On the optimal use of loose monitoring in agencies

Transcription

1 Rev Account Stud (2011) 16: DOI /s y On te optimal use of loose monitoring in agencies Qi Cen Tomas Hemmer Yun Zang Publised online: 19 April 2011 Ó Springer Science+Business Media, LLC 2011 Abstract We study te governance implications of firms being privately informed of teir potential productivity before contracting wit an agent to supply unobservable effort. We sow tat it can be optimal for ig potential firms to ave loose monitoring in te sense tat te monitoring system is less perfect tan wat is implied by a standard agency model a la Holmstrom (Te Bell J Econ 10:74 91, 1979). Loose monitoring is used to acieve separation among different types of firms suc tat firms wit low potential do not ave incentives to imitate contracts offered by ig potential firms. Our findings imply tat altoug loose monitoring may be a symptom of firms squandering scarce resources provided by investors, it can also arise as an optimal contracting arrangement. Keywords Pay Performance measurement Information system Monitoring JEL Classification D82 D86 J33 J41 Q. Cen Fuqua Scool of Business, Duke University, 100 Fuqua Drive, Duram, NC , USA qc2@duke.edu T. Hemmer Jones Graduate Scool of Business, Rice University, 6100 Main Street, Houston, TX 77005, USA tomas.emmer@rice.edu Y. Zang (&) George Wasington University Scool of Business, Suite 601C Funger Hall, 2201 G St. NW, Wasington, DC 20052, USA yunzang@gwu.edu

2 On te optimal use of loose monitoring in agencies Introduction We study wy some firms may coose to commit to loose monitoring in te sense tat te monitoring systems tey implement are less informative tan wat is implied by a standard agency model a la Holmstrom (1979) wile oter firms tat employ similar agents do not. Our basic idea is tat identical agents may be differentially useful to different firms but, to some extent, suc differential usefulness will be private information to firms insiders. Wile many observably quite different firms can benefit from using te inputs of te same type of talent, it may not be obvious to prospective employees were tey can best use teir talents. Tus, it may be optimal for firms to find credible ways to communicate teir differences in tis respect to potential employees. Tis paper sows tat suc credible communication to prospective employees can take place via te terms of employment offered, specifically, and of particular interest from an accounting perspective, via te level of monitoring provided by teir internal and external accounting systems. A few anecdotal examples may be elpful for fixing ideas before proceeding. Consider a company suc as Google tat is currently enjoying significant successes. Despite being unique in many respects, tere are still many large competitors for te talent tat Google relies on for its successes. Tese competitors, like Google, face constant sifts in teir potential fortunes. Te issue of specific interest to us in tis example, owever, is tat, at least anecdotally, Google is generally viewed as providing a work environment wit less oversigt and more individual freedom tan its competitors. As also seems to be te case, firms wit a reputation for engaging in loose monitoring of employees often are ones tat are viewed as aving relatively iger potential for future successes. Te seemingly lax oversigt of employees appears to at least reinforce tis perception by conveying a message of room for excesses. Firms wit iger potential sould be better able to afford not to scrutinize te activities and accomplisments of teir employees. However, being lax in tis way may also be perceived as not pursuing te interest of sareolders. Te fact tat stronger firms are better able to manage teir workforce and related expenditures less vigorously does not imply tat tey sould do so, owever, as tis would appear to be in direct conflict wit te interest of sareolders. A key result of our analysis is tat offering terms of employment wit features suc as loose monitoring can actually be an effective as well as efficient way for ig potential firms to communicate teir productive advantage to employees. Te alternative, wic is to appear indistinguisable from low potential firms by utilizing te best monitoring available, may actually cost sareolders more. Te intuition is te following. In traditional agency settings, te key binding constraint is te agent s incentive compatibility (IC) constraint, wic implies inefficient risk saring (relative to te first-best situation). Tere, te principal always cooses te best information system as better information reduces compensation-related risk for te agent and ence mitigates te adverse risk-saring implications of te IC-constraint. Precisely because te best information system improves contracting efficiency, it also invites imitation.

3 330 Q. Cen et al. Imitation arises because wen te low potential firms type is known, tey need to expose teir employees to more incentive related risk to motivate te same level of effort, wic in turn results in iger expected wage payment tan ig potential firms. Tus low potential firms benefit if tey cannot be distinguised from ig potential ones. We sow tat in te optimal separating contract arrangement, te contracts tat ig potential firms offer generally deviate from te standard singlefirm-type contracts. Specifically, te optimal separating contracts are caracterized by overpayment to agents, or less empasis on efficient risk-saring in te sense tat contracts may be based on a less precise monitoring system tan tose used by te low potential firms, or bot. Wile te deviations from te standard second-best contracts discourage profitable imitation by low potential firms, tey noneteless make ig potential firms appear careless wit teir monitoring and teir sareolders money. Wat is important to note ere is tat, in te case of multiple unobservable firm types, suc accusations could be unwarranted. Te alternative to te separating contract is a contract wic allows imitation by low potential firms. Hig potential firms find it optimal to separate because separation dominates te alternative of being viewed as low potential firms. Accordingly, our analysis suggests tat firms tat appear to squander sareolder value may be doing te opposite; te standard second best is unavailable due to te presence of firms wit lesser potential. Noteworty from an accounting perspective, te optimality of a loose monitoring system implies an endogenous upper bound on te value of information system quality for ig potential firms wen tere are multiple types of firms. To gain furter insigts into tis issue, we consider ow best to design lax monitoring systems. In particular we examine te role of biases and analyze wat kind of news it is better to represent less accurately: good or bad. As we sow, if te optimal employment arrangement involves bot loose monitoring and overpayment, ten te monitoring system sould be designed to be lenient in tat it is more likely to (mis-)report bad news as good news rater tan te oter way around. In oter words, our teory suggests tat firms wit looser oversigt sould ave more optimistic reporting systems in place tan firms wit more intense monitoring. As suc, our paper also provides an empirically testable implication about te determinant of biases in accounting systems. Tere are certainly oter ways firms can communicate information credibly. Indeed, firms suc as Google clearly differ in many observable ways from teir competitors. However, many of tese key observable differences among te prospective employers relate to teir business models and cannot easily be canged for te purpose of attracting a particular employee. Furtermore, as suggested earlier, most companies operate in igly dynamic environments were te nature of te competition and te company s fortunes can cange witout notice so tat differences in track-records provide little guidance on future fortunes. Terefore, many observable differences do not enable prospective employees to differentiate firms potential productivity. 1 Suc companies may terefore need to continuously 1 For example, wile in some labor markets Honda is competing for te same talent as Caterpillar, to te prospective employees it may be less tan obvious wic company offers te best overall opportunities. Yet Honda is Honda and Caterpillar is Caterpillar, and tey are obviously different.

