Centralize an Deentralize Deiion Making in Organization Ján Zábojník, Univerity of Southern California an Queen Univerity Thi artile ientifie a new type of ot aoiate with entralization. If worker are liquiity ontraine, it may be le otly to motivate a worker who i allowe to work on hi own iea than a worker who i fore to follow the manager iea. Thu, it may be optimal to let worker eie on the metho for oing their job even if manager have better information. Thi onluion hol even if more general ontrat are oniere that are bae on ommuniation of information between the worker an the manager, a long a thee general ontrat are not entirely otle. I believe people will o muh more with their ba iea than they will with your goo iea. (Dave Chekett, preient an CEO of Maion Square Garen [Boek 1996]) I. Introution In reent year, many U.S. ompanie have aopte innovative work pratie, frequently inluing greater eentralization of eiion making. In a reent urvey of private-etor etablihment with 50 or more I am grateful to Mihael Walman for hi invaluable omment an uggetion throughout the evelopment of thi artile. I woul alo like to thank Patrik Legro, Robert Gibbon, an the eminar partiipant at Britol Univerity, Cornell Univerity, Queen Univerity, Stokholm Shool of Eonomi, Texa A&M Univerity, Univerity of Pompeu Fabra, Univerity of Roheter, an Univerity of Southern California. [ Journal of Labor Eonomi, 2002, vol. 20, no. 1] 2002 by The Univerity of Chiago. All right reerve. 0734-306X/2002/2001-0001$10.00 1
2 Zábojník employee, about 45% of nonuperviory worker iretly involve in proution ha ubtantial iretion over the metho for oing their job (Oterman 1994). An extreme example may be the epartment tore Nortrom, whih iue it worker only one intrution: Ue your own jugment (Eonomit 1995). The quetion of entralize eiion making veru elegation ha long been preent in the management literature. The typial fou ha been on a trae-off between two oppoite effet of elegation: on the one han, elegation lea to a better utilization of information attere throughout the lower level of the firm hierarhy; on the other han, it entail a lo of ontrol for the upper-level manager. Thi artile ientifie a new type of ot aoiate with entralize eiion making. Thi ot ome from the interplay among Bayeian upating, moral hazar, an worker liquiity ontraint. In thi environment, it may be more otly to inue a worker to work on omeone ele (i.e., the manager ) iea than on hi own iea. For illutration, onier a reearh team of two, a bo an a worker, trying to evelop a ommerially viable alternative to ga-fuele ar. Suppoe that the manager eie that they will follow her (the manager ) iea an onentrate on alternative fuel, ay alohol. If the worker originally believe that they houl rather onentrate on olar energy, he i now quite peimiti about their hane to uee. Therefore, he may not be very enthuiati about proviing effort an nee a trong inentive ontrat to get motivate. However, if the worker i liquiity ontraine, a tronger inentive ontrat will be more otly. The reaon i that it i har to punih him for a failure an therefore he mut be reware more for ue. I how that, beaue of thi motivation effet, it may be optimal to elegate eiion-making authority to the worker even if the manager i better informe than the worker. Moreover, for ome parameter value, elegation to a le informe worker i optimal, even if a more general la of ontrat i allowe in whih the projet hoie an the agent pay epen on ommuniation of information between the prinipal an the agent. The ret of thi artile i organize a follow. In Setion II I iu the relate literature, an in Setion III I eribe the aumption an the bai moel with one manager an one worker. In Setion IV, I provie a omparion of entralize an eentralize eiion making, an in Setion V I allow for general ontrat that onition the agent pay an the projet hoie on whether the agent an the manager agree on whih projet i optimal. In Setion VI I onlue. All proof are in the appenix. II. Relate Work Muh of the reearh ealing with optimal eign of hierarhial organization oe not look at the optimal alloation of eiion-making
Deiion Making in Organization 3 authority. Rather, it i onerne with the ot of ommuniating an proeing information an with the tehnologial apet of thi problem. 1 An early analyi of eentralization i the omparion of unitary (U-form) veru multiiviional (M-form) ompanie by Chanler (1962) an Williamon (1975). Aoring to Chanler, a a U-form firm expan, it experiene ineffiienie beaue of the lo of ontrol by top management, an it i replae by a more effiient, le entralize M-form organization. One reent work relate to the urrent artile i that of Prenergat (1995), who onier a moel in whih the manager eie whether to arry out a tak herelf or to aign it to a uborinate. He how that beaue of a moral hazar problem, the manager will arry out more tak than i effiient beaue by oing o he an earn future rent through on-the-job learning. However, Prenergat i not onerne with optimal ex ante alloation of eiion-making authority within the firm, whih i entral to the urrent artile. Three paper whoe fou i loe to the fou of the urrent artile are Aoki (1986), Athey et al. (1994), an Aghion an Tirole (1997). Aoki (1986) argue that eentralization houl be prevalent where quik repone to hanging tehnologie an environment i neeary an the flow of new information i upwar through the hierarhy. On the other han, entralization an have benefiial oorination effet. Athey et al. (1994) tuy management by exeption, whih an be eribe a a tateontingent eiion making uner whih the manager interfere in the lower level of hierarhy only in exeptional tate of the worl. Thi arrangement erve to onerve are managerial reoure. Finally, Aghion an Tirole (1997) paper i probably the mot loely relate to the urrent artile. In their moel, a in the urrent one, elegating formal authority to the worker inreae hi inentive to provie effort, beaue it inreae hi expete payoff. However, in Aghion an Tirole, thi higher expete payoff ome from a private benefit erive from the projet that the worker hooe. In the urrent moel, it ome from the fat that, uner elegation, the agent work on hi own iea. Thi mean that he may be more optimiti about the poibility of ue than if he wa fore to work on the manager iea. Alo, while in the Aghion an Tirole tuy, inentive ontrat play no intereting role, they are eential in the urrent moel. In fat, in thi moel, the ot of entralization i that the inentive ontrat for the worker beome tronger an, therefore, more otly. Finally, thi artile i alo relate to moel that fou on revelation 1 See, e.g., Calvo an Welliz (1978), Roen (1982), Walman (1984), Sah an Stiglitz (1986), Geanakoplo an Milgrom (1991), Raner (1993), an Bolton an Dewatripont (1994), to name a few.
4 Zábojník mehanim, for example, thoe of Meluma an Reiheltein (1987) an Meluma, Mookherjee, an Reiheltein (1992). The onnetion to thi literature will be explore in greater etail in Setion V, whih allow for general ontrat bae on ommuniation of information between the worker an the manager. III. The Moel Preferene. Conier a firm with a rik-neutral owner-manager (a woman) hiring one rik-neutral worker (a man). The manager objetive i to maximize the firm expete profit while proviing the worker with at leat hi reervation utility, u 0. Proution tehnology. The firm an hooe between two projet, 1 an 2, that are mutually exluive (i.e., only one of the two projet an be aopte). Eah projet require an invetment, C 0, inurre by the firm, an effort e {0, 1}, provie by the worker. If the firm oe not invet in a projet, thi projet i not unertaken an the worker annot work on it. After a projet i hoen, the worker eie whether to provie effort ( e p 1) or not ( e p 0). The worker hoie of effort i not obervable to the manager, whih introue a moral hazar problem. The ot of proviing effort i iutility H 0 for e p 1. The projet payoff epen on the tate of the worl an on the worker effort in the following manner. There are two equally probable tate of the worl, enote ( p 1, 2). Projet j ( j p 1, 2) pay V 1 0 if the tate of the worl i p j an the worker provie effort, an it pay W (normalize to zero for impliity) otherwie. In other wor, projet 1 annot be ueful if the tate of the worl i 2, an vie vera. To um up, the firm output y i given by y p kev, where k p 1 if j p an k p 0 if j (. Thu, effort an auray of projet hoie are omplement here. Thi etting oul alo be interprete a a problem of hooing the right tehnology of proution. If the wrong tehnology i hoen, it will not give the eire outome. 2 Complementarity between effort an auray of projet hoie i not ruial here. Appenix B examine the valiity of the moel qualitative reult uner an alternative tehnology peifiation, where effort an auray of projet hoie are ubtitute. It emontrate that the main theoretial reult of thi artile, a repreente by part b in propoition 2, i preerve in thi alternative etting. 2 In yet another interpretation, the worker aumulate firm-peifi human apital intea of proviing effort. In thi interpretation, there woul be two poible type of firm-peifi human apital, ay learning the etail about the firm prout market veru matering a proution tehnology, an the manager woul be able to fore the worker to hooe the type he think i more benefiial. For moel ealing with peifi human apital aumulation, ee Kahn an Huberman (1988), Prenergat (1993), an Zábojník (1998), for example.
Deiion Making in Organization 5 Information truture. The worker an the manager have ifferent abilitie to itinguih between the two projet (tate of the worl). After nature eie whih tate our, both the manager an the worker reeive impreie an inepenent ignal about the tate that wa realize. If tate ourre, the manager reeive ignal with probability q (1/2, 1), o that her belief that ourre i q. Similarly, the worker poterior belief that tate ourre, after oberving a ignal for, i p (1/2, 1). The prior probability of 1/2, a well a the ignal preiion, are ommon knowlege to both agent. Contrating. Note that, beaue the worker effort i not obervable, hi pay mut epen on the outome of the projet; otherwie he woul alway provie zero effort. The worker employment ontrat will therefore be haraterize by a wage he reeive if the projet fail an a wage he reeive if the projet i ueful. In Setion V, thee wage an epen on whether the manager an the worker agree on whih projet i optimal. They are etermine an the employment ontrat i igne before the ignal are reeive. I will aume that there i a lower boun D on the wage, where D u. Thi mean that, if the projet fail, the worker annot be fore to pay a large fine to the manager. Similarly, when entering the employment relationhip, it i not poible for the worker to plae a large bon with the manager that woul be returne only if the projet i ueful. Thi i an important aumption, riving the main reult. Thi aumption eem quite realiti an i quite ommon in the literature. 3 It allow two interpretation. Firt, the worker may be liquiity ontraine beaue of imperfet apital market, o that he annot borrow from a bank to pay a fine to the firm in the ae of a ba outome or to finane hi onumption in earlier perio. Seon, there may be legal proviion in the eonomy uner whih the worker ha limite liability an annot be fore to plae a bon with the firm when hire. It i intereting to note here that, a hown in an earlier verion of thi artile, the moel main reult woul remain unhange if the worker wa rik avere intea of being liquiity ontraine. Deiion making. I will onier three alternative eiion-making arrangement: 1. Deentralization. Here the eiion-making authority i elegate to the worker with no interferene from the manager. Thi inlue elegating to the worker the authority to invet C into the projet of hi hoie. I will ometime refer to thi arrangement a elegation. 3 See, e.g., Sappington (1983) for a iuion an an analyi of the prinipalagent problem with limite liability.
6 Zábojník 2. Centralization. Here the manager make the projet hoie an the invetment without onulting the worker. 3. Joint eiion making. Thi repreent a general mehanim where the manager an the worker announe their repetive ignal an both the projet hoie an the worker pay epen on thee announement. Thi arrangement will be eribe in greater etail in Setion V. Commitment. No renegotiation i allowe after an employment ontrat i igne. More peifially, the manager i able to ommit not to reveal her ignal to the worker or, alternatively, not to reeive any ignal at all. Similarly, he i able to ommit not to obtain any information from the worker regaring the worker ignal. Thi rener all three arrangement feaible an omparable. Parameter retrition. In orer to make proution profitable uner both entralization an eentralization, a well a to limit the number of ae that nee to be oniere, I will aume that the parameter value are retrite a follow. Aumption 1. V 1 max [2H,(H C u)/m], where m p min (p, q). IV. The Analyi of Centralization an Deentralization I will firt ompare entralization an eentralization an how that elegation an be preferre even if the manager i better informe than the agent (i.e., q 1 p). I will then how, in Setion V, that, uner ome parameter value, elegation to a le informe agent remain optimal, even if the thir arrangement i oniere, where the projet hoie an the agent pay epen on ignal announement, a long a thi arrangement i not entirely otle. I will tart with the ae of eentralization. A. Deentralization In thi ae, both the hoie of the projet an the invetment of C are mae by the worker, bae olely on hi own ignal. Therefore, the worker belief that the projet will be ueful i p. A i tanar in moel with rik-neutral agent faing liquiity ontraint, it i optimal to et the worker pay in the ae of failure to be equal to the ontraint D. Thi allow the manager to provie the worker with the tronget poible inentive while holing hi expete pay ontant. Let the wage that the worker reeive in ae of ue be enote b. The ifferene between the two wage, b an D, mut be uh that the worker i willing to provie effort; otherwie, the manager i better off loing the firm. The worker inentive ompatibility onition i thu p(b D) H 0. The worker expete wage i then w p pb (1
Deiion Making in Organization 7 p)d, o that hi partiipation ontraint an be written a p(b D) H u D. Beaue u D 0, the manager hooe the wage b uh that the partiipation ontraint i bining an the worker get exatly hi reervation utility. The liquiity ontraint thu ha no effet on the firm expete profit uner eentralization. Thi profit i p p pv C u H. 4 B. Centralization without a Liquiity Contraint Uner entralization, the liquiity ontraint play an important role. I will firt look at the benhmark ae where there i no liquiity ontraint. In thi arrangement, the projet i hoen an C i invete by the manager, who oe not onult the worker before eiing. After the manager eie, the worker form a poterior belief about the probability of ue given the elete projet. A the problem i ymmetrial with repet to tate of the worl, it i enough to retrit attention to the ae where the manager hooe projet 1. Then there are two poibilitie: (a) the worker get the ame ignal a the manager, an (b) the worker get ignal 2. In the former ae, the worker poterior probability of ue i p(1, 1) p pq/[ pq (1 p)(1 q)], while in the latter ae it i p(1, 2) p q(1 p)/[ p(1 q) (1 p)]. It i eay to hek that p(1, 1) i alway greater than both p(1, 2) an p. Denote the wage in the ae of ue a an the wage in the ae f of failure a. Let the worker ignal be x p 1, 2, o that hi poterior i p(1, x). The worker two inentive ompatibility ontraint are then f ( )p(1, x) H. (1) Beaue p(1, 1) 1 p(1, 2), the ontraint (1) i atifie for both poterior if it hol when the worker poterior i p(1, 2). The worker partii- pation ontraint i f q (1 q) H u. (2) Note that the probability of reeiving the bonu i q in the above partiipation ontraint. Thi follow from the fat that the projet i hoen by the manager, o that the ex ante probability of ue i q. Sine p(1, 2) 1 1/2, aumption 1 implie p(1, 2)V 1 H. Hene, it i op- timal to eliit effort uner both of the worker poterior if thi an be 4 The reaon firt bet an be ahieve here i that the probability of ue uner no effort i zero. Thi, ombine with the fat that the worker ex pot (i.e., after hooing the projet) belief about the probability of ue i the ame a hi ex ante belief, implie that an inentive-ompatible ontrat only nee to offer him hi reervation utility. In app. B, probability of ue uner no effort i poitive, whih mean that firt bet i not alway attainable.
8 Zábojník one without inreaing the worker expete utility above u. Therefore, the bet the manager an o uner entralization in term of ex ante expete profit i p* p qv C H u. Thi profit woul be ahieve if the worker expete utility were exatly equal to hi reervation utility (i.e., if [2] were bining) an if the worker alway provie effort (i.e., if [1] were atifie for the poterior p(1, 2). Beaue one an alway fin f an uh that thee two onition hol, we have the following reult. Propoition 1. If the worker i not liquiity ontraine, then a) the expete profit uner entralization i p* p qv C H u, an b) entralization i preferre to eentralization if an only if the manager ignal i better than the worker ignal, that i, q 1 p. The eon part of the propoition ome from a traightforwar omparion of the expete profit uner entralization, p*, with the profit uner eentralization, p. Thi reult eem intuitive an harly ur- priing the eiion i mae by the party who i better informe. However, in the next ubetion, I will how that when the worker fae a liquiity ontraint, thi reult no longer hol. C. Centralization with a Liquiity Contraint Now uppoe there i a lower boun D on wage. Again, it i optimal f to et p D. To ee how the liquiity ontraint hange the ituation, let 1 be the mallet wage that eliit effort for both of the worker poterior, that i, 1 { H/p(1, 2) D. Uing the wage 1 an D, the partiipation ontraint beome [q p(1, 2)]H (u D)p(1, 2). (3) It i immeiate that if D i loe to u, ontraint (3) hol with trit inequality, the worker enjoy a rent, an the firt bet profit p* annot be attaine. Thi make it poible for elegation to ominate entralization even when the manager i better informe than the agent. I will now invetigate uner what onition thi an happen. There are two poible aniate for the optimal ontrat uner entralization with a bining liquiity ontraint. Thee will be terme a i) the full inentive ontrat, with p 1, in whih the wage i high enough to eliit effort regarle of the worker poterior but the worker an enjoy a rent; 5 an 5 If the optimal wage were 1 1, the liquiity ontraint woul not be bining, the worker oul be hel own to hi reervation utility u, an entralization woul be alway preferre to eentralization for q 1 p. Thi ae i not intereting.
Deiion Making in Organization 9 ii) the partial inentive ontrat, with! 1, in whih the worker get exatly hi reervation utility but provie effort only if hi 6 poterior i p(1, 1). The repetive expete profit uner thee two alternative ontrat are p (i) p qv C H U ( 1), (4) where U ( 1) { q1 (1 q)d H i the worker expete utility when p, an 1 p (ii) p pqv C [ pq (1 p)(1 q)]h u. (5) Thu, elegation i optimal if an only if p 1 max [p (i), p (ii)]. Propoition 2. a) When the worker i better informe ( q! p), the manager prefer elegation. b) For any worker, there i a manager who, for ome parameter value, tritly prefer eentralization even though he i better informe than the worker. Formally, for any given p! 1an u, there exit value for q, H, an V uh that q 1 p an p 1 max [p (i), p (ii)]. ) When q 1 p, elegation beome relatively more profitable a the lower boun on wage, D, inreae an a the worker reervation utility, u, ereae. Part b of propoition 2 repreent the main theoretial reult of thi artile. Aoring to thi reult, the eiion-making authority within organization nee not alway ret with the better informe, or more able, party. The intuition i a given in the Introution : Suppoe that the manager hooe a projet ifferent from the one preferre by the worker. If the manager i only lightly better informe than the worker, the worker poterior belief in ue, p(1, 2), will rop below hi original belief, p. Thi low poterior make it more otly to inue the worker to provie effort. Thi i beaue, ue to the worker liquiity ontraint, it i har to punih him for ba outome. Therefore, the inentive mut be provie by paying a bonu for ue. But the lower i the worker belief that hi effort will make any ifferene, the higher mut be thi bonu an, hene, the worker expete pay. Therefore, if the ifferene between the quality of the agent ignal i low, the worker reeive an expete utility higher than hi reervation utility, an he enjoy a rent. If the worker information i not muh wore than the manager in- 6 In fat, the wage oul alo be o mall that it woul not eliit effort for any of the poterior. However, thi annot be optimal, beaue the maximum value for expete profit in thi ae equal zero.
10 Zábojník formation, thi effet offet the manager higher ability to hooe the orret tehnology an make eentralization more attrative. The intuition for the omparative tati effet in part i imple. An inreae in the worker reervation utility make it le likely that he reeive a rent uner entralization. A ereae in the lower boun on wage ha the ame effet, beaue it ereae the nee to pay the worker a high bonu for ue, thu ereaing hi expete wage. Both of thee effet make entralization relatively more profitable in omparion with elegation. V. Joint Deiion Making In thi etion, I will allow for general ontrat in whih the projet hoie an the worker pay an epen on ignal announement. The goal i to emontrate that, if ommuniating information from the worker to the manager i not entirely otle, thee general ontrat annot ominate both entralization an eentralization, unle the ot of invetment C i relatively high. Thi then implie that, for low value of invetment ot, the main onluion of propoition 2 till hol; that i, elegation an be optimal even if the manager i better informe than the worker. In the joint eiion-making arrangement, the employment ontrat peifie (a) how the worker an the manager announe their ignal, (b) how the projet hoie epen on thee announement, an () how the worker remuneration epen on the announement an on the projet outome. I will onentrate on the following timing: 7 1. The worker an the manager ign a ontrat. 2. Both the worker an the manager reeive their private ignal. 3. The worker announe hi ignal to the manager (not neearily truthfully). It i not poible for the manager to verify the truthfulne of the worker announement. Thu, in the terminology of Aghion an Tirole (1997), the information onveye by the worker i oft. 4. The manager onier the worker uggetion an announe her own ignal (again, not neearily truthfully). I will aume that it may be otly for the manager to onier the worker uggetion an thi ot will be enote a R, R 0. 5. A projet i hoen bae on the above announement (perhap ranomly), a etermine by the ontrat. 6. The worker upate hi belief uing the manager announement an eie whether to provie effort. 7 Qualitatively, very little woul hange if the worker an the manager announe their ignal imultaneouly an not equentially a aume here.
Deiion Making in Organization 11 7. Payment are mae onitional on announement an ue. The arrangement oniere here i more ophitiate than either of the two arrangement oniere earlier. At a firt glane, it main avantage eem to be the poibility to extrat the worker rent by tailoring hi pay epening on whether he an the manager agree on whih projet i optimal. After all, the reaon for the elegation reult of propoition 2 wa that uner entralization with full inentive the worker reeive a rent that oul not be extrate by the manager beaue only one bonu ha to be ue to provie inentive uner two ifferent poterior. Here, in ontrat, the manager an ue two ifferent bonue, whih may eem enough to extrat the worker rent: the bonu oul be high when the two announement iagree an low when they agree. However, thing are more ompliate here than meet the eye. There are two problem with thi heme, whih imply that the worker rent annot be extrate ompletely. Firt, if the bonu i high when announement iagree an low when they agree, then the worker ha an inentive to mirepreent hi ignal. To ee thi, uppoe that the ontrat peifie that, in the ae of iagreement, the projet that i hoen i the one announe by the manager. 8 In thi ae, the worker announement oe not influene the projet hoie; it only affet the worker expete payoff. Hene, the worker ha an inentive to lie, whih in effet mean that hi bonu i high when hi poterior i high an vie vera. If anything, thi make hi rent even higher than before. Seon, the manager ha an inentive to lie, too. Suppoe that the bonue are uh that they eliit effort only if the two announement agree. Then, if the manager ee that her ignal iffer from the worker announement, he know that if he announe her ignal truthfully, the worker will provie no effort. Thu, to eliit effort from the worker the manager mirepreent her ignal, e fato repliating elegation. 9 Neverthele, uner ome onition, joint eiion making an improve on both entralization an eentralization. The relative avantage of thi arrangement i that it pool information of both the worker an the manager. Given thi poole information, ome projet may turn out to be of negative expete profit, even if they have poitive expete profit uner both entralization an eentralization. Thi an happen if the 8 If the ontrat peifie that the projet uggete by the worker houl be hoen, uh a ontrat woul, in effet, repliate eentralization. 9 The firt argument woul apply even if the announement were imultaneou. The eon argument woul, obviouly, not apply. Intea, the ituation where the bonue are not high enough to eliit effort in ae of the lower poterior woul ompletely repliate the outome of the partial inentive ontrat uner entralization.
12 Zábojník invetment ot, C, of the projet i relatively high. Joint eiion making then allow the firm to kip thee negative-expete-value projet. Propoition 3. a) There exit a Cˆ 1 0 uh that if C! Cˆ an R 1 0 ( R p 0), joint eiion making i tritly (weakly) ominate by either entralization or eentralization, an propoition 2 applie. b) There exit parameter value C* 1 0, u* 1 0, an R* 1 0, uh that if C 1 C*, u 1 u*, an R! R*, then joint eiion making i the optimal eiion-making arrangement. Part a of propoition 3 implie that the entral onluion of propoition 2 i preerve here: if the ot of invetment i relatively mall, then elegation to a le able worker may be tritly optimal, provie that ommuniation of information i not entirely otle. A iue earlier, thi part i rather urpriing. Suppoe that the ot R of oniering the worker uggetion i very mall (loe to zero) an that the firt bet profit uner entralization, p*, an be attaine neither by entralization nor by eentralization. Then one might expet that joint eiion making, with it more ophitiate inentive heme an a riher trategy et, houl be able to improve on elegation even if the ot of invetment, C, i very low. Yet, aoring to propoition 3, if C i mall an R i poitive, the joint eiion making i tritly ominate. If R i zero, then the bet that joint eiion making an o i to repliate either entralization or eentralization. The key to thi reult lie in the fat that, if the inentive heme i eigne o a to extrat the worker rent, then either the worker or the manager have an inentive to game the ontrat, a iue earlier. Part b of propoition 3 i quite intuitive. It follow from the fat that poole information allow for better eiion making, whih make it poible for the manager to ave the invetment ot C by orting out projet with negative interim expete value p(1, 2)V C H u. Note that, beaue the information onveye by the worker in hi announement i oft, the game playe between the worker an the manager in thi etion an be viewe a a heap talk problem, a analyze in Crawfor an Sobel (1982). For example, it i eay to ee that there alway exit a babbling equilibrium, in whih the manager ompletely ignore the worker announement, an vie vera. In uh a ae, joint eiion making ha no value, an the onluion of propoition 2 apply automatially. However, the reult in part a of propoition 3 i tronger than one obtaine by relying olely on the exitene of a babbling equilibrium: part a ay that, for ome parameter value, the qualitative reult of propoition 2 go through, even if the manager pay attention to what the worker announe. Thi reult an thu be better appreiate, in the ontext of the mehanimeign literature, a aying that the bet revelation mehanim that the
Deiion Making in Organization 13 manager an eign in thi etting i not goo enough to alway make joint eiion making tritly better than both plain entralization an eentralization. Therefore, if there i a ot, no matter how mall, aoiate with joint eiion making, then the latter an ometime be tritly ominate by either entralization or eentralization, in whih ae one an revert to the onluion of propoition 2. The analyi in thi etion i thu relate to the literature on elegation an the value of ommuniation, a exemplifie by Meluma an Reiheltein (1987) or Meluma et al. (1992), among other. The fou of Meluma an Reiheltein (1987) i on ientifying the onition uner whih elegation an o equally well a an optimally eigne revelation mehanim. In their moel, though, unlike in the urrent artile, the prinipal ha no private information. They, therefore, o not tuy what happen if the prinipal i better informe than the agent, whih i a ae that play an important role here. Meluma et al. (1992) invetigate the value of elegation when a revelation mehanim i otly. A hown by Myeron (1982), if the ue of a revelation mehanim i otle, then elegation ha no value, beaue it i alway weakly ominate (a i any other organizational arrangement) by entralize eiion making that relie on a revelation mehanim (joint eiion making in the ontext of the urrent artile). Myeron reult i very elegant, but, a Meluma, Mookherjee, an Reiheltein (1997) point out, it make it har to explain why elegation i ue o often in organization. For elegation to be optimal, it mut therefore be that there i ome ot aoiate with the ue of a revelation mehanim. In the urrent artile, thi ot i repreente by R, the ot to the manager of oniering the worker uggetion. In Meluma et al. (1992), thi ot i aoiate with ommuniating information. They evelop a moel in whih the prinipal an either ontrat iretly with two agent, or, alternatively, let agent 1 ontrat with agent 2. The latter arrangement i more flexible, but it entail a lo of ontrol for the prinipal. It i thi trae-off that i entral to their paper. Again, they o not onier the poibility that the manager i better informe than the agent, whih play an important role in the urrent artile. VI. Conluion Thi artile ientifie a new type of ot aoiate with entralize eiion making when effort an auray of projet hoie are omplement. Uner entralization, a manager an hooe a projet that the worker ilike. Thi an make it otly to motivate the worker to work on thi projet if he i liquiity ontraine. Delegation thu may be the optimal organizational arrangement even if the manager i better able to hooe a profitable projet. Thi reult i robut to introution of more
14 Zábojník general employment ontrat, bae on ignal announement by the worker an the manager. An impliation of the moel, not mentione in the main text, i worth mentioning here. Note that the entral reult of thi artile, eribe by part b of propoition 2, ha fore only if the ifferene between the abilitie of the worker an the manager i not too big. Thi implie that the firm manager might prefer hiring a le able worker, who woul be more inline to trut the manager eiion. Caual obervation ugget that thi might be onitent with the pratie of ome firm who are not willing to onier overqualifie worker (e.g., Ph.D. ) for ome poition. Appenix A Proof of Propoition Proof of Propoition 2 a) The highet expete profit attainable uner entralization i p* p qv C H u, whih i le than p p pv C H u when q! p. b) p 1 p (i) if an only if an p 1 p (ii) if an only if H(1 q)(2p 1) (q p)v u D 1 0, (A1) 1 p p(1 q)v [ p(1 q) q(1 p)]h 1 0. (A2) Fix a reervation utility u an a ontraint D. Let A { (1 q)(2p 1), B { (1 p)(q p), u { (u D)(1 p), an M { 1 p(1, 2). Then (A1) an (A2) reue to AH 1 BV u an MV 1 H, repetively. If AM B ( 0, one an alway fin V an H uh that (A1) an (A2) hol with equality for given p an q. V an H are given by V p u/(am B) an H p um/(am B). Now, AM B 1 0 if an only if 2 (1 q) (2p 1)p 1 (1 p)(q p). p(1 q) q(1 p) If thi onition hol, then both V an H are poitive. But it i eay to ee that for any p 1 1/2 there exit a q 1 p uh that the above onition hol it i enough to take q uffiiently loe to p. Chooe uh a q. Now, if AM B 1 0, then it i poible to fin DV an DH uh that (A1) an (A2) hol for Vˆ p V DV an for Hˆ p H DH. To ee thi, note that inequalitie (A1) an (A2) hol for V ˆ an Hˆ if an only if DVM 1 DH an DHA 1 BDV. An beaue AM B 1 0, uh DV an DH exit. ) Thi reult follow from a traightforwar ifferentiation of (A1), noting that (A2) i inepenent of u an D. Q.E.D.
Deiion Making in Organization 15 Proof of Propoition 3 Without lo of generality, let D p 0. Part a For the moment, et R p 0. I will how that, for C p 0, joint eiion making (JDM) i weakly ominate by either entralization or eentralization. By ontinuity, thi reult will hol alo for mall C 1 0. Firt, note that it i uffiient to onentrate on ontrat that fore both the worker an the manager to reveal their ignal truthfully. Thi follow from the revelation priniple. Let a be the probability aigne by the ontrat to projet j if both partie announe ignal j, an let b be the probability aigne by the ontrat to projet j if the manager announe j an the worker announe i ( j. Beaue both partie announe their ignal truthfully, it follow that it i optimal to alway et a p 1 an to et b p 1 if q 1 p an b p 0 if q! p. To ee thi, uppoe firt that a! 1. Then if both partie announe ignal j (truthfully) an the ontrat all for the projet i ( j, the expete ue of the projet, a well a the worker poterior, i 1 p(1, 1). But 1 p(1, 1)! p(1, 1). Hene, the probability of ue i lower an the bonu neee to eliit effort i higher in thi ae than if the ontrat alle for projet j (reulting in the poterior p(1, 1)). Higher a an therefore inreae the firm expete profit. The ame reaoning applie for b, where the argument i omplete by noting that p(1, 2) 1 1 p(1, 2) if an only if q 1 p. So, let a p 1. Step 1. Aume q! p. By the above analyi, it i optimal to et b p 0, o that the worker uggetion i alway followe. In uh a ae, the expete revenue i pv. Sine the worker mut get at leat hi reer- vation utility, the expete profit in thi ae annot be higher than pv C u H, whih i p, the profit uner eentralization. Step 2. Now uppoe q 1 p, o that it i optimal to et b p 1, that i, the projet i alway hoen aoring to the manager uggetion. Suppoe that the worker bonu i ( ) if the two announement oinie (iffer). For the worker to be willing to reveal hi ignal truthfully, it mut be. Otherwie, he ha an inentive to lie in orer to influene the probability that hi announement iffer from the manager ignal. If he announe hi ignal truthfully, thi probability i v1 p 1 pq (1 p)(1 q); otherwie it i v2 p pq (1 p)(1 q) 1 v 1. So uppoe. Step 3. A in the ae of entralization, there are two aniate for the optimal ontrat here. Cae (i) The worker alway provie effort. To eliit effort uner both poterior, it mut be that 1 { H/p(1, 2). The worker expete utility i then qp q(1 p) H, whih i greater than U ( 1) { q 1 H, o that the worker rent i no lower (an the firm profit no higher) than uner
16 Zábojník Cae (ii) entralization with full inentive. The worker provie effort only when hi poterior i p(1, 1) (if 1, it i not poible to eign a ontrat where the worker provie effort only when hi poterior i p(1, 2), beaue p(1, 2)! p(1, 1) ). Beaue the worker oe not provie effort when hi poterior i p(1, 2), with thi poterior, the expete profit i zero an the manager ha an inentive to mirepreent her ignal in orer to make the worker poterior equal to p(1, 1) intea of p(1, 2). But then the manager oe not alway reveal her ignal truthfully, whih i a ontraition. Thu, the bet that JDM an ahieve if C p 0 an R p 0 i to repliate either entralization or eentralization. Therefore, if R 1 0, JDM i tritly ominate by either entralization or eentralization. By ontinuity, there then exit a Cˆ 1 0 uh that thi reult hol for all C! Cˆ. Part b Suppoe the bonu i, an the interim expete profit p(1,2)(v ) C i negative. Then, uner JDM, the manager invet only if her ignal i the ame a the worker uggetion, o that the ex ante expete JDM profit i p p pqv R [ pq (1 p)(1 q)](c H) u. Thi i more than p (ii) (given by [5]) if an only if [ p(1 q) q(1 p)]c 1 R. (A3) JDM Similarly, p i more than p (i) (given by [4]) if an only if [ p(1 q) q(1 p)](c H) 1 R q(1 p)v. (A4) Finally, JDM yiel higher expete profit than eentralization if an only if [ p(1 q) q(1 p)](c H) 1 R p(1 q)v. (A5) Let q 1 p. Then, if C i high enough an R mall enough, (A3) an (A4) hol, an (A5) alo hol, beaue q 1 p. Alo, if (A4) hol, then, if u i large enough, p(1, 2)(V ) C i negative a aume at the beginning of the proof. Similarly, if p 1 q, then if (A5) hol, (A3) an (A4) hol too, an if u i large, p(1, 2)(V ) C i negative. Therefore, the laim follow. Q.E.D. Appenix B Effort an Auray of Projet Choie a Subtitute The purpoe of thi appenix i to examine the valiity of the moel qualitative reult in a etting with an alternative peifiation of proution tehnology. In partiular, intea of being omplement, effort an auray of projet hoie are ubtitute here. Formally, thi i repreente by a tehnology y p kv (1 k)ev, where, a before, k p 1 if
Deiion Making in Organization 17 j p an k p 0 if j (. Thu, while uner the tehnology ue in the main text effort exerte on a goo projet wa more proutive than effort exerte on a ba projet, here the ituation i revere. The goo projet i a ure ue even if the agent exert no effort, while a ba projet require effort to be ueful. Uner thi peifiation, the agent inentive ompatibility an partiipation ontraint, a well a the firm expete profit, are given a follow. Centralization Uner entralization, the agent inentive ompatability ontraint are f given a H p(1, x) [1 p(1, x)], x p 1, 2, whih reue to f ( )[1 p(1, x)] H 0, x p 1, 2. i) Full inentive. In thi ae, the agent provie effort regarle of hi poterior, whih mean that the partiipation ontraint i H u. ii) Partial inentive. In thi ae, the agent provie effort only when hi poterior i p(1, 2), an hi partiipation ontraint i f [q (1 q)p] (1 q)(1 p) H[ p(1 q) q(1 p)] u. iii) No inentive. In thi ae, the agent never provie effort, o that hi partiipation ontraint an be written a f q (1 q) u. f Uing p D, the expreion for expete profit uner entralization are a follow: i) Full inentive. When the agent alway provie effort, the firm expete profit i pi p V C H U (i), ( ) (B1) where U (i) p max u, D {H/[1 p(1,1)]} i the agent expete utility uner the full inentive ontrat. ii) Partial inentive. pii p V[q (1 q)p] C H[ p(1 q) q(1 p)] U (ii), (B2) where U (ii) p max {u, D H[q p(1 q)]/[1 p(1, 2)]} i the agent expete utility uner the partial inentive ontrat. iii) No inentive. Sine in thi ae the agent provie no effort, the expete profit i p p Vq C u. (B3) iii
18 Zábojník Deentralization Uner eentralization, the agent inentive ompatibility ontraint i f ( )(1 p) H 0. i) Full inentive. Uner thi ontrat, the agent alway provie effort, an hi partiipation ontraint i H u. ii) No inentive. When the ontrat never inue the agent to provie effort, hi partiipation ontraint i Again, uing f p D, f p (1 p) u. the profit are pi p V C H U (i) (B4) uner the full inentive ontrat, where U (i) p max {u,d [H/(1 p)]} i the agent expete utility uner thi ontrat, an pii p Vp C u. (B5) The Effet of a Liquiity Contraint on the Optimal Deiion- Making Arrangement Propoition 4 below eribe the effet of a liquiity ontraint on the optimal eiion-making arrangement when effort an auray of projet hoie are ubtitute. Propoition 4 an be viewe a a ounterpart of propoition 2 in thi alternative etting. Propoition 4. a) For any given H 1 0 an q (1/2, 1), there exit parameter value for p, D, an V uh that, in the abene of a liquiity ontraint, eentralization i tritly optimal, but in the preene of a liquiity ontraint, entralization i tritly optimal. b) For any given H 1 0 an q (1/2, 1), there exit parameter value for p, D, an V uh that in the abene of a liquiity ontraint entralization i tritly optimal, but in the preene of a liquiity ontraint, eentralization i tritly optimal. Proof of propoition 4 (a). Suppoe, firt, there i no liquiity ontraint. Comparing profit uner entralization with thoe uner eentralization, one an ee that pi 1 pi iff q 1 p, (B6) pii 1 pi iff V[1 p(1, 1)]! H, (B7) pi 1 pii iff V(1 p) 1 H, (B8)
Deiion Making in Organization 19 Fig. B1. Deentralization i optimal in the abene of a liquiity ontraint (i.e., D! D ), but it i uboptimal when a liquiity ontraint i preent uh that D! D! D. 1 pii 1 pii iff V[1 p(1, 2)] 1 H, (B9) piii 1 pii iff q 1 p. (B10) Fix an H 1 0 an a q (1/2, 1). Conier p p q, an hooe V uh that V[1 p(1, 1)] p H, where 1 0 i loe to zero. Thi mean that the revere of (B7) hol. Then, by (B6), pi p pi ; by (B7), p ii! p i ; an, by (B10), piii p p ii. Therefore, without a liquiity ontraint, elegation i tritly optimal uner thee parameter value. Now introue a liquiity ontraint. Note that there exit a D 1 0, uh that pi i inepenent of D for D D1 an i linear an ereaing in D for D 1 D1 (ee fig. B1). Similarly, for pi ( pii), there exit a D2 ( ), uh that D3 pi ( pii) i ontant for D D2 ( D D 3) an linearly e- reaing in D for D 1 D2 ( D 1 D3). Now, the revere of (B6) implie that (B8) hol, beaue 1 p(1, 2) 1 1 p(1, 1). Thi mean that pii 1 pii if D i not bining (i.e., for D! D 3). Moreover, even when D i bining, looking at figure B1, one an ee that there exit a parameter value D 1 D3 uh that pii 1 pii for D! D. Next, ompare pii an pi uner a liquiity ontraint. After a few algebrai manipulation, it turn out that p 1 p if an only if ii i V[1 p(1, 1)]! H D, (B11)
20 Zábojník Fig. B2. Centralization i optimal in the abene of a liquiity ontraint (i.e., D! D 2 ), but it i uboptimal when a liquiity ontraint i preent uh that D! D! D. where [ ] p(1, 1) 1 1 D p H. pq 1 p 1 p(1, 2) Beaue 1 p! 1 p(1, 2), it follow that D 1 0. Alo, if i hoen uffiiently mall (o that! D), then (B11) hol, an there exit a D! D (ee fig. B1) uh that pii 1 pi for D 1 D. Hene, for p p q, pii 1 max (p i, p i ) if D (D, D ). Continuity then implie that imilar reult hol alo for p ( q if p i loe to q. Thi onlue the proof of part a of propoition 4. Proof of propoition 4 (b). Again, tart by hooing p very loe to q, but p! q. Next, elet V large enough o that (B7) hol. Then en- tralization i tritly optimal in the abene of a liquiity ontraint, beaue pii 1 max (p i, p ii). Now introue a liquiity ontraint, an onier p p q. Comparing pi an p i, it follow that pi 1 p i, beaue 1 p(1, 1)! 1 p, an thi implie U (i) 1 U (i). By ontinuity, there exit a D (ee fig. B2) uh that pi 1 pi alo for p lightly lower than q. Next ompare pi an p ii. It i immeiate from (B11) that if p p q an V i hoen large enough, then pi 1 p ii. Again, uing ontinuity, pi 1 pii even when p! q if p i loe enough to q. Finally, ompare pi an piii for p lightly maller than q. In the abene of a liquiity ontraint, p 1 p if an only if V(1 q) 1 H, whih hol beaue (B11) hol. i iii
Deiion Making in Organization 21 Therefore, there exit a uh that D 1 D pi 1 piii whenever D! D. Thu, in the preene of a liquiity ontraint, there exit a nonempty interval (D, D) uh that eentralization i tritly optimal if D (D, D). Q.E.D. Part b of propoition 4 i a qualitative equivalent of part b of propoition 2, an it emontrate that thi reult i robut to extenion into etting with alternative proution tehnology. On the other han, part a in propoition 4 iffer from part a in propoition 2: when effort an auray of projet hoie are ubtitute, it i poible that the preene of a liquiity ontraint make entralization optimal where otherwie it woul be ominate by eentralization. However, when effort an auray of projet hoie are omplement, thi i never poible. The intuition for thi ifferene in the part a of propoition 2 an 4 i a follow. Conier eentralize eiion making. When effort an auray of projet hoie are omplement, a in the main text, it i relatively heap to eliit effort from the agent, beaue the projet an be ueful only if the agent provie effort. Without proviing effort, he get no bonu. On the other han, when effort an auray of projet hoie are ubtitute, a in thi appenix, the projet an be ueful even if the agent provie no effort. Thi make it expenive to eliit effort in the preene of a liquiity ontraint, an the profitability of eentralization eline a the ontraint beome more bining. Thi make it poible for entralization to ominate. Referene Aghion, Philippe, an Tirole, Jean. Formal an Real Authority in Organization. Journal of Politial Eonomy 105 (February 1997): 1 29. Aoki, M. Horizontal v. Vertial Information Struture of the Firm. Amerian Eonomi Review 76 (Deember 1986): 971 83. Athey, Suan; Gan, Johua; Shaefer, Sott; an Stern, Sott. The Alloation of Deiion in Organization. Grauate Shool of Buine Reearh Paper no. 1322. Stanfor, CA: Stanfor Univerity, 1994. Boek, Greg. Big Apple Sport Supplier Chekett See Garen Come into Full Bloom. USA Toay (November 20, 1996), p. 1C. Bolton, Patrik, an Dewatripont, Mathia. The Firm a a Communiation Network. Quarterly Journal of Eonomi 109 (November 1994): 809 39. Calvo, Guillermo A., an Welliz, Stanilaw. Superviion, Lo of Control, an the Optimum Size of the Firm. Journal of Politial Eonomy 86 (Otober 1978): 943 52. Chanler, Alfre D., Jr. Strategy an Struture: Chapter in the Hitory of the Inutrial Enterprie. Cambrige, MA: MIT Pre, 1962. Crawfor, Vinent P., an Sobel, Joel. Strategi Information Tranmiion. Eonometria 50 (November 1982): 1431 51. Eonomit. Trut in Me. (Deember 16 22, 1995), p. 61. Geanakoplo, John, an Milgrom, Paul. A Theory of Hierarhie Bae on Limite Managerial Attention. Journal of the Japanee an International Eonomy 5 (September 1991): 205 25.
22 Zábojník Kahn, Charle, an Huberman, Gur. Two-Sie Unertainty an Upor-Out Contrat. Journal of Labor Eonomi 6 (Otober 1988): 423 44. Meluma, Nahum; Mookherjee, Dilip; an Reiheltein, Stefan. A Theory of Reponibility Center. Journal of Aounting an Eonomi 15 (Deember 1992): 445 84.. Contrat Complexity, Inentive, an the Value of Delegation. Journal of Eonomi an Management Strategy 6 (Summer 1997): 257 89. Meluma, Nahum D., an Reiheltein, Stefan. Centralization veru Delegation an the Value of Communiation. Journal of Aounting Reearh 25, upp. (1987): 1 18. Myeron, Roger. Optimal Coorination Mehanim in Generalize Prinipal-Agent Problem. Journal of Mathematial Eonomi 10 (June 1982): 67 81. Oterman, Paul. The Role of Promotion in Inuing Speifi Human Capital Aquiition. Quarterly Journal of Eonomi 108 (May 1993): 523 34.. Superviion, Diretion, an Work Organization. Amerian Eonomi Review, Paper an Proeeing 84 (May 1994): 380 84. Prenergat, Canie J. A Theory of Reponibility in Organization. Journal of Labor Eonomi 13 (July 1995): 387 400. Raner, Roy. The Organization of Deentralize Information Proeing. Eonometria 61 (September 1993): 1109 46. Roen, Sherwin. Authority, Control, an the Ditribution of Earning. Bell Journal of Eonomi 13 (Autumn 1982): 311 23. Sah, Raaj Kumar, an Stiglitz, Joeph E. The Arhiteture of Eonomi Sytem: Hierarhie an Polyarhie. Amerian Eonomi Review 76 (September 1986): 716 27. Sappington, Davi. Limite Liability Contrat between Prinipal an Agent. Journal of Eonomi Theory 29 (February 1983): 1 21. Walman, Mihael. Worker Alloation, Hierarhie an the Wage Ditribution. Review of Eonomi Stuie 51 (January 1984): 95 109. Williamon, Oliver. Market an Hierarhie: Analyi an Antitrut Impliation. New York: Free Pre, 1975. Zábojník, Ján. Sale Maximization an Speifi Human Capital. Ran Journal of Eonomi 29 (Winter 1998): 790 802.