CEO Pay and the Lake Wobegon Effect

Transcription

1 CEO Py nd the Lke Wobegon Effect Rchel M. Hyes nd Scott Schefer December 11, 2008 Forthcoming in Journl of Finncil Economics Abstrct The Lke Wobegon Effect, which is widely cited s potentil cuse for rising CEO py, is sid to occur becuse no firm wnts to dmit to hving CEO who is below verge, nd so no firm llows its CEO s py pckge to lg mrket expecttions. We develop gme-theoretic model of this Effect. In our model, CEO s wge my serve s signl of mtch surplus, nd therefore ffect the vlue of the firm. We compre equilibri of our model to full-informtion cse nd derive conditions under which equilibrium wges re distorted upwrd. Hyes: Dvid Eccles School of Business, University of Uth. rchel.hyes@uth.edu. Schefer: Dvid Eccles School of Business nd Institute for Public nd Interntionl Affirs, University of Uth. scott.schefer@uth.edu. We re grteful for the finncil support of the Kellogg School of Mngement t Northwestern University, where Scott Schefer ws visiting professor while completing this work. We thnk Hnk Bessembinder, Mike Lemmon, nd Pul Oyer for helpful discussions, nd seminr prticipnts t Uth nd Arizon for comments.

2 1 Introduction CEO py levels in the US hve risen ten times s fst s verge worker wges since the 1970s (The Economist, 2006). These ever-incresing pychecks continue to ttrct the ttention of policymkers, the medi, nd the public. One much-discussed potentil cuse for the increse in CEO py hs come to be known s the Lke Wobegon Effect. In public rdio host Grrison Keillor s mythicl home town of Lke Wobegon, Minnesot, ll the children re bove verge. And so it is climed with CEOs no firm wnts to dmit to hving CEO who is below verge, nd so ech firm wnts its CEO s py pckge to put him t or bove the medin py level for comprble firms. It is well known tht firms commonly disclose n intention to py well; Bizjk et l. (2008) report tht 73 out of 100 rndomly selected firms mention trgeting t lest one component of py t or bove the peer group medin or men. Of course, not every CEO cn be pid more thn verge, nd so (it is climed) we see ever-incresing levels of CEO py. The resoning behind this effect ws perhps best summrized by former DuPont CEO Edwrd S. Woolrd, Jr., speking t 2002 Hrvrd Business School roundtble on CEO py (Elson, 2003): The min reson compenstion increses every yer is tht most bords wnt their CEO to be in the top hlf of the CEO peer group, becuse they think it mkes the compny look strong. So when Tom, Dick, nd Hrry receive compenstion increses in 2002, I get one too, even if I hd bd yer... (This leds to n) upwrd spirl. A remrkble rnge of commenttors hve referenced the Lke Wobegon Effect in discussing CEO py, including consultnt turned py-critic Gref Crystl (The Wshington Post, 2002), former Hrvrd Business School den Kim Clrk (2003, 2006), nd the director of the SEC s Division of Corportion Finnce, Aln Beller (2004). The Effect hs even been cited by disgruntled shreholders in picking proxy fights with mngement over py levels. After Business Week rnked Alco worst ntionlly in the reltion between CEO py nd stock price performnce, The Ctholic Funds introduced shreholder resolution citing the Lke Wobegon Effect nd instructing the bord to review the firm s py prctices. The resolution filed. Despite the prevlence of the Lke Wobegon Effect rgument mong pundits nd commenttors, there hs been no ttempt to model it in the lrge cdemic literture on CEO py. In this pper, we offer forml, gme-theoretic model of the Lke Wobegon Effect in CEO py. 1 We use this model to sk whether the Lke Wobegon Effect cn increse CEO py in 1 Other reserch exmines Lke Wobegon Effect in employee evlutions, where supervisors re unwilling to rte employees honestly nd thus mrk everyone s bove verge (Morn nd Morgn, 2001, McLeod, 2003). 1

3 equilibrium, nd if so, under wht conditions. We build our model of the Lke Wobegon Effect on three key ssumptions. First, there must be symmetric informtion regrding the mnger s bility to crete vlue t the firm. Second, the py pckge given to mnger must convey informtion bout the mnger s bility to crete vlue t the firm. Third, the firm must hve some preference for fvorbly ffecting outsiders perceptions of firm vlue. We build in these three key ssumptions by modeling firm nd mnger who privtely observe prmeter tht ffects the productivity of their mtch. Stock mrket prticipnts cnnot observe this prmeter, but ttempt to infer it from observing the mnger s wge. The firm mximizes weighted sum of short-run nd terminl firm vlue, nd so my wish to distort the publicly observble wge to ffect the mrket s beliefs regrding firm vlue. We pply the stndrd tools of informtion economics to compre the Perfect Byesin Equilibrium of our model to the outcome in full-informtion benchmrk cse. Within our model, we define Lke Wobegon Effect to occur when the wge schedule tht obtins in the full-informtion cse cnnot be prt of Perfect Byesin Equilibrium of the symmetric informtion cse. We present three min results. First, we show the Lke Wobegon Effect cn occur. Tht is, there re instnces of our model in which the full-informtion benchmrk is not n equilibrium, nd firms distort py upwrd to ffect mrket perceptions of firm vlue. Second, we chrcterize the settings in which the Lke Wobegon Effect does occur. We show tht our three key ssumptions symmetric informtion, mngeril rents, nd corporte myopi re not sufficient to gurntee upwrd distortions in py. In the bsic version of our model, two dditionl conditions re necessry: (1) the mrginl effect of increses in mngeril bility on mtch surplus defined s the difference between the prties output when working together nd when pursuing their outside options is positive, nd (2) the weight plced by the firm on short-run shre prices is greter thn the frction of the mtch surplus tht is cptured by the mnger. Third, we find tht the tempttion to distort py upwrd is stronger when the informtion symmetry pertins to chrcteristics of the firm rther thn chrcteristics of the mnger. When the mnger s bility is uncertin, increses in the mnger s py do boost the mrket s ssessment of mngeril bility; however, the mnger not the firm cptures rents ssocited with increses in mngeril bility. Thus, the mrginl increse in firm vlue ssocited with dollr increse in mngeril py is low when the uncertinty pertins to 2