4 On te optimal use of loose monitoring in agencies 331 communicate to current and prospective employees teir usefulness to teir specific organization. Terms of employment (specific to individual employees) seem to be a natural coice for doing tis. Our paper makes new and specific testable predictions about observable monitoring differences between firms. Our paper is related to te informed principal framework pioneered by Myerson (1983) and Maskin and Tirole (1990, 1992). Tey study a general mecanism design setting were te principal as private information and te agent can infer tis information from te mecanisms offered. Several papers subsequently apply te general framework to study contracting problems in an oterwise standard moral azard setting (Beaudry 1994; Inderst 2001; Cade and Silvers 2002). Tese works focus on wage payments as te only separation tool and are closely related to te efficiency wage literature (e.g., Sapiro and Stiglitz 1984), 2 wic argues tat firms pay employees more tan teir competitive wages to provide incentives for employees to work. A limitation of te efficiency wage argument is tat it assumes tat firms cannot offer more sopisticated performance based compensation contracts. Te extant informed principal literature sows tat efficiency wage still arises even wit firms utilizing performance based contracts. In contrast, our focus and innovation are on te use of information systems to acieve separation among firms. Our paper also relates to te growing literature in accounting aimed at understanding wen (more) noise in accounting information systems may be optimal. Prior studies ave suggested tat a noisy system may be optimal wen it can be used as a substitute for commitment device in a multi-period setting (Arya et al. 1998; Demski and Frimor 1999; Cristensen et al. 2002), or wen it can reduce incentives for earnings management (Dye and Sridar 2002; Cen et al. 2007). We extend tis line of inquiry by focusing on private information on te part of te principal and by allowing firms to design information systems wit regard to te presence of teir competitive peers in te labor market. Our paper provides an alternative explanation for te observed variations in te use of information systems and suggests tat using loose monitoring as represented by a seemingly noisier-tan-necessary information system, can be optimal for firms seeking to separate temselves from teir labor market competitors in order to more efficiently recruit and motivate employees. 3 Te paper proceeds as follows. Section 2 lays out te basic model, derives its solution, and discusses its implications. Section 3 extends te analysis to study measurement biases and provides related empirical predictions. Section 4 provides concluding remarks. 2 Model set-up Our model captures te core aspects of te general penomenon tat we ave in mind as follows. A principal/firm contracts wit an agent to supply a productive 2 Also see Weiss (1990), wic offers an excellent overview of te efficiency wage literature. 3 Ayra and Mittendorf (2005) sow tat optimal contracts may vary in order to screen agents talent. However, as discussed in Sect , switcing private information from te principal to agent in our setup does not give rise to a noisy information system.

5 332 Q. Cen et al. action, a 2fa ; a l g; wic is only observable to te agent. Action a stocastically influences te realizations of te economic income, x 2fx; xg, wit x [ x [ 0. Specifically, Prðxja l Þ¼0 and Prðxja Þ¼p [ 0. Tus, picking a l wic we will refer to as working less ard or sirking leads to low economic income (x) for sure, wile working ard (a ) generates good economic income (x) wit some strictly positive probability p 2 fp l ; p g; were te sub-script refers to te exogenously given potential of te firm. Te probability measures te marginal productivity of te agent s action conditional on te type of te firm te agent works for. It can be eiter low or ig. Since te agent is more productive if e works for a ig potential firm, p [ p l. We assume tat p is privately observed by te firm (principal). Te agent as access to te common prior Prðp ¼ p Þ¼t and can also update is beliefs about te principal s type based on te contract offered by te principal. For te principal, te only contractible variable available is a performance metric (call it accounting earnings) denoted by e 2fe; eg, wit e [ e, tat is informative about te underlying economic income x. Te principal designs and determines te accuracy of te performance evaluation system tat generates te earnings number ex-ante. Te accuracy of te system is denoted by q 2ð1=2; 1Š, wit Prðe ¼ ejx ¼ xþ ¼Prðe ¼ ejx ¼ xþ ¼q. In essence, q is te probability wit wic te information system correctly captures te economic income and te coice of q is directly observable to te agent. To igligt te endogenous cost of a precise information system, we assume tat tere is no exogenous cost of implementing a perfect information system. Tus, a type p i 2 fp ; p l g firm s contract specifies q i as well as wage compensation to te agent ðw i ; w i Þ as a function of realized accounting earnings wit w i (w i ) paid to te agent wen e (e) is observed. For a scematic overview, see Fig. 1. Te principal is risk neutral and te agent is risk averse wit an increasing concave utility function U(w). Witout loss of generality, we assume tat te agent incurs an incremental disutility of m wen working ard and as a reservation utility normalized to zero independent of te type of firm e works for. Finally, assume tat x is sufficiently iger tan x tat te principal, regardless of is type, always wants to elicit ig effort (a ) from te agent. Te last assumption allows us to concentrate on te use of te information system as a separation tool. If we were to allow multiple levels of effort, it is possible tat te ig potential firms migt separate by reducing te level of effort required of te agent but keeping te information system intact. Reduced effort would lower te expected true output. Wen te impact of effort on output is ig (wic is te case wen x is very large Fig. 1 p i firm wit contract of ðw i ; w i ; q i Þ

