Working Paper Wage Bargaining and Turnover Costs with Heterogeneous Labour: The No-screening Case

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1 econtor Der Open-Acce-Publikationerver der ZBW Leibniz-Informationzentrum Wirtchaft The Open Acce Publication Server of the ZBW Leibniz Information Centre for Economic Strand, J. Working Paper Wage Bargaining and Turnover Cot with Heterogeneou Labour: The No-creening Cae Memorandum, Department of Economic, Univerity of Olo, No. 4/998 Provided in Cooperation with: Department of Economic, Univerity of Olo Suggeted Citation: Strand, J. (998 : Wage Bargaining and Turnover Cot with Heterogeneou Labour: The No-creening Cae, Memorandum, Department of Economic, Univerity of Olo, No. 4/998 Thi Verion i available at: Standard-Nutzungbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wienchaftlichen Zwecken und zum Privatgebrauch gepeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich autellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfaer die Dokumente unter Open-Content-Lizenzen (inbeondere CC-Lizenzen zur Verfügung getellt haben ollten, gelten abweichend von dieen Nutzungbedingungen die in der dort genannten Lizenz gewährten Nutzungrechte. Term of ue: Document in EconStor may be aved and copied for your peronal and cholarly purpoe. You are not to copy document for public or commercial purpoe, to exhibit the document publicly, to make them publicly available on the internet, or to ditribute or otherwie ue the document in public. If the document have been made available under an Open Content Licence (epecially Creative Common Licence, you may exercie further uage right a pecified in the indicated licence. zbw Leibniz-Informationzentrum Wirtchaft Leibniz Information Centre for Economic

2 Wage bargaining and turnover cot with heterogeneou labor: The no-creening cae By Jon Strand Department of Economic Univerity of Olo Box 095, Blindern 037 Olo, Norway May 998 Thi paper i part of the reearch project "Employment and the labor market" at SNF-Olo.

3 Abtract We tudy the effect of mobility cot in a model of wage bargaining between heterogeneou worker and firm, where there i intantaneou matching, free firm entry, and worker individual productivitie are dicovered by firm only after being hired.we derive the employment level and the minimum quality tandard, in the market olution and in the ocially efficient olution. We how that the minimum quality tandard choen by firm i alway overoptimal. The rate of hiring among wanted worker i alo overoptimal when worker have low bargaining power, but uboptimal when thi bargainig power i high. In the latter cae overall employment i alo uboptimal. The compoition of the employed labor force i alway inefficient, with a too high average quality of labor. Hiring tandard increae when diipative firing cot for tenured worker increae, and drop when cot of firing unwanted worker increae. An increae in the latter may raie overall employment.

4 . Introduction The purpoe of thi paper i to tudy effect of hiring and firing cot on employment when worker bargain individually with their employer over the wage. We extend the tandard bargaining/matching model (e.g. Piaride (985, 987, 990 in two new direction. Firt, worker are no longer identical but intead have different but given productivitie, known to each worker but not to the firm at the time the worker i hired. With heterogeneou labor the iue of firing become relevant even when there are no (idioyncratic or general hock, ince firm may wih to replace their initially hired worker with other, more productive, one. Secondly, we aume both hiring cot (paid for by the firm and correponding to recruiting cot in Piaride, and cot of getting rid of worker once engaged by firm. While hiring cot do not directly affect firing deciion, firing cot do. We ditinguih between three type of firing cot: a the cot to the firm of immediately getting rid of an unwanted worker; b a pure (diipative cot paid by the firm, which vanihe to the firm-worker relationhip, when a "tenured" (or initially wanted worker leave the firm; and c a redundancy payment from the firm to a tenured worker upon eparation. Worker productivitie are dicovered upon hiring, and firm wih to retain thoe worker who have the highet productivitie, and may wih to fire immediately thoe with productivitie below ome minimum level. Since firm are identical, all chooe the ame cutoff level for productivity, z, beyond which worker are retained. A implification relative to the tandard matching model i that our proce of matching worker and firm involve no friction, and that operating firm uffer no vacancie. Thi implification make the analyi tractable and ha few diadvantage in term of lack of generality. Secondly, with our approach a tandard competitive olution now arie when worker relative bargaining trength goe to zero, making it poible to invetigate the iue of market efficiency in thi important pecial cae. The paper integrate a modified verion of the Piaride-Mortenen matching/bargaining theory for the labor market, with recent literature on turnover cot. It make a firt tep in the direction of endogenizing imultaneouly worker hiring tandard and overall employment when worker have unobervable productivity difference, and point out the implication of turnover cot on labor market performance in uch a context. Several of our reult are novel, in particular thoe decribing how the efficiency of hiring tandard and employment depend on worker bargaining trength, and how employment may depend on the cot of firing worker immediately.

