UNIVERSITY OF ILLINOIS LIBRARY 'AT URBANA-CHAMPAIGN BOOKSTACKS D^-1 CENTRAL CIRCULATION BOOKSTACKS The person charging this material is re- sponsible for its renewal or its return to the library from which it was borrowed on or before the Latest Date stamped below. You may be charged a minimum fee of $75.00 for each lost book. Theft, mwHIotl*!!, and underlining of books are reasons for dUclpUnary action and may result in dismissal from the University. TO RENEW CALL TELEPHONE CENTER, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA CHAMPAIGN APR 2 9 1998 AUG 3 1998 When renewing by phone, write new due date below previous due date. LI 62 ; -. STX ---35 IdO'^ COPY 2 1 BEBR FACULTY WORKING PAPER NO. 1424 A Model of Efficiency Wages as a Signal of Firm Value THE Library of the Lanny Arvan ^pp '^ 7' ]CP2 Hadi S. Esfahani -f UNlVLRblfY Oh ILLIINUIS ••--AM- -^ -A i^M WORKING PAPER SERIES ON THE POLITICAL ECONOMY OF INSTITUTIONS NO. 5 College of Commerce and Business Administration Bureau of Economic and Business Research University of Illinois, Urbana-Champaign Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/niodelofefficienc1424arva BEBR FACULTY WORKING PAPER NO. 1424 College of Commerce and Business Administration University of Illinois at Urbana- Champaign December 1987 WORKING PAPER SERIES ON THE POLITICAL ECONOMY OF INSTITUTIONS NO. 5 A Model of Efficiency Wages as a Signal of Firm Value Lanny Arvan, Associate Professor Department of Economics Hadi S. Esfahani, Assistant Professor Department of Economics We would like to thank the participants of the Economic Theory Workshop at the University of Illinois at Urbana- Champaign for several helpful suggestions, many of which found their way into the paper. Abstract Worker-posted performance bonds are a potential solution to trie agency problem which arises when worker effort is not perfectly observable by tne firm Yet the explicit posting of performance bonds is rarely observed Since the firm should prefer a contractual arrangement which entails performance bonds to one which relies on efficiency wages, because the bonding contract yields lower unit labor cosis, an explanation for the iaci< of bonds in actuality is required. We propose such an explanation based on the idea that the implicit contract must resolve the firm moral hazard conc^erninq bona expropriation. We model this moral hazard as a loan default problem When the value of tne firm is less than the value of the posted performance bonds, the i firm will expropriate the bonds and go out of business. Workers will willingly post performance | bonds when thy know that this inequality is reversed. In an environment v/here the firm is subject to a series of random snocks which are not observed by its workers, these workers will be , unable to determine the value of the firrri Vv'e. aemonstrate that in such an environment the ■ > t t I optimal implicit contract may require the firm to pay wages to workers in excess of their ; J reservation wage, when labor productivity and thus labor demand is high. These efficiency wages " act both as a signal to workers that there is no tnreat of bond expropriation and as an inceniive devic.e to elicit effort . I. Introduction Worker -posted perforrriance bonds oooear lo be a viable soiuiion lo tne agencv Drobierri which arises when worker ei'fort is not perfecuy ooservabie by The firm and, consequcnr ly , wnen the firm must generate incentives for its worKers to put forth effort Such oonamg conrracts, if feasible, obviate the need for the firm to pay its workers in excess of tneir reservation wage, as suggested by the recently developed efficiency wage theory ^ However , the explicit posting of performance bonds is rarely observed. Moreover, recent work by Abraham and Farber ( 1 987) suggests that even implicit bonding arrangem.ents, in the form of uoward sloping w.^ge- earnings profiles steeper than their concomitant productivity profiles, are less significani i.nan was previously suspected/' Thuf;, one is led to :<-eK explanations for why ooncing does not occur more often. The main theoretical argument that has been advanced to date as an expianation for mis puzzle is that workers are liguidity constrained and, thus, unaDle to put up the reguisite bond. Although this explanation may be plausibie in ceriam cases, its general appiicaoiiity faces severe limitations, because the explanation appears to reguire that wnen workers are somewnat iiguia the firm will require these worKers to oost ail available casn as performance oono, so 'hat worker compensation need not be as high as it would oe were there exclusive reliance on efficiency wages. This implies that the firm, should rank its job applicants, who are otnerv/ise similar , on the basis of their relative liquidity. Moreover , to tne extent that the firm can oerceive liauidity differences among its existing workforce, internal wage differentials should arise We oeiieve thai tnis is the wrong line of approach to explain the lack of bending in actuality, though liquidity constraints m,3y bind in many instances ' See, for example, Shapiro and Stiglitz (198'1) and Bulow and Summers i;986) Vellen (1964). Akerlcf and Yellen (1986), and Kalz (1966) provide interesting reviews of tne efMciency wage literature 2 See. for example. Medoff and Abraham (1980). Oij" preferred exp;ar;a*ior, taKe? as its oasis the ;' irm rnoral tiazard concerning bond e'xDroDr ia;ion in ine eiticiency wage literature, this morai r:azarG is usuaiiv described as the firm deiiberateiy mislabeiing its workers as shirkers, it nas oeen argueo tnat tnis moral hazard is soived Through the firm's desire to maintain its reputation in me lahor marKet.