6 On te optimal use of loose monitoring in agencies 333 Fig. 2 Time line relative to x), ten separation troug effort reduction will be very costly for ig potential firms. One neat feature of separation troug information systems is tat modifications to te information system cange only te agent s wage payment and do not affect te actual output. Te principal s objective is to minimize te expected compensation to te agent wile encouraging te agent to work ard. Figure 2 below provides te time line of te model. At Date 1 te principal becomes informed of is own type p i after wic e proposes a contract ðw i ; w i ; q i Þto te agent. At Date 2, te agent revises is belief about te principal s type based on te offered contract and decides weter to accept or reject te contract conditional on is revised belief. If te contract is accepted, te agent ten decides weter to work or to sirk. At Date 3, earnings are realized and te contract in place is executed accordingly. For notational ease, we define PrðjjiÞ; were i; j 2 f; lg, as te probability of observing a ig earnings number (e), conditional on te agent working ard (a )in a firm of type p i wic uses te accounting information system q j and offers as te compensation payments, i.e. w j ; w j Prðjji Þ Prðeja ; q j ; p i Þ¼p i q j þ ð1 p i Þ 1 q j : Similarly we define PrðijiÞ as: PrðijiÞ Prðeja ; q i ; p i Þ¼p i q i þ ð1 p i Þð1 q i Þ: We focus on separating contracts and solve te following program: 4 min q i ;w i ;w i ;i2f;lg Pr ð iji Þw i þ ½1 PrðijiÞŠw i s:t: PrðjlÞw þ½1prðjlþšw PrðljlÞw l þ ½1 PrðljlÞŠw l ; ðpicðlþþ PrðljÞw l þ½1prðljþšw l PrðjÞw þ ½1 PrðjÞŠw ; ðpicðhþþ PrðijiÞUðw i Þþ½1PrðijiÞŠUðw i Þmð1 q i ÞUðw i Þþq i Uðw i Þ; ðaicðiþþ PrðijiÞUðw i Þþ½1PrðijiÞŠUðw i Þm0: ðairðiþþ Let w i ; w i ; q i, i 2 f; lg be te solution to te above program. Tis solution constitutes te best (i.e. least costly) fully revealing equilibrium from te principal s perspective. Te rigt-and side (RHS) of PICðLÞ is te low type principal s expected compensation cost under contract ðw l ; w l ; q l Þ and te left-and side (LHS) 4 We acknowledge te potential for te existence of oter equilibria tan tis fully separating one. We provide furter detailed discussions on tis issue after Proposition 1 in te next section.

7 334 Q. Cen et al. is is expected compensation cost if e pretends to be te ig type and offers contract ðw ; w ; q Þ instead. Te PICðLÞ constraint tus guarantees tat te low type as no incentive to offer te ig type s contract. Similarly, te PICðHÞ constraint guarantees tat te ig type as no incentive to adopt te low type s contract. Upon observing w i ; w i ; q i, te agent ten infers perfectly te principal s type. Conditional on te agent s perfect inference of te principal s type, te solution satisfies te agent s participation constraint (AIR(i)) to ensure tat te agent receives at least is reservation utility as well as te relevant incentive compatibility constraint (AIC(i)) tat ensures te agent prefers working ard to sirking. 5 Te next section caracterizes te solution to tis program. 2.1 Basic analysis We start by establising tat te solution to te above program differs from te standard solution wen te principal and te agent are identically informed about te production function prior to contracting. Specifically, Lemma 1 sows tat te standard second best contracts for eac of te two types considered ere do not satisfy te PIC(i) constraints. Lemma 1 (a) If p i is common knowledge, ten te optimal contract is te second best contract given by q SB i = 1, w SB i ¼ U 1 m p i, and w SB i ¼ U 1 ð0þ, wit i 2 (b) ðw SB i ; w SB i ; q SB i Þji ¼ ; l does not satisfy te principal s PIC(L) constraint. f; lg; Under te informativeness principle of Holmstrom (1979), it never elps to add noise to te information system in a standard moral azard setting. Tis implies q SB i = 1 in te second best contracts wit accounting earnings revealing te true economic outcome wit 100% accuracy. Te second best contracts also ave bot te agent s IR and IC constraints binding. Tus w SB i and w SB i can be solved for simply by substituting q i = 1 into te agent s relevant IC and IR constraints. For Lemma 1(b), notice tat under te second best contracts, te ig type firm offers te same payment as te low type firm wen earnings are low (w SB ¼ U 1 ð0þ ¼ w SB l ) but pays te agent less w SB ¼ U 1 m p \w SB l ¼ U 1 m p l Þ wen earnings are ig. Tis suggests tat, wen p i is privately observed by te principal, te low type principal as incentives to imitate te ig type s contract offer. Indeed, te second best contracts do not satisfy te PIC(L) constraint and terefore cannot be used to acieve separation wen p i is privately known by te firm. Proposition 1 below presents a reduced program tat greatly simplifies te task at and and also seds ligt on te primary tension in te model. Proposition 1 Wen te firm privately observes its type, te best separating contracts are te solution to te following program: 5 Tis formulation assumes tat te principal as te bargaining power, wic implies tat in a standard single type model, te principal would never (need to) provide te agent wit more tan is reservation utility. Our results are not sensitive to tis assumption. See Sect for detailed discussion.