4 chrcteristic of the mnger. While our nlysis shows tht the Lke Wobegon Effect is theoreticl possibility, we note tht, within our model, the three key ssumptions re not sufficient conditions for the Lke Wobegon Effect. In the bsic version of our model, there is no Lke Wobegon Effect if the mtch surplus does not grow s mngeril bility grows. Further, there is no Effect if the firm s myopi is less thn the shre of mtch surplus cptured by the mnger. These dditionl necessry conditions my strike some reders s extreme, nd thus our findings my be tken s grounds for dismissl of the Lke Wobegon Effect s n explntion for recent CEO py increses. However, we think the first dditionl necessry condition tht mngeril bility increses mtch surplus is likely to be met in t lest some cses. It is, in some sense, specific humn cpitl condition. If bility is relted to generl cognitive skills, then it is resonble tht higher bility would boost the mnger s productivity both inside nd outside the firm, which could push the mtch surplus in either direction. But if bility is complement to firm-specific knowledge, then the firm s output could well grow fster with bility thn does the mnger s vlue when producing elsewhere. The second condition on the reltive mgnitudes of myopi nd mngeril brgining power is more difficult to ssess. While it is commonly lleged tht public firms vlue high short-run shre prices, we re not wre of ny empiriclly mesurble nlogue to the myopi prmeter commonly used in models like ours. Further, even with extremely detiled informtion on CEO py, it is not cler how one would mesure mngeril brgining power. Brgining power is the shre of mtch surplus cptured by the mnger; ssessing this figure empiriclly would require knowledge of the mnger s py in his next most ttrctive job, the firm s vlue when employing its second-choice mnger, nd the vlue the prties crete when working together. Difficulties in mesuring both the CEO s shre of mtch surplus nd the firm s degree of myopi imply tht while our model shows the Lke Wobegon Effect cn occur, it remins to be shown whether it ctully does occur. Our model is consistent with some existing empiricl evidence. In the model, py cn be too high becuse mrket prticipnts mke inferences bout firm vlue from observing py. If py levels re not disclosed, then there is no reson for firms to boost py levels to increse short-run mrket vlues. Prk et l. (2001) study how py levels t Cndin firms chnged fter 1994 disclosure mndte, nd report increses in the level of CEO py in the postdisclosure period reltive to pre-disclosure. This evidence is consistent with other theories, however, nd thus cnnot be interpreted s confirming the existence of Lke Wobegon Effect. 3

5 Devising shrper tests of the model will require some wy of ssessing cross-firm vrition in myopi nd mngeril brgining power, nd even this will be complicted by the possibility tht myopi t one firm will ffect py t nother, if the firms compete in the lbor mrket. Finlly, we note tht some discussions of the Lke Wobegon Effect focus exclusively on the effects of peer-group comprisons on CEO py. Crystl (1991), for exmple, hs rgued tht py-benchmrking combined with strtegic choice of peer groups cn rtificilly inflte py. We rgue, however, tht the quottions from Woolrd nd others suggest forces beyond peer-group benchmrking re t work. Specificlly, peer-group benchmrking is by itself not necessrily problemtic for the py process; py should be positively relted to peer group py under lmost ny model of well-functioning lbor mrkets. Further, if strtegic choice of peer groups drives py up, one wonders why bords cnnot simply undo these strtegies by collecting their own peer-group smples. While our model does not spek directly to the question of why firms would wnt to py well reltive to peers in prticulr, it does offer justifiction for the prctice of pying well reltive to some mrket expecttion of py, which, s noted, might derive from peer groups. In our model, firms py well to look strong, even if doing so is not necessitted by lbor mrket competition, nd even if peer groups re chosen non-strtegiclly. 2 Model Outline We consider single-period gme with four dtes nd no discounting, s depicted in Figure 1. At dte 1, the firm is mtched with potentil mnger. The firm nd potentil mnger costlessly lern firm- nd mnger-specific productivity prmeters, nd mtch-specific productivity prmeter. We denote the firm- nd mnger-specific productivity prmeters s q [q L, q H ] nd [ L, H ], respectively. Let the vlue of the output generted when the mnger works for the firm be the differentible nd incresing function f(q, ; γ), where γ [γ L, γ H ] is mtchspecific productivity prmeter. We ssume these prmeters re common knowledge between the firm nd the mnger, but my not be observble to others. Note the firm- nd mngerspecific productivity prmeters my ffect both the prties outside options nd the rent they split if they enter into n employment reltionship nd work together. We therefore interpret the mnger s productivity prmeter s mesure of generl-purpose skill or bility. We cn interpret the firm-specific productivity prmeter q s some mesure of the firm s technology or investment opportunities. If employment is efficient, the firm nd mnger negotite n employment contrct t dte 4