5 We preent the baic model in ection 3, and in ection 4 we derive the olution choen by a ocial planner ubject to the ame technological and cot condition a market agent, and compare thi to the market olution in ection 3. The concluion are ummed up in the final ection 5, where we alo point out ome potential direction for future reearch. 2. The baic model. Conider an economy with a large exogenou number of worker, normalized to one, and a large (endogenou number F of active firm, each employing exactly one worker. All firm and worker are rik neutral. Since the number of active firm equal the number of employed worker, L, F=L. All job are identical and have fixed productivitie over time. There are no capital cot. 2 Labor i heterogeneou, and worker productivitie denoted by z, ditributed according to a continuou ditribution G(z, with upport [0, z ]. z i known to the worker but not to the firm m at the time he i hired. When the worker i hired, the firm incur a hiring cot H, after which the 3 worker productivity i immediately revealed to the firm. The firm chooe to retain the worker given that hi productivity fall in the domain [z,z ], where z $ z. Worker with z<z are m 0 conequently eparated immediately. 4 5 There i free firm entry and, apart from H, no etablihment cot for firm. Aume that all worker remain in the market for an infinite period of time. For a wanted worker (with z$z who i currently unemployed, hi lifetime dicounted value of labor market participation, U(z, i given by 2 A trivial extenion would be to aume a given rental cot of capital per job, a in Piaride (990, with no conequence for the main concluion in the following. 3 H may alo include any recruiting cot expended by the firm. Note that we aume that no part of H i paid by the worker, e.g. due to limitation on worker aet or acce to credit market, by legal retriction on uch worker payment, or by an aumption that H mut be incurred before the worker i actually engaged by the firm. 4 The aumption that worker productivitie are dicovered immediately can eaily be relaxed without any of the main reult being altered. One alternative would be to aume that worker have to go through a traineehip or tet period, whoe length i tochatic and exponentially ditributed. 5 We will demontrate below that the profitability of employing worker in our model alway increae trictly in z, for all firm. 2

6 ( ru(z = b + h[w(z - U(z], where b i the level of income (or income-equivalent utility in the unemployed tate, h i the continuou rate of tranition from unemployment to employment for qualified worker, and W(z i the expected dicounted lifetime utility in the employed tate. For an employed worker (with z $ z the equivalent dicounted lifetime value i determined by (2 rw(z = w(z + [U(z + F - W(z]. 2 Here w(z i the wage earned by a worker of ability z, and i an exogenou rate of job exit. We conequently aume, throughout, that the only reaon why a worker at equilibrium can loe hi job, i becaue hi job ceae to exit. Aume (apart from immediate eparation that the cot to the firm of eparating a worker at the firm initiative i F = F + F, where F repreent real 2 diipative cot incurred by the firm, while F i a required redundancy payment from the firm 2 to the worker. From (-(2 we now find (3 W(z r% [w(z% F 2 % U(z] (r%h[w(z% F 2 % U(z] r(r%%h (4 U(z h[w(z% F 2 ]%(r%b. r(r%%h Denote the preent dicounted value to the firm, of having a job filled with a worker of quality z, by J(z. Conider a poition filled with a worker of quality z, where the hiring cot H i unk and the worker creened. Given that the worker i not fired immediately (i.e., z $ z, J(z i given 6 by (5 rj(z = z - w(z + [-F - J(z], 6 Thi require that z-w(z be trictly increaing in z, which hold in all cae tudied below. 3

