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Auctioning off labor contracts: Legal restrictions reconsidered
Auctioning Off Labor Contracts: Legal Restrictions Reconsidered D O R O T H E A KI]BLER
Institut f u r Wirtschafistheorie I, Humboldt-Universitdt zu Berlin, Berlin, Germany E-mail: kuebler@wiwi, hu-berlin, de
The paper analyzes the effects of various non-discrimination rules when the employer uses an optimal screening mechanism in the presence o f moral hazard and adverse selection. T h e optimal contracting mechanism for heterogeneous workers (with different probability distributions over types) exhibits third-degree wage discrimination, which is beneficial for on average less productive workers. Imposing non-discrimination restrictions on wages and hiring decisions may harm the on average less productive group and reduces efficiency. Affirmative action programs are neutral with respect to rent distribution and efficiency. © 1997 by Elsevier Science Inc. I. I n t r o d u c t i o n
W h e n employers have vacancies, they often have to choose a m o n g a n u m b e r of applicants who are not all equally suited to the job. It is difficult to find the best candidate if educational records, past work experience, and general abilities that can be tested via j o b interviews are of relatively little relevance to the worker's actual performance on the job. But workers themselves often know better than the employer how well they are suited to a job. T h e model presented below applies to such a situation where the n u m b e r of j o b candidates is limited. Workers know that there is some competition for the job, but they also try to exploit their private information by misrepresenting their true productivity. In a situation like this, it is optimal for the employer to use an auction-like mechanism that selects the best applicant and provides work incentives at the lowest possible wage. The optimal contracting mechanism can be described as follows: The employer offers a m e n u o f contracts, each of them specifying a wage and a certain output. The wage not My thanks go to H u g h Gravelle, Peter Jost, Steinar Vagstad, Elmar Wolfstetter, a n d conference participants at the EALE 1995 in Bern. I am especially indebted to three anonymous referees a n d an editor for their helpful suggestions. Financial support from the Norwegian Research Council (Ruhrgas) a n d the Deutsche Forschungsgemeinschafl, SEB 373 ("Quantifikation u n d Simulation 6konomischer Prozesse"), is gratefully acknowledged.
International Review of Law a n d Economics 17:63-74, 1997 © 1997 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
0144-8188/97/$17.00 PII S0144-8188(96)00059-2
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only d e p e n d s on output, b u t also on the rivals' a n n o u n c e d types. Applicants choose a level o f o u t p u t (implying an e x p e c t e d wage), a n d thereby reveal their type. T h e n the e m p l o y e r decides w h o m he will actually employ. W h e n incentive contracts are auct i o n e d off, the auction m e c h a n i s m chooses the best applicant a n d the contract assures that the worker does n o t shirk. As has b e e n shown by Laffont a n d Tirole (1987, 1993) in a p r o c u r e m e n t setting, optimal incentives are invariant to the n u m b e r of c o m p e t i n g workers (separation property). O n l y the profit o f the e m p l o y e r a n d the information r e n t of a g o o d type d e p e n d on the n u m b e r of c o m p e t i n g j o b applicants. Now, consider the case in which workers are h e t e r o g e n e o u s in that they have different probabilities for being a g o o d o r a bad type. It is assumed for simplicity that there are only two possible types o f workers. If the e m p l o y e r can distinguish between groups o f applicants on the basis o f visible characteristics such as race, sex, or age, 1 he will, in the optimal mechanism, offer different m e n u s o f contracts to different groups. This is a form of third-degree wage discrimination where g r o u p characteristics are used as a signal for the productivity o f its members. It is a well-known result from the theory of auctions with asymmetric bidders that it can be optimal to favor a b i d d e r with a lower average valuation, i.e., the item m i g h t be awarded to s o m e o n e o t h e r than the b i d d e r who values it most. This extends to an auction of contracts where a worker whose probability o f being a b a d type is high should be favored. T h e p a p e r confronts the optimal m e c h a n i s m with legal restrictions on third-degree wage discrimination. T h e general principle is that workers may be g r o u p e d a n d treated differently only on the basis of " r e l e v a n t " characteristics, z T h e laws governing differential t r e a t m e n t o f workers have b e c o m e m o r e a n d m o r e specific over the past few decades, b u t G e r m a n labor law seems to take notice of new forms o f contracting only to a limited extent. Jurisdiction is mostly c o n c e r n e d with cases where discrimination entails disadvantages for on average less productive worker groups. A l t h o u g h this effect o f discrimination exists in a n u m b e r o f contexts, the p a p e r shows that it is necessary to investigate discrimination in different contracting environments carefully if the legal rules are to have the desired impact on efficiency a n d distribution. In Section II the m o d e l of Laffont a n d Tirole (1987, 1993, Ch. 7) is r e f o r m u l a t e d in terms o f the labor contract setting with h e t e r o g e n e o u s workers. 3 Section III introduces various legal restrictions and analyzes their impact on efficiency and distribution. Finally, Section IV draws some conclusions. Proofs are relegated to the A p p e n d i x .
~This is also the starting point for theories of statistical discrimination that argue that wage differentials between certain distinguishable groups o f workers can be explained by different expected productivities o f these groups. An assumption underlying this result is that all types f r o m o n e g r o u p o f workers are pooled, i.e., there are no intra-group wage differentials. See for e x a m p l e Phelps (1972) or Arrow (1973). ZHowever, it is not always clear which are the relevant ( " s a c h g e r e c h t " ) a n d the irrelevant ( " s a c h f r e m d " ) characteristics of a worker or a g r o u p of workers with respect to a particular task. In the United States, e m p l o y m e n t discrimination law even restricts the use of seemingly neutral selection criteria that have an adverse impact on a protected g r o u p (disparate impact doctrine). If a selection criterion excludes workers o f a specific race, sex, or ethnicity at a significantly higher rate than it excludes workers o f a n o t h e r group, the e m p l o y e r has to prove that the criterion is in fact j o b related. 3For an application of the L a f f o n t / T i r o l e m o d e l to the labor context see also Gibbons (1987). A classical screening m o d e l is Salop and Salop (1976) where the worker's propensity to quit is private information. Guasch and Weiss (1981) develop a m o d e l where workers are screened via tests including test fees that have to be paid in advance a n d function as an e n t r a n c e fee.
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II. O p t i m a l Mechanism The Model
W o r k e r i p r o d u c e s an o u t p u t Yi, which d e p e n d s o n h e r " p r o d u c t i v i t y " 0 i a n d h e r effort e,. T h e p r o d u c t i o n function takes the additive form Yi = Oi + ei. T h e e m p l o y e r observes the worker's o u t p u t Yi, b u t n e i t h e r h e r type 0i n o r h e r effort e~. T h e r e are two types o f workers with productivity 0 (productive type) a n d 0_ (unproductive type) with A0 = 0 - 0__> 0. Visible characteristics exist by which the e m p l o y e r can distinguish different groups o f applicants. Assume that worker H a n d worker L (which are drawn from g r o u p H a n d L) differ with respect to their probability o f b e i n g productive, vi, with vH> vL. F o r example, the probability of a w o m a n for b e i n g a productive type may be lower t h a n the probability of a m a n for b e i n g productive. T h e s e probabilities are c o m m o n knowledge, a n d a worker knows h e r actual type 0 before the c o n t r a c t is offered. T h e r e are two workers c o m p e t i n g for the j o b , o n e from g r o u p H a n d one from g r o u p L. W o r k e r i (i = H, L) chooses an effort level ez which is assumed to be strictly positive over the relevant r a n g e of e q u i l i b r i u m efforts. 4 Effort e; causes h e r to have a disutility o f d~(ei). Total utility o f a risk-neutral worker i is given by the difference between h e r wage w i a n d h e r disutility o f effort, w i - d? (ei). T h e reservation utility is zero. A g o o d type c h o o s i n g the same y as a b a d type earns a r e n t o f ~ ( e i ) with di'(ei) = d~(ei) - d?(ei- A0). T h e disutility function is strictly increasing a n d convex in effort, d~' > 0 a n d qb" > 0, a n d the third derivative is non-negative, qb" -> 0, which makes the r e n t function ~(ei) convex. T h e e m p l o y e r ' s profit is equal to Yi - wi. With full i n f o r m a t i o n the e m p l o y e r forces the worker to choose the first best level e'* with d~' (e*) = 1 a n d pays h e r a wage o f ~b(e*). It is assumed that, in the case o f full information, the e m p l o y e r makes a positive profit even if a b a d type is hired, _0 + e* - ~b(e*) > O.
Solution
T h e revelation principle implies that the search for the optimal allocation rule can be restricted to direct mechanisms. T h e optimal incentive c o m p a t i b l e m e c h a n i s m relates the probability of winning xi(0_~t,{)£), the wage wi (0/-/, 0£), a n d the o u t p u t level Yi(~)H, {)L) to the a n n o u n c e d types (OH, 0L), i = H, L. T h e time structure o f a direct m e c h a n i s m is the following: First, the e m p l o y e r a n n o u n c e s a set of functions (xi(.), wi(. ), Yi(.)). T h e n b o t h workers reveal their types. Finally, one of the workers is selected, p r o d u c e s an output, a n d receives a wage a c c o r d i n g to the contract. T h e probabilities o f winning are non-negative a n d must satisfy the b u d g e t constraint (there is only o n e vacancy), +
1
X,(t,, tI) ~ O
(1)
i-~- H, L.
4This assumption is made for the sake of expositional clarity, see Laffont and Tirole (1993).