6 2. We ignore morl hzrd on the prt of the mnger, nd ssume the firm s terminl vlue is non-contrctible. Under these ssumptions, the employment contrct simply consists of wge w. 2 We ssume the terms of this wge contrct re publicly observble. 3 If employment is inefficient, then the prties seprte, receive their reservtion vlues, nd the gme ends. Note tht the model cn be interpreted s pplying either to the negotition of hiring-dte py pckges or to the negotition of yerly slry levels for n incumbent CEO. At dte 3, round of trding in the firm s shres occurs. The dte 3 mrket vlue of the firm s shres which we refer to s the firm s interim vlue is conditioned on the dte 2 contrct between the firm nd mnger. However, the interim vlue cnnot be conditioned (directly) on f, becuse this is observed only by the firm nd the mnger. Insted, stock mrket prticipnts form beliefs bout f bsed on the observed dte 2 contrct. At dte 4, production occurs. The shreholders receive the firm s output f minus the wge pid to the mnger. We refer to this pyment to shreholders s the firm s terminl vlue. 4 The gme ends. We build in our three key ssumptions s follows. First, we ssume tht some spect of productivity one of the mtch-specific productivity, the mnger-specific productivity, or the firm-specific productivity is not observed by mrket prticipnts. Thus, there is symmetric informtion bout the firm s terminl vlue. Second, we ssume tht the mnger hs sufficient brgining power to cpture some prt of the rent resulting from the mtch. This implies tht contrct terms will vry with the vlue 2 The ssumption of non-contrctibility of terminl vlue cn be justified by imgining tht some production tkes the form of n investment tht does not yield returns until fter the mnger s tenure in office hs ended. It is strightforwrd to extend the model to llow for py-for-performnce contrcting nd morl hzrd by ssuming the mrginl return to unobservble CEO effort is mtch-specific (see Schefer, 1998). In this cse, py levels cn be distorted upwrds nd incentives cn be too strong reltive to the full-informtion benchmrk. This py-for-performnce extension of our bsic model lso suggests tht the Lke Wobegon Effect cn led to reductions in socil welfre. In the simple version presented here, there re no welfre consequences of the Lke Wobegon Effect, becuse increses in mngeril py re trnsfer. See lso Hyes nd Schefer (2005) for signling model of yerly bonuses in reltionl contrcts setting. 3 Specificlly, we ssume tht the firm must truthfully disclose the wge pid to the mnger. As will become cler, the firm my fce n incentive to over-report py. If firms cn costlessly report py tht is higher thn the mnger s ctul wge, then py disclosures become uninformtive chep tlk. 4 The timing of the pyment to the mnger is not importnt in the nlysis nd cn redily be shifted to dte 2. If the firm cn costlessly borrow, then pyments to the mnger cn be mde t ny time. 5

7 Dte 1: Mtching Dte 2: Contrcting Dte 3: Trding Dte 4: Production Figure 1: Timeline. of the firm, nd thus tht stock-mrket prticipnts will condition their beliefs bout the firm s terminl vlue on the pyment mde to the mnger. Third, we ssume tht the firm hs some preference for high interim shre price. Mny justifictions for the ssumption of corporte short-termism or myopi hve been proposed in the literture. Miller nd Rock (1985), for exmple, ssume tht shreholders hve exogenously differing time horizons. In their model, shreholders re ex nte identicl, nd lern their specific time horizons fter the firm s dividend policy is chosen; thus, ll shreholders hve some preference for high interim shre prices. In Stein (1988), corporte rider considers purchsing ll of the firm s shres immeditely fter corporte ction is tken, but before the terminl pyoff. The expected pyoff to current shreholders is therefore the weighted sum of interim nd terminl vlues, with the weights determined by the probbility of tkeover. In our nlysis, we follow Stein (1989) by suppressing the precise resons underlying corporte myopi. We ssume tht the firm plces weight k on the interim vlue nd 1 k on the terminl vlue. The vrible k prmeterizes the firm s myopi, with higher k implying greter concern for interim shre prices. The twin ssumptions of symmetric informtion nd corporte short-termism hve been widely used in the finncil economics literture. For exmple, Myers nd Mjluf (1984) nd Miller nd Rock (1985) who study cpitl structure nd dividend policy, respectively ssume tht shreholders cre bout short-term shre prices, nd tht mngeril compenstion contrcts induce mngers (who ctully mke the cpitl structure nd dividend policy decisions) to vlue high short-run shre prices s well. This literture hs been criticized by Dybvig nd Zender (1991), who rgue tht shreholders need not write contrcts tht motivte mngers to cre bout short-run shre prices. Indeed, given tht equilibri in these models typiclly involve inefficient investment, shreholders re best off writing contrcts tht give 6

8 mngers different objective function thn shreholders themselves hold; essentilly, Dybvig nd Zender offer delegtion-s-commitment s solution to strtegic problem, s in Fershtmn nd Judd (1987). The delegtion-s-commitment literture hs been criticized by Ktz (1991), Persons (1994), nd others on the grounds tht such contrcts re not renegotition-proof. If secret renegotition of contrcts is possible, then delegtion my be strtegiclly irrelevnt. Dewtripont (1988) counters this clim by noting tht informtionl problems my impede renegotition, thus restoring strtegic role for contrcts. We remin gnostic on the debte over delegtion-s-commitment, for two resons. First, our nlysis differs from the corporte finnce literture in tht it is the mngeril wge contrct itself rther thn choice of cpitl structure or dividend policy which, in turn, is function of the wge contrct tht is ffected by the informtion symmetry nd myopi. Thus, n ppropritely constructed mngeril incentive contrct cnnot help here. Second, the prescription of Dybvig nd Zender (1991) tht myopic shreholders should credibly delegte decisions to n intermediry whose preferences re mnipulted using contrcts is potentilly descriptive of sttus quo institutionl rrngements, where py decisions re delegted to subcommittee of the bord. We re unwre, however, of ny studies of the reltive myopi of shreholders vs. directors. 3 Anlysis In this section, we develop severl vrints of our bsic model. We consider idiosyncrtic mtching, where the prties outside options re ssumed to be equl to their individul-specific productivity prmeters. We exmine three cses, ech corresponding to different source of informtion symmetry regrding firm vlue. First, we suppose tht mngeril bility is unknown to stock mrket prticipnts. Second, we ssume tht stock mrket prticipnts re uninformed regrding the firm s individul productivity q. Third, we ssume tht the informtion symmetry pertins to the mtch-specific productivity prmeter γ. For ech cse, we chrcterize the settings in which the Lke Wobegon Effect occurs. 3.1 Asymmetric Informtion Regrding Mngeril Ability We first consider the effects of symmetric informtion regrding mngeril bility,. To focus on this effect, we mke number of ssumptions. Let the firm s individul productivity prmeter q be common knowledge mong ll plyers of the gme. Let the prties output 7