7 yielding (5a J(z [z&w(z& F] r% Denote by N the probability that the firm ample a deirable worker, when drawing among the ma of unemployed worker. Thi i given by (from the appendix (6 N [&G(z ] (%hg(z %[&G(z ]. The denity in the firm ampling ditribution over z level among deirable unemployed worker, g (z, i given by (alo from the appendix (7 g (z (%hg(z %[&G(z ] g(z, z 0 [z, z m ], and where g (z/n i the conditional denity for worker who are not immediately fired. Calling the cumulative ampling ditribution G (z, note alo that by definition N = - G (z. Note here that N < - G(z. Thi implie that the probability of ampling an acceptable worker from the pool of the unemployed i lower than the fraction of acceptable worker in the entire labor force, ince the unemployment rate of coure i lower among the former. The cot of the firm firt ampling given a vacancy i H. Provided that thi worker doe not have the required quality (i.e., z<z, the cot of the next (and poible following ampling( i H+F, where F i the cot to the firm of firing a worker immediately, after being hired. F may contain a mandatory redundancy payment, and a diipative component. F 0 may be mall, and will be aumed maller than F. The total expected cot of filling the job with a worker of ability z $ z i now given by 2 (8 C = H + (-N(H+F 0 + (-N (H+F = [H + (-NF 0]/N. 7 A tranfer component of F 0 may repreent alary to the worker in an initial tet period over which the worker productivity i dicovered, cf. alo footnote 3 above. 4

8 Define EJ a the expected value to the firm of a filled job (with a worker of productivity z $ z. We then find, integrating (5a over z, (9 E J z m J(zg N m (zd z z0 z m r% N m z0 [z&w(z]g (zdz & r% F. At equilibrium EJ = C, implying the condition 8 (0 z m [z&w(z]g r% m (zd z z0 H % N r% F % (&NF 0. We aume that each firm can unilaterally elect the level of z (= z beyond which a worker i retained, and below which he i immediately fired. The wage for each retained worker i determined in an aymmetric Nah bargain between the worker and the firm, with relative bargaining trength $ and -$, where $ 0 (0,. 3. The bargaining olution We will now aume that the threat point of the bargaining olution, relevant both to worker and firm, involve no redundancy payment to a worker who leave the firm while the firm i operating. Thi implie for one thing, that if a worker were to quit voluntarily, he would receive no final payment F from the firm. It alo implie that the firm can in effect force a worker to quit, 2 e.g. by committing to a tream of zero wage payment making it optimal for the worker to utilize 9 the option of leaving the firm. Conider now an ongoing relationhip, i.e., one that wa not broken up immediately. For uch a relationhip W(z and U(z are till given by (3-(4. The net utility of the worker from the match, 8 We here aume that uch a condition can be fulfilled for h 0 (0, 4 and with z given from (5 below. Thi implie that H and the F i are all not in exce of certain level. In the oppoite cae no firm could profitably enter the market, and there would be no employment. 9 The viability of uch a olution require an aumption that an operating firm i in principle allowed to make zero wage payment to worker and till ecape the final redundancy payment, provided that the worker actually quit; and i the Stackelberg leader in the game initiated by a zero wage payment by the firm. Then the worker quitting option will define the default utility of the firm, relevant in the bargaining olution decribed below. 5

9 S(z, i given by W(z - U(z, i.e. by ( S(z r% [w(z % F & ru(z] w(z&b% F 2 2. r%%h Likewie, the net urplu, Q(z, of the firm i given by the urplu over the default utility in the cae of a worker quit, J(z + F : (2 Q(z r% [z & w(z % r F & F 2 ]. Defining E z a the conditional expectation of z given z $ z, we may now characterize market c equilibrium, a follow. Propoition : Given a Nah bargaining olution, market equilibrium i characterized by the following equation: (3 w(z $(r%%h r%%$h (z % r F % (&$(r% r%%$h b & F 2 (4 z b % %$(r%h F &$ & r%%$h &$ F 0 (5 E c z b % &$ 6[%$(r%h]F % (r%%$h( H N % &N N F > 0 (6 L h %h [&G(z ], provided that z 0 [0, z ]. m $ -$ Proof: (3 i derived directly, etting w(z to maximize the Nah product S(z Q(z, where U(z i taken a given in (. (4 i then found, uing that J(z = - F 0, and recognizing that firm 6