8 On te optimal use of loose monitoring in agencies 335 s:t: min q ;w ;w Prðj Þw þ ½1 PrðjÞŠw PrðjlÞw þ ½1 PrðjlÞŠw ¼ p l w l þ ð1 p l Þw l ðpicðlþþ PrðjÞUðw Þþ½1PrðjÞŠUðw Þm0 ðairðhþþ m Uðw ÞUðw Þ¼ p ð2q 1Þ ðaicðhþþ Uðw l Þ¼ m ; p l Uðw l Þ¼0; q l ¼ 1: Proof (All proofs are included in te appendix.) Te program in Proposition 1 is designed to identify te contract tat attains te best (i.e. least costly) fully revealing (separating) equilibrium from te ig type principal s perspective. However, for tis type of model, te existence of a particular equilibrium always depends on te specification of te off-equilibrium belief. To provide some sense of te validity and generality of te results in Proposition 1, we appeal to te Intuitive Criterion by Co and Kreps (1987), wic requires any off-equilibrium belief to be reasonable. Specifically in our setting, if te low potential firm would not coose a given contract regardless of wat te agent believes, a reasonable off-equilibrium belief by te agent is tat any principal wo does coose tat contract cannot be (i.e., as zero probability of being) te low type. Proposition A1 of te appendix sows tat under te Intuitive Criterion, all pooling equilibria are eliminated, and tat te only separating equilibrium tat survives is indeed te best separating one identified by te above program. 6,7 Proposition 1 establises tat between PICðHÞ and PICðLÞ, only PICðLÞ is binding. Tat is, only te low type firm as incentives to imitate te ig type. Proposition 1 furter reveals tat te optimal separating contracts entail tat te low type cooses te second best contract wit te most accurate information system (i.e., q l = 1). Tis result is reminiscent of te classic result in te mecanism design literature tat tere is no production distortion for te type tat as incentives to imitate te oters (see, e.g., Laffont and Tirole 1986), except tat no distortion ere means te contract is identical to te second best contract. Lastly, Proposition 1 sows tat in bot principals contracts, te agent s IC constraint is binding. Te intuition is te same as in Lemma 1. A slack AIC constraint means a larger tan necessary spread in te agent s compensation to induce effort. Te larger spread imposes unnecessary risk on te agent, wic is always suboptimal for te principal wen te agent is risk-averse. 6 If firms can coose an equilibrium before tey learn teir types, tey strictly prefer pooling. Tis can be easily establised due to te agent s risk aversion and te need for firms to (costly) signal. However, tis commitment to pooling requires tat firms resist te temptation to deviate after teir types are privately known. 7 In a two-sided adverse selection setting, Cella (2005) finds tat pooling always dominates separation. Our setting differs from is in two significant ways. First, our setting is a case of common value wile is deals wit private value. Second, we impose ex post IC and IR constraints wile is pooling equilibrium is obtained under interim IC and IR constraints. Ex post IC and IR imply interim IC and IR but te reverse is not true.

9 336 Q. Cen et al. Togeter wit Lemma 1, Proposition 1 implies tat in order to create te separation, te ig type principal as to offer a different contract tan te second best to satisfy PIC(L). Specifically, e can do so by coosing an imprecise accounting system (q \ 1). To capture tis more succinctly, we re-parameterize te simplified program in Proposition 1 as follows: min PrðjÞU 1 U þ ½1 PrðjÞŠU 1 ðu Þ q ;U 0 s:t: PrðjlÞU 1 U þ ½1 PrðjlÞŠU 1 ðu Þ ¼ p l U 1 U l þ ð 1 pl ÞU 1 ðu l Þ ðpicðlþ 0 Þ mq U Uðw Þ ¼ U 0 þ p ð2q 1Þ U Uðw Þ ¼ U 0 þ mðq 1Þ p ð2q 1Þ U 0 0 U l ¼ m p l ; U l ¼ 0; q l ¼ 1: Here U 0 denotes te agent s expected utility under te optimal contract in te ig type firm, i.e., U 0 ¼ PrðjÞUðw Þþ½1PrðjÞŠUðw Þm. Tis equation, togeter wit te fact tat AIC(H) is binding, enables us to uniquely pin down U and U in terms of q and U 0. Consequently, we can express te AIRðHÞ constraint as U 0 C 0 and replace te AICðHÞ constraint wit te implied expressions for U and U. Te principal s coice variables are now q and U 0, and te re-parameterized problem as te same solution as te original program. Lemma 2 below provides some preliminary insigts on ow PICðLÞ 0 could be satisfied wit U 0 and q and on te relation between tese two tools. Lemma 2 (a) Holding q constant, te LHS of PICðLÞ 0 strictly increases in U 0. (b) Holding U 0 constant, te LHS of PICðLÞ 0 strictly decreases in q. (c) Holding PICðLÞ 0 at equality implicitly defines U 0 as a function of q, wit du 0 dq [ 0. Recall tat te LHS of PICðLÞ 0 represents te expected wage cost for te low type firms wen tey imitate te ig types contract offer. Lemma 2(a) sows tat a iger U 0 increases tis cost and terefore elps satisfy te PICðLÞ 0 constraint by increasing its LHS witout canging te RHS. Lemma 2(b) implies tat te low type s cost to imitate te ig type s contract is iger wen q is lower (i.e., wen te ig type adopts a less tan perfect information system). Te intuition is tat introducing noise into te information system weakens te link between effort and performance measurement. As a result, a risk averse agent demands iger expected wage payment, tus making it costly for te low type principal to misrepresent is type. Lastly, Lemma 2(c) suggests tat te two tools are substitutes for eac oter. A small increase in U 0 frees up te principal s PICðLÞ 0 constraint (as implied by Lemma 2(a)) and enables q to increase as an optimal response (as implied by Proposition 1 and Lemma 2(b)). Tis substitution can potentially create a net benefit

10 On te optimal use of loose monitoring in agencies 337 to te principal wen te gains from te latter outweig te losses caused by te former. To summarize, te key new ingredient of our model derives from te PICðLÞ 0 constraint. In te traditional agency setting, te optimal q is always set at te upper bound of 1 (assuming zero out-of-pocket implementation cost) as te principal always benefits from acieving better risk saring wit te agent. However, Lemma 2 indicates tat, for a ig type firm, a iger q brings an endogenous cost in our setting: it induces te low type to imitate by making PICðLÞ 0 arder to satisfy. As a result te optimal q may not be 1 anymore. Similarly, in te traditional agency setting, paying te agent iger tan is reservation utility as no benefits but only costs to te principal. If te principal as te bargaining power, te optimal contract would keep te agent s IR constraint binding. In contrast, providing te agent wit excess utility as a benefit ere by making PICðLÞ 0 easier to satisfy. Tus, wen te principal is privately informed of is type, te optimal contract for ig type incorporates a trade-off between te relative costs and benefits of tese two means of separation. In te next section we explore tis trade-off furter by identifying sufficient conditions for wen te ig type firm optimally cooses q \ 1 (in Proposition 2) or sets U 0 [ 0 (in Proposition 3). 2.2 Sufficient conditions for separation We first investigate te determinants for te quality of te monitoring system adopted by te ig type firm. Te principal ere is always in a position to coose q = 1 wit no direct cost. A sufficient condition for im to coose q \ 1 would be tat if te expected compensation embedded among all possible contracts tat satisfy te constraints of te simplified program in Proposition 1 is increasing in q at q = 1, i.e., deðw Þ j dq q ¼1 [ 0: Proposition 2 identifies a sufficient condition under wic tis is te case. Proposition 2 A sufficient condition for te optimal q \ 1 is U w ;q ¼1 U w ;q ¼1 U 0 w ;q ¼1 þ U 0 w ;q ¼1 w ;q ¼1 \ ð1þ w ;q ¼1 2 were w ;q ¼1 and w ;q ¼1 are te optimal wage compensation to te agent by te ig type firm wen q is restricted to 1. A sufficient condition for (1) is U 000 ðwþ[ 0. To understand te intuition beind Proposition 2, we first need to recognize te potential benefit of q \ 1 in our setting. One migt tink tat q \ 1 can never be optimal because it introduces noise and increases te risk premium demanded by te risk-averse agent. Tis intuition turns out to be incomplete. In a standard agency model were te principal as no private information, te principal s problem is to trade off between te risk imposed on te agent and te need to motivate te agent

11 338 Q. Cen et al. to work. Ten it is true tat distorting te information system as no value. (Tis is also establised in Lemma 1.) However, in our setting, on top of a traditional moral azard problem te principal also desires to separate among different types. In tis case, as Lemma 2 sows, a noisy system wit q \ 1 can potentially elp separation. Te next step in understanding te intuition beind Proposition 2 is to recognize tat a noisy system urts te ig type relatively less on te margin tan it does te low type. To illustrate tis, let us first pick any contract tat satisfies te agent s AIC constraint. Note tat sligtly decreasing q i wile olding te agent s expected utility constant increases te principal s expected wage payment. In formal terms, oeðw i Þ ¼ o½prðijiþw i þð1prðijiþþw i Š oq i oq " i m ¼ ð2p i 1Þðw i w i ÞPrðijiÞ U 0 ðw i Þð2q i 1Þ 2 # m þð1 PrðijiÞÞ U 0 ðw i Þð2q i 1Þ 2 \0: Te usual single crossing property ere calls for o2 Ew i oq i op i [ 0. Tat is, altoug a smaller q increases te expected wage payment for bot types, it increases less for te ig type principal. Note tat o2 Ew ð i Þ [ 0 if and only if oq i op i UðwÞUðwÞ \ 2U0 ðwþu 0 ðwþ w w U 0 ðwþþu 0 ðwþ : ð2þ It is easy to verify tat (1) is a more general condition tan (2) because (2) is derived by olding te agent s expected utility constant, wic is more restricted tan Proposition 2. To see wy a noisy system urts te ig type less on te margin, note tat conditional on te agent exerting ig effort and olding wage payments constant,a noisy system decreases te expected wage payment of te ig type but increases tat of te low type. Specifically, fix any two wage payments of w and w wit w [ w. Under te perfect information system, te agent is paid w wen te true output is ig and w wen te output is low. As Fig. 1 sows, a noisy system (q \ 1) increases te expected wage payment for bot types wen te true output is low, but decreases te payment wen te true output is ig. Since te low type firm is more likely to end up wit true low output, its expected wage payment increases more tan te ig type under te noisy system. Te above illustration olds w and w constant and does not consider te effect of introducing noise on te optimal wage payments to motivate effort. Wile a noisy system costs te ig type less on expected wage payment wen te agent works, it makes it arder to motivate effort to begin wit. Condition (1) ensures tat tis incentive cost of noisy systems does not overwelm teir benefit in elping te ig type separate. Wile seemingly tecnical, Condition (1) actually speaks to te agent s risk preference. As sown in te appendix, it is satisfied for all utility ð Þ

12 On te optimal use of loose monitoring in agencies 339 functions tat exibit non-increasing absolute risk aversion, suc as logaritm, power, and negative exponential utility functions. Tis is not surprising given tat risk aversion is te fundamental reason for te ig type to be able to use noisy systems to separate. In particular, te ig type s advantage in separation wit q \ 1 is iger wen te agent is more risk averse; in te extreme case wen te agent is risk-neutral, te ig type cannot use q \ 1to separate at all. In Proposition 2, we start at te igest q = 1 and terefore te igest wealt given to te agent (i.e., rely solely on overpayment to separate by Lemma 2). Wile decreasing te agent s wealt benefits te principal, it makes PICðLÞ 0 arder to satisfy and terefore invites imitation by te low type. Wit decreasing risk aversion, owever, reducing te agent s wealt increases is risk aversion, wic provides te ig type te comparative advantage in reducing q to keep PICðLÞ 0 binding. To complete te caracterization of te optimal contract, we note tat te agent s IR constraint may not be binding. Our next proposition identifies sufficient conditions for tat to be te case. Proposition 3 Let w ;U 0 ¼0 and w ;U 0 ¼0 be te wage payments to te agent and q ;U 0 ¼0 be te optimal q in te ig type firm olding U 0 = 0. Ten a sufficient condition for te optimal U 0 [ 0 is U w ;U 0 ¼0 U w ;U 0 ¼0 U 0 w ;U 0 ¼0 þ U 0 w ;U 0 ¼0 w ;U 0 ¼0 [ : ð3þ w ;U 0 ¼0 2 A sufficient condition for (3) is te agent is U 000 ðwþ\0. Similar to Proposition 2, to prove Proposition 3, we start wit a feasible contract were U 0 = 0 and ten sligtly increase U 0 wile maintaining all te constraints. Under Condition (3), te principal s expected wage payment strictly decreases wit U 0 at U 0 = 0, i.e., de ð w Þ du 0 j U0 ¼0 \0. Ten, it as to be case tat te optimal U 0 is strictly iger tan te agent s reservation utility of 0. A sufficient condition for Condition (3) is U 000 ðwþ\0, wic implies tat te agent exibits increasing risk aversion. To see te intuition, note tat at U 0 = 0, te agent exibits te least risk aversion, wic means tat te ig type s advantage in signaling troug q is te weakest. Wen U 000 ðwþ\0, increasing is wealt would make im more risk averse, wic makes separation troug q relatively more attractive. It may seem counter-intuitive to set U 0 [ 0 as te single crossing property does not appear to be satisfied for U 0. One can easily verify tat o½prðjiþw þð1prðjiþþw Š ou 0 [ 0 and o2 ½PrðjiÞw þð1prðjiþþw Š ou 0 op i [ 0. Tis means everyting else equal, a iger U 0 increases te expected wage payment for bot types of principals, and te increase is more for te ig type tan for te low type principal. Tis suggests tat, compared wit q,u 0 would be a costly, and ence an inferior separation device for te ig type principal. However, tis intuition fails to recognize te subtle interaction between U 0 and q, wic comes from te fact tat increasing U 0 can

13 340 Q. Cen et al. elp relax te PICðLÞ 0 constraint and tus makes room for potential improvement on q. However, te improvement in q will invite imitation by te low type. In order to keep te low type at bay, it as to be tat te ig type maintains is comparative advantage in signaling troug q. As discussed earlier, tis advantage is ig wen te agent is more risk averse. Terefore, wen te agent exibits increasing risk aversion, increasing U 0 elp maintain te ig type s advantage. We want to reiterate ere tat Conditions (1) and (3) are sufficient conditions. Moreover, tey are not complement sets to eac oter altoug tey do ave te appearance of being so. Te values bot sides of tese conditions take vary, depending on were tese expressions are evaluated. Condition (1) is evaluated at te point were q = 1 and U 0 [ 0, wile Condition (3) is evaluated at te point were U 0 = 0 and q \ 1. In general, weter Condition (1) or (3) is met depends on te local curvature of te utility function, wic relates to te agent s risk preference as well as is wealt level. 2.3 Additional analyses and discussions Numerical examples Two numerical examples below elp provide more intuitive illustrations of our results. Te first one sows tat loose monitoring (i.e. te optimal q \ 1) can arise in te best separating contract. Assume te following parameter values: UðwÞ ¼LnðwÞ; p ¼ 0:4; p l ¼ 0:2; m ¼ 0:3: wen q = 1, from PICðLÞ 0 binding, we can get U ¼ 0:32684 and U 0 [ 0. Plug tese values in te objective function, we ave te expected wage payment at Now, reduce q from 1 to Again, a binding PICðLÞ 0 implies tat U ¼ 0:31592, under wic U 0 [ 0 still olds. Te new expected wage payment, owever, is , strictly less tan te expected wage payment wen q = 1. Hence, te optimal contract must ave q \1. Te next numerical example sows ow increasing U 0 can benefit te principal. Assume te following parameter values: p ffiffiffiffiffiffiffi pffiffiffii UðwÞ ¼0:5 0:5ð2 w 2 Þ 2 for w 2 2=3 ; 2 ; p ¼ 0:4; p l ¼ 0:2; m ¼ 0:06: wen U 0 = 0, from AIR, AIC, and PICðLÞ 0 binding, we can solve for te optimal contract as w ¼ 1:22876; w ¼ 0:88983; q ¼ 0:6236, under wic te ig type s expected wage payment is Now increase U 0 a little bit to and solve for te optimal contract again. We ave w ¼ 1:21582; w ¼ 0:90195; q ¼ 0:6321g. Under te new contract, te information system becomes more accurate, te spread (ence risk imposed on te agent) between w and w is lower, and te principal s expected wage payment is also lower at Hence, te optimal contract must ave U0 [ 0.