9 be f(q, ), where the function f is common knowledge nd the mtch-specific productivity prmeter γ is suppressed. Finlly, we ssume tht the outside options of the firm nd mnger re given by q nd respectively. 5 Under these ssumptions, the mtch surplus tht is, the difference between the prties output when working together nd when pursuing their outside options is given by f(q, ) q. If ll plyers in the gme cn observe mngeril bility t dte 1, then there is no reson for the firm to behve strtegiclly to try to ffect the firm s interim vlue. We ssume tht in this cse, the firm nd mnger split the mtch surplus ccording to Nsh brgining. Here, we re ssuming tht there re rents tht is, vlue in excess of the prties outside options in the mngeril lbor mrket, nd tht these rents cn be shred between the firm nd the mnger. 6 Assuming the mnger hs brgining power α, he will commnd wge of w() = + α ( f (q, ) q ). (1) Let the wge schedule w() be full-informtion benchmrk. 7 Suppose, however, tht is observed by the firm nd mnger t dte 1, but tht mrket prticipnts cnnot lern directly until dte 4 when the firm s terminl vlue is reveled. 8 5 This ssumption is without loss of generlity. Suppose is some mesure of mnger s generl cognitive skill (IQ perhps). Let g(q, ) be the output when the mnger works for the firm, nd let v( ) be the the mnger s outside option, where both g nd v re strictly incresing in nd differentible. To trnsform this setup into ours, simply define = v( ) nd f(q, v( )) = g(q, ). Differentiting both sides of the definition of f with respect to, it follows tht f is strictly incresing in. 6 Severl theories in lbor nd personnel economics predict tht workers (nd especilly top executives) cn ern rents. Such theories include tournments, firm/worker mtching, firm-specific humn cpitl, efficiency wges, nd rent extrction. See Lzer nd Oyer (2007) for descriptions of these models nd relted empiricl work. Note the setting where the firm cptures ll of the rents (α = 0) is specil cse of our model. 7 Within our frmework it is cler tht mny forces including chnges in f or α could explin why CEO py hs incresed. We do not use this frmework to exmine ll possible resons for recent CEO py increses, but insted use it to develop conditions under which firms re eger to py well reltive to some externl benchmrk. 8 We hve in mind setting where the firm nd mnger know the vlue of the mnger s next best job option even without job offer being mde. Outsiders lck specific knowledge of the lbor mrket, nd thus do not know the mnger s outside option unless job offer is publicly nnounced. It is not importnt tht the firm nd mnger know the outside option with certinty; they must merely hve better informtion thn outsiders. A potentilly useful nlogy is tht finnce professor s deprtment chir might know resonbly well whether 8

10 Given this, the firm my wnt to distort the mnger s py upwrd in n ttempt to ffect outsiders perceptions of terminl vlue, which will then influence the mrket-determined interim vlue. In equilibrium, of course, such ttempts to fool the mrket must fil, so wge schedule tht is prt of Perfect Byesin Equilibrium (PBE) must stisfy set of no-mimic constrints. A firm whose mnger hs bility must not prefer to mimic firm whose mnger hs bility â. Denoting the PBE wge schedule under symmetric informtion s ŵ(), we see tht type- firm s interim vlue when mimicking type-â firm is f(q, â) ŵ(â). Note here tht interim vlue cn be incresing in the wge pid to the mnger. Pying higher wge cn increse the mrket s perception of the vilble mtch surplus. Stock mrket prticipnts therefore expect higher terminl vlue, nd would hve higher willingness-topy for the firm s shres t the dte 3 interim stge. Ordinrily, of course, higher fctor prices reduce firm vlue, but this need not be the cse given the informtion symmetry here. A type- firm s terminl vlue when mimicking type-â firm is f(q, ) ŵ(â). The firm plces weight k on its interim vlue, so its pyoff when mimicking type-â firm is given by k ( f(q, â) ŵ(â) ) + (1 k) ( f(q, ) ŵ(â) ). If type- firm insted elects not to mimic nother type, then its interim nd terminl vlues re identicl, nd equl to f(q, ) ŵ(). A type- firm will not mimic nother type if ŵ() stisfies f(q, ) ŵ() k ( f(q, â) ŵ(â) ) + (1 k) ( f(q, ) ŵ(â) ) (2) for ll â. 9 A wge schedule must stisfy this condition for ll in order to be prt of PBE. To build intuition, note tht there re both costs nd benefits to type- firm mimicking the professor s thret to obtin high-slry offer from nother university is credible. An outsider such s den or provost, lcking specific knowledge of the field, my not know whether this thret is credible until n offer is ctully mde. 9 Note tht in equilibrium, the interim nd terminl mrket vlues re lwys the sme, s required by mrket 9

11 type-â firm, where â >. Becuse we hve ssumed f > 0 (where the subscript denotes prtil derivtive), mimicking higher type cuses the mrket s conjecture bout the firm s dte 4 output to increse. However, the firm must lso increse the employee s wge from ŵ() to ŵ(â) this cost is felt both t dte 3 nd dte 4, reducing both the interim nd terminl vlues. As noted bove, our centrl im is to exmine conditions under which the firm distorts py levels upwrd; tht is, we wnt to know when the full-informtion wge schedule w() cnnot be prt of PBE. To this end, we replce ŵ() in Inequlity (2) with w() from Eqution (1). We ssume the mnger s brgining power is sufficient to gurntee tht he will lwys ern t lest w(), so devitions from the equilibrium tht involve pying less thn this mount re not considered. Thus, for ll nd for ll â >, we must hve f(q, ) w() k ( f(q, â) w(â) ) + (1 k) ( f(q, ) w(â) ). Additionl lgebr shows tht this condition is equivlent to for ll nd for ll â >. Next define f(q, â) f(q, ) (1 α) (k α) â f mx = mx [ L, H ] f (q, ) nd note tht our ssumption tht f is differentible implies In words, we define f mx tht f(q,â) f(q,) â f(q, â) f(q, ) sup = f mx. <â [ L, H ] â to be the lrgest vlue tken by f over the intervl [ L, H ]. Note lso is the verge rte of increse in f over the intervl [, â]; if f is differentible, then this quntity cn be equl to or rbitrrily close to, but never greter thn, f mx. Thus, the sttement tht for ll nd for ll â > is implied by f(q, â) f(q, ) (1 α) (k α) â (1 α) (k α)f mx. efficiency. The driver of our model is the observtion tht the interim nd terminl vlues could differ off the equilibrium pth. If firm were to devite from the equilibrium wge schedule, then these vlues could differ s the mrket is fooled by the high py. The equilibrium is constructed by stting tht such devitions re never profitble, nd therefore tht interim nd terminl vlues re lwys the sme in equilibrium. (3) 10