10 et z unilaterally, given an internal olution for z. (5 can then eaily be derived, uing (0. (6 define L. Q.E.D. We ee from (3 that w(z (apart from the term -F i a weighted um of the term z+rf (the 2 net current value to the firm of continuing rather than ending the employment relationhip and b (the current utility of the worker outide option, with weight that tend to $ and -$ a h tend to zero, and (for given $>0 to and 0 a h tend to infinity. In addition, an increae in F 2 lead to a drop in w(z, by F. An increae in F here implie no improvement in the worker 2 2 attachment value, only that more of thi value take the form of a final redundancy payment, and le the form of wage. A a condition for Propoition, we aume that z 0 [0, z ]. A ufficient condition for z > 0 i m rf < b, which will be aumed here and in the following. With regard to z, a ufficient condition 0 m for z < z, both here and in cae 2 below, i m (7 z m > b % &$ [($r%f & (r%f 0 ], for all relevant value of $ and F, which will alo be aumed to hold. i Conider a marginal worker a viewed by firm, i.e., z = z. For uch a worker, (8 S(z $ &$ (F & F 0. Since F < F, there i a poitive net urplu aociated with, and going to, a marginal employed 0 worker. Thu a worker with productivity lightly below z would now have been able to enjoy a poitive net urplu from not having hi match broken immediately but rather continuing it. The reaon why the match i till immediately broken (unilaterally by the firm i that when F < F, 0 then for a marginally profitable worker it i advantageou to break up the match immediately 7

11 0 rather than later, ince thi reduce diipative firing cot. An important and intereting quetion i whether the olution for z from (8 i unique. To addre thi iue, define 2(z = E z - z, given by c (9 E c z & z r%%$h &$ N (H % F. 0 We may then formulate the following reult. Propoition 2: Equilibrium a characterized in Propoition i unique given that (20 &G(z g(z > E cz & z & (r%(%h (&$ H%F 0 &G(z hold everywhere. Proof: We have from (6 that (6a N % %h G(z &G(z. Inerting from (6a in (9 and differentiating (9 with repect to z yield d2/dz < 0 everywhere if and only if (20 hold everywhere. Moreover, for a given z we have from (4 that there i a unique equilibrium value of h, implying that w(z and L are given uniquely from (3 and (6. Thu (20 i a ufficient condition for equilibrium to be unique. Q.E.D. The poibility of multiple olution i here in principle open. In uch cae (4 implie that high level of z go together with high level of h. Since higher z for given h implie lower employment, and higher h higher employment, employment level cannot generally be ranked among uch equilibria. In the following dicuion we will however generally aume that 0 A conequence of thi i that ome worker with z in ome range below but cloe to z will have an incentive to make an up-front payment to the firm upon joining, in order for the firm not to fire them immediately. We here rule out uch up-front payment. 8

12 equilibrium i unique. The effect of change in the cot variable H, F and F on the key variable h and z can be found 0 from differentiating (4 and (5 with repect to h and z and the cot variable (inerting for L from (6. Note initially that change in F have no effect on h and z. One may readily how 2 that z i increaed when H and F increae. The reaon i partly that the general cot level then increae. Moreover, higher F raie worker bargaining threat point and thu the wage. Firm then become more elective with repect to what worker to keep at the time of recruiting. Note that from (6, (2 d L (%h 2[&G(z ]d h & h %h g(z d z. Total employment mut then drop when H and F increae. We find, in appendix B, that z decreae with F, and h mot likely decreae a well. A lowering of z however in addition 0 reduce creening cot in individual firm ince fewer worker type are immediately dimied, and reduce the pool of undeirable worker, thu lowering average creening cot. Thi raie firm entry and thu alo poibly h, and tend to make the effect on employment of a higher F 0 more poitive when creening i imperfect. 5. Efficient olution Becaue of the mechanim for determining the wage (bilateral bargaining and aggregate employment (firm entry to make net profit equal to zero, there i no reaon to expect either of the derived market olution to be efficient. We will in thi ection derive the contrained efficient olution, and compare it to the two market olution derived above. Our procedure i to find the level of z and h, and conequently L, that would be et by a ocial planner who could et thee directly, given that uch a planner face real hiring cot H, real diipative firing cot F for 0 00 worker to be dimied and F for worker to be kept, and i ubject to the ame creening 0 technology a that facing firm. Define the total match value for a given z, once the worker i employed, H unk and the worker 9