(2)
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For truth telling to be a Bayesian-Nash equilibrium, it must h o l d that 0/~-- OH maximizes the utility o f worker H given that worker L tells the truth, 0H~ arg max EoL [wit (OH, OL) -- XH(~)H, OL)+(yH(~)H, OL) -- OH)] for 0 n = 0,0
(3)
a n d analogously for worker L. T h e two participation constraints for each type o f worker H are E% [wH(0/_/, 0L) - x/-/(0H, OL)d~(yH(O,, 0L) - On)] --> 0 for OH= _0,0
(4)
with two c o r r e s p o n d i n g constraints for worker L. T h e e m p l o y e r maximizes his e x p e c t e d profit subject to the constraints (1), (2), (3), a n d (4) as well as the constraints corres p o n d i n g to (3) a n d (4) for worker L. Solving this c o n s t r a i n e d p r o g r a m leads to the following proposition, which is a straightforward generalization o f Proposition 7.1 in Laffont a n d Tirole (1993). PROPOSITION 1: (1) If a good type competes with a bad type, the good type is always awarded the
contract, irrespective of t_he_group she belongs to. If both applicants are good types, any solution is optimal as long as x14 (0, O) + x L (0, O) = 1. If both workers are bad types, the workerfrom group L is awarded the contract. (2) The optimal effort level of a good type equals thefirst best level in both groups of worhers, gH = ~1. = e*. The optimal effort level of a bad type is lower for worher H than for worker L, eH < eL < e*. (3) The rent of a good type from group H who competes with a bad type from group L is zero, but a good type from group L who competes with a bad type from group H earns an information rent. Wage is equal to the disutility of effort if two good types or two bad types compete. T h e e m p l o y e r discriminates between h e t e r o g e n e o u s workers. It is optimal for him to favor m e m b e r s o f the disadvantaged group. In the case o f two b a d types, worker L is e m p l o y e d because h e r o u t p u t is closer to the first best level than the o u t p u t o f a b a d type o f worker H. Therefore, worker H w h o is m o r e efficient in expectation receives no rent as a g o o d type because she loses h e r j o b with certainty when mimicking a b a d type. Wages are discriminatory as WH (0, 0) = ~b(e*), but, WL (_90,0) = 6 ( e * ) + XL (0_, O)~(ez) (with x L (0, 0) = 1 if the e m p l o y e r does n o t exclude all bad types ex ante; see Corollary 1). Thus, worker L is e m p l o y e d as a b a d type a n d receives an i n f o r m a t i o n r e n t as a g o o d type. 5 Notice also that the wage of a g o o d type o f worker L d e p e n d s on h e r rival's type as she does not earn a r e n t when c o m p e t i n g with a g o o d type, WL (0, 0) = ~b(e*). COROLLARY 1: If the probability of being a good type in group L is sufficiently high, no bad type
will be employed and good types from both groups do not earn a rent. PROOr: See expression (14) in the A p p e n d i x . It can be optimal for the e m p l o y e r to only offer a contract to the g o o d type, 6 i.e., xH(_0, 0_) = xL(O, 0) = 0. T h e n , the information r e n t o f a g o o d type o f worker L is r e d u c e d to zero because she c a n n o t mimic a bad type without losing the j o b with certainty. 7 As a b a d type o f worker H never gets the job, the cutoff rule is only relevant for worker L. 51f g r o u p s H a n d L differ with respect to the s u p p o r t o f 0 a n d g r o u p H is o n average m o r e productive, the optimal m e c h a n i s m has the following properties. If0/4 > 0L, t h e n A0H > A0 L a n d thus _eL > ell j u s t as above w h e r e v n > v L. But if 0 f t > _0L, then A0 H < A0 L a n d thus _eL < .~, which reverses the result. T h e smaller the difference between types ( h o l d i n g the distribution constant) a n d the smaller the probability o f a g o o d type ( h o l d i n g the difference between types constant), the m o r e this g r o u p is favored over the other. Olt is a s s u m e d that a wage o f w = 0 does not attract a worker even if h e r disutility o f effort is zero. Thus, a bad type is n o t e m p l o y e d as l o n g as she does n o t receive a positive wage i n d u c i n g a positive effort level. 7In an earlier version o f the p a p e r [K/ibler (1995) ], a Vickrey auction o f f r a n c h i s i n g contracts is analyzed w h e r e a
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In auctions with asymmetric bidders where a g o o d instead of a contract is sold, probabilities of winning are used to elicit higher bids from bidders with a higher willingness to pay. McAfee and McMillan (1989) and earlier Myerson (1981) show that the auctioneer's optimal policy is discriminatory in that one bidder may win although another bidder assigns a higher value to the object. In a second price a u c d o n optimal favoritism can be implemented by a simple rule (constant price preference), but the rule becomes rather complex when a first price auction is used [see Branco (1994)]. If a contract is auctioned off, the employer controls an additional variable (the wageoutput scheme), which he uses to extract rents. It may then be profitable not to employ the best worker applying for the j o b if her effort is more distorted. 8 T h e optimal mechanism selecting the best worker is not Pareto efficient. It may fail to employ a worker in state (_0,_0), although there are possible gains from the contract. 9 This leads to u n d e r e m p l o y m e n t due to asymmetric information between the worker and the employer. The higher the probability of a g o o d type in g r o u p L, the more likely a bad type will not be offered a contract. Thus, an increasing n u m b e r of qualified workers may cause u n d e r e m p l o y m e n t of the unqualified workers for reasons of information costs. The model allows for the fact that g r o u p H earns more on average than group L and workers of g r o u p H are employed more often because the situation where a g o o d type of worker H c o m p e t e s with a bad type of worker L is very likely. Thus, wage differentials can be reduced by raising the average productivity of g r o u p L. III. Legal Restrictions on Wage Discrimination Wage differentials on the grounds of irrelevant properties such as race, sex, religion, origin, political conviction, belief, language, or union membership are prohibited. 1° In addition, the Treaty of Rome made discrimination on the basis of nationality unlawful) 1 Equal treatment of men and women has received growing attention over recent years. Apart from the constitutional guarantee of equal rights, 12 there are rules requiring equal pay 1B and prohibiting indirect discrimination by the employer, a4 The enforcem e n t of these rules interferes with the employer's ability to use the optimal mechanism described above. In two o f the following three subsections, a non-discrimination restriction is imposed on the m e n u of contracts, which requires worker H a n d worker L to be offered the same menu. This rule seems to be undisputed and relatively easy to enforce. However, the hiring decision and randomization between equally qualified workers cannot be observed as easily as a contract. The case of perfect observability and the case of complete bad type of group H is cut off with a higher probability than a bad type of group L (via minimum bids). Thus, discrimination is also favorable for worker L when franchising contracts are auctioned off. ~l'he finding that the best worker is always employed is an artifact of the two-type case. Only the highest type, 0, is always employed, regardless of which group she belongs to. '~A crucial assumption of the model is that the terms of the contract cannot be changed either unilaterally by the employer or by mutual consent after the worker has announced her type. In an auction-like mechanism the best type must be picked before production takes place. Thus, there is always an incentive to adjust the inefficient effort e to e* or to hire a worker in state (_0,0_). The optimal mechanism is only implementable if the employer can commit himself to the menu of contracts. l°In Germany this follows from Art. 3 III GG. llSee Art. 48 III EWGV. 12See Art. 3 II GG. 13See Art. 119 EWGV and §612 III 1 BGB. 14See §611a BGB and Stllner (1988).
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non-observability are analyzed below. A third possibility to restrict the o p t i m a l mechanism is to stipulate that the same wage be paid for the same output, which a m o u n t s to disallowing for wages that are c o n t i n g e n t on the rival's type.
Non-Discriminatory Wages and Symmetric Tie Rule Suppose the courts can enforce the rule that equally productive workers must receive the same contract when the context, i.e., the rival's productivity, is the same. Thus, wage a n d o u t p u t have to be equal for worker L a n d H in each possible state o f the world:
w,:/(0, 0) = wz(0, 0), w,0(0, _0) = w,;(0, ~),
w,:,(0, 0) = wL(0, 0), w~(_0, ~) = w/.(~, 0).
(5)
T h e same must h o l d for efforts e/:/(. ) a n d e£(. ). Assume that after the workers choose from the m e n u , i.e., reveal their types, the firm's hiring decision can be observed. C o n s i d e r an e n f o r c e a b l e rule that states that equally qualified workers should be awarded the contract with equal probability. 15 In addition, hiring rules must be symmetric when worker types differ. Thus, for i = H, L x,-(0, 0) = xr(_0, _0) = ½, XH(0, _0) = x/:(_0, 0), x~,(_0, 0) = X£(0, _0).
(6)
T h e e m p l o y e r maximizes his profit subject to the legal constraints i m p o s e d on the contract a n d on the hiring decision. T h e p r o p e r t i e s of the optimal contract are summarized in PROPOSITION 2: (1) If a good type competes with a bad type, the good type is always awarded the
contract and receives an information rent. I f two good types or two bad types compete, the wage is equal to thedisutilit_t_tj o f effort_ (2) The optimal effort level of a good type is equal to the first best level, e/~(0, 0) = e£(0, O) = ei~(O, ~ = e£(O_,"0) = e*. The optimal effort level of a bad type is smaller than the optimal level of a bad type without a non-discrimination rule, ell(O_, 0_) = e£(O, 0_) < eL < e*. Thus, welfare is lower than in the unrestricted mechanism. W o r k e r H gains from the non-discrimination rule. As an u n p r o d u c t i v e type, she is e m p l o y e d with a probability o f 50% and as a g o o d type she earns an information r e n t o f 1/2+ (e,e/(_0,_0)). W o r k e r L's information r e n t is lower than in the unrestricted mechanism for two reasons. First, the effort o f a bad type is lower (e£(0, _0) < eL) and, second, she receives only 50% o f the m a x i m u m rent +(e/:(0, _0)). T h e e m p l o y e r is worse off u n d e r this non-discrimination regime because additional constraints are i m p o s e d on his decision. O u t p u t is affected by the legal rules only in state (_0,_0). Because it is smaller than in the unrestricted mechanism, the non-discrimination restrictions r e d u c e efficiency.