12 One finl step of lgebr shows tht if then the full-informtion wge schedule forms PBE. k α + 1 α, (4) f mx Inequlity (4) yields our first min result. Becuse k nd α cn tke vlues on the [0,1] intervl nd f mx > 0, it is possible for this inequlity to be violted. In our model, there re instnces for which the full-informtion wge schedule is not PBE. In these cses, firms distort py upwrd in n ttempt to ffect short-run mrket vlutions. Thus, the Lke Wobegon Effect cn occur. Inequlity (4) lso estblishes our second min result: the Lke Wobegon Effect cn occur only if dditionl necessry conditions re met. Specificlly, py is distorted upwrd only if the firm s myopi level is sufficiently high. To fcilitte comprisons between the cse of symmetric informtion regrding mngeril bility nd the cses of symmetric informtion regrding q nd γ (which we discuss below), we define the firm s myopi threshold to be the lrgest k stisfying Inequlity (4). We mke three observtions bout the comprtive sttics of this threshold: Note first tht higher α mens higher myopi threshold. Why? A high α mens tht greter shre of the mtch surplus is cptured by the mnger rther thn the firm. This both increses the mrginl cost nd reduces the mrginl benefit of ttempts to boost the mrket s perception of mngeril bility. The mrginl benefit flls becuse n increse in perceived mtch surplus hs smller effect on interim vlue. The mrginl cost rises becuse lrger wge increse is required to move mrket perceptions of mngeril bility. Becuse high α mkes it both more costly nd less beneficil to overpy mnger, firm would hve to be very myopic in order to overpy when it hs high α. Second, if f mx the mximum of the mrginl effect of mngeril bility on output is less thn or equl to one, then the right-hnd side of (4) is greter thn or equl to one, nd hence the full-informtion wge schedule is lwys prt of PBE regrdless of the vlue of α. Becuse mtch surplus is given by f(q, ) q, boosting mrket perceptions of mngeril bility cn positively ffect interim vlue only if f mx > Economiclly, 10 To see why this is true, note tht the firm s terminl vlue is f(q, ) w(). Under the full-informtion wge schedule, w is lwys greter thn or equl to one, becuse the mnger s outside option increses by one for ech one-unit increse in. So, if f mx 1, then hving better mnger does not increse firm s terminl vlue. As result, the firm would never wnt to pretend its mnger is better thn he is. 11

13 f mx > 1 mens there is some for which n increse in mngeril bility increses the mtch surplus f(q, ) q. 11 Our nlysis shows tht this is necessry condition for py to be distorted upwrd. Third, in the cse where f mx f mx grows. > 1, increses in f mx reduce the firm s myopi threshold. As grows, the mrginl effect of n dditionl dollr of wges on the firm s interim vlue Becuse overpying the mnger increses the firm s ssessment of mngeril bility, nd beliefs bout bility hve lrger effect on interim vlue when f mx overpying becomes more ttrctive option when f mx is lrge. is lrge, As these observtions indicte, the three ssumptions of the Lke Wobegon Effect re not sufficient to gurntee tht mngers will be overpid reltive to the full-informtion cse. Overpyment cn occur only if f mx reltive to the mnger s brgining power. > 1, nd only if the firm s myopi is sufficiently lrge Given one dditionl ssumption, it is strightforwrd to chrcterize seprting PBE when the full-informtion wge schedule cnnot be prt of n equilibrium. We ssume f is concve, which llows us to replce the globl no-mimic constrints in (2) with the locl nomimic constrint: for ll. 12 We begin by considering the cse where ŵ kf (5) k > α + 1 α f ( H ). Here, the fct tht f is decresing mens tht the full informtion wge schedule does not stisfy (4) for ny [ L, H ]. Applying the stndrd refinement of miniml signling, we cn 11 Recll tht we ssumed tht mngeril bility is identiclly equl to the mnger s outside wge. Absent this normliztion, the condition tht f mx g v 0 for ll. 1 would, using the nottion from footnote 5, tke the form tht 12 Concvity insures tht if it is profitble for type- firm to mimic type-â > firm, then it is lso profitble for the type firm to mimic type- + ɛ firm, where ɛ is rbitrrily smll. The locl no-mimic constrint in (5) which sttes tht mimicking the +ɛ type must be unprofitble for ech thus implies the globl no-mimic constrint in (2). As Lffont nd Mrtimort (2002) observe, it is difficult to obtin generl results in signling gmes with continuous types without mking ssumptions to insure tht locl incentive constrints imply globl. Note tht our min result bove chrcteriztion of the firm s myopi threshold ssumed only tht f ws differentible nd incresing. 12

14 derive the PBE by solving the differentil eqution in (5). Our boundry condition comes from the ssertion tht ech mnger s brgining power is sufficient to gurntee he is pid t lest w(). Thus, our boundry condition is ŵ( L ) = w( L ) = L + α ( ) f(q, L ) q L. We therefore hve tht for k > α + (1 α)/f ( H ), the PBE wge schedule is the solution to Next, we consider the cse where w = kf w( L ) = L + α ( f(q, L ) q L ). α + 1 α f ( L ) < k < α + 1 α f ( H ). Here, the full-informtion wge schedule stisfies the no-mimic constrint for some but not ll vlues of. The PBE wge schedule in this cse is given by ŵ() = mx [ w(), w() ], where w() is the solution to the differentil eqution w = kf with boundry condition w( L ) = L + α ( f(q, L ) q L ). In this cse, it is possible tht py is distorted upwrd reltive to the full-informtion cse for low-bility mngers, but not for high-bility mngers. To illustrte the construction of equilibrium wge schedules, we consider simple numericl exmple. Assume f(q, ) = 8 q, nd let q = 1.5 be common knowledge. Let [1, 2]. If α = 0.25, then the full-informtion wge schedule is given by w() = It is strightforwrd to verify tht if k > (4 + 6)/ , then the full-informtion wge schedule cnnot be prt of PBE. So if, for exmple, k = 1/2, the PBE wge schedule is the function w tht solves w = 6 w(1) =