13 (22 M(z r% (z & b & F 0. retained (i.e., z $ z, by M(z, where rm(z = z - b - F + (-M(z, implying A match breakup 0 involve a ocial firing cot of F and lo of the match value M(z. Denote by EM the expected 0 ex ante value of a ucceful match (i.e., a match where z $ z i realized, including cot unk in order to accomplih uch a match. Thi i given by EM = E[M(z] - [H + G (z F ]/[-G (z ], 0 00 where a before G (z i the ampling ditribution over z for hiring firm, from the pool of unemployed worker. Define T a the ex ante value of all ucceful matche in exitence at a given time. Since the rate of employment among wanted worker (with z $ z i h/(+h, total employment L i [-G(z ][h/(+h]. T may be expreed by: (23 z m T(z,h h %h 6 m & 6 (%h zz z&b& F 0 g(zd z r% G(z % [&G(z ]>H 0 & (%h G(z F 0 0 >. The government objective i to maximize (23 directly with repect to z and h. The olution to thi problem can be formulated in the following propoition. Propoition 3: The government contrained optimal olution for z and h i given by (24 z b & (r%h H 0 % F 0 & (r%(%h F 00 A oppoed to in e.g. Hoio (990 and Piaride (990, uch a maximization i meaningful here even when there i poitive dicounting (r>0, ince there i intantaneou matching of firm. Thi implie that we can in principle view the market olution a reulting from the optimal tock of worker being hired at a given intant of time. (25 expree the ocial value of uch hiring provided that employment i kept at a contant level over time, after the initial hiring. 0

14 (25 E c z b % F 0 % (r%h 0 % (%h2 (r% 2 G(z &G(z (H 0 %F 0 0, provided that z 0 [0, z, and G(z trictly poitive. m Proof: Maximizing (23 with repect to z and h yield (26 d T d z h %h g(z 6&z %b% F 0 r% % H 0 & %h (H 0 %F 0 0 > # 0 (27 d T d h h(%h T & h (%h G(z (H 0 %F 00 $ 0. (26 here hold with equality if and only if z 0 [0, z ]. (27 alway hold with equality. Inerting m for T from (23 in (27 then yield (24-(25. Q.E.D. In (24-(25, the cot of orting out unwanted worker, in the form of increaed firing cot F 00 and ubequent hiring cot H, affect the (contrained and econd-bet optimal olution. The 0 effect in (24 of increaed H and F i to reduce z below it uncontrained optimal level, 0 00 reducing overall orting cot when fewer worker type are creened out at equilibrium. The econd-bet optimum trade off thi aving in orting cot againt the efficiency lo from retaining worker with too low productivitie. Note alo that it can never be efficient to have full employment among deirable worker, i.e., h mut be finite. To ee thi, conider h64. But then the market equilibrium would imply (from appendix a that G (z i very cloe to, i.e., (almot all worker in firm ampling ditribution over unemployed worker would be unwanted. Clearly thi cannot be efficient, ince the marginal hiring and firing cot, aociated with hiring one additional qualified worker, would go to infinity. It may eem urpriing that an increae in H reduce the minimum hiring tandard z.when 0 interpreting the effect of an increae in H on z in (24, note that (+h/ expree the rate at 0 which "unqualified" worker are ampled veru "qualified" one, in term of the original

