( ) = zt. As statd arlir, markt tightnss θ is dtrmind by fr markt ntry for firms, quation (11). Substituting th wag quation (7) into th Bllman quations (8) and (9), and using th abov dscribd job dstruction condition and quation (11), I driv (for calculations s Appndix A) + λ r + λ ɛu [ ] (x ) dg(x) = [(r + λ) + (r + λ(1 G( )))θq(θ)] p + mt rzt as th job dstruction condition (furthr JD) and [ɛ u ] (r + λ) zt = c q(θ) as th job cration condition (furthr JC). Equations (12) and (13) simultanously solvd dtrmin th quilibrium valus of rsrvation productivity and markt tightnss θ for givn policy paramtr T and th judicial mistaks m and z. Sinc unmploymnt is dtrmind by inflows (λg( )(1 u)) and outflows (θq(θ)u) according to th job dstruction and job cration dcisions of firms, th stady stat quilibrium unmploymnt is also dtrmind by quations (12) and (13). In stady stat, th chang in unmploymnt is zro and th unmploymnt rat is givn by u = (12) (13) λg( ) λg( ) + θq(θ). (14) Sinc, as alrady mntiond abov, in quilibrium no workr shirks, bcaus firms pay th no-shirking wag, no inflows into unmploymnt rsult from ral disciplinary dismissals in quilibrium. 8

9 3 Changs in Judicial Mistaks and Employmnt Protction As mntiond abov, th ffcts of judicial mistaks concrning mploymnt protction on th unmploymnt rat hav hardly bn tackld. But taking into account that in Grmany dismissal disputs wr takn to court with a probability of 27% in 2001 (s Grman Council of Economic Exprts 2003) 9, this issu sms to hav som importanc. Thrfor, this sction dscribs th ffcts of a chang in judicial mistaks on unmploymnt. Furthrmor, th ffcts of changing mploymnt protction in prsnc of judicial mistaks is analyzd. First, th ffcts of th chang in th mistak of falsly allowing shirkrs to rciv rdundancy paymnts is analyzd (dm). Scond, th ffct of rducing th mistak of falsly blaming workrs to b shirkrs who ar not is takn a look at (dz). Last, th ffcts of a chang of mploymnt protction in prsnc of judicial mistaks is analyzd. For major mathmatical calculations s Appndix B. 3.1 Rducing th typ I mistak A rduction of th probability for a shirkr to falsly rciv rdundancy paymnts can b calculatd by totally diffrntiating th JD and JC with rspct to th ndognous markt tightnss θ and rsrvation productivity with rspct to m. This yilds d dm = 1 D { c q(θ) 2 q (θ) [(r + λ) + (r + λ(1 G( ))θq(θ)] T } > 0, (15) and whr D = dθ dm = 1 { [ T 1 + [r + λ(1 G(ɛ ]} d))]θq(θ) < 0, (16) D r + λ [ [ r + λ (r + λg()) + λg( ) p + mt [ r + λ [r + λ(1 G())] p + mt ] ] θq(θ) ] [θq(θ)]. c q(θ) 2 q (θ) As can b sn, D < 0, bcaus th first trm is ngativ (du to q (θ) < 0) and th scond trm, which is subtractd, is positiv. Equation (15) shows that th rsrvation productivity incrass with incrasing judicial mistak of falsly allowing a shirkr for rdundancy pays. Th markt tightnss dcrass whn doing so (s quation (16)). 9 S also Gork and Pannnbrg (2004) for a mor dtaild analysis about th paymnt of svranc paymants btwn 1990 and Thy find out that on avrag, 14% of all mploymnt rlationships trminatd wr accompanid by svranc paymnts. 9