-" ^ Tne argument is that upon reneging, recruiting costs go up sufficiently to more than offset the gains resulting from bond expropriation. In a recent paper , we argue Thai Donding will dominate efficiency wages, when such reputational effects are viaDie,^ However , the resulting equilibrium does not yield the first best solution. Although the labor market clears in this equilibrium , firms miust earn reputational renis whicn are themselves distortiongry , when comparea to the solution where the firm moral hazard is apsent in our curren* paper , we assume instantaneous anc certain detection of bona expropriation, in order lo simplify the model ana avoid extraneous issues, pariiculariy The quesTion ()i now oetection of The i'.r^'. moral hazarc occurs.'' inen we view the firmi moral hazard as a loan default problem Thai is, when the firm expropriates bond it takes the bond of all Us workers simultaneously."^ We also assume tnat ihe firm ceases operation once ■-"' See, for example, Akerlof ana Yellen i'l'j'dS). ^ Several authors have suggested mechanisms other than reputation to resolve the f'-rm mioral hazard probienri in contracts with tiondinq. For example, Carmichael ( 1965) argues that the problem can be eliminated through the use of thira party repositories for the performance bonds and through the designation of recipients of performance bonds tnat are appropriated m the event that some workers are detected shirking, other than the firm. Other authors, eg , Dickens et al (1987), 'r)3\'e taken the opposite approach, arguing that there are lirriits to bonding arrangements aside from the fi'~nri moral hazard In particular, it is argued that incentive schemes which rely on disproportionately large punishments as compared to the crime they dre designed to deter, cannot be in-ipiemiented, i e , such punishments will not hold up in a court of law. Still others, e g , Halcolmson ( 1964'. suggest that the problem can be resolved through the use of r,?nk order tournaments, whereby the firms compensation to its workforce is made state independent yet incentives for workers to put forth effort are preserved We a priori rule out the possibility of utilizing third parties, to avoid the issue of the limitations placed on contracts through legal enforcement constr'aints. We also note that the option for the firm to default on its labor contract is typically ignored as a possibility in the tournament literature Thus, our approach can be viewed as filling In this gap 5 See Arvan and Esfahani (1987) ^ This assumiption is also made in Arvan and Esfahani ( 1987) See note 8, ' In Arvan and Esfahani (1987) we show that there is no ioss in generality lo restricting attention to the case of full bond expropriation, since the maximum credible punishment will be applied to the firnri when it expropriates, regardless of how many workers lose their bond. exproDriation ha? taken olace,'^ Then, -vvorkers will be reluctant to post bond unless tnev believe mat the value ol Uie firm given thai the firm honors the implicit coniract eACeeas ihe value ot ;he firm given that the firm reneges via bond expropriation We question the viability of the reputation mechanism by considering a stochastic, environment with information asymmetries. We assume that the firm experiences random productivity shocks. These productivity shocks affect the value of the firm Workers are assumed to be unable to determine whether default is an attractive option to the firm , because workers cannot observe the realization of the current shocK. In this respect our model borrows from tne literature on implicit contracts under asymmetric information '^ It turns out that in our model bond expropriation is an attractive option to the firm when it is actually in tne low productiviiy state but clairris to be in the hign productiviTy si.ate. The optimal contract must either convince workers that bond expropriation is not a thre.at, Dy giving a signal to workers about the firm's True state, or compensate them for the possidiI iTy oi expropriation risk. 