15 ditribution G(z. Since (+h/ >, the overall burden of hiring cot aociated with unqualified worker i greater than that aociated with qualified one. Thi implie that there i an overall efficiency gain to be had from grouping more worker in the qualified category, when H 0 increae. (24-(25 are contructed to facilitate a comparion with the market olution. We are here in particular intereted in deriving the condition for a contrained efficient olution to be implementable by the market in thee two cae. We aume that the government can freely tax or ubidize hiring and firing cot, and that H - H and F - F, i =,2, repreent net government 0 i i0 ubidy rate (or tax rate when negative. There are no net cot to the government aociated with poitive net ubidie to firm, nor are there gain due to net taxe. We impoe no prior contraint on H or F, i.e., either of thee could be negative a part of an implemented efficient i olution. An efficient olution can then in principle alway be implemented in both cae and 2 above, by 2 only etting H and the F i at appropriate level. The intereting iue in our context i what propertie ditinguih the efficient from the unregulated market olution. To hed light on thi iue we conider the following two example. Example a: $ 6 0. In thi cae, note that (4-(5 now can be written a (4a (5a E c z z = b + F - (r+f 0 b % F %(r%h % (%h(r% G(z &G(z (H%F 0. Given that H = H and F = F, i=0,, comparing (4a to (24 reveal that z i unambiguouly 0 i i0 higher in the market olution than in the efficient olution. A a reult, minimum hiring tandard are inefficiently high in the unregulated market olution. The intuitive reaon for thi i again the negative externality related to dimiing a worker that i initially engaged, ince uch a dimial 2 The iue of implementation of efficient olution in the market, tarting from a nonefficient olution, i however more complex than the dicuion here indicate, ince it may then be neceary to alo decribe the optimal path to a new tationary equilibrium. Thi will not be dicued further in the following. 2

16 lead to a "contamination" of the unemployment pool, and increae the hiring (and ubequent firing cot of other firm. Comparing (5a to (25 imilarly reveal that h i overoptimal in the market olution (ince E z c increae trictly in z for given h, and mut conequently be greater in (5 than in (27. Thi i due to a negative externality related to firm etablihment and ubequent hiring in the market. Aborbing a high-quality worker from the unemployment pool namely alo "contaminate" the pool of the unemployed, in a imilar way a when a low-quality worker i fired. The overall conequence of thee concluion i that when worker bargaining power i very low, too few worker type are retained by firm, but the rate of employment among thoe retained i inefficiently high. The overall effect of thi on employment i difficult to judge in general. Example b: F = F = 0, i =,2. In thi cae there are no firing cot. Now z = b from (4. i i0 Conequently the market-determined hiring tandard i till above the contrained optimal level. To tudy the effect for h, note that (5 now can be written a (5b E c z b % r%%$h %h G(z [% &$ &G(z ]H. We again find that when $ i low, h mut be higher at the market olution than at the contrained efficient olution. When $ grow higher and approache one, by contrat, we ee that E z for c given h i increae and approache infinity in the limit. Thi implie that h mut approach zero, and in fact hit zero at a level of $ below one (ince z i a contant, from (4, and thu E z a c contant. The implication of thi i that a $ increae from zero, h i reduced, from an overoptimal level (a expoed in example a to a uboptimal one. For a ufficiently high $, of coure, there can be no market olution a h in our model i below zero. The interpretation of thi cae i that with ufficiently high $, no firm find it profitable to enter the market, when there are poitive hiring cot. An overall concluion from thee two example i that the minimum worker hiring tandard i 3

17 alway higher than the contrained optimal tandard choen by a ocial planner. The rate of hiring and thu employment among thoe above the minimum tandard i alo overoptimal when worker have very low bargaining power, but fall (to a uboptimal level when thi bargaining power increae. A far a the overall level of employment, thi could be higher or lower than the contrained optimal level when worker have low bargaining power, but i alway uboptimal when worker bargaining power i high. 5. Concluion We have tudied a model of the labor market where there i intantaneou matching and ubequent wage bargaining between individual worker and firm, worker differ in their productivitie, and it i cotly for firm to hire and fire worker, and firm cannot oberve worker individual productivitie prior to hiring them. In ection 3 above we have derived the minimum quality tandard beyond which worker are retained by firm, and the equilibrium wage level of worker a a function of their productivitie, among thoe retained. In the model, regular firing cot are incurred only when worker loe their job becaue firm (exogenouly cloe down. Severance payment to uch worker then have no allocation effect, and only affect the ditribution of the worker attachment value between wage and redundancy payment. Diipative firing cot (that are lot to the worker-firm relationhip however reduce employment and increae the minimum hiring tandard. An increaed cot of immediately dipoing of newly hired worker alway reduce thi tandard and ha an ambiguou effect on employment. The reaon why employment then may increae i two fold. Firt, lower hiring tandard implie that the rate of hiring among wanted worker would drop given that overall employment i contant, and thi drop reult in a lower wage, through a weakening of worker bargaining poition. Secondly, the lowering of the quality tandard implie a poitive externality for the labor market a a whole, whereby overall cot of recruiting and teting new worker are reduced. Both thee effect reduce the overall cot of firm, purring firm entry and thu employment. In ection 4, we then derived the contrained efficient olution, implemented by a ocial planner facing the ame technological contraint a thoe facing firm in the market. To undertand the reult derived here, note that there are ocial recruitment cot aociated with orting out 4