15 Wge k 1 Equilibrium Wge Schedule k 0.75 Equilibrium Wge Schedule k 0.5 Equilibrium Wge Schedule Full Informtion Wge Schedule Figure 2: This figure demonstrtes how the equilibrium wge schedule vries with k. As the firm becomes more myopic, the equilibrium wge schedule shifts up. The specific exmple considered here is f(q, ) = 8 q, q = 1.5, α = 0.25, nd [1, 2]. This works out to w() = We plot both the full-informtion wge schedule w nd the symmetric informtion wge schedule w (using vrious vlues for k) in Figure Asymmetric Informtion Regrding Firm Chrcteristics Next, we consider the cse where the informtion symmetry pertins to the firm s individulspecific productivity prmeter q. Let the mnger s individul productivity prmeter be common knowledge mong ll plyers of the gme. Let the firm s output be f(q, ), where the function f is common knowledge nd the mtch-specific productivity prmeter γ is suppressed. 14

16 Define the full-informtion wge schedule s w(q) = + α ( f(q, ) q ). (6) To study the symmetric-informtion cse, ssume tht mrket prticipnts cnnot observe q directly, but insted condition their beliefs regrding firm vlue on the observed wge pyment to the mnger. A type-q firm will not mimic nother type if the equilibrium wge schedule ŵ(q) stisfies f(q, ) ŵ(q) k ( f(ˆq, ) ŵ(ˆq) ) + (1 k) ( f(q, ) ŵ(ˆq) ) (7) for ll ˆq q. We proceed by developing resoning similr to tht in Section 3.1. We exmine conditions under which the full-informtion wge schedule is PBE by substituting w(q) from (6) into (7). Algebr yields for ll q nd for ll ˆq > q. define Here, it is low vlue of f(ˆq,) f(q,) ˆq q f(ˆq, ) f(q, ) (α k) α ˆq q tht mkes it hrder to stisfy this constrint, so we f min q = min q [q L,q H ] f q(q, ). Substituting nd re-rrnging, we see tht the no-mimic constrint is stisfied by the fullinformtion wge schedule if ( k α 1 1 f min q ). (8) The mgnitude of the myopi threshold tht is, the minimum k stisfying (8) gin depends on two prmeters: (1) the mnger s brgining power α, nd (2) fq min, the minumum of the mrginl effect of the firm s productivity prmeter output. Higher α mens higher myopi threshold, nd the resoning behind this result is gin tht higher α mkes overpying the mnger less ttrctive. Notbly, however, the effects of f min q myopi threshold is decresing in f mx is incresing in f min q here re the reverse of those of f mx bove. While the when uncertinty pertins to, the myopi threshold when uncertinty pertins to q. To see why these results hold, note tht the firm cptures ll of ny increse in its outside option q, but must shre increses in the mtch surplus f(q, ) q with the mnger. When f min q is smll, the firm does not need 15

17 to increse the mnger s wge by much in order to convince the mrket tht q is high. This mkes it more ttrctive to distort py upwrd to influence interim mrket vlues. 13 A comprison of Inequlities (4) nd (8) yields our third min result: For fixed α, myopi thresholds re higher when the mrket s uncertinty pertins to chrcteristics of the firm rther thn to chrcteristics of the mnger. In the cse of informtion symmetry regrding, the firm s myopi threshold is lwys greter thn or equl to α, while the threshold is lwys less thn or equl to α in the q cse. Incentives to overpy the mnger to boost interim vlues re stronger when the mrket is uncertin bout firm chrcteristics. This sttement holds for ny vlues of f min q nd f mx. The intuition behind our third min result is esiest to explin fter we hve developed the cse where informtion symmetry pertins to the mtch-specific productivity prmeter γ. As such, we briefly defer this discussion nd turn next to our finl cse Asymmetric Informtion Regrding Mtch Qulity Finlly, we consider the cse where the informtion symmetry pertins to mtch-specific productivity prmeter γ. Agin, we mke number of ssumptions to focus specificlly on the effect of symmetric informtion regrding γ. First, ssume tht both the mnger s nd the firm s individul-specific productivity prmeters, nd q, re commonly known to ll plyers s of dte 1. Next, suppose tht the mtch vlue is given by f(γ) = γ, where γ [γ L, γ H ]. 15 Here, we hve suppressed the role of the individul-specific productivity prmeters in f. Becuse these prmeters re common knowledge, it is necessry for us to consider only the role of γ in determining the mtch vlue. Define, s bove, the full-informtion wge schedule s w(γ) = + α ( γ q ). 13 If f min q 1, then (8) is violted for ny k > 0. Note however tht if f min q < 1, then the mnger s full informtion wge in (6) is ctully decresing in q. Becuse we ssume the mnger s brgining power insures tht he is lwys pid t lest w(q), it is not fesible for firm to mimic higher type in this cse. 14 It is gin strightforwrd to compute the PBE in the cse where the firm s myopi exceeds the myopi threshold. For exmple, if k > α 1 1 f q(q L, then the PBE wge schedule is the solution to the differentil ) eqution w q = kf q with boundry condition w(q L) = + α`f(q L, ) q L. 15 The restriction tht f(γ) = γ is without loss of generlity, becuse the scle of this mtch prmeter is rbitrry. The function f is necessry to the nlysis in Sections 3.1 nd 3.2 bove, s it specifies the reltive rtes t which increses in mngeril bility nd firm chrcteristics ffect the firm s output nd the prties outside options. 16

