The rise of individual performance pay

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1 The rse of ndvdual performance pay Ola Kvaløy y and Trond E. Olsen z Aprl 28, 2011 Abstract Exstng emprcal evdence suggests that ndvdual performance pay s more prevalent n human captal ntensve ndustres. We ntroduce a model that can contrbute to explan ths. In a repeated game model of relatonal contractng, we analyze the condtons for mplementng peer-dependent ncentve regmes when agents possess ndspensable human captal. We show that the larger the share of values that the agents can hold-up, the lower s the mplementable degree of peer-dependent ncentves. In a settng wth complementary tasks, we show that whle team-based ncentves are optmal f agents are dspensable, t may be costly, and n fact suboptmal, to provde team ncentves when the agents become ndspensable. JEL Class caton: D23, J33, L14 Keywords: relatonal contracts; multagent moral hazard; human captal, hold-up 1 Introducton Frm value s ncreasngly dependent on human captal. The share of physcal captal n publcly traded corporatons has dramatcally decreased snce We thank two referees and Derek Clark, Bob Gbbons, Hdesh Itoh, Hdeo Owan, Jack Stecher, and semnar partcpants at the Htotsubash Unversty, Erasmus Unversty, the MIT Sloan School of Management, the EIASM Workshop n Accountng and Economcs, the CESfo Conference on Employment and Socal Protecton, the Conference of the European Assocaton of Labour Economsts, and the Congress of the European Economc Assocaton for helpful comments. y Unversty of Stavanger, 4036 Stavanger, Norway. E-mal: ola.kvaloy@us.no z Norwegan School of Economcs and Busness Admnstraton, Helleveen 30, 5045 Bergen, Norway. trond.olsen@nhh.no 1

2 the 1970s, (see e.g. Blar and Kochan, 2000). At the same tme we observe a hgher degree of ndvdual performance pay n modern corporatons (see e.g., Brown et al., 1998; Brown and Heywood, 2002, and Lemeux et al., 2009). Are these trends related? Several studes ndcate so. Long and Shelds (2005), Lemeux et al. (2009) and Henneberger et al. (2007) nd that ndvdual performance pay s more lkely to be found n rms wth hghly educated employees. A recent study by Barth et al. (2008) shows that the frequency of group-based ncentves s decreasng for those wth hgher educaton, and ncreasng for blue-collar workers; whle ndvdual performance pay s found to be strongly assocated wth rms wth a hghly educated workforce. 1 Group-based ncentve schemes (as n partnershps) are stll qute common n certan hgh-sklled professonal servce ndustres such as law, accountng, nvestment bankng and consultng, but researchers have noted that there s a trend away from equal sharng partnershps towards productvtybased "eat what you kll" partnershps (Levn and Tadels, 2005). 2 One explanaton for the ncreased use of ndvdual performance pay s that advances n nformaton and communcaton technology have made t easer to measure ndvdual performance (Lemeux et al., 2009). A queston then s whether t has become relatvely more easy to assess the performance of hgh-sklled workers. There s apparently no evdence that ths s the case, and n fact, MacLeod and Parent (1999) nd that ncomplete ncentve contracts based on looser performance assessments are assocated wth complex jobs. Barth et al. (2008) suggest that one should expect a postve relatonshp between human captal and ndvdual performance pay because the qualty and e ort of hgh-sklled workers have larger mpacts on productvty than the qualty and e ort of other groups of workers. They lend support from Brown (1990) who argues that n hgh-sklled jobs, worker output s more senstve to worker qualty than n jobs requrng lower sklls. Henneberger et al. (2007) show that hgh-sklled workers tend to self-select 1 Long and Shelds (2005) and Barth et al.(2008) have the most detaled data on the lkelhood of ndvdual performance pay. They show that f the share of the workforce wth a college degree ncreases wth 1% pont, the share of workers on ndvdual performance pay schemes ncreases wth 0,18% and 0,24% pont n Canada and Norway, respectvely. There s about 20% lower probablty of havng ndvdual performance pay plans f you are a worker n a rm where no-one has a degree compared to a rm where everybody has a degree. For the U.S., Lemeux et al. (2009) show that the average years of schoolng s about one year longer for those who work n performance pay jobs compared to those who work on xed salares only. 2 In addton to the evdence mentoned, several studes show that rms wth low unon coverage are more wllng to use ndvdualzed ncentve schemes (see e.g. Brown, 1990; Parent, 2002, Long and Shelds, 2005, Lemeux et al. 2009), and unon coverage s lower among hgh-sklled workers (Acemoglu et al. 2001). 2

3 nto jobs wth performance pay, supportng Lazear s (1986) model. Along the same lne, studes by Kato (2002) and Torrngton (1993) show that workers wth more educaton are partcularly nterested n recevng rewards talored to ndvdual performance. In our vew, these are plausble explanatons. However, there are some remanng puzzles. Indvdualzed ncentves are not desrable when teamwork s mportant, or when t s d cult to verfy each worker s contrbuton to rm value, but t s hard to see that ths apples less to hgh-sklled than to low-sklled workers. In fact, several scholars n human resource management have argued that knowledge ntensve organzatons emphass on nnovaton, teamwork and projects calls for ncentves that are group-based rather than based on ndvdual performance (see e.g. Balkn and Bannster, 1993). We should thus look for an explanaton sayng that group-based ncentves are desrable, but not feasble. Focusng on rms nablty to fully commt to ncentve contracts, the lterature has ponted out that groupbased ncentve schemes are harder to mplement and thus less feasble than schemes based on relatve performance evaluaton (Carmchael, 1983; Malcomson, 1984; Levn, 2002, Kvaløy and Olsen, 2006). In ths paper we focus nstead on the workers lack of ablty to commt to ncentve contracts, whch we beleve s a central feature of human captal ntensve rms, and show that ths feature makes ndvdual performance pay easer to mplement than most peer-dependent schemes. We recognze here two features of human captal that - as we wll argue below- necesstate a hgh degree of ndvdual performance pay. Frst, the true performance of hgh-sklled workers s often d cult to verfy by thrd partes. Incentves based on subjectve performance evaluaton are therefore typcally used for more complex jobs where comprehensve objectve measures are d cult to specfy and/or measure (MacLeod and Parent, 1999). Consequently, ncentve contracts specfyng crtera for performance pay are seldom perfectly enforceable by the court. Ths enforcement problem also apples to low-sklled workers, but as noted above, ncomplete ncentve contracts are more common n the hgh-sklled workforce. Second, human captal blurs the allocaton of ownershp rghts. Accordng to the standard vew of ownershp, t s the owner of an asset who has resdual control rghts; that s the rght to decde all usages of the asset n any way not nconsstent wth a pror contract, custom or law (Hart, 1995). If the crtcal asset nvolved n the worker s producton s hs own mnd and knowledge, t may thus be complcated to decde whether t s the employer or worker who has resdual control rghts. An ndspensable "knowledge worker" can therefore threaten to walk away wth deas, clents, technques, etcetera. As noted by Lebesknd (2000), human-captal-ntensve rms must nduce ther employees to 3