18 unwanted worker, in the form of immediate firing cot and cot of ubequent neceary hiring. Thee recruitment cot are reduced when the group of unwanted worker i mall, relative to the group of wanted worker. Recruitment cot are reduced when the minimum worker quality tandard i reduced (thu leaving fewer worker unwanted ; and when fewer among the wanted group are hired (thu leaving more of thee in the pool of the unemployed, and increaing the probability that a earching firm will find one of thee when recruiting in the market. In ection 4 we alo demontrate that the market olution alway entail a too high quality tandard. We then how that the rate of hiring among wanted worker i too high when worker have very low bargaining power, but i reduced, to a uboptimal level, when worker bargaining power increae. Thi implie that overall employment may be too low or too high when worker bargaining power i low, but i alway too low when thi power i high. In all cae, the compoition of the employed labor force i inefficient, in the direction of firm being too elective and thu the average quality of employed worker too high. Thee reult can be contrated to thoe obtained in a related model, where we intead aume "perfect hitory creening", implying that firm do not incur orting cot (i.e., at the time a worker i firt hired, the firm already know whether the worker i in the deirable group or not; although the firm doe not know the worker actual productivity. Such a cae i explored in an accompanying paper, Strand (997. I then how that the market-determined minimum productivity level for worker i inefficiently low, i.e., the diametrically oppoite cae to that derived here. The reaon i that in thi cae the hiring cot become a net burden aociated with recruiting a worker, which firm in the market have no incentive to conider once hiring already i done. With perfect hitory creening we alo find, in contrat to the current cae, that the rate of hiring among deirable worker i alway too low, while it i alway too high in the current model given that worker have a low bargaining power. The implication i that many of the reult derived from the current and preumably related model, are enitive to detailed aumption with repect to the ability of firm to ditinguih worker type prior to hiring them. Clearly, thee concluion call for more reearch along related line. 5

19 An important feature of our model i that the implementation of an efficient olution require the correct determination of two independent variable (namely the hiring tandard and the rate of employment. An efficient olution thu cannot in general be implemented jut by requiring $ to take a certain value (a in the model dicued by Piaride (990. In addition at leat one cot 3 variable facing firm mut be et by the government. In focuing on the effect of turnover cot and labor heterogeneity, we have deliberately diregarded a number of potentially important feature. In our model all actual firing among deirable ("tenured" worker are fully exogenou. Our analyi i thu quite ditinct from other recent contribution where worker turnover and turnover cot are central, uch a Bentolila and Bertola (990, Bertola (990 and Lazear (990 dealing with turnover cot in more partialequilibrium etting, and Mortenen and Piaride (994, Bertola and Caballero (994 and Saint-Paul (995 who conider bargaining model with turnover and turnover cot but where labor i aumed to be homogeneou. Extenion of our framework, which are poible avenue for future reearch, may be to incorporate productivity variation (a e.g. in Mortenen- Piaride, on-the-job earch (a in Piaride (994, tochatic match value (a in Bertola- Caballero, and the poibility of rehiring laid-off worker. Incorporating uch alternative aumption could alo further erve to integrate the theorie of contract and matching and clarify their relationhip when there are poitive turnover cot. 3 The baic property that efficiency require the efficient determination of other variable than the hare parameter $, i common with other recent related work which take on a more complicated tructure than the baic Piaride model, e.g. Bertola and Caballero (994. 6