18 We ssume tht mrket prticipnts cnnot observe γ directly, but insted condition their beliefs regrding the firm s terminl vlue on the observed wge pyment to the mnger. A type-γ firm will not mimic nother type if the equilibrium wge schedule ŵ(γ) stisfies γ ŵ(γ) k (ˆγ ŵ(ˆγ) ) + (1 k) ( γ ŵ(ˆγ) ) (9) for ll ˆγ γ. Anlysis similr to tht in Sections 3.1 nd 3.2 revels tht (9) holds if k α. (10) Thus, the condition under which w(γ) is n equilibrium wge schedule tkes n especilly simple form. If the firm s myopi k is less thn the mnger s brgining power α, then then w(γ) is PBE wge schedule, nd otherwise not. 16 Compring (10) to (4) nd (8) bove, we see tht the myopi thresholds tht is, the smllest k stisfying ech inequlity vry mrkedly, depending on the source of the mrket s uncertinty. When the mrket s uncertinty pertins to chrcteristics of the mnger (the prmeter in our model), the firm s myopi threshold is lwys wekly greter thn α. When the mrket s uncertinty pertins to mtch qulity γ, the firm s myopi threshold equls α. When the mrket s uncertinty pertins to firm chrcteristics q, the firm s myopi threshold is wekly less thn α. We show the reltions mong these myopi thresholds grphiclly (using specific exmple) in Figure 3. We plce α nd k on the x nd y xes, respectively, nd depict the firm s myopi thresholds in ech of the three cses. The dshed line is Inequlity (4); it therefore shows how the firm s myopi threshold vries with α in the cse where mrket uncertinty pertins to mngeril bility. The solid line is the firm s myopi threshold for the γ cse (from Inequlity (10)), nd the dotted line is the myopi threshold from the q cse (from Inequlity (8)). Focusing, sy, on α = 0.5, we see tht myopi thresholds rise from 0.36 to 0.50 to 0.60 s the source of mrket uncertinty shifts from firm chrcteristics to mtch qulity to mngeril bility. To explin the intuition for the differences in myopi thresholds, we focus on the cse where the informtion symmetry pertins to γ. Consider, in this cse, the effect on interim firm 16 If k > α, then the PBE wge schedule is given by the solution to w γ = k with boundry condition w(γ L) = + α`γ q. 17

19 k α Figure 3: This figure shows how myopi thresholds vry with α, nd by the source of the informtion symmetry. The specific exmple considered here is f(q, ) = 8 q, nd q, [1, 2]. The dshed line is the inequlity from (4) ssuming q = 1.5. If the informtion symmetry pertins to, then the full-informtion wge schedule is PBE for ll (α, k) below the dshed line. The solid line is the inequlity from (10). If the informtion symmetry pertins to γ, then the full-informtion wge schedule is PBE for ll (α, k) below the solid line. The dotted line is the inequlity from (8) ssuming = 1.5. If the informtion symmetry pertins to q, then the full-informtion wge schedule is PBE for ll (α, k) below the dotted line. vlue when the firm pys the mnger one dditionl dollr in wges. Pying n dditionl dollr in wges is the equilibrium ction of firm of type ˆγ, where ˆγ is defined by α (ˆγ γ ) = 1. Thus, firm pying n dditionl dollr in wges is behving s though its mtch surplus is higher by 1/α. Becuse the firm cptures frction 1 α of the mtch surplus, pying n dditionl dollr in wges increses the firm s interim vlue by (1 α)/α. Now suppose the informtion symmetry pertins to mngeril bility, nd gin consider the effect on interim vlue when the firm pys the mnger n dditionl dollr in wges. Pying one dditionl dollr in wges is the equilibrium ction of firm of type â, where â is defined 18

20 by 1 = â + α ( f(q, â) â f(q, ) + ) = (1 α)(â ) + α ( f(q, â) f(q, ) ). Here, becuse the informtion symmetry pertins to the mnger s bility nd hence to his outside option, only prt of the dditionl dollr in wges is ttributed to n increse in the mtch surplus. As result, firm pying n dditionl dollr in wges is behving s though its mtch surplus is higher, but by n mount strictly less thn 1/α. Becuse the firm cptures frction 1 α of the mtch surplus, pying n dditionl dollr in wges increses the firm s dte 3 mrket vlue by n mount strictly less thn (1 α)/α. Becuse the mrket ttributes prt of ny increse in wges to n increse in the mnger s outside option nd therefore not to n increse in the mtch surplus, the mrginl effect of wge increse on interim vlue is smller when the informtion symmetry pertins to mngeril bility rther thn to mtch-specific productivity prmeter γ. Thus, the set of (α, k) vlues for which the mnger s wge is distorted upwrd reltive to the full-informtion cse is lrger when the informtion symmetry pertins to γ. Finlly, suppose the informtion symmetry pertins to firm productivity q, nd gin consider the effect on interim vlue when the firm pys the mnger n dditionl dollr in wges. Pying one dditionl dollr in wges is the equilibrium ction of firm of type ˆq, where ˆq is defined by α ( f(ˆq, ) f(q, ) (ˆq q) ) = 1. A firm pying n dditionl dollr in wges is behving s though its mtch surplus is higher by 1 α 1 α. Note, however, tht the increse in interim vlue is strictly lrger thn α, becuse higher mtch surplus mens higher vlue of q. Tht is, by pying the mnger more, the firm increses the mrket s ssessment of the mtch surplus. Becuse the only unknown ffecting mtch surplus is the firm-specific productivity prmeter q, n increse in mtch surplus mens the firm s outside option is higher s well. Thus, the mrginl effect of dollr of wges on interim vlue is highest when the informtion symmetry pertins to q, second highest when γ is unknown, nd lowest when is unknown. This explins the pttern evident in Figure 3. The resoning outlined in the preceding four prgrphs on the mrginl effect of dollr of wges on interim vlue cn lso be used to describe the implictions of mrket uncertinty regrding the mnger s brgining power, α. Suppose tht α is privtely observed by the firm nd mnger, but, γ, nd q re public. In this cse, disclosure of the mnger s wge contins 19