4 stay around long enough so that the rm can establsh some ntellectual property rghts wth respect to the deas generated by these employees, or else these rms run the rsk of beng exproprated or held-up by ther own employees. Why do these two features - ncomplete contracts and ndspensable human captal - prepare the way for ndvdual performance pay? In other words: Why s t d cult to mplement peer-dependent ncentves when performance s unver able and workers possess resdual control rghts? The answer s ntutve when we thnk of the ncentves facng an agent who s a full resdual clamant. He smply gets the values he has produced; the market ncentves are not lnked to what other agents produce. Hence, f a prncpal wants to mplement a peer-dependent ncentve contract, she faces a problem f her agents have resdual control rghts. Wth relatve performance evaluaton (RPE) an agent s not pad well f hs peer performs better, whle wth team ncentves - or jont performance evaluaton (JPE) - he s not pad well f hs peer s performance s poor. Ths peer-dependence may lead to contract breach: an agent who s pad a low bonus after realzng a hgh output has ncentves to hold-up hs output and renegotate payments. Of course, a hold-up strategy s only possble f the agent actually s able to prevent the prncpal from realzng the agent s value added ex post producton. But f hold-up s possble, then RPE and JPE schemes are more susceptble to hold-up than ncentve schemes based on ndependent performance evaluaton (IPE). 3 The partes can mtgate the hold-up problem through repeated nteracton,.e. through self-enforcng relatonal contractng where contract breach s punshed, not by the court, but by the partes who can refuse to cooperate after a devaton. 4 But snce a hold-up wll be regarded as a devaton from such a relatonal contract, the self-enforcng range of the contract s lmted by the hold-up problem. And snce the hold-up problem s most severe under jont or relatve performance evaluaton, we can expect a larger fracton of ndependent performance pay when hold-up s feasble for the agents. Is ths a problem? Yes, from the nformatveness prncple (Holmström, 1979, 1982) we know that an ncentve contract should be based on all var- 3 Our argument bears some smlartes to Oyer (2004), who shows that t may be optmal to let pay vary wth the agent s outsde opton. But he focuses on the costs of adjustng ncentve contracts and does not dscuss the problem of mplementng peerdependent relatonal ncentve contracts. 4 In uental models of relatonal contracts nclude Klen and Le er (1981), Shapro and Stgltz (1984), Bull (1987), MacLeod and Malcomson (1989), Baker, Gbbons and Murphy (1994, 2002) and Levn (2003). There s also a growng body of emprcal work on relatonal contractng, see n partcular Ryall and Sampson (2009). 4

5 ables that provde nformaton about the agents actons. Stochastc and/or technologcal dependences between the agents then typcally call for peerdependent ncentve schemes. By tyng compensaton to an agent s relatve performance, the prncpal can lter out common nose so that compensaton s based more on real e ort, and less on random shocks that are outsde the agent s control (see Holmström, 1982; and Mookherjee, 1984). 5 And by tyng compensaton to the jont performance of a team of agents, the prncpal can explot complementartes between the agents e orts. 6 Hence, from the nformatveness prncple t s puzzlng that we actually observe ncentve schemes based on ndependent performance evaluaton. The drawbacks of team ncentves and relatve performance evaluaton can partly explan why: Team ncentves may be susceptble to free-rdng (see e.g. Alchan and Demsetz, 1972; and Holmström, 1982), whle RPE s susceptble to colluson (see e.g. Mookherjee, 1984). RPE may also nduce sabotage and dscourage cooperaton (see Lazear, 1995, for a dscusson of the costs and bene ts of RPE and team ncentves). In ths paper we provde a new argument for ndependent performance evaluaton; an argument that s not based on these classcal drawbacks, but rather on the mplementablty of peer-dependent ncentves. Our man result then says that the maxmum dependence between agent s bonus and agent j s output that the prncpal can mplement, decreases wth the share of values that the agents can hold-up ex post. Wth respect to team e ects we consder the case of complementary tasks. We nd that the optmal mplementable scheme becomes less based on team ncentves and more based on ndvdual performance pay the larger the share of values the agents can hold-up. We also show that f agents d er n e ort productvty and/or nherent ablty, the most productve agent s - for a gven hold-up power - gven more ndvdualzed ncentves than the less productve agent. Moreover, the e ect of a hgher hold-up power s stronger for the hgh-ablty agent than for the low-ablty agent. We argue that ths result may contrbute to our understandng of why performance pay ncreases wage nequalty. Broadly speakng, our contrbuton s to consder the e ect of resdual 5 See also Lazear and Rosen (1981), Nalebu and Stgltz (1983) and Green and Stokey (1983) for analyses of RPE s specal form, rank-order tournaments. 6 In addton, JPE can promote cooperaton snce an agent s rewarded f hs peers perform well (see e.g. Holmström and Mlgrom, 1990; Itoh 1993; and Macho-Stadler and Perez-Castrllo, 1993). JPE can also provde mplct ncentves not to shrk (or exert low e ort), snce shrkng may have socal costs (as n Kandel and Lazear, 1992), or nduce other agents to shrk, whch agan reduces the shrkng agent s expected compensaton (as n Che and Yoo, 2001). 5

6 control rghts n a multagent moral hazard model. In the vast lterature on multagent moral hazard, t s (mplctly) assumed that resdual control rghts are exclusvely n the hands of the prncpal. And n the lterature dealng wth optmal allocaton of control rghts, the multagent moral hazard problem s scantly consdered. 7 Our basc set-up wth two agents, bnary e ort and bnary output, s smlar to Che and Yoo (2001). As shown by these authors, peer montorng s a ratonale for makng use of peer-dependent ncentves such as JPE. We ntroduce and explore nstead technologcal complementartes n ths settng. And more mportantly, we extend and complement ther analyss by assumng non-ver able output, and that agents are able to hold-up values ex post. 8 The paper proceeds as follows. In Secton 2 we present the model and deduce the optmal ncentve contract. In Secton 3 we study how varatons n complementarty between the agents tasks, and d erences between the agents productvty and ablty levels a ect ncentve desgn. Secton 4 o ers some concludng remarks. 2 The Model Consder an economc envronment consstng of one prncpal and two agents ( = a; b) who each perod produce ether hgh, Q H, or low, Q L, values for the prncpal. Each agent s e ort level can be ether hgh or low, where hgh e ort (e 1 ) has a dsutlty cost of c and low e ort (e 0 ) s costless. The prncpal can only observe the realzaton of the agents output, not the level of e ort they choose. Smlarly, agent can only observe agent j s output ( 6= j; j = a; b), not hs e ort level. 9 Moreover, we assume that output s non-ver able to a thrd party. Hence, contracts on output cannot be enforced by the court. The agents outputs are stochastcally ndependent, and each agent s success probablty depends on the agent s own as well as hs peer s e ort. Let q (e ; e j ) denote ths probablty, where e 2 fe 0 ; e 1 g and e j 2 fe 0 ; e 1 g refer 7 Ths lterature begns wth Grossman and Hart (1986) and Hart and More (1990), who analyze statc relatonshps. Repeated relatonshps are analyzed n partcular by Halonen (2002) and Baker, Gbbons and Murphy (2002). Although Hart and Moore (1990) analyze a model wth many agents, they do not consder the classcal moral hazard problem that we address, where a prncpal can only observe a nosy measure of the agents e ort. 8 Kvaløy and Olsen (2008a) consder a model on cooperaton (help) between agents wth hold-up power, whle Kvaløy and Olsen (2008b) endogenze the agent s hold-up power n a smpler model wth no team e ects. 9 Whether or not the agents can observe each other s e ort level s not decsve for the analyss presented. However, by assumng that e ort s unobservable among the agents, we do not need to model repeated peer-montorng. 6

7 to the agent s own and hs peer s e ort, respectvely. To model technologcal complementarty between the agents tasks, we assume that there are three levels of the success probablty for each agent: 10 q (e 1 ; e 1 ) = q 1 (1) q (e 1 ; e 0 ) = q10 q (e 0 ; e 1 ) = q (e 0 ; e 0 ) = q0, where q0 q10 q1, q0 < q1: The dea here s that the peer s e ort has a postve e ect when the agent s own e ort s hgh, but has no e ect when own e ort s low. Note also that q 10 = q 1 corresponds to no team e ects (ndependent technology), whle q 10 = q 0 corresponds to perfect complementarty; n the sense that slackng by one agent leads to low success probablty for both agents, even f the other agent exerts hgh e ort. Throughout the paper we assume that the value of hgh e ort exceeds ts cost, n the sense that q Q > c, (2) where q = q 1 q 0 and Q = Q H Q L. It s moreover assumed that all partes are rsk neutral, but that the agents are subject to lmted lablty: the prncpal cannot mpose negatve wages. 11 Ex ante reservaton wages are assumed to be zero, for convenence. The prncpal may o er each agent a wage contract sayng that agent receves a bonus ( HH; HL; LH; LL) ex post value realzatons, where the subscrpts refer to agent s and agent j s realzatons of Q k and Q l, (k; l = H; L), respectvely. For each agent, a wage scheme exhbts jont (JPE), relatve (RPE) or ndependent (IPE) performance evaluaton f, respectvely, ( HH ; LH ) > ( HL ; LL ), 12 ( HH ; LH ) < ( HL ; LL ), and ( HH ; LH ) = ( HL ; LL ). Wth JPE an agent s pad more f hs peer does well, n RPE he s pad more f hs peer does poorly, and n IPE hs payment s ndependent of hs peer s performance. Snce outputs are not ver able, a contract must be selfenforcng to be sustanable. We now descrbe the contractng envronment n more detal. 10 The model can be generalzed to account also for stochastc dependence n the form of postvely correlated outputs. As s well known, such dependence favors RPE relatve to JPE and IPE, but t can be shown that all our results go through as long as the degree of ths dependence s not too hgh. 11 Lmted lablty may arse from lqudty constrants or from laws that prohbt rms from extractng payments from workers. 12 The nequalty means weak nequalty of each component and strct nequalty for at least one component. So a JPE scheme has HH HL and LH LL wth at least one nequalty beng strct. 7

8 Each perod the prncpal and the agents face the followng contractng stuaton. 1. The prncpal o ers a contract sayng that agent receves a bonus ( HH; HL; LH; LL) condtonal on outputs as descrbed above. 2. The agents smultaneously choose e orts. Provded the contract s honored, agent = a; b then gets an expected wage (e ; e j ; ) q q j HH + q (1 q j ) HL +(1 q )q j LH + (1 q )(1 q j ) LL (3) where the success probabltes depend on agent s and agent j s e orts; e and e j, respectvely, so q = q (e ; e j ) and q j = q j (e j ; e ), wth e ; e j 2 fe 0 ; e 1 g. 3. The agents value realzatons, Q k and Q l, (k; l = H; L), are revealed. 4. The prncpal decdes whether or not to honor the contract. If the prncpal reneges on the contract by refusng to pay, she bargans wth the agent and pays a spot prce s for the good. 5. If the prncpal honors the contract, the agent chooses whether or not to delver the good and accept the payment. If he accepts, trade takes place accordng to the contract. If not, he bargans wth the prncpal and obtans a spot prce s. The tmng of events s summarzed n Fgure 1. The prncpal offers a contract The agents choose effort Qualty of output s revealed The prncpal decdes whether or not to honor the contract The agents decde whether or not to delver the good Fgure 1: Tmelne Whle the three rst stages are standard ngredents n prncpal-agent relatonshps, the fourth stage s also standard n ncomplete contractng models where the prncpal has dscreton over her choce whether or not to actually pay the promsed bonus. The last stage s less standard. Usually t s assumed that values accrue drectly to the prncpal n the process of producton, but we assume that agents are able to hold-up values f they are not sats ed wth the prncpal s o er n the fourth stage. Ths knd of modellng s common n blateral buyer-suppler relatonshps, but not n multagent relatonshps as presented here. 8

9 Now f stage 4 or 5 ends up n spot barganng, we assume that the spot prce s determned by Nash barganng. In stage 4 agent s able to ndependently attan Q k, 2 [0; 1] n an alternatve market. In Nash barganng, agent wll then receve Q k plus a share of the surplus from trade.e..the spot prce wll be s k = Q k + (Q k Q k ) = Q k where = + (1 ). The parameter can be nterpreted as an ndex of the agent s total hold-up power. As we wll see, ncreased hold-up power to agents does not reduce total surplus n our model. Rather, t ncreases the agents rent and reduces the prncpal s exblty when desgnng ncentves. An agent s hold-up power ( ) s here an ncreasng functon of ex post barganng power ( ) and ex post outsde optons, ( ). The outsde opton parameter depends on the spec cty of the agent s value-added. The more rm spec c value-added or the more narrow the agent s skll set the lower s. But, mportantly, note that even f = 0, the agent can stll acheve a share = ex post. Ths share of the surplus from trade s determned by ex post barganng power, and wll typcally ncrease wth the ndspensablty of the agent: If an agent possesses essental human captal that makes hm ndspensable for ex post value extracton, then s hgh. But f values accrue drectly to the prncpal n the process of producton, then the agents have no hold-up power: = = 0, so that = 0. So to obtan a postve spot prce, the agents must be able to hold up values n stage 3. The model allows us to study the e ects of varatons n hold-up power and d erences n productvty and ablty between the agents. Whle the levels of the success probabltes q1 and q0 are related to the nherent ablty or talent of the agents, the rato q =c s a measure of the agents e ort productvty. Hgh-sklled workers wll typcally have hgher q =c, hgher q1; q0 and hgher. We wll analyze how varatons n these parameters a ect ncentve desgn. When analyzng d erences n productvty and ablty, we assume that the hold-up power s the same for both agents (and thus suppress superscrpts on ). Ths makes t easer to dstngush the e ects of varatons n hold-up power from the e ects generated by d erences n e ort productvty and ablty. Before proceedng, t should be noted that we consder a statonary model where the envronment (technology) does not depend on the output obtaned n prevous perods. Hence, hgh performance n one perod does not a ect the future performance of the rm. Moreover, we do not analyze the ncentves to nvest n rm-spec c human captal (as n e.g. Kessler and Lülfesmann, 2006). Rather, we just assume that agents become ndspensable n the process of producton (as n e.g. Halonen, 2002). We thus follow the relatonal contractng lterature, and abstract from human captal accumulaton. 9

10 The magntudes of Q k and Q k are therefore assumed to be exogenously gven and constant each perod. Ths smpl es the analyss and hghlghts the statonary e ect of ex post hold-up power on the prncpal s ncentve desgn. 2.1 The spot contract A spot contract s a perfect publc equlbrum (PPE) 13 of the contractng game descrbed above. In stage 4, agent wll renege f hs promsed bonus for the gven outputs s lower than the spot prce ( kl < s k ), and honor otherwse. In stage 4, the prncpal wll renege f kl > s k, and honor otherwse. Hence, at least one party wll renege, unless kl = s k. The only payment that can be mplemented for agent when he has output Q k s thus s k = Q k. Antcpatng ths, agent wll n stage 2 exert low e ort f the cost of hgh e ort exceeds the hgher expected spot prce nduced by ths e ort,.e. f c > (q (e 1 ; e j ) q ((e 0 ; e j )) Q. Recallng our assumptons (1) we see that low e ort s thus a strctly domnant strategy f q Q < c (4) Hence, we see that the spot contractng game has a unque contnuaton equlbrum from stage 2 f (4) holds. Each agent then exerts low e ort and receves the expected spot prce S = (Q L + q0q). In our smple model, a contract to motvate hgh e ort s only necessary f the parameters satsfy (4), snce f not, the agents hold-up power provdes them wth su cent ncentves. Hence, throughout the paper we assume that (4) holds, so that the prncpal has to mplement an ncentve contract n order to nduce hgh e ort. Snce outputs are non-ver able, the partes must rely on self-enforcng (relatonal) ncentve contracts. An mportant reason for why a contract can be self-enforcng s that the partes ncur reputatonal costs f they renege on the contract. The contract s honored f these costs are su cently hgh. Such reputatonal costs can be measured by the loss of future surplus. Modelng self-enforcng relatonal contracts as a repeated game provdes us wth a rgorous tool for analyzng the trade-o between short term gans and long-term losses from contract devatons. The repeated game approach s partcularly relevant n employment relatonshps, whch are typcally repeated n nature. 13 In a PPE each player s strategy s based on publc nformaton (not on prvately observed e orts) and the strateges consttute at each stage a Nash equlbrum for the remander of the game. 10

11 2.2 Relatonal contracts Now, for the prncpal to mplement hgh e ort through a contract, the contract must be ncentve compatble (IC) and self-enforcng, where a selfenforcng (relatonal) contract s a perfect publc equlbrum of the n ntely repeated game n whch the stage game descrbed above s played every perod. We consder rst the IC constrant. Focusng on statonary contracts, an mplementable ncentve scheme,, s ncentve compatble f 14 (e 1 ; e 1 ; ) c (e 0 ; e 1 ; ), = 1; 2 (5) The left hand sde (LHS) shows the expected wage mnus the cost from exertng hgh e ort, whle the rght hand sde (RHS) shows the expected wage from exertng low e ort. The condton (5) ensures that hgh e ort from both agents s an equlbrum, gven the contract. The agents equlbrum s unque for the gven contract f hgh e ort s a domnant strategy,.e. f (e 1 ; e 0 ; ) c (e 0 ; e 0 ; ) holds n addton to (5). The optmal wage schemes we deduce n ths paper wll ensure ether such a unque hgh-e ort equlbrum, or a hgh-e ort equlbrum that s not Pareto domnated by a low-e ort equlbrum. 15 Consder now the condtons for the ncentve contract to be self-enforcng,.e. the condtons for mplementng a relatonal ncentve contract. The relatonal ncentve contract s self-enforcng f all partes honor the contract for all possble values of Q k and Q l, k; l 2 fl; Hg. There are many possble self-enforcng contracts, but we focus here on trgger strategy equlbra n whch the partes enter nto spot contractng forever after one party reneges (as n e.g. Baker, Gbbons and Murphy, 2002; and Levn, 2002). We consder a multlateral punshment structure where any devaton by the prncpal trggers low e ort from both agents. The prncpal honors the contract only f both agents honored the contract n the prevous perod. The agents honor the contract only f the prncpal honored the contract wth both agents n 14 We consder only statonary contracts, whch are not restrctve when partes are rsk neutral and there s no lmted lablty (Levn, 2003). When partes have lmted lablty, statonary contracts are not necessarly optmal. Fong and L (2009) show, however, that under lmted lablty the optmal contract reaches a statonary equlbrum after a probaton phase. 15 One can show that there s a threshold for the degree of complementarty such that for hgh complementarty there s a low-e ort equlbrum, whle for low complementarty there s no low-e ort equlbrum. Moreover, an agent s payo n the low-e ort equlbrum s strctly smaller than hs payo n the hgh-e ort equlbrum, except under perfect complementarty, where the payo s are equal. 11

12 the prevous perod. Thus, f the prncpal reneges on the relatonal contract, both agents nsst on spot contractng forever after. And vce versa: f one (or both) of the agents renege, the prncpal nssts on spot contractng forever after. A natural explanaton for ths s that the agents nterpret a unlateral contract breach (.e. the prncpal devates from the contract wth only one of the agents) as evdence that the prncpal s not trustworthy (see Bewley, 1999, Levn, 2002). 16 Now, (gven that (5) holds) the prncpal wll honor the contract f, for all realzatons of output Q k ; Q l, k; l 2 fh; Lg, by agents a and b, respectvely, we have a kl b lk + 1 (Q l + Q k ) + 1 X QL + q1q (e 1 ; e 1 ; ) X QL + q0q S ; (EP) where s a common dscount factor. The LHS of the nequalty shows the prncpal s expected present value from honorng the contract, whch nvolves payng out the promsed bonuses and then recevng the value assocated wth hgh e ort n all future perods. The RHS shows the expected present value from renegng, whch nvolves spot tradng of the realzed outputs, and then recevng the value assocated wth low e ort and spot tradng n all future perods. Agent wll honor the contract f kl+ 1 ( (e 1 ; e 1 ; ) c ) Q k + 1 S, all k; l 2 fh; Lg (EA) where smlarly the LHS shows the agent s expected present value from honorng the contract, whle the RHS shows the expected present value from renegng. 2.3 Optmal ncentves Gven hgh e ort from both agents, the prncpal s wage cost for agent s (e 1 ; e 1 ; ) = q1 q j 1 HH + (1 q1)hl j + (1 q 1 ) q1 j LH + (1 q1) j LL (7) 16 Modellng multlateral punshments s also done for convenence. Blateral punshments wll not alter our results qualtatvely (see also Schottner, 2008, for a dscusson of multlateral punshments n a relatonal contractng model wth two agents and several tasks). 12

13 If one agent devates from hgh to low e ort, hs own success probablty wll be reduced from q1 to q0 and hs partner s from q j 1 to q10. j The IC condton (5) for hgh e ort (e 1 ; e 1 ) c > (e 0 ; e 1 ; ) can then be wrtten as q1 q j 1 HH + (1 q1)hl j + (1 q 1 ) q1 j LH + (1 q1) j LL c q0 q j 10 HH + (1 q10)hl j + (1 q 0 ) q10 j LH + (1 q10)ll j (IC) The optmal contract mnmzes the total wage costs P (e 1 ; e 1 ; ), subject to the constrants gven by lmted lablty, ncentve compatblty (IC), and enforceablty (EP and EA). 17 As a reference case and to buld ntuton, consder rst the case of ver- able outputs, for whch the enforceablty constrants are not relevant. The costs per agent can then be mnmzed separately. It s ntutve that an agent wll not be pad a bonus for low output and hence that LL = LH = 0. Gven ths, we can see from IC and (7) that costs can be reduced by reducng HL and ncreasng HH so that IC s just sats ed (see (16) and the ensung paragraph n the appendx). Ths mples that costs are mnmal when also HL = 0, and hence that each agent s optmally pad a bonus only when both agents have hgh outputs ( HH > 0). The mnmal such bonus that yelds su cent ncentves for hgh e ort s found from IC, and we see that t s gven by: HH(q; c ) = q1q j 1 q0q j 10 The assocated mnmal wage cost for agent s then from (7) seen to be V (q; c ) = HH(q; c )q1q 1, j.e. c V (q; c ) = q1q j 1 q1q j 1 q0q j c (8) 10 Comparng ths contract to a contract wth ndependent evaluaton ( HH = HL H), we see from IC that the latter can mplement hgh e ort wth a bonus H = c =q. But snce ths bonus s pad every tme the agent has hgh output, t yelds hgher costs than the JPE scheme, whch pays a bonus only when both agents have hgh output (q1c =q > q1q 1 j HH(q; c )). The ntuton s that when tasks are complements, low e ort from agent yelds a negatve externalty on agent j. Wth jont performance evaluaton the agent s punshed for ths,.e. JPE nternalzes the externalty to some extent. Ths makes t less costly to mplement hgh e ort under JPE than 17 These constrants also ensure that all partes are at least as well o wth the relatonal contract as wth a spot contract. 13

14 under ndependent or relatve performance evaluaton. The optmal ncentve scheme for ver able output s thus a scheme wth a very stark form of jont performance evaluaton and a hgh degree of peer dependence, n that agents are only pad bonuses f both of them realze hgh outputs. We wll now see that for non-ver able outputs, the enforceablty constrants assocated wth relatonal contracts, and n partcular the degree of agent hold-up re ected n those constrants, can severely modfy the optmal ncentve scheme and lead to consderably less peer dependence. For non-ver able outputs, the prncpal wll mnmze total wage costs subject to lmted lablty, ncentve and enforceablty constrants. It s nstructve to rst analyze ths problem wthout takng account of the enforceablty constrant for the prncpal, and then check ths constrant ex post. In ths procedure the costs per agent can be mnmzed separately, snce the relevant constrants pertanng to one agent do not nvolve the ncentve scheme for the other agent. To state the result, recall our mantaned assumpton that spot ncentves are nsu cent for hgh e ort; see (4), whch can equvalently be expressed as We then have the followng: < 0 = mn c f q Q g: Proposton 1 Provded Q L s not too small, then for above some threshold ( 1 < < 0 ) the ncentve scheme that mnmzes costs subject to ncentve and enforceablty constrants for the agents (IC and EA) has the followng features: ) Each agent s pad a xed salary ( LH = LL) plus a bonus ncrement for hgh output ( Hk Lk). The bonus ncrement exceeds the spot reward ncrement for hgh output ( Hk Lk Q), s peer dependent, and s of the jont performance evaluaton (JPE) type ( HH > HL). ) The enforceablty constrants EA are bndng for all bonuses except HH, and the bonuses satsfy (9-10) below. ) As the hold-up parameter ncreases, the degree of peer dependence ( HH HL) decreases. v) Each agent s xed salary component ( Lk) and the mnmal wage cost for the prncpal are ncreasng n the hold-up parameter and decreasng n the dscount factor. The mnmal wage cost exceeds the cost V (q; c ) assocated 14

15 wth ver able output. LH = LL = HL Q (9) HH = 1 HL + c q1q j 1 q0q j q Q (10) 10 The man message from the proposton s that f contracts are not enforceable by the court and the agents have hold-up power, then they cannot commt to stay n a relatonal contract wth strong team ncentves. If agent has produced Q H whle hs peer has produced Q L, then the contract enttles hm to HL, whle he can acheve Q H by renegotatng wth the prncpal. Hence, for a relatonal ncentve contract to be sustanable, the bonus HL must be hgh f s hgh. Ths s re ected n (10), whch clearly shows that the bonus ncrement HH HL s smaller, the larger s the agent s hold-up power. For symmetrc agents we also see that n the lmt, as the hold-up power becomes su cently hgh (! c q Q ), only ndvdual performance pay (where HH = HL) becomes feasble. Hence, ex post barganng power and/or outsde optons do not only ncrease the agents rents (as s well know from the lterature), but also change the form of compensaton towards more ndvdualzed ncentves. Ths result contrbutes to explanng why ndvdual performance pay s more common n human captal ntensve ndustres, where agent hold-up s an mportant ssue. So far we have gnored the dynamc enforceablty constrant for the prncpal (EP). To be fully feasble a contract must also satsfy ths constrant. It s straghtforward to show (proof avalable from the authors) that the scheme n Proposton 1 s mplementable (sats es the prncpal s enforceablty constrant EP) f the dscount factor exceeds a threshold () < 1. The larger the hold-up parameter (for < 0 ), the smaller ths threshold s, and hence the easer t s to mplement the relatonal contract. Ths follows ntutvely from the fact that a hgher reduces the prncpal s gan from devatng from the contract. A hgher s not socally dsadvantageous here snce t s the agents and not the prncpal, who exert e ort n ths model. Hold-up power ncentvzes the agents, but lmts the form of compensaton that the prncpal can use. 3 Complementarty, heterogenety and ncentves We wll now study n more detal how ncentve desgn s a ected by varatons n the degree of complementarty between the agents producton tech- 15

16 nologes, and by d erences between the agents productvty and/or ablty levels. When analyzng the e ects of d erences between the agents (heterogenety) we wll keep the level of complementarty constant. If there s no complementarty between the agents, the analyss of heterogenety becomes less nterestng, as ndvdual performance pay s then always (weakly) optmal. Smlarly, when studyng varatons n complementarty, we wll keep the level of heterogenety constant, and for expostonal smplcty we wll then consder dentcal agents. 3.1 Incentves for heterogenous agents We start by studyng the e ects of d erences between the agents. Consder rst d erences n e ort productvty, and suppose agent s more productve n ths respect (so c < cj ). Then we see from (10) that f the hold-up q q j power becomes su cently large (! c = q Q 0), agent s ncentves wll become ndependent of hs partner s performance ( HH = HL), whle the ncentves of the other agent wll reman peer dependent. Thus we have: Proposton 2 As the hold-up parameter ncreases, the degree of peer dependence ( HH HL) decreases, but not at the same rate for the two agents. As gets large (! 0 ) the ncentve scheme for the most productve agent (wth c < cj ) approaches a scheme wth ndependent performance evaluaton (IPE), whle the scheme for the other agent remans q q j JPE. Thus we see that f agents d er wth respect to e ort productvty, the most productve agent - for a gven hold-up power - s gven more ndvdualzed ncentves than the agent wth low e ort productvty, even f ther hold-up powers are equal. In the lmt (as gets large,! 0 ) the less productve agent s o ered a bonus that depends on the performance of the most productve agent, but where the reverse s not true. Ths contrbutes to explanng why lower-level employees are often gven team ncentves based on the rm s overall performance, whle those at hgher levels are o ered ndvdual performance pay (see e.g. Barth et al and Mohn et al., 2010). We also nd that the e ect of a hgher hold-up power on the expected wage depends on the agents abltes. For smplcty, we here assume perfect complementarty (q 10 = q 0). It then turns out that the margnal e ect of hgher hold-up power on the expected (e 1; e 1 )) s largest for agent 16

17 f (q q j ) + ( q 1 q j q j q j 1 q ) > 0 (11) q 0 0 (See the appendx.) For gven e ort costs and e ort productvtes, the LHS n (11) ncreases n both q1 and q0 whle t decreases n q j 0 and n q1. j Hence, hgher hold-up power ncreases the wage d erence between hgh- and lowablty workers. Ths result contrbutes to our understandng of why performance pay ncreases wage nequalty. Lemeux et al. (2009) show that wages are less equally dstrbuted n performance pay jobs because the return to productve characterstcs s hgher n such jobs. Our result suggests that ncreased hold-up power to agents may renforce ths tendency. As we wll now explan, the man results n Propostons 1 and 2 can be llustrated by a smple gure. Gven that each agent s pad a xed salary for low output (ndependent of the other agent s output, LH = LL), and ths salary s set as low as permtted by the enforceablty constrants for these wage payments, we see from (EA) that the correspondng constrants for the payments assocated wth hgh output take the form Hk Q LH = LL, k = H; L (EA ) Ths relaton says that the bonus ncrements for hgh output HH LH and HL LL must both exceed Q, whch s the addtonal value of hgh output for the agent outsde the relatonshp. These relatons are represented by the lnes marked EA n Fgure 2. Only bonuses n the northeast regon delneated by ths L-shaped curve satsfy the enforceablty constrants for the agent. Bonus schemes wth ndependent performance evaluaton are represented by ponts on the dagonal lne (IPE), and those wth jont (relatve) performance evaluaton by ponts above (below) that lne. To be ncentve compatble wth hgh e ort, bonuses must satsfy IC, and ths can here be represented by ponts above a lne such as IC n the gure. 18 Moreover, t s straghtforward to verfy that an socost curve for the wage cost (e 1 ; e 1 ; ) wll be represented by a lne whch s more steeply sloped than IC, as ndcated by the dashed lne n the gure. Gven these facts, t s clear that the bonus scheme that mnmzes costs subject to EA and IC wll be at the ntersecton pont between EA and IC above the dagonal n the gure. Ths pont represents a scheme wth jont performance evaluaton. The agent s then pad a bonus ncrement for hgh output ( Hk Lk) that depends on the other agent s output, and s larger when the latter s hgh 18 The IC constrant s lnear n the bonuses, and can be expressed n terms of the bonus ncrements when LH = LL. 17

18 (k = H) than when t s low (k = L). The bonus ncrement strctly exceeds the value of hgh output for the agent outsde the relatonshp (.e. the EA constrant s not bndng) only when the other agent s output s also hgh. As the hold-up parameter ncreases, the EA constrants become tghter, and the EA lnes shft northeast n the gure, as ndcated by the arrow. Ths mples that the soluton pont for the optmal scheme moves downwards on the IC lne towards the dagonal,.e. towards a scheme wth ndependent performance evaluaton. The vertcal dstance from the soluton pont along EA to the dagonal s gven by HH HL and s thus a measure of the extent to whch agent s bonus for hgh output depends on the other agent s output. Ths can be taken as a measure of peer dependence n the bonus scheme, and we see that ths dependence decreases as the hold-up parameter ncreases. Two dentcal agents would have dentcal IC lnes and hence dentcal bonus schemes. In the lmt as approaches 0, ths common scheme would become an IPE scheme (on the dagonal) and thus have no peer dependence. By de nton of 0 t s the case that for symmetrc agents and 0 the spot contract provdes su cent ncentves for hgh e ort. Ths contract has no peer dependence, and for approachng 0 (from below) we see that the relatonal contract then cannot have such dependence n the lmt ether. Heterogenous agents wll have separate IC lnes, as llustrated by IC and IC j n the gure. Here agent s most productve, n the sense of havng the smallest cost per unt probablty ncrease nduced by hgh e ort,.e. < cj. Geometrcally the IC lne for agent then ntersects the dagonal q j closer to the orgn (at bonus ncrements equal to c As the hold up c q q ). parameter then ncreases towards 0, we see that the optmal scheme for agent approaches an IPE scheme, whle the scheme for the least productve agent j remans JPE. 18

19 Fgure 2: Illustraton for Proposton Complementarty and ncentves To study varatons n complementarty, represented by varatons n the parameter q10, we consder for expostonal smplcty dentcal agents. Recall that (droppng superscrpts) q 10 s the probablty of obtanng hgh output for a hard workng agent, gven that hs partner shrks. The partner s mpact s larger, the smaller s q 10, all else equal. A hgher level of complementarty between the agents s thus represented by a reducton of q 10. Frst, t should be noted that the nsght from Proposton 1 that the degree of peer-dependence decreases wth hgher hold-up power s robust to varatons n the degree of complementarty. In addton we have the followng: Proposton 3 ) The degree of peer dependence ( HH HL ) decreases wth more complementarty (reduced q 10 ). Ths e ect s smaller (n absolute value), the larger the hold up parameter s. ) The mnmal wage cost decreases wth more complementarty. Even though complementarty makes t optmal for the prncpal to offer a JPE scheme, we see that hgher complementarty does not lead to a starker scheme; n fact t s the other way around: Under team ncentves, hgher complementarty ncentvzes the agents because each agent s e ort 19

20 mproves hs peer s output. Hgher complementarty thus reduces the team bonus ncrement HH HL necessary to mplement hgh e ort. The emprcal mplcaton s that the degree of peer dependence n the ncentve scheme should not be expected to ncrease wth the degree of technologcal nterdependence between the agents. These results can be llustrated by Fgure 3, whch s smlar to Fgure 2. For gven parameters there s here one common IC lne for the two (dentcal) agents. For ver able outputs, where there are no enforceablty constrants, the optmal contract s then a stark JPE contract, represented by pont J n the gure. For the relatonal contract, the enforceablty constrants for the agents (represented agan by EA ) clearly force the optmal contract to be less extreme. The optmal contract s stll JPE (represented by the ntersecton pont between IC and EA above the dagonal), but t moves towards an IPE contract as the hold up parameter ncreases. Regardng varatons n the degree of complementarty, as measured by the probablty q 10, t can be seen that a hgher q 10 wll rotate the IC lne clockwse around ts ntersecton pont wth the dagonal. A hgher degree of complementarty (a lower q 10 ) wll lead the IC lne to rotate as ndcated n Fgure 3,.e. to a less steep lne (IC ). As explaned above, ths wll relax mplementaton of JPE contracts, and the gure llustrates how ths mples that the optmal contract wll have a lower degree of peer-dependence. (The optmal pont shfts down along EA.) It also llustrates that ths e ect s smaller the larger the hold-up parameter s. 20

21 Fgure 3: Illustraton for Proposton 2 We nally note that, f the agents producton technologes are ndependent,.e. f q 10 = q 1, then the IC lne wll be parallell to an socost curve. Snce any pont on IC wll then yeld mnmal costs, we see that a scheme wth ndependent performance evaluaton (.e. on the dagonal) wll be optmal n that case. 4 Concludng remarks There s stll lmted theoretcal research on the relatonshp between human captal and ncentve provson. Our approach has been to consder the e ect of employee hold-up n a settng wth multple (two) agents, but the model can be extended n varous ways. We have not consdered dynamc e ects of nvestments n human captal, nor the knd of hold-up problem that appears when rms ncentves to nvest n ther workers human captal are mtgated by the workers ablty to capture the return from these nvestments (by e.g. explotng outsde optons). Our model can also be generalzed further to more agents (n > 2) and possble blateral contractng wth d erent groups of agents (as n Levn 2002). And t can be extended to account not only for technologcal dependence, but also for stochastc dependence between the agents, or socal dependence such as peer pressure To model peer pressure n ths framework, we may assume that there are costs assocated wth lowerng the peer s wage by realzng low output,.e. that the agents experence 21

22 Nevertheless, we beleve our model can elucdate some mportant recent developments. In an nterestng revew of the hstory of employment relatonshps, Peter Cappell (2000) argues that the last twenty years have seen a dramatc shft from tradtonal bureaucratc employment structures to "nsde contractng systems (...) shaped by ndvdualzed ncentves and pressures from outsde labor markets". Along the same lnes, Levn and Tadels (2005) argue that greater competton n the labour market and changes n market nformaton have made t less valuable to commt to the pro t sharng plans of professonal partnershps. We o er a model that helps explan ths rse of ndvdual performance pay. We have shown that compensaton ted to peer performance can nduce employee hold-up and obstruct the mplementaton of relatonal ncentve contracts. The model presented can thus explan the tendency to use ndvdual performance pay n human-captal-ntensve ndustres. Tremblay and Chenevert (2005) and Appelbaum (1991) note that even f knowledgebased ndustres are characterzed by teamwork, the challenge to retan the most crtcal resources ncreases the pertnence of rewardng ndvdual performance. Our model supports ths conjecture. APPENDIX Proof of Proposton 1. The proposton follows from the lemma below. 20 Lemma 1 There s Q L > 0 such that for Q L >Q L the followng holds. There s 1 < 0 = mnf c g such that for 2 ( q Q 1; 0 ) the ncentve scheme that mnmzes costs subject to ncentve and enforceablty constrants for the agents (IC and EA) has the followng features: ) The EA constrants are bndng for all bonuses except HH, and the bonuses are gven by (9-10) n the text and (13) below. ) The mnmal wage cost for agent s (e 1 ; e 1 ) = V (q; c ) + q0q 1 q j 1 q j 10 q1q j 1 q0q j Q + LL (12) 10 dsutlty from beng the "weakest lnk". In an extended verson of the paper (avalable from the authors upon request), we show that whle peer pressure makes team ncentves optmal when agents are dspensable, team ncentves becomes suboptmal once the agents enforcement constrants (EA) bnd. 20 To smplfy notaton we gnore as an argument n () n what follows. 22

23 where V (q; c ) s gven by (8), and LL = (; ; Q L ; q; c ) = Q L c q 1 q 0 Q q 0q j 10 q 1q j 1 q 0q j 10 (13) ) The cost (e 1 ; e 1 ) and the bonus LL are ncreasng n and decreasng n. Proof of the lemma. Wrte the IC constrant as c q1q j 1 q0q j 10 HH + q1(1 q1) j q0(1 q10) j HL (14) + (1 q1)q j 1 (1 q0)q j 10 LH + (1 q1)(1 q1) j (1 q0)(1 q10) j LL De ne p kl as the term multplyng kl n (14),.e. p HH = q 1q j 1 q 0q j 10 > 0 (15) p HL = q 1(1 q j 1) q 0(1 q j 10) p LH = (1 q1)q j 1 (1 q0)q j 10 p LL = (1 q1)(1 q1) j (1 q0)(1 q10) j < 0; where the nequaltes follow from q j 10 2 q0; j q1 j, and note that p kl = 0. Now substtutng for HH from (14) nto the expresson (7) for costs we obtan, after some algebra " # (e 1 ; e 1 ) q 1q j 1 c + q0q 1 q j 1 q j 10 HL (16) p HH + q j 1q j 10 q 1 q 0 p HH p HH LH + (1 q1)(1 q1) j q1q j 1 p LL p HH LL The terms multplyng HL; LH and LL are postve, hence these bonuses should be mnmal. For ver able output t would thus be optmal to set HL = LH = LL = 0, and the mnmal cost would be V (q; c ) = q1q 1c j =p HH, whch s precsely the cost gven n (8). For non-ver able output, the EA constrants of the relatonal contract must be taken nto account. Ignorng non-negatvty constrants for the moment (these wll be checked ex post), the mnmal cost s then acheved when 23

24 the EA constrants for the bonuses HL; LH and LL are bndng, and thus LH = LL = Q L + S 1 (e 1 ; e 1 ) + c = HL Q (17) where S = (Q L + q0q). Substtutng LH = HL Q = LL nto (16), whch must then hold wth equalty, we nd after some algebra that the RHS of (16) and hence the mnmal cost (e 1 ; e 1 ) s gven by the expresson n (12). Consder now the optmal bonus LL. The mnmal cost s gven by (12), where the bonus LL sats es (17). These condtons mply that the bonus LL must be gven by the expresson n (13). To see ths, we can substtute for LL = Q L + 1 [S (e 1 ; e 1 ) + c ] from (17) nto (12) and solve for (e 1 ; e 1 ) to obtan! (e 1 ; e 1 ) = (1 ) V + q0q 1 q j 1 q j 10 q1q j 1 q0q j Q + Q L + S + c (18) 10 where S = (Q L + q0q). Some algebra shows that ths condton and (12) mply that the bonus LL must be gven by the expresson n (13). It remans to check non-negatvty for ths soluton for the bonus LL. De ne 1 as the value of that makes the expresson n (13) postve for all < 1, e let 1 be gven by ( 1; 1; Q L ; q; c ) = 0. For Q L > 0 we see that c 1 < (q1 q 0)Q 0. Also, snce 1 s smaller, the larger s Q L > 0, there s Q L > 0 such that for Q L > Q L we have maxf 1; j 1g 1 < mnf 0; j 0g 0. Snce then (; ; Q L ; q; c ) > 0 for 2 ( 1 ; 0 ) and < 1 t follows that LL n (13) s postve and hence optmal, and that the mnmal cost s ndeed gven by (12). From the bndng EA constrants we have LH = LL = HL Q (see (17)), and by the IC constrant (14) and the de ntons (15), the optmal bonus HH s then gven by HH = = 1 p HH 1 p HH c p HL HL p LH LH p LL LL c + (p LH + p LL)Q + HL where the last equalty follows from p kl = 0. Ths ver es the expresson (10) for HH, snce p LH + p LL = (q 1 q 0). So far we have proved statements () and () n the lemma. Statement 24