Corporate fraud and investment distortions in efficient capital markets

Transcription

1 AND Journa of Economics Vo. 4, No. 1, Spring 29 pp Corporate fraud and investment distortions in efficient capita markets Praveen Kumar and Nisan Langberg Inefficient investment aocation induced by corporate fraud, were informed insiders strategicay manipuate outside investors beiefs, as been endemic istoricay and as recenty attracted muc attention. We reconcie corporate fraud and investment distortions wit efficient capita markets, buiding on sareoder-manager agency conficts and investment renegotiation in active takeover markets. Because investments tat are ex post inefficient are not renegotiation proof, te optima renegotiation-proof contract induces overstatements by managers, accompanied by overinvestment in ow return states and underinvestment in ig return states by rationa investors. Our framework aso eps expain wy easy access to externa capita appears to faciitate corporate fraud. 1. Introduction Corporate fraud as attracted muc attention recenty because of prominent cases of corporate mafeasance were insiders were abe to attract investment troug overy optimistic representations of financia performance and economic prospects e.g., Wordcom and Enron). An important consequence of tis type of fraud is investment inefficiency. Compared to te efficient aocation, tere is overinvestment in certain industries or sectors as uninformed investors direct capita fows to not ony te firms manipuating teir beiefs; owever, tere is underinvestment in oter sectors, as te presence of fraud makes investors generay more cautious. Manipuation of outside investors by better-informed strategic insiders as a ong istory, and appears to ave existed from te onset of organized trading and investment. 1 A istorica review points to te crucia roe of asymmetric information and agency conficts in te manipuation University of Houston; pkumar@u.edu, nangberg@u.edu. We tank te editor, Mark Armstrong, and two anonymous referees for very epfu comments. We aso tank Larry Ausube, Micae Fisman, Tomas George, Itay Godstein, Peter Hammond, Miton Harris, Andrew Hertzberg, Diip Mookerjee, Oguzan Ozbas, Adriano ampini, Avri avid, Cester Spatt, Matt Spiege, Jeremy Stein, S. Viswanatan, and seminar participants at Ben Gurion University, Haifa University, Hebrew University, University of Houston, Te Aviv University, te Duke-UNC Corporate Finance Conference 26), te American Finance Association Meetings 27), and te Uta Winter Finance Conference 27) for usefu comments. A remaining sortcomings are our responsibiity. 1 Notabe eary exampes incude te Sout Sea Trading Company in te 18t century, U.S. rairoad firms in te 186s, and utiities in midwestern states in te 192s. See Skee 25) for numerous oter exampes. 144 Copyrigt C 29, AND.

2 KUMA AND LANGBEG / 145 of investors beiefs and te attendant investment distortions. Because of te separation between ownersip and contro Bere and Means, 1932), insiders are typicay more informed tan outsiders about expected returns on investment, especiay for new tecnoogies and markets. 2 However, in spite of considerabe anecdota and more systematic empirica findings empasizing overinvestment reative to te first-best) as an attendant cost of corporate fraud, 3 te iterature rarey presents frameworks were fraud and overinvestment occur in equiibrium wit rationa investors. Tere is in fact a iterature arguing tat, in efficient capita markets, strategic manageria discosures aimed at infating firm prospects soud be discounted by rationa market participants e.g., Stein, 1989; Narayanan, 1985). Moreover, modes wit private information on investment prospects typicay predict underinvestment rater tan overinvestment, because of te adverse seection probem in equity financing e.g., Myers and Majuf, 1984; Greenwad, Stigitz, and Weiss, 1984) or capita rationing by debt markets e.g., Stigitz and Weiss, 1983). 4 Our contribution is to deveop a teory of fraud and generaized investment distortions, tat is, bot under- and overinvestment, wit rationa expectations and perfect capita markets. Specificay, we construct and caracterize an equiibrium wit rationa investors were underand overinvestment can bot occur wit positive probabiity, tat is, ow-capita productivity firms receive more tan teir efficient eves of investment capita, and conversey for ig-capita productivity firms. Our framework is buit on two fundamenta caracteristics of modern corporations operating in we-deveoped financia markets. First, tere are sareoder-management agency conficts because managers derive private benefits from controing arger investments and ave private information on te investment opportunity set e.g., Stuz, 199; Hart, 1995). Second, sareoders cannot crediby precommit to investment tat is inefficient ex post, because suc investment poicies are renegotiated in active takeover markets e.g., Grossman and Hart, 1986). As is typica in optima contracting wit asymmetric information, te second-best or ex ante incentive-efficient contract in our setup requires precommitment to investment poicies tat are inefficient ex post i.e., conditiona on knowing te true state of te word). eative to te firstbest, investment is owered in te ig-productivity state and raised in te ow-productivity state. But investment eves tat are inefficient ex post ead to a transparent undervauation of te firm and generate a profitabe takeover opportunity for any investor wo acquires contro of te firm and resets investment to te ex post efficient eves. Indeed, in our setting, any renegotiation-proof investment poicy tat is, one tat does not generate profitabe takeover opportunities must be ex post or conditionay) efficient. We terefore igigt te infuence of an active corporate takeover market on te design of incentive contracts between managers and sareoders, and provide an institutionay compeing motivation for te renegotiation-proofness probem see Dewatripont, 1988; Boton and Dewatripont, 25). Our main insigt is tat te ex post investment efficiency constraint substantiay affects te information optimay induced from te privatey informed agent, and terefore aso te equiibrium aocation of capita across productivity states. We find tat, for a range of mode parameters, te optima renegotiation-proof contract induces misreporting by insiders wit a 2 For exampe, Wordcom s caim in 1996 since proved frauduent tat Internet traffic was doubing every 1 days not ony bostered its own stock price but aso apparenty induced overinvestment in fiber-optic capacity see, e.g., Dreazen, 22; Sidak, 23). Wordcom s misrepresentations on te rate of growt of Internet traffic ad credibiity because suc information is igy proprietary to carriers: Wordcom used [te] asymmetry of information to exaggerate te vaue of its stock by overstating te growt of Internet voumes Sidak, 23). 3 For instance, during , investment in teecommunication infrastructure to service te nascent internet industry grew from about $62 biion per year to over $135 biion per year in constant 1996 doars), and resuted in a gut in fiber-optic cabe capacity wit utiization rates at ony 2.5 3% Brenner, 23; page 9). But te iterature is now presenting more compreensive evidence tat corporate fraud is associated wit overinvestment. For exampe, Kedia and Piippon 27) find tat firms tat commit accounting fraud i.e., ave to restate earnings) aso invest more tan comparabe nonfrauduent firms during te misreporting period. 4 Oter agency modes tat empasize te asset substitution probem Jensen and Mecking, 1976) and te debt overang probem Myers, 1977) aso ead to underinvestment. See Stein 23) for a very usefu survey. C AND 29.