10 Th rason for this is straightforward. As can b sn in quation (7), a highr judicial mistak m incrass th no-shirking wag, which is th minimum wag that firms hav to pay. Highr wags yild highr labour costs. That mans that a job to pay must b mor productiv and rsrvation productivity incrass on th on hand. As working costs incras, rlativly lss jobs ar mor productiv, on th othr hand. Lss vacancis ar offrd and markt tightnss dcrass. Thus, dcrasing th judicial mistak of falsly allowing a shirkr to rciv svranc paymnts (dm < 0) dcass th rsrvation productivity (through lowr wags) and incrass markt tightnss (through mor vacancis). That maks unmploymnt unambiguously fall, as can b sn in quation (14). 3.2 Rducing th typ II mistak Again, a rduction of th probability for a non-shirkr to falsly not rciv rdundancy paymnts can b calculatd by totally diffrntiating th JD and JC with rspct to th ndognous markt tightnss θ and rsrvation productivity, this tim with rspct to z. This yilds and d dz = 1 D { [ ] T {[r + λ(1 G( ))] p + mt } [θq(θ)] c r q(θ) 2 q (θ)} < 0, (17) dθ dz = 1 { [ [ ] ]} T λg( ) + D r + λ p + mt λg( )θq(θ) < 0. (18) Equation (17) shows that th rsrvation productivity incrass with incrasing judicial mistak of falsly not allowing a non-shirkr for rdundancy pays. Not that an incras of this mistak mans an incras of (1 z) and thrfor, a dcras of z! Markt tightnss incrass whn doing so (s quation (18)). This can b xplaind as follows. First, an incras in th judicial mistak (1 z) (dcras of z) incrass th no-shirking wag, bcaus workrs hav to b compnsatd for th loss of scurity of rciving a svranc paymnt whn bing dismissd as non-shirkr (s quation (7)). Th firm s labour costs incras. Scond, th xpctd costs of dismissals (zt ) dcras, which maks th firm dcid to lay off workrs arlir according to th JD (s quation (12)). Thrfor, rsrvation productivity incrass. Sinc th xpctd firing costs zt dcras, th valu of a nw job incrass, which incrass th offr of vacancis and thrfor, markt tightnss incrass. Hnc, dcrasing this judicial mistak (1 z) by incrasing z, dcrass rsrvation productivity and markt tightnss. That inducs lss inflows into unmploymnt, but at th sam tim, lss outflows out of unmploymnt. Th ffct on th unmploymnt rat is ambiguous, as can again b sn in quation (14). 10

11 3.3 Changing mploymnt protction T Th ffcts of mploymnt protction on unmploymnt (in this stup, svranc paymnts) hav widly bn discussd. Highr mploymnt protction dcrass dismissals but at th sam tim dcrass job cration which maks its ffct on th unmploymnt rat ambiguous, s Mortnsn and Pissarids (1999, 2001). Or, in cas of pur svranc paymnts, complt and prfct markts nutraliz th ffct on mploymnt, s Lazar (1990). In th prsnc of judicial mistaks, th ambiguity may partly b dismantld. Again totally diffrntiating th JD and JC, this tim with rspct to mploymnt protction T, yilds d dt = 1 D 1 D { ( c r { cη(θ) η(θ) + q(θ)(1 η(θ)) θq(θ) whr 0 < η(θ) = q (θ) θ < 1 and q(θ) dθ dt = 1 {[ D r + λ λg() + λg( ) (r + λ) θq(θ) + (r + λ(1 G()) [ ]) [ ]} p + mt + λ(1 G( ))q(θ)(1 η(θ)) p + mt z } m, (19) [ ] ] [ p + mt θq(θ) z [r + λ(1 G(ɛ ] } d))]θq(θ) m < 0. r + λ (20) As can b sn in quation (20), markt tightnss dcrass unambiguously whn incrasing mploymnt protction. This is du to th fact that highr mploymnt protction T inducs highr xpctd costs of dismissals which maks th valu of nw firms dcras and thrfor, fwr vacancis ar offrd. But in prsnc of judicial mistaks, as can b sn in quation (19), th ffct of an incras in mploymnt protction on th rsrvation productivity is ambiguous. It dpnds on how typ I and typ II mistaks stand to ach othr. If th trm in brackts of quation (19) is positiv, markt tightnss dcrass and th standard rsult applis. But if th trm is ngativ, rsrvation productivity unambiguously incrass, which mans mor dismissals tak plac whn incrasing svranc paymnts T. Rwriting th trm in brackts of quation (19), this is th cas if z m < [1 + (r + λ(1 G( )) θq(θ)] cη(θ) [ ], (21) rcη(θ) + (1 η(θ)) (r + λ(1 G( )) θq(θ) + mt q(θ) p }{{} =A whr z/m is th rlation of th probabilitis of having to pay th svranc paymnt T du to th two typs of mistaks from th firm s point of viw and A > From a thortical point of viw, it cannot b said if A is smallr or biggr than unity. It dpnds on th xognous vacancy costs c, th discount rat r, th probability of a shock, λ, th ncssary ffort lvl, th inspction probability, p, th lvl of svranc paymnts, T, and th magnitud of th typ I mistak, m, itslf, as wll as on th ndognous valus for markt tightnss, θ, and rsrvation productivity, (which ar dtrmind by th xognous variabls). 11

12 Equation (21) shows that for rsrvation productivity to incras whn incrasing th lvl of svranc paymnts, z/m < A has to hold. That mans that th probability of rciving a svranc paymnt as a no-shirkr, z, has to b rlativly small compard to th probability of rciving a svranc paymnt as a shirkr, m, wightd by A. A small probability z yilds a rlativly high typ II mistak, (1 z). Thrfor, rlativly high typ II mistaks mak it vry likly that dismissals incras whn incrasing th lvl of svranc paymnts and hnc, unmploymnt incrass (bcaus at th sam tim, markt tightnss dcrass, as can b sn in quation (20)). 11 Th intuition for this is straightforward. Whn incrasing svranc paymnts T, workrs fac a highr compnsation whn bing dismissd du to oprational rasons. As shirking is positivly influncd through th typ I mistak, - th highr m, th highr th probability to obtain th svranc paymnt T whn bing dismissd bcaus of shirking - th rsrvation wag has to incras on th on hand. On th othr hand, rsrvation wag can b dcrasd for a small typ II mistak (high z), bcaus workrs ar rlativly assurdly compnsatd for a dismissal du to oprational rasons, which maks thm shirk lss (s quation (7)). Thrfor, th ffct on th firm s labour costs (wags) whn incrasing svranc paymnts dpnds on th magnitud of ths ffcts. Furthrmor, a rlativly small typ II mistak [high z] maks firms dismiss workrs latr (s quation (17)). Hnc, if rsrvation productivity incrass or dcrass with svranc paymnts highly dpnds on th rlation of th magnituds of th two typ of mistaks. For th bnchmark cass z = 0, giving th highst possibl typ II mistak, and m = 0, giving th lowst possibl typ I mistak, quation (21) allows for som prdication. 12 For a positiv typ I mistak (z > 0) and typ II mistak bing zro (m = 0), saying that no shirkr falsly rcivs svranc paymnts, but still som no-shirkrs falsly do not, rsrvation productivity falls, yilding ambiguous ffcts on th unmploymnt rat. For a positiv typ I mistak (m > 0) and th highst possibl typ II mistak (z = 0), rsrvation productivity incrass which unambiguously incrass unmploymnt. For both typs of mistaks bing positiv, no clar cut thortical prdiction can b mad (bcaus th xact magnitud of A cannot b dtrmind thortically) and at last mor mpirical rsarch about th magnituds of th ffcts is ndd. But intrstingly, quation (21) shows that A is smallr for high lvls of svranc paymnts, T (and givn typ I mistak, m, and typ II mistak, (1 z) and thrfor, z). Thus, starting from a situation with high lvls of svranc paymnts, an incras of thos svranc paymnts mak it likly that fwr dismissals tak plac. Th intuition is similar to th abov. For high lvls of svranc paymnts, T, an incras of thos paymnts nds a vry high typ II mistak, (1 z) [low z], rlativ to th typ I mistak, m, for rsrvation productivity to incras. In this situation, th abov dscribd wag ffct dos 11 For th rsults of Galdón-Sánchs and Güll (2003) to hold, A > 1 has to hold, sinc m = z. But, as alrady mntiond, this cannot b assurd from a thortical point of viw. 12 Not that for th lattr cas, m would hav to b switchd to th rhs by multiplying quation (21) with m bfor assuming m = 0 to b mathmatically corrct. 12

13 not compnsat th xpctd dismissal costs and thrfor, firms dcid to dismiss latr. Thn, th ffct on unmploymnt is ambiguous. Summing up, th ffct of unmploymnt is still ambiguous whn incrasing mploymnt protction, as long as th typ II mistak (1 z) is low nough (with z bing high). For th mistak m to b high nough rlativ to th probability of paying svranc paymnts du to an oprational dismissal, z, unmploymnt unambiguously incrass whn incrasing th lvl of svranc paymnts, bcaus of mor dismissals and fwr vacancis. 4 Improving th Judicial Systm with dpndnt Mistaks It sms to b rasonabl to assum that typ I and typ II mistaks ar not indpndnt from ach othr. If on mistak is tackld through som political action - lts say, courts hav th right to gt bttr information (proofs) about th firms policy whn having to dcid about a dismissal disput -, th othr on might b affctd by this action as wll. Morovr, whn improving th judicial systm, th assumption that both, typ I and typ II mistaks dcras, can b justifid. That yilds dm < 0 and d(1 z) < 0 (dz > 0), whn th judicial systm is improvd. Thrfor, th improvmnt of judicial mistaks lads to th following ffcts on rsrvation productivity and markt tightnss, which ar simply drivd from quations (15) in combination with (17) and (16) in combination with (18) d = 1 [ ] c D q(θ) 2 q (θ) [(r + λ) + (r + λ(1 G( ))θq(θ)] T }{{} dm }{{} ( ) ( ) + 1 [ { [ ] }] T [r + λ(1 G( ))] D p + mt [θq(θ)] c r q(θ) 2 q (θ) }{{} dz < 0 }{{} (+) (+) (22) 13

14 and dθ = 1 ( T 1 + [r + λ(1 G(ɛ ) d))]θq(θ) D r + λ }{{} dm }{{} ( ) (+) + 1 ( [ ] ) T D r + λ λg() + p + mt λg( )θq(θ) }{{} dz. }{{} (+) (+) (23) Equation (22) shows that through an improvmnt of th judicial systm, rsrvation productivity unambiguously falls and thrfor lads to fwr dismissals. That is th cas bcaus through this improvmnt, whn bing dismissd, th probability for a shirkr to rciv rdundancy paymnts dcrass, as th probability for a no-shirkr to rciv svranc paymnts incrass. This dcrass th non-shirking wag and thrfor labour costs, as can b sn in quation (7). Additionally, th xpctd cost for a dismissal, zt, incrass, which maks firms dismiss latr. Th sign of quation (23) is ambiguous. An improvmnt of th judicial systm on th on hand lads to lowr labour costs through a dcras of th no-shirking wag (through dm < 0 and dz > 0). This incrass th xpctd valu of nwly cratd jobs which inducs markt tightnss to incras. On th othr hand, th xpctd costs of an oprational dismissal incras (through dz > 0) which dcrass th xpctd valu of nwly cratd jobs. Which of th ffct dominats dpnds highly on th magnituds of th changs of th mistaks. Evn for th xtrm assumption that th xpctd probabilitis of having to pay th svranc paymnt chang by th sam amount, dm = dz, thr is no clar cut answr possibl. For dm = dz = dx, quation (23) can b rwrittn to dθ = 1 D {[ p + mt ] λg( )θq(θ) T r + λ [1 + q(θ)][r + λ(1 G())] } dx, whr dx < 0 whn improving th judicial systm. As can b sn, for th improvmnt of th judicial systm to incras firm s incntiv to crat nw jobs (which incrass markt tightnss), [ ] th trm in brackts nds to b positiv (rmmbr that D < 0). That yilds + mt λg(ɛ p d )θq(θ) > T [(r + λ(1 G(ɛ (r+λ) d)))(1 + θq(θ))]. If this condition holds, markt tightnss incrass which thn unambiguously dcrass unmploymnt. Th only clar thortical rsult that can b adhrd is that for high inspction probability, p, this is likly to happn which is quit intuitiv - mor inspctions lowr th no-shirking wag and thrfor labour costs. Rcapitulating, it can b said that improving th judicial systm unambiguously dcrass dismissals on th on hand. On th othr hand, it has ambiguous ffcts on markt tightnss. 14

15 For incrasing markt tightnss, unmploymnt unambiguously dcrass. That is possibl for high lvls of inspction probability, p, in combination with fairly quivalnt changs of th probabilitis of having to pay svranc paymnts du to typ I and typ II mistaks (dm dz). For dcrasing markt tightnss, th ffct on unmploymnt stays ambiguous. From a thortical point of viw, it is not clar if an improv of th judicial systm dos hav th dsird ffct of lowring unmploymnt through bttr incntivs for firms to offr jobs as is claimd by many politicians and officials. It might hav th advrs ffct. 5 Conclusion Th aim of this papr was to highlight th importanc of considring judicial mistaks concrning mploymnt protction. It is shown that dcrasing th typ I mistak, falsly allowing a shirkr for svranc paymnts, unambiguously dcrass unmploymnt. This is mainly du to th fact that th no-shirking wag dcrass, which rducs labour costs. Thrfor, fwr dismissals tak plac and th incntiv to crat mor vacancis incrass. Th ffct of rducing typ II mistak of falsly not allowing a no-shirkr for svranc paymnts on th unmploymnt rat is ambiguous. That rsults bcaus, on th on hand, fwr dismissals tak plac, sinc labour costs (wags) dcras whn rducing this mistak and th xpctd costs of dismissals incras. On th othr hand, lss jobs ar cratd, bcaus through highr xpctd dismissal costs, th valu of nwly cratd jobs dcrass. Incrasing th lvl svranc paymnts and thrfor mploymnt protction has ambiguous or positiv ffcts on th unmploymnt rat. Th unmploymnt rat is likly to incras for rlativly high typ II mistaks compard to typ I mistaks. In this cas, wags to prvnt workrs from shirking - and thrfor, firm s labour costs - incras, whil th incras of dismissal costs is rlativly small. That lads to mor layoffs, whil th incntiv to crat nw vacancis dcrass. In this cas, th rsults of Galdón-Sánchs and Güll (2003) can b approvd. But in th cas of rlativly low typ II mistaks compard to typ I mistaks maks wags fall whil dismissals ar rlativly xpnsiv. Incrasing mploymnt protction in this situation maks firms dismiss fwr workrs which dcrass rsrvation productivity. Bcaus th xpctd valu of nwly cratd firms dcrass through an incras of mploymnt protction, th ffct on th unmploymnt rat is ambiguous. An improvmnt of th judicial systm, lowring typ I and typ II mistaks at th sam tim, dos dcras rsrvation productivity and thrfor lads to fwr dismissals. That is du to th fact that wags can b dcrasd, bcaus th incntivs to shirk dcras, whil dismissals thmslvs gt mor xpnsiv. Th ffct on markt tightnss and thus, on job cration is ambiguous. Through lowr wags, th incntiv to crat mor nw jobs incrass, whil it dcrass through highr xpctd dismissal costs du to oprational layoffs. If th two typs of mistaks ar dcrasd in a way that th probabilitis of having to pay th svranc paymnts chang alik and th inspction probability is high, it is likly that job 15

16 cration incrass. But this ffct cannot b approvd through a thortical argumnt and it is possibl that job cration vn dcrass whn improving th judicial systm. Th dscription abov yilds svral conclusions. First of all, it has bn shown that whn daling with mploymnt protction, possibl judicial mistaks should b considrd. Th xistnc of judicial mistaks may chang th standard rsults whn analyzing th ffcts of mploymnt protction. Som ambiguitis can b rsolvd (or at last it can b said undr which circumstancs that can b don) whil additional ambiguitis ar addd. Thrfor, I agr with Ichino t al. (2003) that it is crucial to do mor thortical and mpirical rsarch to find out about th magnituds of th mistaks. Thortical rsarch can includ to discovr and analyz mchanisms to rduc th incntiv for not rporting th tru rason for dismissals. This crtainly also includs modling costs of going to court. Sinc this, and most othr modl framworks that I know daling with mploymnt protction in this vin, assum risk-nutral agnts, risk-avrsion and htrognity should b includd. Additional rsarch on how and why judicial mistaks can b dtrmind is crtainly ndd. 13 Empirical rsarch is ndd, bcaus for any political advis concrning an incras or dcras of mploymnt protction or th improvmnt of th judicial systm, th magnituds of th mistaks mntiond can dfin th outcom of a political action of that kind. Furthrmor, whn intnting to dcras unmploymnt, it sms to b dsirabl to rduc typ I mistaks if it was possibl to tackl th mistaks apart. Mor prcisly, rduc th probability for shirkrs to rciv svranc paymnts. In Grmany and many othr Europan countris, this could b don by, for xampl, rvrsal of th burdn of proof. Whn going to court, th firm nds to proof that th workr has bn dismissd du to disciplinary rasons. This givs som inscurity of th ral dismissal costs. If th burdn of proof was rvrsd, this might prvnt som shirkrs from going to court. All th sam, on has to b carful with this conclusion. Mor rsarch on this topic, as mntiond abov, might rvrs this argumnt. Additionally, it can b said that a crtain lvl of typ II mistak might b positiv for th conomy. This is bcaus typ I mistaks probably can nvr b fully liminatd and thrfor som lvl of typ II mistak is positiv for th incntiv to crat additional mploymnt. Espcially,, whn incrasing th lvl of svranc paymnts. But, as alrady mntiond, th ffcts of judicial mistaks on labour markt outcoms sm to b an intrsting and important fild of furthr rsarch. 13 Not that th aim of this papr was to highlight th implications of th xistnc of judicial mistaks in wll known labour markt modls. Thrfor, in a first stp, th standard assumptions wr mad. Nvrthlss, risk-avrsion, htrognity on both sids, and th dtrmination of how and why thos mistaks occur ar a vry important rsarch topic. 16

17 Mathmatical Appndix A Job Dstruction and Job Cration To calculat rsrvation productivity and th markt tightnss, th valus of continuing and nwly cratd jobs hav to b calculatd. Substituting th no-shirking wag, quation(7), into quation (8) yilds [ ] (r + λ)j(ɛ) = ɛ [(r + λ) + (r + λ(1 G( )))θq(θ)] p + mt [ ɛu ɛu ] +λ J(x)dG(x) W (x)dg(x). (24) Thrfor, th firm valu can b calculatd from as (r + λ) [J(ɛ) J( )] = (ɛ ) J(ɛ) = (ɛ ) (r + λ) zt. (25) Not that J( ) = zt. Using quation (25) and th just mntiond condition to valuat quation (24) for th rsrvation productivity yilds [ ] (r + λ)j( ) = (r + λ)zt = ɛ [(r + λ) + (r + λ(1 G( )))θq(θ)] p + mt + λ (r + λ) ɛu (x )dg(x) λzt which can b transformd into quation (12). To calculat th prsnt discountd valu of a nwly cratd job, I combin quations (9), (7), J 0 = J(ɛ u ) from quation (25), and J( ) = zt, yilding (r + λ) [ J 0 J( ) ] = (ɛ u ) which in combination with quation (11) yilds quation (13). B Effcts on Rsrvation Productivity and Markt Tightnss I totally diffrntiat quations (12) and (13) with rspct to θ,, m, z, and T. Thn I put th ndognous variabls d and dθ on th lhs, whil putting th xognous ons, dm, dz, and dt on th rhs. Writing th systm of quations as a matrix yilds 17

18 = ( [ ] (r + λg(ɛ r+λ d)) + λg( )θq(θ) + mt p (r + λg( )) [ ] + mt ) [θq(θ)] p cq (θ) q(θ) 2 } (r+λ) {{ } =B ( dɛd dθ ( [(r + λ) + [r + λ(1 G(ɛd ))]θq(θ)] T rt m [(r + λ) + [r + λ(1 G( ))]θq(θ)] rz 0 T z ) ) dm dz dt (26). With D = dt(b), rarranging quation (27) yilds [ ] ) = 1 cq (θ) (r + λg(ɛ q(θ) 2 d )) + mt [θq(θ)] p D (r + λg(ɛ (r+λ) r+λ d)) + λg( )θq(θ) ( dɛd dθ [ p + mt ] ( [(r + λ) + [r + λ(1 G(ɛd ))]θq(θ)] T rt m [(r + λ) + [r + λ(1 G(ɛ d ))]θq(θ)] rz 0 T z ) dm dz dt which finally yilds quations (15) to (20). Rfrncs Brtola, G. (1990). Job Scurity, Employmnt and Wags, Europan Economic Rviw 34, Brtola, G. (1999). Microconomic Prspctivs on Aggrgat Labor Markts, in O.Ashnfltr and D.Card (dt.), Handbook of Labor Economics, Volum 3C, Elsvir, Amstrdam, Galdón-Sánchs, J. E. and Güll, M. (2000). Lt s got to Court! Firing Costs and Dismissal Conflicts, Princton Univrsity, Industrial Rlations Sction, Working Papr 444. Galdón-Sánchs, J. E. and Güll, M. (2003). Dismissal conflicts and unmploymnt, Europan Economic Rviw 47, Garibaldi, P. (1998). Job Flow Dynamics and Firing Rstrictions, Europan Economic Rviw 42, Grman Council of Economic Exprts (2003). Staatsfinanzn konsolidirn - Stursystm rformirn, Elsvir Group, Rutlingn. 18

19 Gork, L. and Pannnbrg, M. (2004). Bruflich Witrbildung on-th-job und Auflösung von Bschäftigungsvrhältnissn, Diskussionspapir dr Forschrgrupp Htrogn Arbit 04/22. Güll, M. (1999). Employmnt Protction and Unmploymnt in an Efficincy Wag Modl, Princton Univrsity, Industrial Rlations Sction, Working Papr 432. Ichino, A., Polo, M., and Rttor, E. (2003). Ar judgs biasd by labor markt conditions?, Europan Economic Rviw 47, Kittnr, M. (2000). Kündigungsschutz in Dutschland und dn USA, Btribs-Bratr 55, Bilag 4. Lazar, E. P. (1990). Job scurity provisions and mploymnt, Quartrly Journal of Economics 105, Mortnsn, D. T. and Pissarids, C. (1994). Job Cration and Job Dstruction in th Thory of Unmploymnt, Rviw of Economic Studis 61, Mortnsn, D. T. and Pissarids, C. (1999). Nw Dvlopmnts in Modls of Sarch in th Labor Markt, in O.Ashnfltr and D.Card (dt.), Handbook of Labor Economics, Volum 3B, Elsvir, Amstrdam, Mortnsn, D. T. and Pissarids, C. (2001). Taxs, Subsidis, and Equilibrium Labour Markt Outcoms, CEPR Discussion Papr, Muthoo, A. (1999). Bargaining Thory with Applications, Cambridg Univrsity Prss, Cambridg, Nw York and Mlbourn. OECD (2004). Employmnt Outlook, Paris. Pissarids, C. (2000). Equilibrium Unmploymnt Thory, Cambridg USA: MIT Prss. Rochtau, G. (2002). Working tim rgulation in a sarch conomy with workr moral hazard, Journal of Public Economics 84, Shapiro, C. and Stiglitz, J. E. (1984). Equilibrium Unmploymnt as a Workr Disciplin Dvic, Amrican Economic Rviw 74,