20 Appendix A: Derivation of the firm ampling ditribution over worker qualitie We here wih to derive the ampling ditribution G (z, for firm ampling of worker from the pool of unemployed. Firt define the ditribution over qualitie for the entire et of unemployed worker, G (z. The fraction of worker in the entire labor force that ha z<z i G(z, and the u equivalent fraction among the unemployed i denoted by G (z. Note that u (A N G(z = U G (z = U, u where U i the total number of unemployed worker, and U i the number of unemployed worker with z<z, ince all worker with z<z are unemployed at equilibrium (when each i employed by firm only for an infinitely hort period of time after being hired. For a worker with z$z, the unemployment rate u equal the average fraction of the time pent 2 in unemployment, /(+h, while the employment rate equal the fraction of the time pent in employment, h/(+h. Denoting by U and N the number of worker with z$z in unemployment 2 2 and employment repectively. We then have (A2 U 2 N[&G(z ] %h (A3 h N 2 N[&G(z ] %h. Since U = N G(z, N = 0, we then find (A4 G u (z (%hg(z %hg(z Since G (z ha denity proportional to G(z, piecewie on [z,z and on [z,z ], we find u 0 m 7

21 (A5 G u (z %h %hg(z G(z, z<z (%hg(z %hg(z % %hg(z [G(z&G(z ], z$z. Since the relative frequency with which a worker with z<z will be ampled by the firm i one, the probability that the firm ample uch a worker i (A6 G (z G u (z G u (z %&G u (z &N, which yield, uing (A4, (A7 &N (%hg(z (%hg(z %[&G(z ]. The firm ampling ditribution i then given by (A8 G (z (%h (%hg(z %[&G(z ] G(z, z<z (%hg(z (%hg(z %[&G(z ] % (%hg(z %[&G(z ] [G(z&G(z ], z$z. 8

22 Appendix B: Comparative-tatic reult of change in F. 0 The effect of change in F on h and z are: 0 (B dh & df 0 D (r%%$h D(z &$ & (%h r%%$h &$ &2G(z (&G(z 2g(z (H%F &N % 0 N (B2 dz df 0 & D r%%$h &$ [ $ (&$N ((&$%$NF %H%$(&NF 0 % (r%%$h(h%f 0 G(z &G(z ], where (B3 % $ D (&$N [H%(&N%$ND(z F %(&D(z F ] 0 &G (r%%$h[g% $ &$ ((&2G(z (%h(f &F ](H%F., 0 0 which i poitive by virtue of the econd-order condition for an internal optimal olution being fulfilled. 9

23 Reference Bentolila, S. and Bertola, G. (990, Firing cot and labour demand: How bad i Eurocleroi? Review of Economic Studie, 57, Bertola, G. (990, Job ecurity, employment and wage. European Economic Review, 34, Bertola, G. (992, Labor turnover cot and average labor demand. Journal of Labor Economic, 0, Bertola, G. and Caballero, R. J. (994, Cro-ectional efficiency and labour hoarding in a matching model of unemployment. Review of Economic Studie, 6, Hoio, A. On the efficiency of matching and related model of earch and unemployment. Review of Economic Studie, 57, Lazear, E. P. (990, Job ecurity proviion and employment. Quarterly Journal of Economic, 05, Mortenen, D. T. and Piaride, C. (994, Job creation and detruction in the theory of unemployment. Review of Economic Studie, 6, Piaride, C. (985, Short-run equilibrium dynamic of unemployment, vacancie and real wage. American Economic Review, 75, Piaride, C. (987, Search, wage bargain, and cycle. Review of Economic Studie, 54, Piaride, C. (990, Equilibrium unemployment theory. London: Bail Blackwell. Piaride. C. (994, Search unemployment with on-the-job earch. Review of Economic Studie, 6, Saint-Paul, G. (995, The high unemployment trap. Qaurterly Journal of Economic, 0, Strand, J. (987, Unemployment a a dicipline device with heterogeneou labor. American Economic Review, 77, Strand, J. (997, Wage bargaining with heterogeneou labor and turnover cot: Perfect hitory creening. Working paper, Department of Economic, Univerity of Olo. 20