Equal-Pay-for-Equal-Work Rule and Non-Observability of Randomization In this section, the m e n u o f contracts does n o t only have to be the same for both workers H a n d L, but workers must also be p a i d the same wage for the same output. This equal-pay-for-equal-work rule implies that the context, for e x a m p l e the n u m b e r a n d ability o f c o m p e t i n g workers who could do the j o b , may n o t be a d e t e r m i n a n t o f wages. ~Whether employers abide by this rule can be checked either if the act of randomizing is monitored by the court (flip a coin for example) or, more importantly, by observing a series of hiring decisions of an employer over time.
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In Germany, there are rather strict criteria to ascertain equivalence of jobs that necessitate equal pay. 16 This implies, for example, that workers on equivalent jobs must receive the same wage although there are many equally qualified workers for one j o b whereas there is only one qualified applicant for another job. The second new assumption made in this section is that the employer's randomization between equal types is not observable) 7 Thus, the_employ__er is obliged to offer the wage ~ for a good type's effort level e/~(0, 0) = eL(O, O) = ei:l(O, 0_) = eL(O_, "6) and w for a bad type's effort level e~/ (0_, 0) = e£(0_, _0), but he can choose any probabilities xA0_, _0) and x¢(0, 0), i = H, L. PROPOSITION 3: (1) If two good types compete, worker L always gets the contract. If two bad types compete, worker L gets the contract with probability xL(O_, ~ = 1/(2 - vH). A good type who is awarded the contract always receives an information rent. (2) Effort in state (0_, 0_) is smaller than in the unrestricted mechanism, ei:l(O_, O_O_OQ = eL(O, O) < e L. Thus, total welfare is below that of the unrestricted mechanism. The strict non-discrimination rule with respect to wages together with the optimal probabilities leads to efficiency losses compared to the full discrimination case. 18 The freedom to choose optimal probabilities when both workers are equally qualified means that the employer always chooses worker L in state (0, 0) (remember that he was indifferent in the unrestricted mechanism). However, worker L is not always employed in state (_0,_0) as in the unrestricted mechanism, but only with probability 1/(2 - vn). Thus, the effect of the restrictions is ambiguous because a good type of worker His never employed in the case of a tie, but rent is redistributed from worker L to worker H.
Affirmative Action Suppose g r o u p L's lower average productivity results from historical discrimination, which manifests itself in lower levels of education. Affirmative action programs or equivalent rules that exist in some of the German states t9 are m a n d a t e d to compensate for past discrimination. These programs induce unfair competition by using asymmetric rules. Assume that employers can be forced to employ worker L with certainty if a tie Occurs
xL,(O, 0) = xL,(0_, _0) = 1, x~r (0, 0) = x/_r(_0, _0) = 0.
(7)
We assume third-degree wage discrimination to be allowed if it benefits the protected g r o u p L. PROPOSITION 4: Affirmative action leads to the same rent distribution as in the unrestricted mechanism, but worker L is always employed in state (0, 0). Welfare is the same as in the unrestricted mechanism. PROOF: M a x i m i ~ the employer's profit in expression (11) subject to equation (7). 168¢e §612 BGB and Schaub (1988), RdNr.262-268. 17I am very grateful to an anonymous referee who indicated the interesting consequences of this set of assumptions and who made me think about the efficiency effects of non-discrimination rules in general. 181t is straightforward to show that this also holds for the strict non-discrimination rule in combination with the symmetric tie rule. 19One of the rules for employment in the public sector states that when two job applicants are equally qualified and one of them is a woman, the woman should be employed.
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When incentive contracts are auctioned off, affirmative action programs have almost no effect on the o u t c o m e if "reverse" wage discrimination is allowed, i.e., if worker L may be paid more for the same output than worker H. The only difference is that the rule favoring worker L results in the g o o d type of g r o u p L being employed more often than she would be without the rule. Effort in state (_0,_0) and thus total welfare defined as the sum of the employer's and the worker's rent are the same as in the unrestricted mechanism.'m We have assumed in all three subsections that hiring decisions are expost optimal, i.e., that it does not pay to exclude bad types ex ante to reduce information rents. However, u n d e r e m p l o y m e n t may occur in all three settings if the expected profit from employing a worker in state (_0, _0) is smaller than the expected rent payment in all other states (analogous to Corollary 1). In this case the employer offers only one contract, which violates a bad type's participation constraint and leaves no rent to a g o o d type. IV. Conclusion Some of the results in this paper contradict conventional knowledge about discrimination on the labor market. First, optimal screening mechanisms can lead to preferential treatment of on average less productive workers. Second, legal remedies against discrimination such as the prohibition of wage discrimination on the basis of visible characteristics or rules governing the hiring decision can have adverse effects on the on average less productive group. Third, if the prohibition of wage discrimination is justified by arguments of fairness and equal treatment, not by redistributive goals, legislators must still take into account that total welfare can be affected by these measures. Finally, the relevance of screening contracts for labor markets should be discussed. Auction-like hiring and contracting procedures are mainly found in areas where great uncertainty about the value of the j o b and the ability o f the applicants prevails. In transition economies m or in business areas undergoing rapid technological change or change in consumer tasteY thcre are no fully functioning labor markets where information about applicants and jobs can be derived from long-term observation. Weiss (1995) argues that the more highly developed a society, the greater is the proportion of jobs for which productivity is not directly observable and the more important screening becomes. Rules governing labor contracts have to adjust to the contracting practices used in these situations to achieve the desired allocative and distributional ends. Appendix
Proof of Proposition Some reformulations are helpful to transform the constrained maximization problem into an unconstrained program. O u t p u t y is replaced by 0 + e and the expected rent payments U/, i -- H, L, are used to eliminate wages, ~°Interesting effects have been discovered in experiments as to how agents actually respond to a contractual and legal environment. For example, in tournaments with asymmetric agents, affirmative action programs can increase the principal's profits. In theory, affirmative action programs favoring less productive agents in a tournament setting lead to lower effort levels of the favored group, therefore also to lower effort levels of the competing group of more productive agents and to lower profits of the tournament administrator. The experiments of Schotter and Weigelt (1992) suggest, however, that profits may increase with affirmative action because fewer low-productivity agents drop out with dropouts leading to lower effort levels of the high-productivity group. 21There is evidence from China that managers are selected via auctions and are subsequently forced to pay a fixed sum to the municipal authorities. See Groves et al. (1995). 22An example given in Milgrom and Roberts (1992) and McAfee and McMillan (1987) is the mechanism used by IBM to elicit information from their sales persons about the potential of a sales territory.
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E0,,0L [U/(0~, 00] = E0,,0L [wi(0H, 00 -xi(OH, 00+(yi(0H, 00 -0i)].
(8)
Only the incentive constraint of a g o o d type a n d the participation constraint of a b a d type are binding. Using these constraints and ~ ( • ), the e x p e c t e d rent of a g o o d type of w o r k e r H can be written as E0L [ UH(-6, eL)] :VLXI-I(O__, -6)~(eH(0, -6)) + (1 -vL)xn(O_, _0)~(er/(_0, _0)),
(9)
a n d of w o r k e r L Eo. [ UL(OH, -6)] = VHXL(-6, O_)dP(eL(-6, 0_)) + (1 - V.)XL(O__, O__)dP(eL(O__, _0)).
(10)
Plugging in the rents and writing out the e x p e c t e d value, the profit P of the e m p l o y e r becomes v , ~ L [ x ~ O , 0)(o + e~(O, 0) - +(ell(O, o)) + x L (0, 0)(0 + eL(O, O) -- +(eL(O, 0))] + v~l
(11)
- vL)[xn(O, 0__)(-6+ en(O, 0_) - +(en(-6, 9_)) + x L (-6, _0)(_0+ eL(-6, _0) - +(eL(-6, 0_))]
+ vL(1 - vH)[x~(0, -6)(0 + e ~ 0 , -6) - + ( e ~ 0 , -6)) + x L (0_, 0)(0 + eL(O,-6) -- +(eL(O_, -6))]
+ (1 - VH)(1 - VL[Xn(O, 0_)(0__+ eo(O_, 0_) - +(en(O, 0_)) + x L (0_, 0_)(0_ + eL(O , 0__)-- +(eL(O , _0))1 - VI4VL[XH(O_, -6)dP(e/4(_O, -6)) + XL(-6, _O)dP(eL(-6,0))]
- (1 - VL)VHXo(O_, O__)¢P(eH(O_,0__))-- (1 -- YH)PLXL(O, O_)~P(ez(O__,0))] subject to the constraints i - XH(k, I) - xL(k, l) > 0 Vk, l = 0_, -6
with the L a g r a n g e multipliers h 1, h2, h3, a n d h4, a n d non-negativity of all xi(On, 0 i ) . Expression (11) is m a x i m i z e d with respect to ~q (0~r, 0L) a n d ei(On,_OL .2a The_oj~timal effort levels follow f r o m the K u h n - T u c k e r conditions, en(0, 0) = ell(0, 0__) = eL(0 , 0) -- eL (_0, -6) = e* and ])i
t
+'(e~) = 1 - _--_---~ 1 • (e~), i = H , L
(12)
with e H = ell(_0, -6) = el-i(o_o_,_0) and ~ = eL(-6, 0_) = eL(0, 0_). F r o m equation (12) and the convexity of +(e) follows that the o p t i m a l effort of a b a d type, e~, is lower than the first best effort level e*. Differentiating e q u a t i o n (12) with respect to vHyields 0 e l l / Or/4 < 0. This proves s t a t e m e n t 2 of Proposition 1. F r o m the K u h n - T u c k e r conditions" follows 2SThe first-order conditions are sufficient for a m a x i m u m , because the objective function is concave in el(OH, OL), linear in xi(On, Or), a n d all cross-derivatives except P'i~, a n d P,i,i vanish. Thus, the Hessian matrix is negative semidefinite.