3 146 / THE AND JOUNAL OF ECONOMICS positive probabiity. Te roe for randomized reporting arises in our setting because attempts to induce trut teing troug wage contracts wen investment is constrained to be ex post efficient) can be costy. Specificay, trut teing can be induced even wit te constraint of renegotiation-proof investment by paying te ow-productivity agent information-based rents troug ig wages) tat compensate im for te utiity oss from receiving a ower investment eve reative to te arger investment aocated to te ig-productivity state. But tese rents can be ig if tere is a arge difference between te efficient investment eve in te ig- and ow-productivity states. Le Cateier s principe ten suggests tat it may be cost effective to induce randomized reporting, because randomization owers expected wage costs by moving te Bayes-rationa or renegotiation-proof) investment in te direction of te second-best. Indeed, te optima reporting noise or probabiity of misreporting) is determined by trading off te expected cost of investment distortion from te incorrect report wit te reduction in te expected wage costs. In our mode, tere generay can be randomized reporting by bot te ow- and te igproductivity manager because te incentive compatibiity constraints are binding bot upward and downward in te second-best. Te reason is tat te incentive-efficient contract expoits te tradeoffs between wages and utiity of contro to give zero wages to te ig-productivity manager, and make is incentive constraint bind. However, under a range of parameters, it is optima to induce randomization ony by te ow-productivity manager. Tis is because randomization by te igproductivity agent imposes investment distortion costs because tere is underinvestment wit positive probabiity and increases expected wage costs because te agent receives positive, rater tan zero, wages wenever e reports ow productivity. Tus, as ong as te apriori ikeiood of te ig-productivity state is not too ow and te capita productivity in te ow state is not too ig, it is suboptima to induce randomization by te ig-type agent. But under tese conditions, it is sti optima to ave te ow-type randomize as ong as te opportunity cost of investment and te manager s subjective benefits of contro are in an intermediate range. In sum, we estabis te existence of, and caracterize, a noisy reveation equiibrium were te ow-productivity manager infates is reports wit positive probabiity, and tere is overinvestment in te ow state but underinvestment in te ig state. Comparative statics around tis equiibrium revea tat te ikeiood of fraud is negativey reated to te cost of capita or externa financing), and positivey reated to te ratio of ow- and ig-capita productivities. Tese comparative statics aow us to reate te extent of investment inefficiency to saient mode parameters. Te desire to understand te causes and consequences of corporate) fraud as an equiibrium penomenon dates at east back to Becker 1968). One strand of te existing iterature on fraud empasizes te roe of manageria myopia e.g., Narayanan, 1985; Stein, 1989; Von Tadden, 1995; Kedia and Piippon, 25). Suc myopia is sometimes motivated troug imperfections in ong-term incentive contracting. Anoter strand examines fraud in modes wit imits on communication e.g., Dye, 1988; Demski, 1998). 5 And a more recent iterature assumes some form of market irrationaity in reconciing fraud wit market equiibrium e.g., Jensen, 25; Boton, Sceinkman, and Xiong, 25). 6 Our anaysis differs from te iterature, because we empasize te roe of capita markets in te incidence of corporate fraud; in fact, capita markets ave payed a prominent roe in severa recent corporate scandas and istoricay in episodes of fraud. Instead of reying on manageria myopia, imitations on communication and contracting, mutitasking, or investor irrationaity, we focus on te inabiity of financia markets to resist vaue-increasing investments. Tat wedeveoped or reativey frictioness) financia markets wi expoit te profit opportunities afforded 5 In Dye 1988), tere is asymmetric information of two dimensions wereas te informed agent can ony provide a one-dimensiona report eading to nontrutfu reporting wit some probabiity). In Demski 1998), earnings management is actuay beneficia because tat is te ony way te manager can communicate te eve of future earnings. 6 See aso Guttman, Kadan, and Kande 26) for a partiay reveaing signaing mode wit costy manipuation of earnings. C AND 29.

4 KUMA AND LANGBEG / 147 by transparent undervauation of assets is a compeing argument; terefore, our perspective appears to rest on rater unexceptionabe foundations. 7 We organize te remaining artice as foows. Section 2 sets out te basic mode. Section 3 defines optima contracting and its equiibrium representation. Section 4 records te first- and second-best bencmark outcomes. Section 5 presents te main resuts, and Section 6 concudes by discussing some impications of te mode. A proofs are paced in te Appendix. 2. Te mode Tecnoogy. Tere are tree time periods in te mode, t =, 1, 2. Te firm as a tecnoogy tat stocasticay converts investment at time t = 1, denoted by k, to earnings or output) at time t = 2, denoted by y. For simpicity, we normaize units so tat earnings take ony two possibe vaues: a ig vaue, y = 1, and a ow vaue, y =. Te probabiity distribution of earnings is infuenced by te firm s capita productivity, s {s, s },1> s > s, and investment k). Te probabiity of ig earnings is given by sf k), were f = 2 k is defined on te feasibe investment set [, k max ], suc tat k max 1/4s 2.8 Ownersip, contro, and manageria preferences. Te firm is controed by a risk-neutra manager wo receives two types of utiity from managing te firm. He receives utiity from consuming wages, w, tat are paid at te time of te firm s iquidation. Te manager aso receives benefits from contro tat are a mixture of subjective utiity and noncontractibe pecuniary benefits, and tey increase wit te size of te capita assets. We represent tese benefits by a bk) = k, were >. Terefore, te manager s utiity from possiby uncertain wages and investment eve k is Uw, k) = Ew) k. Moreover, te manager as no initia weat and enjoys imited iabiity, and terefore wages must be nonnegative. Finay, te manager s reservation utiity is normaized to zero. 9 Te firm is pubicy ed and its sares are traded in a frictioness capita or equity ownersip) market. For simpicity, we assume tat a of te firm s sares are ed by a risk-neutra active sareoder ereafter, te origina owner. Firm ownersip and contro, owever, may vary over time. In particuar, a potentia raider may gain contro of te firm we discuss tis in detai beow). Te origina owner and te potentia raider ave a common opportunity cost of investment, namey te gross rate of return. 1 In te ast period, time t = 2, output y is reaized, wages w are paid to te manager, and te firm is iquidated. Te payoff to te owner of te firm at te time of iquidation, given an investment eve k, output y, and wage w is vw, k, y) = y w k. Information. Te manager privatey observes te productivity of te firm s) before investment takes pace, tat is, before time t = 1. At t =, te manager and te investors sare common prior beiefs about te reaizations of s; te probabiity of observing s and s is μ 7 More broady, our artice is aso reated to te agency iterature, were constraints on te principa s abiity to crediby precommit ex ante imit te amount of information e possesses ex post e.g., Crawford and Sobe, 1982; Laffont and Tiroe, 1988). Two reated appications of tis idea are Arya, Gover, and Sunder 1998) and Krasa and Viami 2). Te focus of tese anayses, owever, is quite different, because tey do not address corporate fraud and its impications for investment. 8 Te feasibiity constraint on k wi not bind in our setting as ong as s 2 < /2andkmax = 1, and tus we make 4s 2 tis assumption trougout te anaysis. 9 Our resuts do not rey on te manager aving a zero reservation utiity. A noisy reveation equiibrium can sti be optima for a stricty positive reservation utiity as ong as te manager earns rents in equiibrium. Neiter does te optimaity of a noisy reveation equiibrium rey on te assumption tat te manager is risk neutra. Kumar and Langberg 26) anayze te existence of te noisy reveation equiibrium in te mode at and wen te agent is risk averse. Te resuts are quite simiar to te ones derived in te current artice. 1 For simpicity, we assume tat te firm is unevered our resuts are materiay uncanged if we reax tis assumption. And atoug te assumption of a singe active sareoder is convenient, our main resuts are robust to more genera ownersip patterns. C AND 29.

5 148 / THE AND JOUNAL OF ECONOMICS and 1 μ, respectivey. A investors know tat te manager wi privatey observe s. Everyting ese in te mode, besides te reaization of s, is observabe and common knowedge. Contracting and te market for contro. From an institutiona perspective, sareoders deegate te responsibiity of wage contracting wit management) to te board of directors. Tese empoyment contracts are enforceabe in te sense tat managers can move te courts to enforce prior wage contracts even toug te ownersip of te firm canges, as te set of equity oders itsef canges. 11 However, owners abiity to crediby commit to arbitrary investment in te firm is imited by te possibiity of a cange in contro of te firm ex post troug a takeover. Because investment at any given point in time is egay te domain of te current capita owners, te new owners can coose any desirabe and feasibe) investment eve. To see te basic point, imagine a situation were sareoders panned investment does not maximize efficiency, conditiona on knowing te true productivity state. But tis inefficient) investment wi ead to a transparent undervauation of te firm s assets, reative to te ex post efficient investment eve. However, transparent undervauation is not a viabe situation wit a frictioness market for contro. Tis is because tere is a cear positive net present vaue NPV) opportunity for a potentia raider to purcase te firm at te undervaued price, reset te investment to te ex post efficient eve, and se or even od) te firm. We can incorporate te commitment issues wit respect to investment by appeaing to te notion of renegotiation-proof mecanisms or contracts see Boton and Dewatripont, 25). We wi say tat te mecanism is renegotiation proof if and ony if te potentia raider cannot benefit from gaining contro of te firm and canging investment. Terefore, te investment poicy described above is not renegotiation proof because tere are incentives for te potentia raider to offer an aternative arrangement to increase efficiency impemented by purcasing te sares of te origina owner. We formaize te notion of renegotiation proofness beow. Incentive mecanisms or contracts. We wi aow te manager to communicate wit te owners regarding is private information on te firm s productivity. Owners can terefore design an incentive mecanism or contract) at te beginning of time t = tat is contingent on te manager s communication of te productivity and on te pubicy observabe earnings. Tis communication occurs ater during tis time period, foowing te manager s observation of te actua productivity. Specificay, te contract is a wage and investment menu. It determines te sareoders investment poicy as a function of te manager s communication; it aso determines te manager s wages as a function of is communication and te observed earnings at time t = 2. However, te investment may cange if te ownersip canges prior to te investment decision). Te possibiity of investment revision or renegotiation impies tat te reveation principe fais to od in our setting. 12 A contract terefore specifies a noisy reporting poicy for te manager, contingent on is type. Let π jr be te probabiity tat a manager wit an actua productivity j reports te productivity r, for j, r {, }. Simiary, te investment poicy or menu) is k r, wie te wage poicy or menu) is {w, r w r }, were r= w r w r ) denotes te compensation wen earnings are positive zero) and te productivity r was communicated. It is notationay convenient to put π jj π j and 11 Indeed, tere is muc evidence tat CEOs are abe to successfuy enforce teir empoyment contracts, especiay te payment of arge severance payments, in te event of job termination and te sae of te firm see, e.g., Murray, 26; Lubin and Turm, 26). Te ex post infexibiity of tese empoyment contracts seems to surprise even boards wo inked te contracts in te first pace Das, 26). 12 Tis is a we-known resut in te iterature tat studies agency modes wit adverse seection in te absence of commitment e.g., Laffont and Tiroe, 1987, 1988, 199; Bester and Strausz, 27). In genera, one may require compex message spaces to caracterize te optima mecanism e.g., Kumar, 1985; Forges, 199); owever, because we ave ony two possibe agent types, we can restrict attention to noisy communications or randomizations) on te space of types witout oss of generaity see Bester and Strausz, 27). C AND 29.

6 KUMA AND LANGBEG / 149 FIGUE 1 TIMING CONVENTIONS OF THE MODEL Contract C determined Manager earns private signa eport made to investors Investment occurs possibe takeover) Output reaized t = t =1 t =2 π = π, π ). Simiary, we et k k, k ) and w = w, w, w, w ). Tus, a contract is te profie C = {π, w, k}. 13 We denote te set of feasibe contracts by = [, 1] 2 4 [,kmax ] 2. Te takeover process. At time t = 1, after te manager s communication but prior to te investment decision, te potentia raider can make a take-it-or-eave-it tender offer to buy te firm from te origina owner. If te origina investor accepts te offer, ten te contro of te firm passes to te raider, wo is ten free to ater any preannounced investment pan, because te raider is te new) owner of te firm s capita at te time of investment. However, te raider must respect te manager s origina wage or empoyment contract w), because it is egay enforceabe. 14 But if te tender offer fais, ten te contro of te firm remains wit te origina owner and te investment pan announced at t = is executed. Timing conventions. Te timing conventions of te mode are described in Figure Te optima contract Admissibe contracts and ex post investment efficiency. A contract C = {π, w, k} is admissibe if te noisy reporting poicy π) is incentive compatibe for te manager and if te investment menu k is renegotiation proof. To quantify tis notion of admissibe contracts, we note first tat for any given w, k), te manager s payoffs wen te true productivity is j, but e reports r, for j, r {, } are [ ] U j r w, k) = 2s j kr w r w r w k r r. 1) Terefore, te manager s expected payoffs wen te true productivity is j and e uses te noisy communication poicy π j,1 π j )are U j π j, w, k) = π j U j j w, k) 1 π j )U j r w, k), r, j {, }, r j. 2) Te manager s reporting poicy π C is incentive compatibe if π j arg max U j ˆπ,w, k), j {, }. ˆπ [,1] Next, we specify te renegotiation-proofness constraints on k by excuding opportunities for a profitabe takeover ex post. FixsomeC, and note tat te probabiity of receiving te report r 13 Notice tat te manager s wage contract at time t = is not directy contractibe on te investment at time t = 1. As in te incompete contracts iterature see Hart and Moore, 1988), we assume tat a compete specification of future investment in te corporation is sufficienty compex to make wage contracts contingent on future investment proibitivey costy to enforce. In fact, manageria compensation contracts are not typicay contingent on te externa investment in te firm Koe, 1997). 14 In principe, te raider coud aso renegotiate te empoyment contract if it is mutuay agreeabe. But notice tat te possibiity of wage contract renogotiation ony faciitates takeovers, for any takeover opportunity tat is profitabe wit te constraint of enforcing te prior wage contract of te manager i.e., w) is at east weaky more profitabe wit te possibiity of a mutuay beneficia renegotiation of te wage contract. However, to ease te notationa burden and simpify te mode specification, we do not consider empoyment contract renegotiation. C AND 29.

7 15 / THE AND JOUNAL OF ECONOMICS {, } under te given contract) is q r C) = μπ r 1 μ)π r. Hence, by Bayes rue, te conditiona expectation of te productivity state s, foowing a report r is Es C, r) = μπ rs 1 μ)π r s μπ r 1 μ)π r. 3) And te market vaue of te firm foowing tis report is, terefore, V C, r) = 2Es C, r) k r [ 1 w r w r ] w r k r. 4) Ten, tere is an opportunity to increase firm vaue ex post tat is, foowing te report r {, } if tere exists some investment eve ˆk r tat improves expected profits reative to te origina investment pan k r ) in te contract. Tat is, if V C,r; ˆk r ) = 2Es C, r) ˆk r [ 1 w r w r ] w r ˆk r > V C, r). 5) A renegotiation opportunity exists if, given 5), te potentia raider can take over te firm and repace k r wit ˆk r. Te contract C) is renegotiation proof if, for eac report r {, }, tere exists no ˆk r tat is vaue improving in te sense of 5)) and impementabe troug a takeover. Ceary, given te takeover process, any ˆk r tat is vaue improving is aso impementabe troug a takeover. Tat is, given any ˆk r tat satisfies 5), te potentia raider can make a tender offer to purcase te firm s sares at a price tat te origina owner wi accept, revise te investment pan, and make positive expected profits. Te ogica cumination of tis argument is tat te requirement of renegotiation-proof investment wi ead to ex post or conditionay efficient, tat is, Bayes-consistent, investment. Tis is te investment eve tat maximizes firm vaue at te information set C, r ). Tere is an equivaence between renegotiation-proof investment and ex post efficiency troug te eimination of profitabe takeover opportunities. Teorem 1. If te investment poicy k r, r {, }, is renegotiation proof i.e., contractuay admissibe), ten it maximizes te vaue of te firm conditiona on te report r, for any given C. Tat is, k r arg max k k max V C,r; k ), r {, }. Wereas Teorem 1 presents sufficient conditions for ex post or conditiona) investment efficiency in te presence of frictioness takeover markets, tis resut is actuay quite robust. For exampe, it woud appy if tere was no potentia raider and te owner of te firm woud simpy revise any prior announced investment in igt of te new information. Wit mutipe bockoders, te aocation of efficiency gains from revising te investment ex post is more compex, but it is difficut to envisage te surviva of ex post investment inefficiency. In effect, enricing te action space of investors in tis case, aowing tem to take over firms to expoit profitabe opportunities resuts in reducing te ex ante incentive efficiency of investment poicy in admissibe contracts. Tis outcome is reated to Dewatripont and Maskin 1995), wo sow tat it may be optima to restrict contractua contingencies wen renegotiation is possibe. Owner s program. At time t =, te initia owner cooses an admissibe contract tat maximizes te ex ante vaue of te firm. Ten, foowing Teorem 1, te optima renegotiationproof) contract Ĉ = ˆπ, ˆk, ŵ ) is a soution to te program max [μπ r 1 μ)π r ]V C, r; k r ) s.t., 6) C r {,} V C, r; k r ) V C, r; ˆk r ), for a ˆk r [, k max ], and r {, } 7) U j π j, w, k) U j ˆπ,w, k), for a ˆπ [, 1], and j {, } 8) k max k r,w r, w r, r {, }. 9) C AND 29.

8 KUMA AND LANGBEG / 151 Equiibrium representation of optima contracts. Teorem 1 above impies tat in any optima contract, te investment k must be optima given te posterior or revised) beiefs of te investors, conditiona on te manager s report. Tat is, k must be a Bayes-rationa rue. Tis observation suggests tat te optima contract cf. equation 6)) may be represented troug a sigty modified form of te perfect Bayesian equiibrium PBE) see, e.g., Fudenberg and Tiroe, 1991) te modification being required to accommodate te contractuay fixed manageria wages. Specificay, a given wage poicy, w, defines a noncooperative game wit incompete information wit associated strategies π from te manager) and k from te owner). Te manager s reporting strategy π and te owner s investment response to reports r {, }, k, comprise a PBE if i) π is optima given k, w), ii) k is optima given w and updated beiefs regarding te firm s productivity, denoted by β s; r), and iii) te beiefs β s;r) are derived using Bayes rue wenever possibe. 15 It is easy to ceck tat any contract C = {π, w, k} is optima in te sense of 6)) iff π, k) is a PBE in te game defined by w, were w is cosen to maximize firm vaue, taking as given te menu π, k)w) tat specifies an equiibrium π, k) for eac w. 4. Important bencmark outcomes To faciitate intuition on te basic forces tat drive our resuts, in tis section we record two bencmark outcomes. Tese are: te compete information or te first-best) outcome; and te information-constrained efficient or te second-best) outcome, were tere is asymmetric information but investors can crediby precommit to any investment poicy. Compete information. Suppose tere is compete information on te productivity. In tis case, te efficient or te first-best) investment poicy is denoted by k j, j =, suc tat s ) 2 k j j =. 1) Because s > s, it foows tat k > k > ; moreover, expected profits are positive in bot productivity states. Consequenty, te manager is not given any wage payment ere, because e enjoys benefits of k j > in eac state. Proposition 1. Wit compete information, for eac j {, }, te investment k j is given by 1) and te wage poicy sets w j = w j =. Asymmetric information wit perfect commitment. Te compete information aocation is transparenty not feasibe wen te manager as private information on capita productivity, because te ow-productivity manager can do stricty better by pretending to be te igproductivity manager. Because owners can crediby precommit to bot wage and investment poicies by assumption), te reveation principe appies. Tus, witout oss of generaity, we can restrict attention to direct mecanisms, were te agent s message space is {, } and trut teing is an optima strategy. A direct mecanism is specified as te pair k, w), and te second-best or optima mecanism is te soution to te program P1) [ ) ] max μ j 2s j k j 1 w {w,k} 6 j w j w j k j, s.t., j= U j j w, k) U j r w, k), r j, r, j {, }, 11) w r, w r, r {, }. 12) 15 Aternativey, et π, k) be te continuation equiibrium for a given w. C AND 29.

9 152 / THE AND JOUNAL OF ECONOMICS Here, 11) are te trut-teing incentive-compatibiity) constraints and 12) are te nonnegativity constraints on manageria wages. We denote te soution to P1) as ˆδ {ŵ, r ŵ, r ˆk r }. r= Because te margina productivity of capita becomes unbounded for infinitesima investment eves, te information-constrained efficient investment eves wi be positive in bot productivity states. Hence, te manager wi obtain positive benefits wic cannot be taxed away by te owners due to te nonnegativity restriction on wages. Terefore, te manager s participation constraint wi not bind in eiter productivity state. Turning to incentive issues, a pooing investment poicy were te investment eve is te same for eac reported) productivity woud triviay be incentive compatibe. Consequenty, managers wi not be paid any incentive wages, tat is, w j = w j =, j {, }. Hence, te optima pooing eve is ) 2 Es) k P =, Es) = μs 1 μ)s, 13) However, te pooing investment poicy is ceary inefficient. Terefore, and except for a pooing range of parameters tat we identify beow, it wi be optima to distort wages and investment poicy reative to te first-best) in order to induce information from te managers. Specificay, tere wi be dispersion in te investment eves across productivity states; tat is, k > k, but intuition suggests tat tis dispersion wi be ower wit asymmetric information reative to te compete information dispersion in order to reax te trut-teing constraint of te ow-productivity type; tat is, k k ) < k k ). Of course, a mecanism wit k > k is not incentive compatibe wit zero wages. Some introspection suggests tat it woud be inefficient to offer a positive wage if te manager reports ig productivity. Te reason is tat suc a mecanism wi ony tigten te trut-teing incentive constraints for te ow-productivity manager. Hence, te optima mecanism wi give a positive wage wen te manager reports ow productivity so as to make im just indifferent between trutfuy reveaing te true state and pretending to be te ig-productivity type. But because te ig-productivity manager receives zero wages, e wi aso be just indifferent between trutfu reporting and sending te aternative message. Terefore, te incentive compatibiity constraints are binding for bot types in te secondbest. Te reason is tat, in our mode, tere are two instruments to provide utiity to te agent: te monetary wage w) and te benefits of contro troug investment ). Te incentive-efficient contract terefore expoits te tradeoffs between wages and te utiity of contro to give te ig-productivity manager zero wages but iger investment aocation. By setting te ig-type agent s wages to zero, te optima mecanism reaxes te ow-type agent s trut-teing constraints wie aso reducing te expected wage costs. 16 Teorem 2. Tere exists a > suc tat under te optima mecanism ˆδ {ŵ r, ŵ r, ˆk r } r=, ŵ = ŵ =, and ŵ = ŵ = ˆk ˆk ). 14) Moreover, if <, ten k < ˆk < ˆk < k, were 2 [ ] ˆk = s 2 ) s 1 μ, ˆk =. 15) μ Finay, if, ten ˆk = ˆk = k P. In tis mode, is aso a measure of te extent of te agency confict between te sareoders and te manager. Intuition ten suggests tat it may be too costy to induce reveation if te agency 16 Tis feature distinguises tis mode from oter mecanism design modes wit idden information were ony te incentive constraints for one of te agent types are binding e.g., Laffont and Tiroe, 199). C AND 29.

10 KUMA AND LANGBEG / 153 confict is too ig, tat is, if is sufficienty arge. Teorem 2 verifies tis argument, indicating tat pooing is optima wen exceeds te tresod vaue. Oterwise, it is optima to induce reveation by distorting te investment and wage poicy reative to te first-best. Comparing te second-best investment aocation cf. 15)) wit tat in te first-best cf. 1)), we find tat investment distortions in te second-best) are positivey reated to. In particuar, investment in te ig ow) state of productivity is decreasing increasing) in, for<. 5. Noisy communication equiibria Te roe of randomized reporting. In te optima renegotiation-proof mecanism cf. 6) 9)), te owners ave significant infuence on te information content or accuracy of te manager s reports troug te initia design of te wage poicy. A main resut of tis artice is tat, for an open set of parameters, tere is noisy reveation of te firm s economic state in equiibrium, tat is, te optima renegotiation-proof mecanism induces randomized reporting by te manager. To motivate te roe of randomization by te agent, we note tat te set of admissibe contracts incude contracts tat induce a fuy reveaing separating equiibrium were te manager reveas te true productivity. Due to ex post efficiency of investment, any separating equiibrium wi impy te first-best investment eves k j, j =,. Terefore, a simpe exampe of a renegotiation-proof separating contract is one in wic te ow-productivity manager receives an output-independent wage w and te ig-productivity manager receives zero wages, suc tat w k = k cf. 8)). But wereas tis contract attains investment efficiency, it imposes a ig-wage cost because te ow-productivity manager extracts information-based rents because w >. Importanty, te rents are proportiona to te difference in te investment aocation across te two states, tat is, w = k k ). On te oter extreme, tere aso exist admissibe contracts tat induce a pooing equiibrium wit noninformative reports). A simpe exampe for suc a contract is one in wic te wage and investment poicies are independent of te manager s report, suc tat w = and k = k = k P were k P is quantified in 13)). But, as we noted above, atoug tis pooing contract does not impose a compensation cost, it is costy for te owners in terms of ig investment inefficiency, reative to te first-best. Tus, te tradeoff between efficient aocation of capita and te compensation cost of extracting information determines te optima information tat is induced from te manager. 17 Le Cateier s principe suggests tat it may often be cost effective to infuence Bayes-consistent investment poicies toward tose prescribed by te second-best by inducing randomized reporting from te manager. Suc noisy communications wi dampen investors Bayes-rationa response to a ig-productivity report and ampify it in response to a ow-productivity report; te equiibrium investment aocation wi, terefore, move toward te second-best aocations see 15)). Of course, we need to sti determine te optima pattern of randomization across agent types: wen is it optima to ave te ow- and/or te ig-productivity-type agent randomize? We note tat in our mode, randomization by bot agent types singy or togeter) may be optima, because te incentive compatibiity constraints bind for bot agent types i.e., upward and downward) in te second-best see Teorem 2). 18 But for te reasons mentioned in te Introduction, we focus first on sowing te existence of, and caracterizing, a noisy reveation equiibrium were te ow 17 See Laffont and Martimort 22) for furter discussion on te respective costs and benefits of separating versus pooing contracts under renegotiation. 18 In a series of papers, Laffont and Tiroe 1987, 1988, 199) examine a two-period agency probem wen idden action and idden information are jointy present, under a variety of contracting and commitment assumptions. In teir basic mode, tere are two agent-types: a ow-cost agent te good type) and a ig-cost agent te bad type). Under te first-best, it is te good type tat as te incentives to defect. Hence, in te second-best, ony te good type s incentive constraints bind. If te principa can ony write sort-term contracts, ten te incentive constraints can be binding for bot types. However, if tere is ong-term contracting wit renegotiation, ten again ony te good type s incentive constraints wi bind. C AND 29.

11 154 / THE AND JOUNAL OF ECONOMICS type randomizes i.e., <π < 1 and π = ). 19 Subsequenty, we provide a range of mode parameters for wic it is indeed optima to ony ave te ow-type agent randomize. Equiibrium fraud and investment inefficiency. It is apparent from 1) and 5) tat an output-contingent wage poicy affects te expected payoffs of bot te manager and te sareoders. Tus, output-contingent wages infuence not ony manageria reports troug 8)) but aso te owner s best investment response to tese reports troug 7)). To faciitate intuition, we terefore conduct te anaysis in two stages. First, we consider wage contracts tat are contingent ony on te manager s reports, but not on output. We ten anayze in Section 7 beow) te more genera case of output-contingent contracts. Wit output-independent wages, we can write w j = w j w j, j {, }. Tus, if <π < 1, tat is, wit positive probabiity te ow-productivity manager overreports te firm s productivity and π = ), ten tis agent type s incentive constraint 8) is w k = w k. 16) Moreover, te renegotiation-proof constraints on investment 7) reduce to ) 2 Es C, j) k j =, j {, }, 17) were Es C, ) = μs 1 μ)π s μ1 μ)π, and Es C, ) = s are given by 3). Terefore, te optima contract Ĉ = ˆπ, ˆk, ŵ ), wit noisy reveation by te ow-type agent and trutfu reporting by te ig-type agent, is a soution to max [μ 1 μ)π ][Es C, )2 k w k ] π,k,k,w,w 1 μ)1 π )[Es C,)2 18) k w k ], s.t., 16), 17), and w j, j {, }. 19) As in te second-best cf. Teorem 2), te optima wage poicy ere is aso to set ŵ =. Tis is because te renegotiation-proofness constraints on investment do not affect te optima poicy of trading off ower wages for iger benefits of contro troug arger investment) for te ig-productivity manager. Tus, constraint 16) reduces to te constraint w = k k ). We now turn to caracterization of te noisy reveation equiibrium at and. Subsequenty, we sow tat suc an equiibrium wi exist for an open range of mode parameters. Teorem 3. Te optima contract Ĉ = ˆπ, ˆk, ŵ ) wit output-independent wages and trut teing by te ig-productivity agent i.e., π = ) is given by ˆk = s ) 2, ˆk = μs 1 μ)ˆπ s ) 2, ŵ μ 1 μ)ˆπ ) =, ŵ = ˆk ˆk ). 2) Moreover, in equiibrium, ˆπ is impicity defined by ) 2Es Ĉ, ) μs s ) 1 =, were Es Ĉ, ) = μs 1 μ)ˆπ s, 21) μ 1 μ)ˆπ provided tat < ˆπ < 1. Te optimaity condition for ˆπ, specified in 21), carifies tat optima randomization by te ow type trades off costs of investment distortion wit te wage savings from reaxing te trut-teing constraints of te ow-type manager. We note tat tere are two types of investment distortions reative to te first-best) induced by te said randomization. First, overstatement of 19 Suc equiibria were tere are ony overstatements of economic performance are of particuar interest. For exampe, BurnsandKedia 26) reporttat 93% ofaccountingfraudduring invovedoverstating net income in te year of misreporting. C AND 29.

12 KUMA AND LANGBEG / 155 FIGUE 2 EQUILIBIUM EGIONS Iustrates te tree equiibrium regions. Te private benefit of contro parameter is te vertica axis wie te annua cost of capita r = 1/5 is on te orizonta axis i.e., r represents te annua return on a project spanning over te duration of five years). Te parameter vaues are s =.7, s =., and μ =.1. productivity by te ow-type manager introduces overinvestment in te ow-productivity state. Second, investors rationay respond to randomization by te ow-type agent by underinvesting in te ig state. Terefore, te margina cost of an increase in te probabiity of over-statement by te ow type π ) is te cost of overinvestment in te ow state, wic is positivey reated to te capita costs. But te incentive gains from randomization are positivey reated to te manager s subjective benefits of contro. Hence, te ratio can be interpreted as an incentive cost-benefit ratio reated to te investment distortion). Te second term in 21) tus refects te margina cost of π. Meanwie, expected wage cost is decreasing in te investment gap k k, wic is increasing in te posterior expected productivity, given a ig report, tat is, Es Ĉ, ), te quantity in te first term in 21). We now turn to examine te feasibiity of a noisy reveation equiibrium, tat is, were < ˆπ < 1. Intuitivey, an interior noisy reveation equiibrium wi obtain if te costs of inducing information from te ow-productivity manager are neiter too ow nor too ig. For, if tese costs are too ow, ten it woud be optima to induce te correct information, tat is, π =. On te oter and, if tese costs are very ig, ten it may be optima not to induce any information at a, tat is, π = 1. It turns out tat tese conditions, tat caracterize te information content of te ow-type agent s reports in equiibrium, can be succincty expressed in terms of te incentive cost-benefit ratio. Teorem 4. Tere exist positive numbers 1 < b < b, suc tat under te optima contract Ĉ, te manager reports trutfuy i.e., ˆπ = ) wen b; manageria reports are not informative i.e., ˆπ = 1) wen b; and, tere is noisy reveation i.e., < ˆπ < 1) wen b, b). Figure 2 iustrates te tree equiibrium regions as a function of te private benefit of contro and te cost of capita. Furtermore, an immediate impication of Teorem 4 is as foows. Coroary 1. Te optima noisy reveation contract Ĉ, wit < ˆπ < 1, stricty dominates a trut-teing equiibrium and a pooing equiibrium wenever b, b). C AND 29.

13 156 / THE AND JOUNAL OF ECONOMICS FIGUE 3 POBABILITY OF OVE-EPOTING THE LEVEL OF PODUCTIVITY Pots te equiibrium ikeiood tat te ow productivity manager makes a ig productivity report, as a function of te private benefit of contro parameter for = 1, and μ =.1). Tree cases are considered: s, s =.7,.1,.65,.5 and.6,. Note tat in a tree cases s s =.6. Indeed, from te optimaity condition 21), one can cacuate anayticay te equiibrium ˆπ : μ ˆπ = 1 μ ) 2 μ μ 1 s s 1 s ) ) s 1 ) ) 1 2 s s,for b, b). 22) From 22), we can deduce te main determinants of ˆπ. In genera, variations in mode parameters tat increase te manager s propensity to overstate productivity wi raise ˆπ, because inducing trutfuness becomes more costy. Tus, ˆπ wi be increasing in, because te manager s incentives for attracting iger investment troug misreporting increase wit is benefits from contro. On te oter and, ˆπ wi be negativey reated to parameters tat increase te cost of investment misaocation due to randomized reporting. Tus, ˆπ wi be decreasing in. We can terefore express tese comparative statics compacty troug variations in te incentive cost-benefit ratio. It is aso apparent from 22) tat ˆπ is increasing in te ratio s s. Effectivey, if te ower productivity parameter s ) rises reative to te iger one s ), ten te cost of investment distortion due to randomization by te ow-type agent fas, wie te incentive benefit increases. But note tat an increase or decrease) in te ratio s s of te productivities s s ). eaves ambiguous te cange in te difference Proposition 2. In equiibrium, te probabiity tat te ow-type manager overstates productivity, ˆπ, is decreasing in te ratio. Moreover, ˆπ is increasing in te productivity ratio s s ;but ˆπ is ambiguousy reated to s s ). Figure 3 pots te equiibrium ˆπ against te private benefit parameter. Tree cases are considered: s =.6, s =.65, and s =.7 wie oding te difference of productivities C AND 29.

14 KUMA AND LANGBEG / 157 fixed, i.e., s s ) =.6). Te equiibrium ikeiood of fraud is increasing in and increasing in te productivity ratio s s, as sown formay in Proposition 2. In te optima contract specified in Teorem 3, tere is no investment distortion foowing a ow-productivity report i.e., ˆk = k ), because wit probabiity 1) ony te ow-productivity manager sends suc a report. But tere are investment distortions foowing a ig-productivity report, in bot productivity states. To anayze te equiibrium investment distortions, it is usefu to compute te eve of investment foowing a ig-productivity report by substituting for ˆπ cf. 22)) in 2) to obtain ˆk = ) 2 Es Ĉ, ) were Es Ĉ, ) = μ ) 2 s s ) 1. 23) Proposition 3. In equiibrium, investment foowing a ig-productivity report satisfies ˆk k P, k ). Moreover, ˆk is increasing in s s ), decreasing in and, and increasing in μ. Te first part of Proposition 3 confirms te intuition tat, in te presence of noisy reveation by te ow-productivity manager, te optima investment foowing a ig-productivity report ies between te pooing and te compete information investment eves. Meanwie, te second part of te proposition indicates tat even in te noisy reveation equiibrium wit te renegotiationproofness constraints, te investment response to a ig-productivity report maintains certain efficiency features: it is negativey reated to te opportunity cost ) and it is positivey reated to te ig-state productivity; moreover, as in te second-best investment poicy cf. 15)), it is negativey reated to te manager s benefits of contro ). However, ˆk aso depends negativey on te ow-state productivity s, because, for a fixed s, iger productivity in te ow state increases te equiibrium ikeiood of overreporting cf. Proposition 3). By contrast, neiter te first-best cf. Proposition 1) nor te second-best cf. Teorem 2) investments in te ig-productivity state depend on s. In te noisy reveation equiibrium, investors posterior expectation for te firm s productivity conditiona on a ig report are bounded beow by te unconditiona expected productivity and bounded above by s, tat is, Es) < Es Ĉ, ) < s. Terefore, wit probabiity 1 μ)π, tere is an overinvestment in te ow-productivity state and, wit probabiity μ, tere is an underinvestment in te ig-productivity state. In reative terms, te extent of overinvestment underinvestment) foowing a ig-productivity report in te ow ig) state is ˆk k k ˆk ), namey, ˆk k ) 2 ) Es Ĉ 2, ) = and k s =. 24) s ˆk Es Ĉ, ) Proposition 4. In equiibrium, foowing a ig-productivity report, tere is overinvestment ˆk reative to te first-best) if s = s, tat is, > 1, but tere is underinvestment reative to k te first-best), if s = s, tat is, k ˆk > 1. In fact, based on 24) and te previous anaysis, we can infer te determinants of te two types of investment distortions, in equiibrium. Specificay, from Proposition 2, we know tat ˆπ is decreasing in te incentive cost-benefit ratio, and increasing in te productivity ratio s s. Consequenty, investors posterior expected productivity foowing a ig-productivity report are positivey reated to and negativey reated to s s. Tus, we obtain te foowing impications for reative investment distortions in Proposition 5. Figure 4 pots te investment distortions foowing a ig-productivity report cf. 24)), as a function of te manager s subjective benefits of contro parameter. C AND 29.

15 158 / THE AND JOUNAL OF ECONOMICS FIGUE 4 ELATIVE INVESTMENT DISTOTIONS FOLLOWING A HIGH PODUCTIVITY EPOT Pots te reative investment distortions foowing a ig productivity report bot under investment and over investment) as a function of te private benefit of contro parameter for = 1, s, s =.7,.5, and μ =.1). Proposition 5. In equiibrium, te reative eve of underinvestment over-investment) k ˆk ˆk )is k decreasing increasing) in s, increasing decreasing) in s, and decreasing increasing) in. Finay, te manager s wage compensation foowing a ow-productivity report can be cacuated from 2) and 21) as ) 2 ŵ = ˆk ˆk ) = Es Ĉ, ) s ) 2. 25) Tus, consistent wit te iterature on mecanism design wit idden information, sareoders in our mode optimay design te wage poicy to purcase more trutfuness from te manager in te ow-productivity state in equiibrium see Eisfedt and ampini, 28; Coe, 1998). Intuitivey, a iger wage for a ow-productivity report w ) resuts in more informative manageria discosures. For exampe,wen te agency confict is more severe i.e., tere is a iger ), or wen te owproductivity parameter s ) rises reative to te iger one s ), te ikeiood of overreporting by te ow-type manager rises, wie w decreases cf. Proposition 2). Proposition 6. In equiibrium, te wage foowing a ow-productivity report, ŵ, is decreasing in and s s. Output-contingent wage contracts. In tis section, we extend te anaysis to aow outputcontingent contracts. As we saw earier, suc contracts are not optima in te bencmark firstor te second-best cases cf. Proposition 1 and Teorem 2). But output-contingent contracts can be potentiay optima, because tey can infuence investors investment response to manageria discosures ex post. Specificay, te optima investment at te information set C, r), r {, }, is ) 1 w r w 2 r ))Es C, r) k r =. 26) C AND 29.

16 KUMA AND LANGBEG / 159 Tus, by varying w r w r ) ex ante, te owner can infuence is consistent investment ex post. However, using output-contingent wages is aso costy, because tis wage poicy diutes te owner s caim on reaized output in te ig-earnings state. Tus, noisy reveation and te use of output-contingent wages are two costy mecanisms tat ameiorate te agency probem tat arises due to te renegotiation-proof constraints on investment. 2 In particuar, setting w w > decreases te investment gap k k ), and reaxes te ow-type manager s incentive constraint. However, a positive wage differentia w w > reduces investment foowing a ow-productivity report, increases te investment gap k k ), and tigtens te ow-type manager s incentive constraint. Moreover, setting w > is not effective in reducing eiter te investment gap or reaxing te ow-type manager s incentive constraints. Teorem 5 beow confirms te intuition tat under te optima contract wit outputdependent wages and genera randomization by bot types, w = and w = w. Moreover, in te mode at and, wit a risk-neutra agent wo as a inear benefit of contro function, te use of output-contingent wages foowing a ig-productivity report is not optima, tat is, w = w. Terefore, in any optima renegotiation-proof contract or PBE), te wage poicy is not output contingent, tat is, w j = w j j {, }. Note tat te wage contract can certainy be contingent on te reported productivity, in particuar Teorem 5 states tat w = w w = w =, in equiibrium. Teorem 5. In any optima renegotiation-proof contract or PBE), te equiibrium wages are not output contingent, tat is, w = w = and w = w. We reiterate tat Teorem 5 ods wie aowing randomized reporting strategies by bot manager types, tat is, wie considering strategies π, π ) [, 1] 2. To see wy te optima mecanism incudes noisy reveation but not a positive wage differentia w w, it is usefu to consider a reaxed version of te optima contracting probem wit te incentive constraint 27) repacing 8): w ) w s f k ) w k k. 27) We commence te proof of Teorem 5 by sowing tat 8) impies 27), tat is, 27) is satisfied wenever 8) is satisfied. Now, considering te reaxed probem, it foows from 26) and 27) tat it is suboptima to set w >, because any suc wage poicy is stricty dominated by an aternative poicy tat sets w = w w and w = : te aternative poicy does not affect te constraint 27), maintains te origina investment foowing a ig report cf. 26)), and owers expected wages. Simiary, w >w aso cannot be optima, because an aternative poicy tat sets w = w = w, wit w = w w )s f k ) w, satisfies 27), but improves te ex post efficiency of k witout raising te expected wages. It is aso te case tat 27) binds at te optimum. Next, te objective function wit w =, w = w, and binding 27) is suc tat te first-order condition wit respect to w is proportiona to 1 w ). Terefore, te optima wage compensation w is on te boundary, but paying w at te upper boundary is suboptima; terefore, w =. We concude te proof by estabising tat te soution to te reaxed probem equas te soution to te origina probem, tat is, te soution of te reaxed probem satisfies te origina incentive constraint 8). Generaized randomization. In Section 5 above, we ave examined te optimaity of inducing randomized reporting from te ow-productivity manager, wie assuming tat te ig-productivity manager reports trutfuy. Now, from Teorem 5 it foows tat te incentive constraints of bot agent types bind at te optimum wit generaized randomization. But we note tat randomization by te ig-productivity manager wi increase investors Bayes-rationa 2 Monotonicity of manageria compensation contracts in performance is an appeaing property and is a common simpification in te iterature. See, for exampe, Innes 199), Nacman and Noe 1994), and DeMarzo and Duffie 1999) for te use of, and potentia justification for, suc restrictions. C AND 29.

17 16 / THE AND JOUNAL OF ECONOMICS investment response to a ow-productivity report, and terefore possiby move equiibrium outcomes toward te second-best. Tus, it may aso be optima under certain conditions) to induce randomization by te ig-type agent by trading off ower expected wages wit te cost of investment distortions. In tis section, we terefore examine randomization by bot agent types, and present sufficient conditions on te mode parameters) for randomization ony by te ow-type agent to be optima. To see te main argument, consider te impications of increasing te probabiity tat te ig-productivity manager under reports, tat is, π. At te margin, tis perturbation imposes investment distortion costs tat equa μ [ r, ) r, )], were r, ) s f k ) k and r, ) [s f k ) k w ] are te expected profits wen te ig-type manager reports trutfuy and fasey, respectivey. We aso know from Teorem 5 tat in any equiibrium, w = k k ). But it foows from Bayes rue tat as π rises, investors posterior expected productivity fas conditiona on a ig report and rises conditiona on a ow report; ence, k π and k π. Hence, increasing π sigty aso yieds a margina benefit of wage reduction tat is proportiona to w π ). We note tat te margina investment distortion cost, μ [ r, ) r, )], is inversey reated to te ow-productivity parameter s ) because te optima k is increasing in s. Tat is, te cost of capita misaocation wen te true state is s,butk is invested, is iger te ower is s. Moreover, te margina investment cost increases wit π ; and, if μ is bounded beow and s is not too ig, ten te objective function is convex in π. As a consequence, under te conditions on μ and s, te optima π ies on te boundary, tat is, π {, 1 π }. 21 However, te boundary soution π = 1 π, as we as te soution π,π = 1,, impement a pooing equiibrium, tat is, reports are not informative and investments are k = k = k P. But, as sown above in Teorem 4, te pooing contract π, π = 1, ) isstricty dominated by te noisy reveation contract wenever b, b), or by te trut-teing contract wenever b. Consequenty, te upper boundary π = 1 π is not optima as ong as > b, eaving te soution π =. To summarize te immediatey preceding arguments, it is optima to induce trut teing from te ig-type agent if te expected production inefficiency cost of under investing in te igproductivity state, tat is, investing k wen te true state is s, is above some tresod. And tis expected inefficiency cost of underinvesting) is inversey reated to te ow-state productivity s ); tat is, te ower is s, te greater is te inefficiency due to underinvestment. But it is positivey reated to te prior beiefs on te ikeiood of te ig-productivity state μ); for exampe, te expected cost of underinvestment is ceary very ow if te prior probabiity of te ig state is itsef cose to zero. Finay, using previous resuts, we know tat pooing i.e., π = 1) is not optima wenever te incentive-cost ratio is above a specified tresod see Teorem 4 and Coroary 1). Putting tese conditions togeter, we can specify conditions tat ensure tat ony randomization by te ow-type agent is optima. Teorem 6. Tere exists < s < 1, suc tat under te optima contract tere is trut teing by te ig-productivity manager i.e., π = ) and randomization by te ow-productivity manager i.e., π < 1) wenever > b, < s < s, and μ> 1. 3 Atoug Teorem 6 impies tat, under te optima contract, tere is noisy reveation <π < 1) by te ow-productivity agent as described in Teorem 3) and trut teing by te ig-productivity manager if b, b), s < s, and μ> 1, furter exporation of te probem 3 numericay confirms tat te conditions on s and μ are sufficient but not necessary. In particuar, Figure 5 pots firm vaue as a function of te randomization probabiities π, π,forμ =.1, 21 As we argue in Teorem 5, a feature of any optima contract is tat π 1 π,asπ = 1 π impements te pooing equiibrium. C AND 29.

18 KUMA AND LANGBEG / 161 FIGUE 5 FIM VALUE WITH ANDOMIZATION BY BOTH MANAGE TYPES Pots firm vaue as a function of te randomization probabiities π, π, for μ =.1, =.1, = 1, and s, s =.7,.5. Te optimum is ocated at π, π =.12,. and sows tat te optima genera randomization strategy is given by π, π =.12,, consistent wit Teorem Summary and concusions Investment inefficiency in certain firms or sectors, induced by corporate fraud were informed insiders manipuate te beiefs of uninformed investors troug exaggerations of economic prospects, as been istoricay prevaent, and as recenty attracted muc attention because of some prominent corporate scandas. However, reconciing suc investment distortions and corporate fraud wit rationa capita markets poses obvious caenges. We provide a new teory were corporate fraud or noisy information reveation) is accompanied by overinvestment in ow-return states and under-investment in ig-return states. Our framework is based on two important caracteristics of modern corporations operating in we-deveoped financia markets: tere are sareoder-management agency conficts because managers derive private benefits 22 Based on te optima wage poicy specified in Teorem 5 and te resuts of Teorem 6, we can briefy comment on te impications of aowing renegotiation of wage contracts cf. footnote 12). Suppose tat r =, in wic case te firm is reveaed to be a ow-productivity firm. Here, w is renegotiation proof because te owner ceary as no information-based incentives to offer an aternative wage; e aso does not ave risk-saring benefits as in Fudenberg and Tiroe, 199), because te agent is risk neutra. Meanwie, te agent wi not accept any wage ower tan w as ong as investment is fixed at k from te ex post efficiency constraint. Next, suppose tat r =, in wic case tere is uncertainty ex post regarding te firm s productivity. However, te owner can induce furter information troug renegotiation ony by inducing te agent to communicate again or to coose from a type-based wage menu). Atoug sequentia mecanism design is outside te scope of our mode, it is an interesting topic for furter researc to examine our mode in suc a setup. C AND 29.