21 no informtion bout the firm s output f. Thus, terminl vlue is strictly decresing in the wge, nd interim vlue will be decresing in the wge s well. Firms therefore hve no incentive to increse py to boost interim mrket vlues. If the mrket cnnot observe in ddition to α, then the min force in our bsic model tht firms my fce incentives to rise wges to boost interim vlue is still present. To see why, consider the mrket s inference when the firm pys n extr dollr of wges. This increse in wge will be ttributed in prt to n increse in the mnger s outside option, in prt to n increse in the mnger s brgining power, nd in prt to n increse in the mtch surplus. The specifics of this inference will depend on the mrket s beliefs bout the distributions of α nd. Before concluding this section, we briefly revisit the quottion from Edwrd S. Woolrd, Jr. tht we discussed in the introduction. Woolrd indictes tht incresing the mnger s py helps mke the compny look strong. Notbly, our nlysis suggests tht the tempttion to overpy mnger to influence mrket beliefs is strongest when there is significnt uncertinty regrding firm-specific productivity nd wekest when there is significnt uncertinty regrding mngeril bility. Overpying mnger to increse the mrket s ssessment of mngeril bility hs smll effect on interim vlue, becuse the mrket expects the gins from increses in mngeril bility to be cptured t lest in prt by the mnger. Overpying mnger to increse the mrket s ssessment of some firm-specific element of productivity hs lrge effect on firm vlue, becuse the mrket expects the gins from increses in firm productivity to be cptured lrgely by the firm. Woolrd s ssertion tht Wobegon Effects re mostly likely intended to mke the compny look strong rther thn mking the mnger look good therefore fits with our findings. 4 Discussion Our nlysis exmines whether three key ssumptions symmetric informtion, mngeril rents, nd corporte myopi cn cuse firms to distort CEO py upwrd in n ttempt to ffect mrket perceptions of firm vlue. We find the three ssumptions re not sufficient to led to Lke Wobegon Effect; two dditionl conditions re necessry. For the cse where the informtion symmetry pertins to mngeril bility, we find tht the Lke Wobegon Effect cn occur only if mngeril bility increses the mtch surplus, nd only if the firm s myopi is strictly greter thn the mnger s brgining power. These conditions my strike some reders s sufficiently restrictive to wrrnt dismissing the Lke Wobegon Effect s n 20

22 explntion for recent CEO py increses. Tht sid, we think the bility increses mtch surplus condition is likely to be met, t lest in some cses. The second condition on the reltive mgnitudes of myopi nd brgining power is hrder to ssess. As we note below, few direct proxies for corporte myopi re vilble, nd it is not cler how one would mesure mngeril brgining power. The effects studied in our model do fit with some existing empiricl evidence. If, for some reson, firms do not disclose py levels, then there is no reson (in our model) to increse mngeril py to boost interim vlues. Requiring disclosure my therefore introduce the effects studied in this pper. The observtion tht py disclosure my spur Lke Wobegon Effect fits with evidence in Prk et l. (2001) regrding 1994 chnge in Cndin disclosure rules. This chnge, which ws not nticipted fr in dvnce, required firms to retroctively disclose CEO py levels from 1992 nd This llows for esy comprison of pre-disclosure nd post-disclosure py pckges. Prk et l. (2001) report tht py levels rose in the postdisclosure period, nd, citing O Reilly et l. (1988), ttribute this to the prctice of setting CEO py in reltion to the py of other CEOs. Our model explins why it might be rtionl for firms to set py in reltion to some externl benchmrk, but only fter py levels re required to be disclosed to cpitl mrket prticipnts. 17 Note, however, tht other theories cn explin the Cndin disclosure evidence; if the disclosure reduces serch costs for firms ttempting to hire new CEOs, then it is possible tht wges would rise s result of the new rules. More reserch is needed before the Cndin disclosure chnge cn be tied directly to the Lke Wobegon Effect. Devising shrp test of the model is likely to be chllenging, however. Like mny models of symmetric informtion, the comprtive sttics of our model relte mostly to quntities tht re hrd to mesure. For exmple, our model suggests tht the Lke Wobegon Effect depends (in vrying wys, depending on the source of the informtion symmetry) on the reltion between the firm s myopi k nd the mnger s brgining power α. Higher k fvors upwrd distortions in py, while higher α fvors the full-informtion wge schedule. While these myopi nd brgining-power prmeters re stndrd in the theoreticl literture, there re no 17 Crighed et l. (2004) nd Swn nd Zhou (2006) lso exmine chnges in CEO py in Cnd post-1994, nd document incresed CEO py-performnce sensitivity. While our model does not ddress this fcet of CEO py directly, it is possible to extend our nlysis to show tht corporte myopi my cuse py to be tied inefficiently closely to firm performnce (see footnote 2). This suggests tht Cndin py-performnce increses my not hve been vlue-mximizing. 21

23 stndrd mesures of these prmeters in the empiricl literture. Some mesures of corporte myopi re vilble (see, for exmple, Bushee, 1998), but it cn be difficult to interpret these mesures s weight on short-run shre price, s our myopi prmeter is defined. Any mesure of brgining power would seemingly require knowledge of the outside options of the mnger nd the firm, nd the output when the two work together, ll of which re difficult to observe. An dditionl compliction rises when our model is embedded in n equilibrium model of lbor mrket. Even if cross-sectionl mesure of corporte myopi were redily vilble, firm s py level cn be ffected by the myopi of its lbor mrket competitors. It is therefore not necessrily the cse tht py should be incresing in myopi within cross-section of firms tht compete for the sme mngeril tlent. Finlly, we note tht it is strightforwrd to extend our model to yield upwrd spirls in CEO py, s suggested by Woolrd. In n erlier version of this rticle, we considered two-firm version of the model with ssorttive mtching. Tht is, we ssumed complementrity between some firm chrcteristic (sy, size) nd mngeril bility. The complementrity implies tht the equilibrium ssignment of mngers to firms will involve sorting: the highest bility mnger will be mtched with the lrgest firm, second highest with second lrgest, nd so on. Assorttive mtching models hve been studied extensively by lbor economists; see Sttinger (1993). The dvntge of this ssorttive mtching pproch is tht it llows us to endogenize the prties outside options. The brgining between, sy, the lrge firm nd the bler mnger is frmed by the possibility tht the lrge firm could hire the second-best mnger or the best mnger could seek employment t the smller firm. The extension of our model yielded two results. First, py for the mnger of the lrge firm is wekly incresing in the myopi of smll firm. Second, if the lrge nd smll firms re eqully myopic, then py for the lrge firm s mnger increses fster (wekly) with tht common degree of myopi thn does py for the smll firm s mnger. 5 Conclusion Our nlysis offers model of the widely discussed Lke Wobegon Effect. In our model, we define the Lke Wobegon Effect to occur when firms distort CEO py upwrd in n ttempt to ffect mrket perceptions of firm vlue. The model relies on three key ssumptions symmetric informtion, mngeril rents, nd corporte myopi nd yields four min conclusions. First, we show simply tht the Lke Wobegon Effect cn occur. Second, we show tht those 22