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Auctioning off labor contracts
that xH (0, 0_), = xL(-0, 0) = 1 a n d x,q(0, 0) + xL(0, 0) = 1. In state (_0, _0), w o r k e r L gets the j o b if the following i n e q u a l i t y h o l d s strictly
eL
-
+(e~)
-
v-----5--L - 1 1 v L qb(et')/> £1-1-+(el-I) -
PH -
vz_i ¢p(eI4)" -
(13)
This is always the case as
- +(a)-
vL
1 - ,,,---~
~(_ec) = m a x
> -~'-
e - ~(e) - 1
+(-~")
> £ H - q~(e_~)
1 - vl~
- - -
- 1 - ,,-----~,t,(_~,).
Thus, x/~(O_.,_0) -- 0 a n d PL
xL(-0, -0) = 1 if_0 + eL - +(£/) - 1 - v L ~ ( £ ' ) ~> 0,
(14)
xL(_0, _0) = 0 otherwise. This proves s t a t e m e n t 1 o f P r o p o s i t i o n 1. S t a t e m e n t 3 follows f r o m the b i n d i n g particip a t i o n c o n s t r a i n t o f a b a d type a n d f r o m p l u g g i n g the o p t i m a l p r o b a b i l i t i e s into equations (9) a n d (10). Proof of Proposition 2 Maximize the e m p l o y e r ' s p r o f i t f u n c t i o n (11), subject to e q u a t i o n (5), a n d the corres p o n d i n g c o n s t r a i n t for efforts, as well as e q u a t i o n (6), a n d the c o n s t r a i n t 1 - xL(0, -0) - xL(-0, 0) t> 0. T h e o p t i m a l effort level w h e n b o t h workers are u n p r o d u c t i v e m a x i m i z e s (1 - vL)(-0 + e,(0 -0) - +(6(_0, _0))) -
(1 - v,.)vtt + (1 - Vl4)V L ¢P(e,(-0, 0_)), i = H, L 2(1 - vt/) (15)
whereas the o p t i m a l eL in the u n r e s t r i c t e d m e c h a n i s m m a x i m i z e s (1 -- VL)(--0 + e.e/..- (~(_.gL) -- OL(I)(e_L))"
(16)
A s v L is smaller t h a n the fraction in e x p r e s s i o n (15), el(-0 , -0) < e L. Proof of Proposition 3 In a s e p a r a t i n g e q u i l i b r i u m , all g o o d types are i n d u c e d to c h o o s e the efficient effort level e* a n d all b a d types receive the wage w = +(el(-0, -0)), i = H, L. M o r e o v e r , the incentive constraints for g o o d types of H a n d L are satisfied. T h e e m p l o y e r always chooses a g o o d type 0 if she r e p o r t s a strictly h i g h e r productivity t h a n h e r rival, b e c a u s e h e r effort is n o t d i s t o r t e d a n d pays h e r the wage w. Define ~H: = vLxi:i (0, 0) + (1 - vL)
D. KI]BLER
73
a n d ~L: = VH(1 -- XH(0, 0)) + (1 -- VH) as the p r o b a b i l i t i e s t h a t w o r k e r H o r w o r k e r L are e m p l o y e d if they r e p o r t 0. T h e incentive c o n s t r a i n t s o f g o o d types can b e written as
~/t [ ~ - +(e~)] I> (1 - v0x,~(0, 0)~(e,~(0, 0)) {c [ ~ - qb(e*)]/> (1 - v , ) ( 1 - xh(_0, 0_))q)(eh(_0, 0)). In e q u i l i b r i u m they m u s t h o l d as equalities. Thus, wage ~ i n d u c e s t r u t h t e l l i n g if it satisfies
W = 6(e*) + max
{(1-- VL)XfI(O_, O) (1-- V/t)(1-- xH(O_, O_))} ~H ' -~L ¢P(eH(O_,0_)).
Because b o t h fractions are m o n o t o n o u s in xt) (0_, 0_), the wage o f a g o o d type is minim i z e d by c h o o s i n g xH(_0, 0_) such t h a t b o t h fractions in the m a x i m u m e x p r e s s i o n are equal. T h i s yields an o p t i m a l x h (0_, O) o f (1 - v / t ) ~ / t
xgt (_0, 0_) - (1 - VL)~L-[- (1 - v/t)~t-/"
(17)
T h e r i g h t - h a n d side o f e q u a t i o n (17) is i n c r e a s i n g in xB(0, 0) which yields x/:/(0, 0) = 0 a n d thus x/:/(0_, 0_) = (1 - v/t) / (2 - v/t). This proves s t a t e m e n t 1 as ~ = ~b(e*) + xt~(0_, O) (I)(e~(_O, _0)). T h e e m p l o y e r c h o o s e s the o p t i m a l effort of a b a d type el(O, _0) by m a x i m i z i n g his profits given the o p t i m a l p r o b a b i l l i t i e s j u s t derived, 1 - v " ~(e,.(O, 0))] (V/t + VL(1-- V11))[ 0 + e* - ~b(e*) - ------~.. v2 _ _ __ + (1 - v/t)(1 - vO[ ~ + e~(0_,_0) - 6(el(0_, _0))]. T h e o p t i m a l e~(0_, 0), i = H, L m a x i m i z e s (1 - VL)[O - + ee (0__,O) + dp(ee(0__,0_9_)]
V/_/'I- VL(1 --
(2--v/~
V/t)
4P(ei (0_, _0)).
(18)
Because the f r a c t i o n in e x p r e s s i o n (18) is g r e a t e r t h a n v L in the u n r e s t r i c t e d m e c h a nism [see e x p r e s s i o n (16)], it follows t h a t e(0_, 0) = eL (0_, 0_) < eL. This proves statem e n t 2.
References ARROW, KENNETHJ. (1973). The theory of discrimination. In Discrimination in Labor Markets. Orley Ashenfelter and Albert Rees (eds.) Princeton, New Jersey: Princeton University Press, pp. 3-42. BRANCO, FERNANDO.(1994). Favoring domestic firms in procurement contracts. Journal of International Economics 37:65-80. GIBBONS, ROBERT. (1987). Piece-rate incentive schemes. Journal of Labor Economics 5:413-429. GROVES,THEOI)ORE,HONG, YONGMXAO,McMILLAN,JOHN, ANDNAUGHTON,BARRY.(1995). China's evolving managerial labor market. Mimeo. GUASCH,J. Luts, and WEiss, ANDREW.(1981). Self-selection in the labor market. American EconomicReview 71:275-284. K~aLER, DOROTHEA. (1995). Auctioning off labor contracts: Legal restrictions reconsidered. Discussion Paper 22, SFB 373, Humboldt Universitfit zu Berlin.
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LAFFONT, JEAN-JAcQUES, AND TIROLE, JEAN. (1987). Auctioning Incentive Contracts. Journal of Political Economy 95:921-937. LAFFONT, JEAN-JACQUES, AND TIROLE, JEAN. (1993). A Theory of Incentives in Procurement and Regulation Cambridge, Massachusetts: MIT Press. MC,AdEE, R. PRESTON, AND McMILLAN, J. (1987). Competition for agency contracts. Rand Journal of Economics 18:296-307. MCAFEE, R. PRESTON, AND McMILLAN, J. (1989). Government procurement and international trade. Journal of International Economics 26:291-308. MILGROM, PAUL, AND ROBERTS,JOHN. (1992). Economics, Organization and Management Englewood Cliffs, New Jersey: Prentice-Hall. MYERSON, ROGERB. (1981). Optimal auction design. Mathematics of Operations Research 6:58-73. PHELPS, EDMUNDS. (1972). The statistical theory of racism and sexism. American Economic Review 62:659661. SALOP, JOANNE, AND SALOP, STEVEN. (1976). Self-selection and turnover in the labor market. Quarterly Journal of Economics 90:619-628. SCHAUB, GUNTHER. (1988). In §612 BGB Munchner Kommentar zum BGB, Schuldrecht AT, 2nd ed, Mfinchen: Beck, pp. 1392-1460. SCHOTTER,A., ANDWEIGELT,K. (1992). Asymmetric tournaments, equal opportunity laws, and affirmative action: Some experimental results. QuarterlyJournal of Economics 52:511-539. StDLLNER, ALLFRED. (1988). 611a BGB In Miinchner Kommentar zum BGB, Schuldrecht AT, 2nd ed., MtSnchen: Beck, pp. 1381-1390. WEISS, ANDREW. (1995). Human capital vs. signalling explanations of wages.Journal ofEconomicPerspeaives 9:133-154.
Institut f u r Wirtschafistheorie I, Humboldt-Universitdt zu Berlin, Berlin, Germany E-mail: kuebler@wiwi, hu-berlin, de
The paper analyzes the effects of various non-discrimination rules when the employer uses an optimal screening mechanism in the presence o f moral hazard and adverse selection. T h e optimal contracting mechanism for heterogeneous workers (with different probability distributions over types) exhibits third-degree wage discrimination, which is beneficial for on average less productive workers. Imposing non-discrimination restrictions on wages and hiring decisions may harm the on average less productive group and reduces efficiency. Affirmative action programs are neutral with respect to rent distribution and efficiency. © 1997 by Elsevier Science Inc. I. I n t r o d u c t i o n
W h e n employers have vacancies, they often have to choose a m o n g a n u m b e r of applicants who are not all equally suited to the job. It is difficult to find the best candidate if educational records, past work experience, and general abilities that can be tested via j o b interviews are of relatively little relevance to the worker's actual performance on the job. But workers themselves often know better than the employer how well they are suited to a job. T h e model presented below applies to such a situation where the n u m b e r of j o b candidates is limited. Workers know that there is some competition for the job, but they also try to exploit their private information by misrepresenting their true productivity. In a situation like this, it is optimal for the employer to use an auction-like mechanism that selects the best applicant and provides work incentives at the lowest possible wage. The optimal contracting mechanism can be described as follows: The employer offers a m e n u o f contracts, each of them specifying a wage and a certain output. The wage not My thanks go to H u g h Gravelle, Peter Jost, Steinar Vagstad, Elmar Wolfstetter, a n d conference participants at the EALE 1995 in Bern. I am especially indebted to three anonymous referees a n d an editor for their helpful suggestions. Financial support from the Norwegian Research Council (Ruhrgas) a n d the Deutsche Forschungsgemeinschafl, SEB 373 ("Quantifikation u n d Simulation 6konomischer Prozesse"), is gratefully acknowledged.
International Review of Law a n d Economics 17:63-74, 1997 © 1997 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
0144-8188/97/$17.00 PII S0144-8188(96)00059-2
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Auctioning off labor contracts
only d e p e n d s on output, b u t also on the rivals' a n n o u n c e d types. Applicants choose a level o f o u t p u t (implying an e x p e c t e d wage), a n d thereby reveal their type. T h e n the e m p l o y e r decides w h o m he will actually employ. W h e n incentive contracts are auct i o n e d off, the auction m e c h a n i s m chooses the best applicant a n d the contract assures that the worker does n o t shirk. As has b e e n shown by Laffont a n d Tirole (1987, 1993) in a p r o c u r e m e n t setting, optimal incentives are invariant to the n u m b e r of c o m p e t i n g workers (separation property). O n l y the profit o f the e m p l o y e r a n d the information r e n t of a g o o d type d e p e n d on the n u m b e r of c o m p e t i n g j o b applicants. Now, consider the case in which workers are h e t e r o g e n e o u s in that they have different probabilities for being a g o o d o r a bad type. It is assumed for simplicity that there are only two possible types o f workers. If the e m p l o y e r can distinguish between groups o f applicants on the basis o f visible characteristics such as race, sex, or age, 1 he will, in the optimal mechanism, offer different m e n u s o f contracts to different groups. This is a form of third-degree wage discrimination where g r o u p characteristics are used as a signal for the productivity o f its members. It is a well-known result from the theory of auctions with asymmetric bidders that it can be optimal to favor a b i d d e r with a lower average valuation, i.e., the item m i g h t be awarded to s o m e o n e o t h e r than the b i d d e r who values it most. This extends to an auction of contracts where a worker whose probability o f being a b a d type is high should be favored. T h e p a p e r confronts the optimal m e c h a n i s m with legal restrictions on third-degree wage discrimination. T h e general principle is that workers may be g r o u p e d a n d treated differently only on the basis of " r e l e v a n t " characteristics, z T h e laws governing differential t r e a t m e n t o f workers have b e c o m e m o r e a n d m o r e specific over the past few decades, b u t G e r m a n labor law seems to take notice of new forms o f contracting only to a limited extent. Jurisdiction is mostly c o n c e r n e d with cases where discrimination entails disadvantages for on average less productive worker groups. A l t h o u g h this effect o f discrimination exists in a n u m b e r o f contexts, the p a p e r shows that it is necessary to investigate discrimination in different contracting environments carefully if the legal rules are to have the desired impact on efficiency a n d distribution. In Section II the m o d e l of Laffont a n d Tirole (1987, 1993, Ch. 7) is r e f o r m u l a t e d in terms o f the labor contract setting with h e t e r o g e n e o u s workers. 3 Section III introduces various legal restrictions and analyzes their impact on efficiency and distribution. Finally, Section IV draws some conclusions. Proofs are relegated to the A p p e n d i x .
~This is also the starting point for theories of statistical discrimination that argue that wage differentials between certain distinguishable groups o f workers can be explained by different expected productivities o f these groups. An assumption underlying this result is that all types f r o m o n e g r o u p o f workers are pooled, i.e., there are no intra-group wage differentials. See for e x a m p l e Phelps (1972) or Arrow (1973). ZHowever, it is not always clear which are the relevant ( " s a c h g e r e c h t " ) a n d the irrelevant ( " s a c h f r e m d " ) characteristics of a worker or a g r o u p of workers with respect to a particular task. In the United States, e m p l o y m e n t discrimination law even restricts the use of seemingly neutral selection criteria that have an adverse impact on a protected g r o u p (disparate impact doctrine). If a selection criterion excludes workers o f a specific race, sex, or ethnicity at a significantly higher rate than it excludes workers o f a n o t h e r group, the e m p l o y e r has to prove that the criterion is in fact j o b related. 3For an application of the L a f f o n t / T i r o l e m o d e l to the labor context see also Gibbons (1987). A classical screening m o d e l is Salop and Salop (1976) where the worker's propensity to quit is private information. Guasch and Weiss (1981) develop a m o d e l where workers are screened via tests including test fees that have to be paid in advance a n d function as an e n t r a n c e fee.
D. KUBLER
65
II. O p t i m a l Mechanism The Model
W o r k e r i p r o d u c e s an o u t p u t Yi, which d e p e n d s o n h e r " p r o d u c t i v i t y " 0 i a n d h e r effort e,. T h e p r o d u c t i o n function takes the additive form Yi = Oi + ei. T h e e m p l o y e r observes the worker's o u t p u t Yi, b u t n e i t h e r h e r type 0i n o r h e r effort e~. T h e r e are two types o f workers with productivity 0 (productive type) a n d 0_ (unproductive type) with A0 = 0 - 0__> 0. Visible characteristics exist by which the e m p l o y e r can distinguish different groups o f applicants. Assume that worker H a n d worker L (which are drawn from g r o u p H a n d L) differ with respect to their probability o f b e i n g productive, vi, with vH> vL. F o r example, the probability of a w o m a n for b e i n g a productive type may be lower t h a n the probability of a m a n for b e i n g productive. T h e s e probabilities are c o m m o n knowledge, a n d a worker knows h e r actual type 0 before the c o n t r a c t is offered. T h e r e are two workers c o m p e t i n g for the j o b , o n e from g r o u p H a n d one from g r o u p L. W o r k e r i (i = H, L) chooses an effort level ez which is assumed to be strictly positive over the relevant r a n g e of e q u i l i b r i u m efforts. 4 Effort e; causes h e r to have a disutility o f d~(ei). Total utility o f a risk-neutral worker i is given by the difference between h e r wage w i a n d h e r disutility o f effort, w i - d? (ei). T h e reservation utility is zero. A g o o d type c h o o s i n g the same y as a b a d type earns a r e n t o f ~ ( e i ) with di'(ei) = d~(ei) - d?(ei- A0). T h e disutility function is strictly increasing a n d convex in effort, d~' > 0 a n d qb" > 0, a n d the third derivative is non-negative, qb" -> 0, which makes the r e n t function ~(ei) convex. T h e e m p l o y e r ' s profit is equal to Yi - wi. With full i n f o r m a t i o n the e m p l o y e r forces the worker to choose the first best level e'* with d~' (e*) = 1 a n d pays h e r a wage o f ~b(e*). It is assumed that, in the case o f full information, the e m p l o y e r makes a positive profit even if a b a d type is hired, _0 + e* - ~b(e*) > O.
Solution
T h e revelation principle implies that the search for the optimal allocation rule can be restricted to direct mechanisms. T h e optimal incentive c o m p a t i b l e m e c h a n i s m relates the probability of winning xi(0_~t,{)£), the wage wi (0/-/, 0£), a n d the o u t p u t level Yi(~)H, {)L) to the a n n o u n c e d types (OH, 0L), i = H, L. T h e time structure o f a direct m e c h a n i s m is the following: First, the e m p l o y e r a n n o u n c e s a set of functions (xi(.), wi(. ), Yi(.)). T h e n b o t h workers reveal their types. Finally, one of the workers is selected, p r o d u c e s an output, a n d receives a wage a c c o r d i n g to the contract. T h e probabilities o f winning are non-negative a n d must satisfy the b u d g e t constraint (there is only o n e vacancy), +
1
X,(t,, tI) ~ O
(1)
i-~- H, L.
4This assumption is made for the sake of expositional clarity, see Laffont and Tirole (1993).
(2)
66
Auctioning off labor contracts
For truth telling to be a Bayesian-Nash equilibrium, it must h o l d that 0/~-- OH maximizes the utility o f worker H given that worker L tells the truth, 0H~ arg max EoL [wit (OH, OL) -- XH(~)H, OL)+(yH(~)H, OL) -- OH)] for 0 n = 0,0
(3)
a n d analogously for worker L. T h e two participation constraints for each type o f worker H are E% [wH(0/_/, 0L) - x/-/(0H, OL)d~(yH(O,, 0L) - On)] --> 0 for OH= _0,0
(4)
with two c o r r e s p o n d i n g constraints for worker L. T h e e m p l o y e r maximizes his e x p e c t e d profit subject to the constraints (1), (2), (3), a n d (4) as well as the constraints corres p o n d i n g to (3) a n d (4) for worker L. Solving this c o n s t r a i n e d p r o g r a m leads to the following proposition, which is a straightforward generalization o f Proposition 7.1 in Laffont a n d Tirole (1993). PROPOSITION 1: (1) If a good type competes with a bad type, the good type is always awarded the
contract, irrespective of t_he_group she belongs to. If both applicants are good types, any solution is optimal as long as x14 (0, O) + x L (0, O) = 1. If both workers are bad types, the workerfrom group L is awarded the contract. (2) The optimal effort level of a good type equals thefirst best level in both groups of worhers, gH = ~1. = e*. The optimal effort level of a bad type is lower for worher H than for worker L, eH < eL < e*. (3) The rent of a good type from group H who competes with a bad type from group L is zero, but a good type from group L who competes with a bad type from group H earns an information rent. Wage is equal to the disutility of effort if two good types or two bad types compete. T h e e m p l o y e r discriminates between h e t e r o g e n e o u s workers. It is optimal for him to favor m e m b e r s o f the disadvantaged group. In the case o f two b a d types, worker L is e m p l o y e d because h e r o u t p u t is closer to the first best level than the o u t p u t o f a b a d type o f worker H. Therefore, worker H w h o is m o r e efficient in expectation receives no rent as a g o o d type because she loses h e r j o b with certainty when mimicking a b a d type. Wages are discriminatory as WH (0, 0) = ~b(e*), but, WL (_90,0) = 6 ( e * ) + XL (0_, O)~(ez) (with x L (0, 0) = 1 if the e m p l o y e r does n o t exclude all bad types ex ante; see Corollary 1). Thus, worker L is e m p l o y e d as a b a d type a n d receives an i n f o r m a t i o n r e n t as a g o o d type. 5 Notice also that the wage of a g o o d type o f worker L d e p e n d s on h e r rival's type as she does not earn a r e n t when c o m p e t i n g with a g o o d type, WL (0, 0) = ~b(e*). COROLLARY 1: If the probability of being a good type in group L is sufficiently high, no bad type
will be employed and good types from both groups do not earn a rent. PROOr: See expression (14) in the A p p e n d i x . It can be optimal for the e m p l o y e r to only offer a contract to the g o o d type, 6 i.e., xH(_0, 0_) = xL(O, 0) = 0. T h e n , the information r e n t o f a g o o d type o f worker L is r e d u c e d to zero because she c a n n o t mimic a bad type without losing the j o b with certainty. 7 As a b a d type o f worker H never gets the job, the cutoff rule is only relevant for worker L. 51f g r o u p s H a n d L differ with respect to the s u p p o r t o f 0 a n d g r o u p H is o n average m o r e productive, the optimal m e c h a n i s m has the following properties. If0/4 > 0L, t h e n A0H > A0 L a n d thus _eL > ell j u s t as above w h e r e v n > v L. But if 0 f t > _0L, then A0 H < A0 L a n d thus _eL < .~, which reverses the result. T h e smaller the difference between types ( h o l d i n g the distribution constant) a n d the smaller the probability o f a g o o d type ( h o l d i n g the difference between types constant), the m o r e this g r o u p is favored over the other. Olt is a s s u m e d that a wage o f w = 0 does not attract a worker even if h e r disutility o f effort is zero. Thus, a bad type is n o t e m p l o y e d as l o n g as she does n o t receive a positive wage i n d u c i n g a positive effort level. 7In an earlier version o f the p a p e r [K/ibler (1995) ], a Vickrey auction o f f r a n c h i s i n g contracts is analyzed w h e r e a
D. KUBLER
67
In auctions with asymmetric bidders where a g o o d instead of a contract is sold, probabilities of winning are used to elicit higher bids from bidders with a higher willingness to pay. McAfee and McMillan (1989) and earlier Myerson (1981) show that the auctioneer's optimal policy is discriminatory in that one bidder may win although another bidder assigns a higher value to the object. In a second price a u c d o n optimal favoritism can be implemented by a simple rule (constant price preference), but the rule becomes rather complex when a first price auction is used [see Branco (1994)]. If a contract is auctioned off, the employer controls an additional variable (the wageoutput scheme), which he uses to extract rents. It may then be profitable not to employ the best worker applying for the j o b if her effort is more distorted. 8 T h e optimal mechanism selecting the best worker is not Pareto efficient. It may fail to employ a worker in state (_0,_0), although there are possible gains from the contract. 9 This leads to u n d e r e m p l o y m e n t due to asymmetric information between the worker and the employer. The higher the probability of a g o o d type in g r o u p L, the more likely a bad type will not be offered a contract. Thus, an increasing n u m b e r of qualified workers may cause u n d e r e m p l o y m e n t of the unqualified workers for reasons of information costs. The model allows for the fact that g r o u p H earns more on average than group L and workers of g r o u p H are employed more often because the situation where a g o o d type of worker H c o m p e t e s with a bad type of worker L is very likely. Thus, wage differentials can be reduced by raising the average productivity of g r o u p L. III. Legal Restrictions on Wage Discrimination Wage differentials on the grounds of irrelevant properties such as race, sex, religion, origin, political conviction, belief, language, or union membership are prohibited. 1° In addition, the Treaty of Rome made discrimination on the basis of nationality unlawful) 1 Equal treatment of men and women has received growing attention over recent years. Apart from the constitutional guarantee of equal rights, 12 there are rules requiring equal pay 1B and prohibiting indirect discrimination by the employer, a4 The enforcem e n t of these rules interferes with the employer's ability to use the optimal mechanism described above. In two o f the following three subsections, a non-discrimination restriction is imposed on the m e n u of contracts, which requires worker H a n d worker L to be offered the same menu. This rule seems to be undisputed and relatively easy to enforce. However, the hiring decision and randomization between equally qualified workers cannot be observed as easily as a contract. The case of perfect observability and the case of complete bad type of group H is cut off with a higher probability than a bad type of group L (via minimum bids). Thus, discrimination is also favorable for worker L when franchising contracts are auctioned off. ~l'he finding that the best worker is always employed is an artifact of the two-type case. Only the highest type, 0, is always employed, regardless of which group she belongs to. '~A crucial assumption of the model is that the terms of the contract cannot be changed either unilaterally by the employer or by mutual consent after the worker has announced her type. In an auction-like mechanism the best type must be picked before production takes place. Thus, there is always an incentive to adjust the inefficient effort e to e* or to hire a worker in state (_0,0_). The optimal mechanism is only implementable if the employer can commit himself to the menu of contracts. l°In Germany this follows from Art. 3 III GG. llSee Art. 48 III EWGV. 12See Art. 3 II GG. 13See Art. 119 EWGV and §612 III 1 BGB. 14See §611a BGB and Stllner (1988).
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Auctioning off labor contracts
non-observability are analyzed below. A third possibility to restrict the o p t i m a l mechanism is to stipulate that the same wage be paid for the same output, which a m o u n t s to disallowing for wages that are c o n t i n g e n t on the rival's type.
Non-Discriminatory Wages and Symmetric Tie Rule Suppose the courts can enforce the rule that equally productive workers must receive the same contract when the context, i.e., the rival's productivity, is the same. Thus, wage a n d o u t p u t have to be equal for worker L a n d H in each possible state o f the world:
w,:/(0, 0) = wz(0, 0), w,0(0, _0) = w,;(0, ~),
w,:,(0, 0) = wL(0, 0), w~(_0, ~) = w/.(~, 0).
(5)
T h e same must h o l d for efforts e/:/(. ) a n d e£(. ). Assume that after the workers choose from the m e n u , i.e., reveal their types, the firm's hiring decision can be observed. C o n s i d e r an e n f o r c e a b l e rule that states that equally qualified workers should be awarded the contract with equal probability. 15 In addition, hiring rules must be symmetric when worker types differ. Thus, for i = H, L x,-(0, 0) = xr(_0, _0) = ½, XH(0, _0) = x/:(_0, 0), x~,(_0, 0) = X£(0, _0).
(6)
T h e e m p l o y e r maximizes his profit subject to the legal constraints i m p o s e d on the contract a n d on the hiring decision. T h e p r o p e r t i e s of the optimal contract are summarized in PROPOSITION 2: (1) If a good type competes with a bad type, the good type is always awarded the
contract and receives an information rent. I f two good types or two bad types compete, the wage is equal to thedisutilit_t_tj o f effort_ (2) The optimal effort level of a good type is equal to the first best level, e/~(0, 0) = e£(0, O) = ei~(O, ~ = e£(O_,"0) = e*. The optimal effort level of a bad type is smaller than the optimal level of a bad type without a non-discrimination rule, ell(O_, 0_) = e£(O, 0_) < eL < e*. Thus, welfare is lower than in the unrestricted mechanism. W o r k e r H gains from the non-discrimination rule. As an u n p r o d u c t i v e type, she is e m p l o y e d with a probability o f 50% and as a g o o d type she earns an information r e n t o f 1/2+ (e,e/(_0,_0)). W o r k e r L's information r e n t is lower than in the unrestricted mechanism for two reasons. First, the effort o f a bad type is lower (e£(0, _0) < eL) and, second, she receives only 50% o f the m a x i m u m rent +(e/:(0, _0)). T h e e m p l o y e r is worse off u n d e r this non-discrimination regime because additional constraints are i m p o s e d on his decision. O u t p u t is affected by the legal rules only in state (_0,_0). Because it is smaller than in the unrestricted mechanism, the non-discrimination restrictions r e d u c e efficiency.
Equal-Pay-for-Equal-Work Rule and Non-Observability of Randomization In this section, the m e n u o f contracts does n o t only have to be the same for both workers H a n d L, but workers must also be p a i d the same wage for the same output. This equal-pay-for-equal-work rule implies that the context, for e x a m p l e the n u m b e r a n d ability o f c o m p e t i n g workers who could do the j o b , may n o t be a d e t e r m i n a n t o f wages. ~Whether employers abide by this rule can be checked either if the act of randomizing is monitored by the court (flip a coin for example) or, more importantly, by observing a series of hiring decisions of an employer over time.
D. K/JBLER
69
In Germany, there are rather strict criteria to ascertain equivalence of jobs that necessitate equal pay. 16 This implies, for example, that workers on equivalent jobs must receive the same wage although there are many equally qualified workers for one j o b whereas there is only one qualified applicant for another job. The second new assumption made in this section is that the employer's randomization between equal types is not observable) 7 Thus, the_employ__er is obliged to offer the wage ~ for a good type's effort level e/~(0, 0) = eL(O, O) = ei:l(O, 0_) = eL(O_, "6) and w for a bad type's effort level e~/ (0_, 0) = e£(0_, _0), but he can choose any probabilities xA0_, _0) and x¢(0, 0), i = H, L. PROPOSITION 3: (1) If two good types compete, worker L always gets the contract. If two bad types compete, worker L gets the contract with probability xL(O_, ~ = 1/(2 - vH). A good type who is awarded the contract always receives an information rent. (2) Effort in state (0_, 0_) is smaller than in the unrestricted mechanism, ei:l(O_, O_O_OQ = eL(O, O) < e L. Thus, total welfare is below that of the unrestricted mechanism. The strict non-discrimination rule with respect to wages together with the optimal probabilities leads to efficiency losses compared to the full discrimination case. 18 The freedom to choose optimal probabilities when both workers are equally qualified means that the employer always chooses worker L in state (0, 0) (remember that he was indifferent in the unrestricted mechanism). However, worker L is not always employed in state (_0,_0) as in the unrestricted mechanism, but only with probability 1/(2 - vn). Thus, the effect of the restrictions is ambiguous because a good type of worker His never employed in the case of a tie, but rent is redistributed from worker L to worker H.
Affirmative Action Suppose g r o u p L's lower average productivity results from historical discrimination, which manifests itself in lower levels of education. Affirmative action programs or equivalent rules that exist in some of the German states t9 are m a n d a t e d to compensate for past discrimination. These programs induce unfair competition by using asymmetric rules. Assume that employers can be forced to employ worker L with certainty if a tie Occurs
xL,(O, 0) = xL,(0_, _0) = 1, x~r (0, 0) = x/_r(_0, _0) = 0.
(7)
We assume third-degree wage discrimination to be allowed if it benefits the protected g r o u p L. PROPOSITION 4: Affirmative action leads to the same rent distribution as in the unrestricted mechanism, but worker L is always employed in state (0, 0). Welfare is the same as in the unrestricted mechanism. PROOF: M a x i m i ~ the employer's profit in expression (11) subject to equation (7). 168¢e §612 BGB and Schaub (1988), RdNr.262-268. 17I am very grateful to an anonymous referee who indicated the interesting consequences of this set of assumptions and who made me think about the efficiency effects of non-discrimination rules in general. 181t is straightforward to show that this also holds for the strict non-discrimination rule in combination with the symmetric tie rule. 19One of the rules for employment in the public sector states that when two job applicants are equally qualified and one of them is a woman, the woman should be employed.
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Auctioning off labor contracts
When incentive contracts are auctioned off, affirmative action programs have almost no effect on the o u t c o m e if "reverse" wage discrimination is allowed, i.e., if worker L may be paid more for the same output than worker H. The only difference is that the rule favoring worker L results in the g o o d type of g r o u p L being employed more often than she would be without the rule. Effort in state (_0,_0) and thus total welfare defined as the sum of the employer's and the worker's rent are the same as in the unrestricted mechanism.'m We have assumed in all three subsections that hiring decisions are expost optimal, i.e., that it does not pay to exclude bad types ex ante to reduce information rents. However, u n d e r e m p l o y m e n t may occur in all three settings if the expected profit from employing a worker in state (_0, _0) is smaller than the expected rent payment in all other states (analogous to Corollary 1). In this case the employer offers only one contract, which violates a bad type's participation constraint and leaves no rent to a g o o d type. IV. Conclusion Some of the results in this paper contradict conventional knowledge about discrimination on the labor market. First, optimal screening mechanisms can lead to preferential treatment of on average less productive workers. Second, legal remedies against discrimination such as the prohibition of wage discrimination on the basis of visible characteristics or rules governing the hiring decision can have adverse effects on the on average less productive group. Third, if the prohibition of wage discrimination is justified by arguments of fairness and equal treatment, not by redistributive goals, legislators must still take into account that total welfare can be affected by these measures. Finally, the relevance of screening contracts for labor markets should be discussed. Auction-like hiring and contracting procedures are mainly found in areas where great uncertainty about the value of the j o b and the ability o f the applicants prevails. In transition economies m or in business areas undergoing rapid technological change or change in consumer tasteY thcre are no fully functioning labor markets where information about applicants and jobs can be derived from long-term observation. Weiss (1995) argues that the more highly developed a society, the greater is the proportion of jobs for which productivity is not directly observable and the more important screening becomes. Rules governing labor contracts have to adjust to the contracting practices used in these situations to achieve the desired allocative and distributional ends. Appendix
Proof of Proposition Some reformulations are helpful to transform the constrained maximization problem into an unconstrained program. O u t p u t y is replaced by 0 + e and the expected rent payments U/, i -- H, L, are used to eliminate wages, ~°Interesting effects have been discovered in experiments as to how agents actually respond to a contractual and legal environment. For example, in tournaments with asymmetric agents, affirmative action programs can increase the principal's profits. In theory, affirmative action programs favoring less productive agents in a tournament setting lead to lower effort levels of the favored group, therefore also to lower effort levels of the competing group of more productive agents and to lower profits of the tournament administrator. The experiments of Schotter and Weigelt (1992) suggest, however, that profits may increase with affirmative action because fewer low-productivity agents drop out with dropouts leading to lower effort levels of the high-productivity group. 21There is evidence from China that managers are selected via auctions and are subsequently forced to pay a fixed sum to the municipal authorities. See Groves et al. (1995). 22An example given in Milgrom and Roberts (1992) and McAfee and McMillan (1987) is the mechanism used by IBM to elicit information from their sales persons about the potential of a sales territory.
D. Kt]BLER
71
E0,,0L [U/(0~, 00] = E0,,0L [wi(0H, 00 -xi(OH, 00+(yi(0H, 00 -0i)].
(8)
Only the incentive constraint of a g o o d type a n d the participation constraint of a b a d type are binding. Using these constraints and ~ ( • ), the e x p e c t e d rent of a g o o d type of w o r k e r H can be written as E0L [ UH(-6, eL)] :VLXI-I(O__, -6)~(eH(0, -6)) + (1 -vL)xn(O_, _0)~(er/(_0, _0)),
(9)
a n d of w o r k e r L Eo. [ UL(OH, -6)] = VHXL(-6, O_)dP(eL(-6, 0_)) + (1 - V.)XL(O__, O__)dP(eL(O__, _0)).
(10)
Plugging in the rents and writing out the e x p e c t e d value, the profit P of the e m p l o y e r becomes v , ~ L [ x ~ O , 0)(o + e~(O, 0) - +(ell(O, o)) + x L (0, 0)(0 + eL(O, O) -- +(eL(O, 0))] + v~l
(11)
- vL)[xn(O, 0__)(-6+ en(O, 0_) - +(en(-6, 9_)) + x L (-6, _0)(_0+ eL(-6, _0) - +(eL(-6, 0_))]
+ vL(1 - vH)[x~(0, -6)(0 + e ~ 0 , -6) - + ( e ~ 0 , -6)) + x L (0_, 0)(0 + eL(O,-6) -- +(eL(O_, -6))]
+ (1 - VH)(1 - VL[Xn(O, 0_)(0__+ eo(O_, 0_) - +(en(O, 0_)) + x L (0_, 0_)(0_ + eL(O , 0__)-- +(eL(O , _0))1 - VI4VL[XH(O_, -6)dP(e/4(_O, -6)) + XL(-6, _O)dP(eL(-6,0))]
- (1 - VL)VHXo(O_, O__)¢P(eH(O_,0__))-- (1 -- YH)PLXL(O, O_)~P(ez(O__,0))] subject to the constraints i - XH(k, I) - xL(k, l) > 0 Vk, l = 0_, -6
with the L a g r a n g e multipliers h 1, h2, h3, a n d h4, a n d non-negativity of all xi(On, 0 i ) . Expression (11) is m a x i m i z e d with respect to ~q (0~r, 0L) a n d ei(On,_OL .2a The_oj~timal effort levels follow f r o m the K u h n - T u c k e r conditions, en(0, 0) = ell(0, 0__) = eL(0 , 0) -- eL (_0, -6) = e* and ])i
t
+'(e~) = 1 - _--_---~ 1 • (e~), i = H , L
(12)
with e H = ell(_0, -6) = el-i(o_o_,_0) and ~ = eL(-6, 0_) = eL(0, 0_). F r o m equation (12) and the convexity of +(e) follows that the o p t i m a l effort of a b a d type, e~, is lower than the first best effort level e*. Differentiating e q u a t i o n (12) with respect to vHyields 0 e l l / Or/4 < 0. This proves s t a t e m e n t 2 of Proposition 1. F r o m the K u h n - T u c k e r conditions" follows 2SThe first-order conditions are sufficient for a m a x i m u m , because the objective function is concave in el(OH, OL), linear in xi(On, Or), a n d all cross-derivatives except P'i~, a n d P,i,i vanish. Thus, the Hessian matrix is negative semidefinite.
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Auctioning off labor contracts
that xH (0, 0_), = xL(-0, 0) = 1 a n d x,q(0, 0) + xL(0, 0) = 1. In state (_0, _0), w o r k e r L gets the j o b if the following i n e q u a l i t y h o l d s strictly
eL
-
+(e~)
-
v-----5--L - 1 1 v L qb(et')/> £1-1-+(el-I) -
PH -
vz_i ¢p(eI4)" -
(13)
This is always the case as
- +(a)-
vL
1 - ,,,---~
~(_ec) = m a x
> -~'-
e - ~(e) - 1
+(-~")
> £ H - q~(e_~)
1 - vl~
- - -
- 1 - ,,-----~,t,(_~,).
Thus, x/~(O_.,_0) -- 0 a n d PL
xL(-0, -0) = 1 if_0 + eL - +(£/) - 1 - v L ~ ( £ ' ) ~> 0,
(14)
xL(_0, _0) = 0 otherwise. This proves s t a t e m e n t 1 o f P r o p o s i t i o n 1. S t a t e m e n t 3 follows f r o m the b i n d i n g particip a t i o n c o n s t r a i n t o f a b a d type a n d f r o m p l u g g i n g the o p t i m a l p r o b a b i l i t i e s into equations (9) a n d (10). Proof of Proposition 2 Maximize the e m p l o y e r ' s p r o f i t f u n c t i o n (11), subject to e q u a t i o n (5), a n d the corres p o n d i n g c o n s t r a i n t for efforts, as well as e q u a t i o n (6), a n d the c o n s t r a i n t 1 - xL(0, -0) - xL(-0, 0) t> 0. T h e o p t i m a l effort level w h e n b o t h workers are u n p r o d u c t i v e m a x i m i z e s (1 - vL)(-0 + e,(0 -0) - +(6(_0, _0))) -
(1 - v,.)vtt + (1 - Vl4)V L ¢P(e,(-0, 0_)), i = H, L 2(1 - vt/) (15)
whereas the o p t i m a l eL in the u n r e s t r i c t e d m e c h a n i s m m a x i m i z e s (1 -- VL)(--0 + e.e/..- (~(_.gL) -- OL(I)(e_L))"
(16)
A s v L is smaller t h a n the fraction in e x p r e s s i o n (15), el(-0 , -0) < e L. Proof of Proposition 3 In a s e p a r a t i n g e q u i l i b r i u m , all g o o d types are i n d u c e d to c h o o s e the efficient effort level e* a n d all b a d types receive the wage w = +(el(-0, -0)), i = H, L. M o r e o v e r , the incentive constraints for g o o d types of H a n d L are satisfied. T h e e m p l o y e r always chooses a g o o d type 0 if she r e p o r t s a strictly h i g h e r productivity t h a n h e r rival, b e c a u s e h e r effort is n o t d i s t o r t e d a n d pays h e r the wage w. Define ~H: = vLxi:i (0, 0) + (1 - vL)
D. KI]BLER
73
a n d ~L: = VH(1 -- XH(0, 0)) + (1 -- VH) as the p r o b a b i l i t i e s t h a t w o r k e r H o r w o r k e r L are e m p l o y e d if they r e p o r t 0. T h e incentive c o n s t r a i n t s o f g o o d types can b e written as
~/t [ ~ - +(e~)] I> (1 - v0x,~(0, 0)~(e,~(0, 0)) {c [ ~ - qb(e*)]/> (1 - v , ) ( 1 - xh(_0, 0_))q)(eh(_0, 0)). In e q u i l i b r i u m they m u s t h o l d as equalities. Thus, wage ~ i n d u c e s t r u t h t e l l i n g if it satisfies
W = 6(e*) + max
{(1-- VL)XfI(O_, O) (1-- V/t)(1-- xH(O_, O_))} ~H ' -~L ¢P(eH(O_,0_)).
Because b o t h fractions are m o n o t o n o u s in xt) (0_, 0_), the wage o f a g o o d type is minim i z e d by c h o o s i n g xH(_0, 0_) such t h a t b o t h fractions in the m a x i m u m e x p r e s s i o n are equal. T h i s yields an o p t i m a l x h (0_, O) o f (1 - v / t ) ~ / t
xgt (_0, 0_) - (1 - VL)~L-[- (1 - v/t)~t-/"
(17)
T h e r i g h t - h a n d side o f e q u a t i o n (17) is i n c r e a s i n g in xB(0, 0) which yields x/:/(0, 0) = 0 a n d thus x/:/(0_, 0_) = (1 - v/t) / (2 - v/t). This proves s t a t e m e n t 1 as ~ = ~b(e*) + xt~(0_, O) (I)(e~(_O, _0)). T h e e m p l o y e r c h o o s e s the o p t i m a l effort of a b a d type el(O, _0) by m a x i m i z i n g his profits given the o p t i m a l p r o b a b i l l i t i e s j u s t derived, 1 - v " ~(e,.(O, 0))] (V/t + VL(1-- V11))[ 0 + e* - ~b(e*) - ------~.. v2 _ _ __ + (1 - v/t)(1 - vO[ ~ + e~(0_,_0) - 6(el(0_, _0))]. T h e o p t i m a l e~(0_, 0), i = H, L m a x i m i z e s (1 - VL)[O - + ee (0__,O) + dp(ee(0__,0_9_)]
V/_/'I- VL(1 --
(2--v/~
V/t)
4P(ei (0_, _0)).
(18)
Because the f r a c t i o n in e x p r e s s i o n (18) is g r e a t e r t h a n v L in the u n r e s t r i c t e d m e c h a nism [see e x p r e s s i o n (16)], it follows t h a t e(0_, 0) = eL (0_, 0_) < eL. This proves statem e n t 2.
References ARROW, KENNETHJ. (1973). The theory of discrimination. In Discrimination in Labor Markets. Orley Ashenfelter and Albert Rees (eds.) Princeton, New Jersey: Princeton University Press, pp. 3-42. BRANCO, FERNANDO.(1994). Favoring domestic firms in procurement contracts. Journal of International Economics 37:65-80. GIBBONS, ROBERT. (1987). Piece-rate incentive schemes. Journal of Labor Economics 5:413-429. GROVES,THEOI)ORE,HONG, YONGMXAO,McMILLAN,JOHN, ANDNAUGHTON,BARRY.(1995). China's evolving managerial labor market. Mimeo. GUASCH,J. Luts, and WEiss, ANDREW.(1981). Self-selection in the labor market. American EconomicReview 71:275-284. K~aLER, DOROTHEA. (1995). Auctioning off labor contracts: Legal restrictions reconsidered. Discussion Paper 22, SFB 373, Humboldt Universitfit zu Berlin.
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LAFFONT, JEAN-JAcQUES, AND TIROLE, JEAN. (1987). Auctioning Incentive Contracts. Journal of Political Economy 95:921-937. LAFFONT, JEAN-JACQUES, AND TIROLE, JEAN. (1993). A Theory of Incentives in Procurement and Regulation Cambridge, Massachusetts: MIT Press. MC,AdEE, R. PRESTON, AND McMILLAN, J. (1987). Competition for agency contracts. Rand Journal of Economics 18:296-307. MCAFEE, R. PRESTON, AND McMILLAN, J. (1989). Government procurement and international trade. Journal of International Economics 26:291-308. MILGROM, PAUL, AND ROBERTS,JOHN. (1992). Economics, Organization and Management Englewood Cliffs, New Jersey: Prentice-Hall. MYERSON, ROGERB. (1981). Optimal auction design. Mathematics of Operations Research 6:58-73. PHELPS, EDMUNDS. (1972). The statistical theory of racism and sexism. American Economic Review 62:659661. SALOP, JOANNE, AND SALOP, STEVEN. (1976). Self-selection and turnover in the labor market. Quarterly Journal of Economics 90:619-628. SCHAUB, GUNTHER. (1988). In §612 BGB Munchner Kommentar zum BGB, Schuldrecht AT, 2nd ed, Mfinchen: Beck, pp. 1392-1460. SCHOTTER,A., ANDWEIGELT,K. (1992). Asymmetric tournaments, equal opportunity laws, and affirmative action: Some experimental results. QuarterlyJournal of Economics 52:511-539. StDLLNER, ALLFRED. (1988). 611a BGB In Miinchner Kommentar zum BGB, Schuldrecht AT, 2nd ed., MtSnchen: Beck, pp. 1381-1390. WEISS, ANDREW. (1995). Human capital vs. signalling explanations of wages.Journal ofEconomicPerspeaives 9:133-154.