14 On te optimal use of loose monitoring in agencies Sensitivity to alternative assumptions We now discuss te robustness of our results to alternative assumptions. 8 Te first is wen te agent, not te principal, privately observes te productivity parameter p.in tis case, te principal needs to offer a menu of contracts to separate different types of agents. As is standard in te adverse selection literature, te ig type agent as incentives to imitate te low type, ceteris paribus, and te optimal screening contract leaves positive rent to te ig type agent. However, te optimal information system is te most accurate one regardless of te agent s type. Tat is, loose monitoring does not arise as part of te optimal screening contract wen agents privately observe p. Te intuition is tat adding noise to te low type agent s contract would lead to an even iger award wen te performance signal is good, wic is a more likely event for te ig type agent and tus generates more incentives for te ig type to imitate. 9 Second, our main set-up follows te standard assumption by giving te principal te bargaining power in designing te contract. Wat we ave in mind is a situation were a relatively large number of oterwise identical job candidates seek employment wit a limited supply of firms wit differing levels of productivity. For example, sales associates at SAP and Oracle probably come from a potentially large pool of candidates wit similar backgrounds. But tere are only a few firms like SAP and Oracle. Terefore, it is not unreasonable to assume tat an industry leader suc as SAP as a muc larger sare of te bargaining power against its employees and at te same time needs to signal its productivity relative to its competitors. Noneteless, it is interesting to see weter our results are sensitive to te assumption about bargaining power. We terefore consider a setting were te agent offers a menu of contracts to te principal suc tat te expected wage payment from te principal cannot exceed a reservation level, i.e., let te IR constraint be for te firm suc tat te firm does not exceed its (exogenous) budget for compensation. As a bencmark, if te firm s productivity is publicly known, te optimal (secondbest) information system is a perfect one. However, wen productivity is privately observed by te firm, under te second-best contract, muc like in our existing setting, te low type principal as incentives to imitate te ig type. Te intuition ere is tat if correctly identified, te low (ig) type firm needs to offer a contract wit a greater (smaller) spread in compensation, leading to a iger (lower) expected wage payment. Tus, to restore incentive compatibility in a separating equilibrium, te principal s IC constraint needs to be satisfied. It can be sown tat adding noise to te information system in te ig type firm can benefit te agent, for intuitions similar to wat we establised earlier in te main model. Hence, our main implication tat te ig type introduces noise to signal is type is not sensitive to sifts in bargaining power. 8 Detailed proof for tis section is available from te autors upon request. 9 Correspondingly, because te low type does not want to imitate te ig type to begin wit, adding noise in te ig type s contract only increases te principal s cost to induce effort from te ig type witout added benefits.

15 342 Q. Cen et al. Tird, our current setting only allows a binary signal. Given q and U 0, te binary wage payments are uniquely pinned down by te agent s binding IC constraint. However, wen tere are more tan two levels of signal realizations, te agent s IC can no longer uniquely determine all wage payments. Tus, in tis case, te principal may ave an additional tool to use for separation. Tat is, for fixed q and U 0 and a binding agent s IC constraint, te principal now as te ability to fine-tune wage payments across different signal realizations to acieve more efficient separation. 10 However, te key message of our paper tat a noisy information system can serve as a separation device remains unaltered as te low type will not coose any q \ 1 to begin wit. Finally, trougout te paper, we ave assumed tat tere are no exogenous outof-pocket costs to implement an information system for stewardsip purpose. Tis assumption allows us to focus on te main insigt of our analysis, i.e., tere is an endogenous cost of aving an accurate information system for stewardsip purposes. Information systems are of course not costless. Wen it is sufficiently costly to set up a perfect stewardsip system, loose monitoring may not be an effective separating tool to te extent tat te low type firms find it easier to imitate by adopting a noisier system to reduce teir monitoring cost. However, we note tat firms often install information systems (potentially wit exogenous set-up cost) for oter purposes suc as decision making and yet tese systems can provide stewardsip uses on te margin. It is conceivable tat, in order to separate, firms simply do not utilize te best available tecnology tat s already acquired but instead noise up te performance measure in order to credibly convey private information to agents. In tis sense, loose monitoring means tat ig potential firms are less likely to utilize te best available existing tecnology for monitoring tan low potential firms Alternative interpretation In our analysis we interpret p as te exogenous difference in firms productivity tat is unobservable to potential employees. Tis difference can be more broadly interpreted in oter ways, one of wic may be tat ig p firms ave better baseline information systems in place (for example, better information infrastructures tat provide feedback to employees to improve teir performance) but te quality of suc systems is unobservable to potential employees. In tis case, q can be interpreted as some observable canges to te baseline information system tat is specific for stewardsip purposes. For example, in a scool setting were scools compete for talented students, ow well exams can test students learning and provide students wit useful feedback to improve teir uman capital (i.e., te quality of te scool s baseline information system) may sometimes be difficult for students to observe. However, te grade assignment sceme (weter to use an A/B/ C/D system or simply a pass/fail system) is usually publicly observable and committed to beforeand. 10 We tank an anonymous referee for tis observation.

16 On te optimal use of loose monitoring in agencies 343 Wile we ave interpreted q as te degree of monitoring intensity or te quality of performance measurement system, one could equivalently interpret te combination of ðq; w; wþ as te principal offering a randomized contract to te agent. Since randomized contracts do not correspond well to wat casual empiricism suggests as used in practice, te information system or te degree of monitoring intensity can be viewed as realistic ways of implementing randomized contracts. Watever te interpretation, owever, our main point stands. Tat is, wen firms need to convey teir private information to potential employees in te presence of imitating competitive peers, te terms of employment contracts in ig potential firms may appear to be inefficient, especially if one insists on comparing tem wit te standard second-best contracts. 3 Biases in information systems Te structure analyzed in te previous section assumes tat any noise introduced is symmetric, i.e., te probability of misrepresenting a good economic income (x) asa low performance measure (e) is te same as tat of misreporting a bad economic income (x) as a ig performance measure (e). In tis section, we relax tis assumption and analyze te situation were te principal can coose bot Prðe ¼ ejx ¼ xþ ¼q 1 and Prðe ¼ ejx ¼ xþ ¼q 2 individually and is not constrained to set q 1 = q 2 (wit q 1 ; q 2 2½ 1 2 ; 1Š and cannot bot be equal to 1 2 ). Figure 3 illustrates te modified information system. Wit tis sligt cange in te model setup, te principal s problem is to coose a contract q 1 i ; q2 i ; w i; w i, were i 2 f; lg; to minimize is expected payment: min PrðijiÞw i þ½1prðijiþšw i q 1 i ;q2 i ;w i;w i ;i2f;lg subject to te AICðÞ; i AIRðÞ; i PIC(L), and PIC(H) constraints as sown in Sect. 2, wit te probabilities modified as follows: were, PrðjjiÞ ¼p i q 1 j þð1p i Þð1 q 2 j Þ; PrðijiÞ ¼p i q 1 i þð1p i Þð1 q 2 i Þ: Similar to te symmetric case, we can sow (details available upon request) tat te optimal contracts ave te same general properties as tose caracterized in te prior section. Furtermore, te conditions in Propositions 2 and 3 for te symmetric case clearly still apply ere: te sufficient conditions under wic a perfect information system is dominated and were te IR constraint (i.e., U 0 [ 0) is slack are still sufficient conditions ere. We call an information system an unbiased system if q 1 = q 2, a ars system if q 1 \ q 2 (because it is more likely to represent a good economic outcome as bad performance tan it is to represent a bad economic outcome as good performance), and a lenient system if q 1 [ q 2 (te opposite of te ars system). A priori, it is not clear wic of tese tree possibilities is optimal as a device to make PIC(L) satisfied, because all tree systems introduce noise into te information system tat will increase te low type s cost to imitate. Te following proposition

17 344 Q. Cen et al. Fig. 3 p i firm wit contract of w i ; w i ; q 1 i ; q2 i sows tat if te optimal contract involves loose monitoring and if te IR constraint is not binding, ten te loose monitoring as to be lenient, i.e., q 1 [ q 2. Proposition 4 If te optimal contract involves bot loose monitoring and U 0 [ 0 ten it must be eiter 1 2 q2 \1 ¼ q1 or 1 2 ¼ q2 \q1 \1. Te intuition can be gleaned from Fig. 3. Observe tat decreasing q 2 increases te probability of classifying a bad economic income x as good performance e and ence increases te expected payment to te agent. A low type principal (p l ) is more likely to reac tis node (i.e., aving a bad economic income) and ence more likely to end up paying a ig wage to te agent. A smaller q 2 terefore affects te ig type principal adversely but to a lesser extent tan it does te low type principal. In contrast, decreasing q 1 increases te probability of classifying a good economic income x as bad performance measure e. Tis would urt te ig type principal more tan te low type because te former is more likely to ave a good economic income and tus as to compensate te agent for te increased compensation risk. Te intuition can also be sown by te single crossing property. Start wit a feasible contract were q 1 = q 2 = 1 and U 0 [ 0. Sligtly decrease q 2 wile keeping te agent s expected utility constant. Te marginal cange in te expected wage payment for a type i principal is oew ð iþ and can be easily sown to be negative. ð Þ oq 2 Furter o2 Ew i oq 2 op [ 0. Tat is, wile a lower q 2 i urts bot principals, it urts te low type more tan it urts te ig type. In oter words, te single crossing property for q 2 is satisfied. However, te same property doesn t old for q 1 : if we sligtly decrease q 1 wile keeping te agent s expected utility constant at 0, oew ð iþ \0 and o 2 Ew ð i Þ oq 1 op i \0. Tus, in fact, it is te low type principal tat as an advantage wen decreasing q 1. To te extent tat external financial accounting earnings are an important input in te compensation contracts to firm management, te above result may be of particular relevance for te contemporary literature on accounting conservatism. Our results suggest tat firms wit brigter prospects may not just pay iger compensation and be more lax in terms of measuring performance; teir performance measure will also exibit more optimistic (or less conservative) bias. Oter implications include using market-to-book as a measure of individual firms growt prospects. Wile firms wit ig growt potential sould enjoy relatively ig market valuation, our result suggests tat tey may also exibit relatively more liberal accounting and tus report iger book values as well. oq 1

18 On te optimal use of loose monitoring in agencies Conclusion We study a setting were a firm (principal) is privately informed of te firm s potential and contracts wit an agent to supply unobservable effort. We sow tat it can be optimal for te firm to ave loose monitoring in te sense tat te monitoring system is less perfect tan wat is implied by a standard agency model a la Holmstrom (1979). Furter, it may be optimal also to provide te agent wit iger expected utility tan is reservation level. Tese contractual features are used to acieve separation among different types of firms suc tat firms wit low potential do not imitate contracts offered by ig potential firms. Our findings imply tat altoug loose monitoring and seemingly excessive compensation to employees may be symptoms of firms squandering scarce resources provided by investors, tey can also arise as an optimal contracting arrangement to maximize sareolders wealt. Of furter interest wen we can identify strict preferences for biases, we sow tat firms tat optimally provide loose monitoring may prefer a lenient information system in te sense tat representing bad news as good is preferred to representing good as bad. Particularly, tis is te case wen te conditions favor slack in te IR constraint. In oter words our teory suggests tat firms wit iger pay and less focus on tigt oversigt sould ave more optimistic or less conservative monitoring systems tan teir more stringent counterparts. Our paper provides direct testable implications about te determinants of reporting biases and teir relation to compensation arrangements and market values. Acknowledgments We received elpful comments from Hengjie Ai, Tim Baldenius, Bob Bowen, Dave Burgstaler, Sane Dikolli, Cristian Hofmann, Pino Lopomo, Brian Mittendorf, and worksop participants at Baruc College, Duke University, Georgetown University, George Wasington University, Pennsylvania State University, Tilburg University, University of Maryland, University of Wasington at Seattle, and te Minnesota Accounting Teory Conference. Special tanks to two anonymous referees and te editor (Stan Baiman), wose constructive comments improved te paper significantly. Appendix Proof of Proposition 1 Proof: We start wit a relaxed program were we ignore PIC(H). Later, we ll sow tat te optimal solution under te relaxed program satisfies PIC(H). Te proof proceeds in several steps. Te IC constraint for te agent in te low type firm (AIC(L)) is binding at te optimal solution. Suppose not. Ten, by continuity, tere exists a [ 0 suc tat PrðljlÞ we can decrease w l by and increase w l by 1PrðljlÞ and still maintain AIC(L) slack. Tis operation maintains te low type principal s expected payoff. At te same time, it relaxes te agent s participation constraint (AIR(L)), wic means te low type principal can ten be made strictly better off by reducing w l