'When the former is tne c.a3e, our model appears similar to the model of Milgrom and Roberts ( 1 986), who analyze price and advertising signals of product quality in an experience good market. Their acnievemeoT is to consider a multidimensional signal , The product-price and advertising-expenditure pair , to explain tne presence of noninformative advertising. Signaling in our model is also acnieved via a multidimiensional signal, the wage, performance bond, and employment triple, in addition to viewing contract offers as signals, our model explicitly considers both tne worker moral hazard concerning shirKing and the firm moral hazard concerning bond expropriation A further feature which differentiates our approacn from Milgrom and Roberts is that they only consider one snot uncertainly while we allow for an underlying stochastic process to generate workers' uncertainty In Milgrom and Roberts' paper, all doubt aoout the firm's underlying characteristics is eliminaTed * 'v^hen oetection of bond expropriation 15 both instantaneous and certain, the firm qomg out of business constitutes ttie maximum credible punist'iment that workers can impose on the firm, as we showed m our previous paper. Weaker forms of punishment, such as increased recruiting costs, wi!! sustain equilipna which are Pareto dominated by the equilibria described in this paper ^ See the entire OJE (1935.) supplement and Hart(l983) for a very good survey of this literature. once Duver?. learn about, the oroduct quality associated with the firm in question Thus, as they readily admit, their mncei is best interoretea as explaining nonini'ormaiive advertising (or a riew product, in our mode: , even if workers are currently sure about the firm's productivity because the current coniraci. offer is a perfectly informative signal, workers will be genuinely uncertain about the value of the firm in the next period because there is a new shock in that period. Indeed, our approach could oe readily applied to the product quality issue to explain persistent advertising. The basic model we consider is essentially an extension of the cogent efficiency wage model develooed by Shaoiro and Stlqlitz ( 1 964) Vve extend their model to a stochastic contract game which allows for tne possibility of performianc^ bonds, and hence for an analysis of the firm moral hazard problem. We viev* the problem of long term contract determination as one of constructing a sequential equilibr'um for rh:s fXinirac' qame. ■ ^ in, fact, we restrict attention to tne particular refinement of sequential equilibrium gwen by tne intuitive or ]terion^ ■ This solution concept is suitable since the issue of whether worKers are willing to post performance bonds depenos crucially on their Del lefs about firm profitability. We assume that the underlying uncertainty of the game is generated by a very simple Markov process. This allows us to provide an explicit characterization of \\\?. equilibrium As a consequence of the workers' uncertainty about firm value, the firmt does not necessarily rely exclusively on performance bonds to provide workers with the appropriate incentives when its productivity, and conse^Duently its employment, is high. Instead, the firm mary utilize efficiency wages, in part The reliance on efficienc-/ w^ages occurs when firm employment is sufficiently great that there would be a risk of bond expropriation, were the firm in the low productivity state Performance bonds will still be utilized by the firm in such an equilibrium, but not to the extent that they would be were the firm's productivity observable Moreover, the greater the value of the firm's shxk in the high productivity state the greater the volume of ^ ^ See Kreps anr! Wilson ( 1 982). ^' SeeChoand Kreps(l987). employment ir; the riiah prcductiviTy state, ana nence, the greater- the reliance on eftiClencv wage? Thus, our model precicts a positive correlation between wages anc firm s;:e, a well f nown sTylizec fact of the labor market that heretofore nas not beer^ explained adequately ' - As an alternative to paying efficiency wages to signal high firm prodiiCtiviTy, [Ue firm might find it preferable to not signal its productivity at all , but instead to comiperisaie wocKers for expropriation risk. This tactic is more favorable for the firm when the workers' prior beliefs put a lot of weight on the firm being in the high productivity state, since the size of tne compensating differential is small in this case. This suggests that when workers are sufficiently optimistic, pooling rather than separating equilibria will prevail However , as we show in the paper, this intuition is not correct. As long as worker prior beliefs are not helc with ceri.ainty , the firm in the high productivity state has sufficient incentive to signal Us oroductiviiv Thai any pooling equilibrium involving compensating differentials is undermined. In addition to explaining wny firms pay efficiency wages, our miodel resolves another paradox which has troubled the efficiency wage literature: When firmis pay efficiency wages to workers, why don't they charge entry fees up front ;n order to recapture the renis emoeddea m the efficiency wage payments? (lore importantly, when such entry fees are uti lizec, doesn't The involuntary unemployment associated with efficiency wage theory vanish, since eacn worker's lifetime compensation, inclusive of the entry fee, eguals wnat the worker coulc earn at nis next best opportunity? ' ^ In our model , we allow the firm to charge eacn worker such an up front paymeni, as per Carmichael's suggestion. