DISCRIMINATION AND EMPLOYMENT PROTECTION

Transcription

1 DISCRIMIATIO AD EMPLOYMET PROTECTIO Stenar Holden Unversty of Oslo Åsa Rosén Stockholm Unversty (SOFI) Abstract We study a search model wth employment protecton legslaton. We show that f the output from the match s uncertan at the hrng stage, a dscrmnatory equlbrum may exst n whch workers wth the same productve characterstcs are subject to dfferent hrng standards. If a bad match takes place, dscrmnated workers wll take longer to fnd another job, prolongng the costly perod for the frm. Ths makes t less proftable for frms to hre dscrmnated workers, thus sustanng the dscrmnaton. In contrast to Becker s model, the exstence of employers wth a taste for dscrmnaton may make t more proftable to dscrmnate, even for frms wthout dscrmnatory preferences. (JEL: J70, J60, J71) 1. Introducton In almost all countres there are large dfferences n the labor market outcomes of dfferent worker groups. Several studes fnd that these dfferences are greater than what can be explaned by objectve crtera. The Organsaton for Economc Cooperaton and Development (OECD, 2008a) shows that second-generaton mmgrants n many countres have 15% 20% lower employment rates than natve-born persons and that only half of ths dsparty can be explaned by dfferences n educaton levels. One possble explanaton for the dfference s dscrmnaton. The exstence of such dscrmnaton s supported by studes showng that a foregn-soundng name on a job The edtor n charge of ths paper was George-Maros Angeletos. Acknowledgments: We are grateful to Björn Brügeman, Espen R. Moen, Kalle Moene, Kjetl Storesletten, Fredrk Wllumsen, Fabrzo Zlbott, four anonymous referees, the edtor George-Maros Angeletos; and partcpants at presentatons at the Unversty of Oslo, the Frsch Centre, ETH Zurch, the orwegan School of Management, the orwegan School of Economcs and Busness Admnstraton, the orwegan Meetng for Labour Economsts, Stockholm Unversty, Umeå Unversty, the CEPR/IZA 2009 Summer Symposum n Labour Economcs, the Socety of Economc Dynamcs Meetng 2009, and the 2010 World Congress of Econometrc Socety for valuable comments. Thanks to ysten Rembar for effcent research assstance. Rosén thanks Rksbankens Jubleumsfond for fnancal support. The paper s part of the research actvtes at the centre of Equalty, Socal Organzaton, and Performance (ESOP) at the Department of Economcs at the Unversty of Oslo. ESOP s supported by the Research Councl of orway through ts Centres of Excellence fundng scheme, project number E-mal: stenar.holden@econ.uo.no (Holden); asa.rosen@sof.su.se (Rosén)

2 Holden and Rosén Dscrmnaton and Employment Protecton 2 applcaton can reduce the lkelhood of beng called for an ntervew by 40% 50% (Bertrand and Mullanthan, 2004; OECD, 2008a; Jacquemet and Yannels, 2011). A vast lterature has tred to understand the reasons for dscrmnaton n the labor market. In one strand of the lterature, ntated by Becker (1957), dscrmnaton s explaned by prejudces or tastes among some employers. However, the exstence of prejudces aganst one group of workers wll lead to lower wages for ths group, makng them more proftable to hre for employers wthout prejudces. In ths case, the exstence of proft-maxmzng employers wll weaken and possbly remove the effect on the labor market outcome of the dscrmnated group (Arrow, 1973). In ths paper, we argue that there s an mportant opposng mechansm that makes workers who are dscrmnated aganst less attractve to other frms. The underlyng dea s that frms often may end up wth a worker that s unproftable, so that the worker s margnal product does not cover wage costs. The reason could be a bad hrng decson, a worker who turned out to be less qualfed than expected, or a change n job characterstcs for an exstng employee so that he or she s no longer up to the requrements of the job. The upshot s that the frm loses money and the worker has lttle hope of hgher wages or a career n the frm. Thus, both partes wll want to termnate the relatonshp for a new, better-suted partner. However, for the frm, t may be costly or dffcult to lay off the worker and t s much better f the worker fnds a new job and leaves the frm voluntarly. However, f the worker s n a dscrmnated group, t may be dffcult to fnd another job. The result may be that the worker remans n the unproftable match for a long tme, leadng to substantal loss for the employer. To avod the rsk of such a loss, the frm may avod hrng workers from a dscrmnated group, precsely because they are from ths group. We show that the outcome may be an equlbrum wth dfferent outcomes for two groups wth dentcal productve characterstcs and where the dscrmnated group has a lower hrng probablty and a hgher unemployment rate. The crucal assumpton and source of dscrmnaton n our model s that t may be costly for the frm to lay off a worker. One mportant reason for ths s employment protecton legslaton (EPL) that s suffcently strct so that t constrans frms layoff decsons. A vast lterature has documented that the extensve EPL n OECD countres affects mportant economc varables, such as unemployment, wages, hrng and frng rates, and nvestments n human captal (see the survey of the lterature n OECD, 2004). Even n the Unted States, whch s among the OECD countres wth the least strct EPL, there s evdence that the adopton of the wrongful dscharge doctrne n most US states durng the 1970s and 1980s reduced the employment rates of certan groups n the labor market (Autor, Donahue, and Schwab, 2006). However, also wthout EPL, a frm may be reluctant to lay off employees, snce dong so can nvolve a negatve sgnal about the frm s fnancal poston 1 or personnel polces. Beng lad off can nvolve hgh costs for employees (e.g., Davs and von Wachter, 2011); so a 1. In a study of 347 frms from Fortune s Amerca s Most Admred Companes, Flanagan and Shaughnessy (2005) fnd a strong, sgnfcant negatve effect of layoffs on corporate reputaton.

3 Holden and Rosén Dscrmnaton and Employment Protecton 3 frm wth a reputaton for layng off workers may have dffcultes hrng or may cause exstng employees to spend tme and effort lookng for other jobs. The basc mechansm presented by our paper, that the exstence of EPL or other frng costs can reduce the hrng and employment rates of specfc groups of workers, s supported by emprcal evdence n a number of papers. Usng mcro data for seven ndustralzed economes, Kahn (2007) fnds that strct EPL rases relatve nonemployment rates for youth and mmgrants. Oyer and Schaefer (2002) fnd evdence that the ntroducton of the Cvl Rghts Act of 1991 led to a negatve trend break n the employment shares of black and female workers n ndustres where these groups had low representaton. Acemoglu and Angrst (2001) show that there was a sharp drop n the employment of dsabled ndvduals after the enforcement of the Amercans wth Dsabltes Act, whch, among other thngs, prohbts dscrmnatory dscharge on the bass of dsablty. The novelty of our paper compared to ths lterature s due to the fact that we explore the mechansm n a general equlbrum search model. We show that there s an mportant nteracton effect n frms hrng strateges: If other frms use dscrmnatory hrng, t wll be harder for the dscrmnated group to fnd a new job. Ths ncreases the costs for the frm assocated wth EPL, whch amplfes the negatve effect on the hrng of ths group. A key mplcaton, whch, to the best of our knowledge, s novel to the lterature, s that ths mechansm can also explan persstent dscrmnatory outcomes for workers wth the same productve characterstcs as other workers. In our model wth two groups wth dentcal productve characterstcs, there also exsts a neutral equlbrum wth no dscrmnaton. However, f we assume that a suffcently large share of the employers dscrmnate as a result of dscrmnatory preferences (see the evdence of, e.g., Charles and Guryan, 2008), t becomes unproftable to hre the dscrmnated group, and therefore also pure proft-maxmzng employers wthout dscrmnatory preferences wll practce dscrmnatory hrng. The upshot s that the neutral equlbrum vanshes whle the dscrmnatory equlbrum stll exsts. Ths s n sharp contrast to the analyss of taste-based dscrmnaton of Becker (1957) and Arrow (1973), where the exstence of proft-maxmzng employers mtgates the extent of dscrmnaton. If the economy s n a dscrmnatory equlbrum, there wll be no mechansm that moves t to a neutral equlbrum, even f the taste for dscrmnaton vanshes. As s clear from Becker (1957) and Arrow (1973), the effect of dscrmnaton on wages plays a crucal role n the exstence of dscrmnaton. In the man text, we assume dscrmnaton has no drect effect on wages, that s, no effect for gven productvty. Ths assumpton can be theoretcally justfed by the use of the outsde opton prncple of Bnmore, Shaked, and Sutton (1989), whch says that an outsde opton puts a lower constrant on the barganng outcome wthout affectng the wage f t s above the outsde opton. The assumpton can also be justfed on more nsttutonal grounds, because f an ndvdual from a specfc demographc group receves a lower wage for the same productvty than ndvduals from other groups, that would be wage dscrmnaton, whch s llegal n many countres. In Onlne Appendx H.2, we adopt the more common assumpton n search models that the wage depends on both

4 Holden and Rosén Dscrmnaton and Employment Protecton 4 productvty and outsde optons, mplyng that workers from a dscrmnated group receve lower wages due to weaker outsde opportuntes. In both cases we show that a dscrmnatory equlbrum may exst. In fact, n a workng paper verson of ths study, we show that a dscrmnatory equlbrum exsts even f we allow workers that are dscrmnated aganst at the hrng stage to "buy" jobs by acceptng an ntal perod wth low or possbly negatve wages. Our paper s not the frst to suggest an explanaton for the exstence of persstent dscrmnaton of ex ante dentcal groups n the absence of preferences for dscrmnaton. 2 One strand s the so-called statstcal dscrmnaton lterature, where employers make decsons on the bass of average features of dfferent worker groups, due to lack of nformaton about the ndvdual n queston. Ths can lead to dscrmnatory outcomes f, for example, hrng decsons nteract wth human captal nvestments, as explored by Lundberg and Startz (1983), or f frms choose one of many applcants (Cornell and Welch, 1996). A second approach, to whch our model adheres, s based on self-fulfllng stereotypes. The specfc mechansms dffer from the one we consder. In Coate and Loury s (1993) model, dscrmnatory equlbrum s due to the nteracton between frms promoton standards and workers nvestment n human captal, whle n Malath, Samuelson, and Shaked (2000) the nteracton s between frms search behavor for workers and workers nvestment n human captal. Furthermore, n Malath et al. (2000), frms can drect ther search toward a specfc group and EPL plays no role, both features n contrast to our specfcatons. Our paper s closer to that of Rosén (1997), snce both papers derve equlbrum dscrmnaton at the hrng stage as a result of the nteractons between the frms hrng polces. However, there are also mportant dfferences: In Rosén (1997), the nformaton about match-specfc productvty s asymmetrc. In equlbrum, non-dscrmnated workers apply only to jobs wth hgh match-specfc productvty, whle dscrmnated workers may also apply to jobs where they have low match-specfc productvty, snce ther outsde alternatve s worse. In contrast, our explanaton s based on symmetrc nformaton and the source of dscrmnaton les n the combnaton of on-the-job search and frng costs. 3 One of the few theoretcal analyses of the nteracton between EPL and dscrmnaton s that of Morgan and Várdy (2009). These authors study a statstcal dscrmnaton model where the test result (sgnal) of productvty contans more nose for one group and where employers engage n optmal sequental search. Among other thngs, Morgan and Várdy show that workers for whch the test (sgnal) s less precse may need due to Bayesan updatng a hgher test result to be hred. However, the model framework dffers from ours and the authors do not consder the nteracton of hrng strateges, whch s the man dea n our paper. 2. The recent studes of Fang and Moro (2010) and Lang and Lehmann (2010) present excellent surveys of the lterature. 3. Lang et al. (2005) show, wthn an urn ball search model, that the wages and utlty of the dscrmnated group are substantally lower for an arbtrarly small taste for dscrmnaton.

5 Holden and Rosén Dscrmnaton and Employment Protecton 5 To undertake our analyss, we develop a search model wth match-specfc productvty and on-the-job search. As Pres and Rogerson (2005), we explore a settng where frms obtan an mperfect sgnal about match-specfc productvty at the hrng stage, where the exstence of EPL makes frngs costly, and where frms optmally choose the hrng standard. However, whle Pres and Rogerson assume that a bad match always results n a layoff, we focus on the possblty that the frm can avod frng costs by watng for the worker to fnd a better job and leave voluntarly. Thus, Pres and Rogerson do not nclude the key feature of our model, whch s that the hrng standard of each frm depends on the hrng standards of other frms. The feature that frms beneft from avodng frng costs s also consdered by Sant-Paul (1995). Thus, n both Sant-Paul (1995) and our paper, frm profts ncrease f a worker n a bad match leaves voluntarly. However, the model and focus are dfferent. In Sant-Paul (1995), the key nteracton s related to frms decson to enter the market. Furthermore, Sant- Paul consders only one group of workers, does not consder dscrmnaton, and does not nclude the sgnal of productvty at the hrng stage. The paper s organzed as follows: The model s presented n Secton 2, whle n Secton 3 we consder the exstence of a dscrmnatory equlbrum. Secton 4 explores modfcatons and applcatons and Secton 5 concludes the paper. Most of the proofs are n Appendces A G, whle the Onlne Appendx H contans extensons and remanng proofs. 2. The Model We consder a sequental search model of the type used by Damond (1982), Mortensen (1982), and Pssardes (1985), wth wages set by barganng. Workers and frms are rsk neutral and have the same dscount rate r > 0. There are two types of workers n the economy, n G Greens and n R Reds, where n G C n R D 1. The workers are ex ante equally productve and there are no other dfferences between the types besdes some observable characterstc that determnes type, such as skn color. Workers are assumed to leave the market at an exogenous rate s > 0. ew workers enter at the same rate, and are ntally unemployed. There s free entry of jobs n the market, so frms can open a vacancy at zero cost. The flow cost of mantanng a vacancy s c > 0. When a frm hres a worker, a random draw determnes whether the match s of hgh or low productvty, wth output y H > y L. We make two key assumptons n ths paper. Frst, we assume that some but not all of the uncertanty about the match-specfc productvty s revealed when the employer and worker meet. In the words of Pres and Rogerson (2005), match qualty s both an nspecton good and an experence good. 4 Specfcally, when a frm s matched 4. The mportance of match-specfc uncertanty s supported by agypal (2007), who presents evdence from French frm-level data, showng that the effect of learnng about match qualty domnates the effect of learnng by dong at tenures above sx months.

6 Holden and Rosén Dscrmnaton and Employment Protecton 6 wth a worker, both partes observe a sgnal that corresponds to the probablty that the match s of hgh productvty. The sgnal s assumed to be ndependent and dentcally dstrbuted over matches and, to keep the model transparent, can take only two values: wth probablty and < wth probablty 1. 5 Havng observed, the frm decdes whether to offer the worker a job and the worker decdes whether to accept the offer. The dea s that when the frm and the worker meet, they wll obtan nformaton that makes t possble to assess the lkelhood that the match wll be of hgh qualty, but they cannot foresee perfectly how the worker wll perform. There s consderable uncertanty n both how well the worker fts n wth the job requrements and wth colleagues. To keep the model as smple as possble, we assume that the match productvty s revealed mmedately after the worker s hred and s then constant over tme. 6 Second, we assume that t s costly for frms to lay off a worker who wants to reman on the job. In many countres, such costs come n the form of EPL. Crucally, employment protecton s assumed to be already at work when match productvty s revealed, so frms cannot fre wthout cost upon dscoverng that productvty s low. 7 The dea s to capture the fact that whle there s often a probaton perod wth lttle or no employment protecton, t may take tme to dscover whether the worker s up to the requrements of the job. Furthermore, the job content or requrements can change at a later stage, turnng a worker who had good productvty for many years nto a less productve worker. As noted n the ntroducton, there s also evdence suggestng that layoffs can nvolve a negatve sgnal about a frm s fnancal poston. Layoffs can also be costly f t makes exstng employees or potental newcomers also fear beng lad off at a later stage. For our purposes, the precse reason for the frng costs s mmateral; the key ssue s that frms proft from a badly matched worker leavng voluntarly. To smplfy the formal exposton, we assume that layoff costs are suffcently hgh that frms wll never beneft from layng off a worker. However, ths smplfcaton s not crucal and, as dscussed below, essentally the same results can be derved f, n some cases, frms actually lay off the workers. We assume that search costs are suffcently low that all workers n lowproductvty matches gan from searchng. However, workers n hgh-productvty matches wll not search, snce all such matches are equal, so there s nothng to gan. For smplcty, search ntensty s assumed to be exogenous and the same for both employed and unemployed workers. The search cost s set to zero. 5. In a prevous verson of the paper, numercal smulatons showed the exstence of a dscrmnatory equlbrum n a smlar model, where the sgnal was drawn from a contnuous nterval. 6. The same results can be derved under the alternatve assumpton that all matches start out wth hgh productvty, combned wth a constant probablty rate 1 that productvty drops to a lower level. However, the analyss would be more cumbersome. 7. In many cases, worker turnover s costly to the frm (e.g., Burdett and Mortensen, 1998), whch mght make dscrmnated workers more attractve and go aganst our results. In a more general model, both effects would apply and dscrmnaton would only preval n equlbrum f the negatve effect domnated. Ths would be smlar to the stuaton n the Onlne Appendx Secton H.2, also wth two opposng effects.

7 Holden and Rosén Dscrmnaton and Employment Protecton 7 Let u denote the unemployment rate, " the fracton of employed workers n bad matches and thus searchng, and v the vacancy rate. Thus, the fracton of workers searchng for jobs s u C ".1 u/. The matchng between vacances and workers s random, ndependent of worker type, and descrbed by a constant returns to scale matchng functon x D x.u C ".1 u/; v/ (1) A worker fnds a vacancy at a rate ' D x=.u C ".1 u// and a vacancy s found by a searchng worker at a rate q D x=v. Constant returns to scale mples that ' and q are functons of the tghtness D v=.u C ".1 u// only and that ' D q. We also assume two boundary condtons: As! 0, '! 0 and q! 1 and, as! 1, '! 1 and q! 0. Workers flow payoff equals ther wages, w, when employed and when unemployed. Furthermore, the expected value to a worker of type, D G; R, condtonal on just beng hred, after observng the sgnal, but before observng whether the match s of hgh or low productvty, s EW./ D W H C.1 /W L ; (2) where W j s the asset value of a worker of type n a match wth productvty level j, where j D L; H. The asset value of an unemployed worker of type, s.r C s/u D C ' p EW. / C.1 /p EW. / p U : (3) Matchng takes place at a rate '. Wth probablty, the sgnal s, n whch case the hrng probablty s p and the expected value s EW. /. Correspondngly, wth probablty 1, the sgnal s, the hrng probablty s p, and the expected value s EW. /. Condtonal on beng matched, the hrng probablty p s gven by p D p C.1 /p (4) and f the worker s hred we must deduct the value of beng unemployed. Workers n a hgh-productvty match do not search; so ther asset value s smply gven by.r C s/w H D w H ; (5) where w H s the wage n a hgh-productvty match for a worker of type. In contrast, a worker n a low-productvty match, earnng wage w L, wll contnue to search and wll fnd a new job at the rate 'p. The asset value for a low-productvty worker s hence.r C s/w L D w L C ' p EW. / C.1 /p EW. / p W L : (6) The asset value of a job flled wth a worker of type n a hgh-productvty match, denoted J H, depends on the flow proft y H w H, as well as the change n asset value f the worker exogenously leaves the market (V s the value of a vacancy): rj H D y H w H C s.v J H /: (7)

8 Holden and Rosén Dscrmnaton and Employment Protecton 8 The value of a match of low productvty, J L, depends, n addton, on the rate at whch the worker fnds a new job 'p : rj L D y L w L C.s C 'p /.V J L /: (8) The expected value to a frm of hrng a worker from group after havng observed s J H C.1 /J L. Usng (7) and (8), we fnd the value to the frm of hrng a worker from group to be a functon of the probablty that the match s of hgh productvty,, and the probablty that, n case of a low-productvty match, the worker s hred when matched to another frm, p J.; p / D r C s.yh w H.1 / C sv / C y L w L C.s C 'p /V : r C s C 'p (9) Snce J H > J L, t follows that J.; p / s strctly ncreasng n. Frms hre a worker f and only f t s proftable, that s, f and only f J > V. Thus, for each color of worker, there are three possble mnmum hrng standards, S (or hrng rules, n pure strateges): Hre all workers, S D ; hre only workers wth a hgh sgnal, S D ; or hre no workers, S >. 8 Let. S / denote the proporton of applcants that have a value of S or hgher. The value of a vacancy for a gven hrng rule s rv./ D c C q G.G S /.E.J ˇ G ˇG S / V / C R. R S /.E.J ˇ R ˇR S / V / ; (10) where s the rato of job seekers of type to all job seekers. Consder now the wage settng, whch takes place mmedately after the match productvty s revealed. As noted above, n the man part of the paper, we assume that the wage depends only on productvty and not on worker type. Ths wll be the outcome f the barganng s modeled usng the outsde opton prncple of Bnmore, Shaked, and Sutton (1989), n whch the outsde optons work as constrants on the barganng outcome. Due to search frctons, the outsde optons wll not bnd. In lne wth Bnmore, Rubnsten, and Wolnsky (1986), the threat ponts should then reflect the players payoffs durng a barganng dspute. We assume that, n ths case, producton does not take place whle the frm does not pay the worker; for smplcty, the threat ponts of both players are then set to zero. Accordng to Bnmore et al. (1986), the barganng power of the worker, ˇ 2.0; 1/, should reflect the players tme preferences, whch are assumed to be the same for both groups. Thus, the wages wll be the same for both worker types. In a match wth hgh productvty, the wage s w H D ˇy H : (11) Further motvaton for assumng the same wage for both groups s that wage dscrmnaton s llegal n many countres; so t s of nterest to explore the mplcatons of equal wages for dscrmnaton. In a match wth low productvty, we assume a 8. Throughout the paper t wll always be the case that workers beneft from acceptng all job offers.

9 Holden and Rosén Dscrmnaton and Employment Protecton 9 bndng mnmum wage w L. Furthermore, we assume that the mnmum wage s hgher than the low productvty output w L > y L ; (12) mplyng that the frm ncurs a loss as long as the match takes place. The crucal assumpton here s that f the match has low productvty, the frm s prevented from reducng the wage down to a value that makes the match proftable for the frm. Clearly, f the frm has the opton of reducng the wage so that the match s proftable, EPL would not be relevant, snce the frm, n that case, would never want to lay off the worker. We take w L as exogenous; t could be gven by some natonal law or from a collectve agreement mposng a mnmum wage. ote also that the mnmum wage could be zero f the low productvty output y L s negatve. The key feature we need s for the match to be unproftable for the frm, wth the frm prevented from makng the match proftable (by cuttng the wage) or layng off the worker Equlbrum We consder an equlbrum where all frms use the same hrng strateges; ths s dscussed further below. The steady-state share of employed workers of type n jobs wth low match qualty, ", s gven by the unemployment rates for both groups are " D s.1 E. ˇˇ S // s C E. ˇˇ S / 'p ; (13) u D s s C 'p ; (14) and the fracton of all job seekers, both unemployed and employed n low-productvty matches, who are of type,, s D n.u C.1 u /" / n G.u G C.1 u G /" G / C n R.u R C.1 u R /" R / : (15) See Appendx A for a dervaton of (13) and (14). Furthermore, when all frms use the same hrng strateges, the workers hrng probabltes are gven by p D 1 f S D ¹ ; º and p D 0 f S > ; (16) 9. If wages are set n negotatons even for low-productvty matches and frng costs enter nto the threat ponts of the frm, as assumed by, for example, Mortensen and Pssardes (1999), (12) would follow f the frng costs are suffcently hgh (see the Onlne Appendx H, Secton H.10).

10 Holden and Rosén Dscrmnaton and Employment Protecton 10 p D 1 f S D and p D 0 f S D or S > : (17) In a steady-state equlbrum, free entry ensures that the value of a vacancy s zero: V./ D 0; wth V gven by (10). Furthermore, frms hre a worker of type f and only f ths s proftable, that s, f and only f wth J.; p / gven by (9). J.; p / = V ; 3.1. Characterzaton and Exstence of Equlbra In ths secton we consder the exstence of varous types of equlbra n the model. To ensure that the economy s productve, we make the followng (suffcent) assumpton on parameter values. Denote the expected value of the sgnal by M, wth M D C.1 /. Assumpton 1 (The Economy s Productve)..1 ˇ/y H > 1 M M.wL y L / (18) Assumpton 1 ensures that the value of a vacancy s postve when there are no frms n the market, that s, V > 0 n the lmt D 0. The exact form s chosen so that ths s true n all the specfcatons we consder. Assumpton 1 also ensures that t s always proftable to hre an applcant wth a hgh sgnal (see Appendx B). ote that Assumpton 1 s more easly satsfed the hgher y H, y L, and M are and the lower ˇ and w L are. Furthermore, t s satsfed for any 0, as long as y H s hgh enough. We start by demonstratng the exstence of an equlbrum condtonal on the hrng strategy (see the proof n Appendx C). Lemma 1 (Exstence of an Equlbrum, Gven a Hrng Rule). Gven G S 2 ; and S R 2 ;, there exsts a unque > 0 where V. / D 0, V./ < 0 for >, /=@ < 0. In the standard search model, the value of a vacancy decreases monotoncally wth labor market tghtness and there s a unque equlbrum. However, ths s not necessarly the case n the present model. A hgher mples that a badly matched worker wll fnd a new job faster, reducng the expected duraton of a bad match. Because of ths effect, the value of a vacancy may actually be ncreasng n for some ntervals and there may be multple equlbrum levels for a gven hrng strategy. Ths

11 Holden and Rosén Dscrmnaton and Employment Protecton 11 sort of multplcty s the focus n Sant-Paul (1995), who shows that as a tghter labor market reduces frng costs because more workers wll leave voluntarly, there may be a multplcty of equlbra n labor market tghtness. Our results do not depend on a multplcty of equlbra n labor market tghtness. To the contrary, f there are several equlbra, we restrct our attenton to only one of them to keep the analyss tractable. Specfcally, f there are several equlbra, we choose that wth the hghest labor market tghtness. 10 (Incdentally, that equlbrum maxmzes the expected utlty of a new worker.) For a suffcently hgh, the value of a vacancy wll always be negatve. Snce V s contnuous n for gven hrng strateges, t follows that there exsts a unque equlbrum where V. / D /=@ < 0, and V./ < 0 for all >. The next step s to explore optmal hrng strateges. The frm wll hre an applcant f and only f the expected profts are postve, that s, f and only f (wth V D 0) J.; p / D r C s.1 ˇ/yH C 1 y L w L 0; (19) r C s C 'p where we use (9) and substtute out for the wage equaton (11). The frst term of (19) s postve, snce the frm profts from a hgh-productvty match. The second term s negatve, snce the frm loses from a low-productvty match. The absolute value of ths term decreases wth 'p, reflectng that the faster a worker n a low- productvty match can fnd a new job, the shorter the expected duraton of the unproftable match for the frm. Thus, an ncrease n p makes t more proftable to hre the worker; ths s the key mechansm n the paper. As wll be clear below, several dfferent equlbra exst n the model. We frst consder the exstence of a dscrmnatory equlbrum, where all frms hre Greens, rrespectve of the value of the sgnal, but Reds are hred only f D. Thus, p G D 1 and p R D. As can be seen from (19), whether ths dscrmnatory hrng strategy s optmal wll depend on the combnaton of parameter values. We want to show that for gven values of the other parameters, there exsts an nterval 0 ; 1 for the value of the low sgnal for whch a dscrmnatory equlbrum exsts. A complcaton s that and thus also ' are endogenous and thus depend on. It can be shown that and ' are contnuous and ncreasng n. 11 Ths s ntutve, because a hgher value of makes t more proftable for frms to enter the market. The bounds of the nterval are defned as follows (wth slght abuse of the notaton to make t clear that the value of a flled job J s a functon of, p, and IJ.; p ; / - recall that ' D q - and the value of a vacancy V s a functon of and ). Defnton 1. Gven the dscrmnatory hrng rule G S D, and R S D, () the values 0 and 0 are defned by J. 0 ; 1; 0 / D 0 and V. 0 I 0 / D 0 and () the values 1 and 1 are defned by J. 1 ; ; 1 / D 0 and V. 1 I 1 / D We conjecture that our results go through for all stable, that s, whenever V./ D 0 < The proof s n Onlne Appendx H.8

12 Holden and Rosén Dscrmnaton and Employment Protecton 12 Thus, for D 0, the frm s ndfferent to hrng a Green worker and, for D 1, the frm sndfferent to hrng a Red worker. Snce J s ncreasng n both and p and p G > p R, t follows that 0 < 1. We are now ready to state our frstman proposton (the proof s gven n Appendx D). Proposton 1. There exsts a non-empty nterval 2 0 ; 1 for whch a dscrmnatory equlbrum exsts, where Greens are hred rrespectve of the sgnal whle Reds are only hred for the sgnal. For outsde ths nterval, a dscrmnatory equlbrum of ths type does not exst. The ntuton behnd the exstence of the dscrmnatory equlbrum s, as explaned above, that a bad match s more costly for the frm f the worker s Red than f the worker s Green. The reason s that other frms hre Green workers even wth a bad sgnal, but they do not hre Red workers, mplyng that the expected duraton of a bad match s longer for a Red worker. Thus, for a value of wthn ths nterval, t s proftable to hre a Green worker wth a bad sgnal, but not proftable to hre a Red worker wth a bad sgnal. For values of above the nterval, t s proftable to hre Red workers wth a low sgnal, even f other frms dscrmnate, n whch case dscrmnaton cannot exst n equlbrum. For values of below the nterval, t s not proftable to hre Green workers wth a low sgnal, even fother frms do so; agan, ths sort of dscrmnaton cannot exst n equlbrum. In ths equlbrum, frms have strcter hrng standards for Red workers than for Green workers. The followng result s mmedate. Corollary 1. In a dscrmnatory equlbrum, the unemployment rate for Red workers s hgher than for Green workers: u R D s=.s C '/ > u G D s=.s C '/. Regardng wages, Green and Red workers have, by assumpton, the same wages for the same productvty. The uncondtonal average wage depends on the proporton of workers n good and bad matches and, dependng on the parameter values, ths can go n ether drecton. (In Onlne Appendx Sectons H.2 and H.3, we explore the case where wages are affected by outsde optons, mplyng that Red workers have lower wages for the same productvty n a dscrmnatory equlbrum.) eutral equlbra also exst n the model: one good, where both groups are hred, rrespectve of the sgnal, and one bad, where a worker, rrespectve of group, s only hred f the sgnal s hgh. The term good refers to the fact that ths equlbrum yelds hgher utlty for a new worker, whle frms n both cases earn zero proft n equlbrum. Formally, we obtan the followng (the proof s gven n Appendx E). Proposton 2. () There exsts a cut-off such that for a neutral equlbrum exsts where S G D R S D and for < D such a neutral equlbrum does not exst. () There exsts a cut-off U such that for U a neutral equlbrum exsts where S G D R S D and for > U such a neutral equlbrum does not exst. D D

13 Holden and Rosén Dscrmnaton and Employment Protecton 13 () D < 0 and U > 1, whch mples that when a dscrmnatory equlbrum of the type S G D and R S D exsts, two neutral equlbra also exst. To understand the ntuton behnd these results, frst observe that whenever a dscrmnatory equlbrum exsts, the exstence of the good neutral equlbrum would hold trvally f labor market tghtness were gven. Clearly, f t s proftable to always hre a Green worker when all other frms do the same, then the same must be true wth a Red worker, snce Red and Green workers are dentcal apart from type. However, s not gven, so we must take nto account the effect of a change n. Consder, frst, the good neutral equlbrum, where Red workers are now also always hred, rrespectve of the sgnal. In ths case the expected duraton of a bad match wth a Red worker s shorter than n a dscrmnatory equlbrum. Ths ncreases the expected profts from hrng a Red worker, whch leads to the entry of more vacances, ncreasng. A hgher value of wll reduce the expected duraton of a bad match, mplyng that frms wll be wllng to hre a worker wth a lower probablty of hgh productvty, that s, even for values of below 0. Thus, the crtcal value D < 0. Clearly, ths good equlbrum wll exst for all hgher values of. Consder, next, the bad neutral equlbrum, where no worker s hred wth a low sgnal. The same effect takes place, but n the opposte drecton. The expected duraton of a bad match wth a Green worker s longer than n a dscrmnatory equlbrum, whch reduces the expected profts from hrng a Green worker. Lower expected profts lead to fewer vacances and a lower, whch mples that there wll be values of above 1 for whch expected profts from hrng a worker wth a low sgnal wll be negatve. Ths bad equlbrum wll exst for all lower values of. A dscrmnatory equlbrum also exsts where the roles are reversed, that s, the Greens are dscrmnated aganst. Agan, f labor market tghtness were gven, t would follow trvally that the reversed dscrmnatory equlbrum would hold for the same nterval for. However, the loss for the employers caused by lower hrng probablty under dscrmnaton and thus longer expected duraton of a bad match s greater the larger the dscrmnated group. Thus, f the Greens are the larger group, the expected proft of a vacancy for a gven s lower n an equlbrum n whch Greens are dscrmnated aganst than one n whch Reds are dscrmnated aganst. Ths leads to the ext of vacances, lowerng. The lower value of ncreases the duraton of a bad match, whch mples that the equlbrum where Greens are dscrmnated aganst exsts for hgher values of. Formally, we have the followng result. Proposton 3. () There exsts a dscrmnatory equlbrum wth G S D and R S D when 2 00 ; 10, () 00 > 0 and 10 > 1 when n G > n R, and () D < 00 and U > 10, mplyng that when a dscrmnatory equlbrum of the type G S D and S R D exsts, two neutral equlbra also exst. Proof. Parts () and () are analogous to the proofs for Proposton 2 and therefore omtted. The proof of part () s gven n Appendx F.

14 Holden and Rosén Dscrmnaton and Employment Protecton 14 Fgure 1. Exstence of equlbra for dfferent values of. Propostons 1 to 3 completely characterze the stable equlbra n the model as long as Assumpton 1 holds, ensurng that workers are always hred wth a hgh sgnal. Fgure 1 shows the ntervals for whch the varous equlbra exst. ote that all the equlbra are stable: If one frm devates from the equlbrum hrng strategy, t wll have very small mpact on the probablty, p, that a worker of type s hred, condtonal on beng matched. Thus, the equlbrum hrng strategy wll stll be optmal for other frms. Furthermore, there does not exst a stable equlbrum n mxed strateges or where frms use dfferent hrng strateges. Ths can be formally proven, along the followng lnes. Assume that all frms hre Greens, rrespectve of sgnal; that a fracton of all frms hres all Reds, rrespectve of sgnal; and that the remanng fracton 1 hres only Reds wth a hgh sgnal. Ths can be an equlbrum only f J. ; p R / D 0. It s straghtforward to show that there exsts a D 0 where J. ; p R / D 0. However, snce J. ; p R / depends postvely on p and hence on, ths equlbrum s unstable, snce J. ; p R / < 0 for < 0 and J. ; p R / > 0 for > Frng Costs and Wage Settng In the basc model, we mpose the strong assumpton that the frng costs are prohbtve. We now show that the man results also hold n a model where some workers are actually lad off. Consder an extenson of the model that ncludes a thrd and lower level of productvty, y M n, wth y M n < y L. Furthermore, assume that y M n s so low that frms prefer to lay off the worker and pay the frng costs. For the ntermedate level y L, frms stll wat for voluntary transtons. Thus, the model now allows layoffs to happen (when y M n s realzed), but t also ncludes the key feature that f a bad match wth ntermedate productvty occurs, the frm wll choose to wat untl the worker leaves voluntarly. Hence, the same dscrmnatory equlbrum as before would exst, gven smlar condtons. In Sectons H.2 and H.3 n the Onlne Appendx H, we explore the more common way to model wage barganng, where wages are affected by outsde optons. Snce

15 Holden and Rosén Dscrmnaton and Employment Protecton 15 dscrmnated workers have worse outsde optons, they obtan lower wages for the same level of productvty. Ths makes them more attractve for frms, gong aganst the dscrmnatory outcome. However, a dscrmnatory equlbrum stll exsts f the costs of a bad match are suffcently hgh. We calbrate the model by the use of emprcal estmates whenever possble and fnd that a dscrmnatory equlbrum exsts under plausble parameter values. In partcular, we fnd that frng costs need to exceed 87% of the average quarterly output to sustan a dscrmnatory equlbrum. Ths s well wthn the parameter range of frng costs explored by Mortenson and Pssardes (1999), whch goes from zero to unty, measured as a fracton of the quarterly output per worker. ote also that n many countres employment protecton may be more strngent or more strctly enforced for mnorty groups subject to dscrmnaton n the labor market. Thus, the frng costs may be suffcent to sustan the dscrmnatory hrng of a mnorty group, even f the frng costs for majorty group workers are lower than the requred threshold value. 4. Dscusson In ths secton we show that by modfyng some of the features of the model, we are able to make a number of novel arguments and predctons. The man pont of the paper s to show how dscrmnaton can arse among proft-maxmzng employers. However, snce there s evdence that some frms have a taste for dscrmnaton (e.g., Charles and Guryan, 2008), t would be nterestng to see how ths affects the model. More specfcally, assume that a proporton m 2.0; 1/ of the vacances, for exogenous reasons, always apply the dscrmnatory hrng rule: G S D and R S D. Thus, these frms are wllng to hre Red workers f they observe a good sgnal but not f they observe a bad one. Such behavor could arse from these employers recevng a certan dsutlty from hrng Red workers, as n Becker s model. Accordng to Becker s argument, the exstence of some dscrmnatory frms makes t proftable for non-dscrmnatory frms to hre the workers that are dscrmnated aganst. In the Onlne Appendx H (Secton H.1), we show that the opposte effect s at work n our model. More specfcally, we show that f the share of frms wth an exogenous dscrmnatory hrng rule exceeds a crtcal value Qm, proft-maxmzng frms wll also apply dscrmnatory hrng n equlbrum. Thus, the equlbrum wth neutral hrng no longer exsts. In ths case, t s neutral hrng that s less proftable, whch mples that t s the non-dscrmnatory hrng that s drven out of the market. Snce both types of frms apply the same hrng rule, they also make the same profts. A thought-provokng mplcaton of ths result s that f the economy s n a dscrmnatory equlbrum, there s no power or mechansm that can take t to a dfferent equlbrum. Ths mples that there s large scope for persstence. Consder a labor market where dscrmnaton has prevaled hstorcally, for reasons of taste and power, and where dscrmnaton was also a part of the legslaton. Then assume that the dscrmnatory legslaton s removed and the taste for dscrmnaton vanshes n the sense that new frms wth neutral preferences gradually replace exstng frms wth

16 Holden and Rosén Dscrmnaton and Employment Protecton 16 a taste for dscrmnaton. However, when the neutral frms enter, they too wll practce dscrmnatory hrng, snce the economy s n a dscrmnatory equlbrum where ths s the proft-maxmzng hrng strategy. Thus, the dscrmnatory equlbrum prevals, n spte of the removal of dscrmnatory legslaton, even f all frms lose ther taste for dscrmnaton. To ext a dscrmnatory equlbrum, some sort of concerted acton would be requred to ensure that frms hre dscrmnated workers even f t s not proftable, or to ensure changes so that t becomes proftable to hre dscrmnated workers. Ths lne of argument s consstent wth descrptons of the evoluton of racal segregaton n the US labor market by Darty and Mason (1998), who argued that dscrmnatory practces were sustaned long after the dscrmnatory legal practces were removed. ext we consder how the outcome s affected by ant-dscrmnatory rules. In many countres, the authortes undertake varous measures to reduce the extent of dscrmnaton. One key measure s a hrng quota, where frms are requred to have a certan proporton of hres from specfc groups perceved to be subject to dscrmnaton n the labor market (for a dscusson of the US experence, see Holzer, 2007). Ths measure s controversal and the effect vares across models. In the mentorng model of Athey et al. (2000), hrng quotas work to reduce dscrmnaton, whle the opposte effect can occur n the human captal nvestment model of Coate and Loury (1993). We capture a hrng quota by assumng that a proporton a of vacances always apply the neutral hrng rule: G S D R S D. Wth ths specfcaton, the hrng quota case s the mrror mage of the case wth a taste for dscrmnaton above. It follows mmedately that f a suffcent fracton of the frms follow the neutral hrng rule, the dscrmnatory equlbrum no longer exsts (see Onlne Appendx H, Secton H.1). Thus, n our model, affrmatve acton n the form of mnmum hrng quotas works to counteract dscrmnaton. If a hrng quota s at work n suffcently many frms, t wll also prevent dscrmnatory behavor n jobs that are not drectly affected by the hrng quota. In our model, workers are homogeneous except for color, so the model cannot address any lnk between dscrmnaton and educaton. It turns out that n all OECD countres, the unemployment gap between mmgrants and natves wdens as the educaton level rses (OECD, 2008b, p. 114). However, f we assume that the costs of a bad match are greater for educated workers than for workers wthout educaton, our model would predct that dscrmnaton s more lkely for the educated workers. One reason for ths assumpton s that captal s complementary wth the use of sklled labor (Hornsten, Krusell, and Volante, 2005) and presumably the ncreased use of captal ncreases the costs assocated wth a badly matched worker. Another reason s that jobs requrng more sklls are often more complex, wth the lkely mplcaton that the output s more senstve to the sutablty of the worker. The mechansm we hghlght may also be mportant for groups for whom there s no underlyng subjectve reason for dscrmnaton, such as racal or cultural prejudce. Old workers are a case n pont. In contrast to mmgrants, there are no ssues of race or cultural or language sklls. Yet n all OECD countres, the hrng rates of workers declne sgnfcantly after the age of 50, more sharply n some countres than

17 Holden and Rosén Dscrmnaton and Employment Protecton 17 n others (OECD, 2006, p. 132). There mght be several reasons for ths, whch are not captured by our model. However, wthn our model, the drop n hrng rates wll have negatve feedback effects on the employablty of older workers, snce frms expect older workers to have a harder tme fndng another job n case the current one does not work out. Thus, gven the lower hrng rates, our model predcts that older workers wll be subject to dscrmnaton n the labor market, n lne wth the OECD (2006) fndngs. Furthermore, our model s also consstent wth the fndngs of Behaghel, Crépon, and Sédllot (2008). These authors fnd that a tax on frms layng off workers aged 50 and above had a negatve effect on frms hrng of workers n the relevant age groups, consstent wth the mechansm proposed n our paper. Autor, Donohue, and Schwab (2006) fnd that the ntroducton of wrongful dscharge laws have reduced state employment rates and that long-term effects are greater for older workers than for younger workers. 5. Concludng Remarks We offer a novel argument for the dscrmnatory outcomes of equally productve groups n labor markets where t s costly for frms to lay off workers. The key mechansm s that workers wth low job-fndng rates are rsky to hre snce they mght stay for a long tme, even n the case of a bad match. Dscrmnaton s self-enforcng, snce t s precsely because a group s dscrmnated aganst that t has lower job-fndng rates and thus becomes less attractve to hre. Whle nondscrmnatory equlbra also exst n our model, these vansh f a suffcently large proporton of employers have a taste for dscrmnaton. Thus, the exstence of dscrmnatory employers also makes t proftable for proft-maxmzng frms to practce dscrmnatory hrng, n sharp contrast to the effect n Becker s model, mplyng that dscrmnaton s the unque equlbrum outcome. However, f we alternatvely assume that a suffcently large share of employers hre accordng to the populaton shares of each group a hrng quota the dscrmnatory equlbrum vanshes. The am of ths paper s to make a theoretcal contrbuton about the possble exstence of dscrmnaton aganst a group of workers wth dentcal productve characterstcs as other workers. However, t s nterestng to see whether key predctons correspond to the actual labor market stuaton of a group for whom there s evdence of dscrmnaton n the labor market, namely mmgrants. One predcton of the model s that workers from the dscrmnated group have a lower rate of jobto-job movement (see Appendx G). Ths s consstent wth recent evdence from orwegan matched employer employee data, where Dap (2013) fnds that frstgeneraton mmgrants have a hghly sgnfcant 40% lower probablty than natves of drect job-to-job movement, controllng for other explanatory varables such as ndustry, county, and ndvdual characterstcs such as age, senorty, a dummy for part-tme work, and educaton (n years). The effect s slghtly smaller but stll hghly sgnfcant wth frm fxed effects. A related predcton of our model s that workers

18 Holden and Rosén Dscrmnaton and Employment Protecton 18 from a dscrmnated group are more lkely to experence an ntermttent spell of unemployment between jobs; Barth, Bratsberg, and Raaum (2011) show that ths s the case for mmgrants n orway. Furthermore, n almost all OECD countres, mmgrants are much more lkely to hold temporary jobs than natve-born persons, consstent wth the dea that employers are reluctant to hre mmgrants drectly nto permanent jobs wth employment protecton. Another predcton of our model s that dscrmnaton s postvely related to the exstence of EPL. One way to explore ths predcton s to look at varatons n EPL across countres and, as noted above, Kahn (2007) fnds supportng evdence usng mcro data from the Internatonal Adult Lteracy Survey for Canada, the Unted States, and fve European countres. However, one problem wth comparsons across countres s that there s large varaton n effectve job protecton wthn countres and mmgrants may fnd employment n other parts of the labor market where legslaton s less strct. Thus, an alternatve s to look at dfferences across sectors. Typcally, employment protecton s much strcter n the publc sector and, ndeed, n almost all OECD countres (Belgum beng the only excepton) mmgrants are underrepresented n publc sector jobs, as compared to natve-born persons (OECD, 2007c, p. 73). In fact, even chldren of mmgrants tend to be underrepresented n the publc sector (OECD, 2007c, p. 85). Whle there are also other possble reasons for the underrepresentaton of mmgrants n the publc sector, such as language requrements, the dfference s nevertheless suggestve. Appendx A: Steady State Condtons Let " denote the share of employed workers of type n jobs wth low match qualty. For both types, the outflow from jobs wth bad matches must equal the nflow to jobs wth bad matches n ".s C 'p /.1 u / D vq. S /.1 E. ˇˇˇ S // : Smlarly, the outflow from good matches equals nflow to good matches Usng the above two equatons gves us n.1 " /s.1 u / D vq. S /E. ˇˇˇ S / : " D s.1 E. ˇˇ S // s C E. ˇˇ S / 'p : As the outflow from unemployment equals nflow to unemployment, we must have Solvng for the unemployment rate n u.s C 'p / D sn : u D s s C 'p :

19 Holden and Rosén Dscrmnaton and Employment Protecton 19 Appendx B: Assumpton 1 mples that J. ; p / > 0 For D, we have that (usng (19) and that V D 0 n equlbrum) J. ; p / > 0,.1 ˇ/y H > r C s.1 r C s C 'p /.w L y L / whch clearly follows from (18) as.r C s/=.r C s C 'p / 1 and.1 /= <.1 M /= M. Appendx C: Proof of Lemma 1 For a gven hrng rule we have that (from equaton (10)) V./ D c=q./ C G. G S/E.J ˇ S G ˇG / C R.R S/E.J ˇ S R ˇG / r=q./ C G.G S/ C R. R S/ Usng that ' D 0 and D n when D 0 gves V.0/ D n G.G S/E.J ˇ S G ˇG / C n R.R S/E.J ˇ S R ˇG // n G.G S/ C n R.R S/ ; Wth (usng equaton (19)) J.; p / D As J.; p / s ncreasng n t follows that E.J ˇˇˇ S / E.J ˇˇˇ S D Thus, or V.0/ M.1 r C s..1 ˇ/yH C sv / C 1 r C s.yl w L C sv / / D M.1 ˇ/yH C sv r C s ˇ/yH C sv r C s C.1 M / yl w L C sv r C s C.1 M / yl w L C sv r C s rv.0/ M.1 ˇ/y H C.1 M /.y L w L / Hence by Assumpton 1 we have that V.0/ > 0. In the lmt, we have lm V D c=r < 0. As V s contnuous n for gven!1 hrng strateges, postve for low values of and negatve for hgh values, t follows that there exst an equlbrum (condtonal on hrng strategy) where V. / D /=@ < 0 and V./ < 0 for all >.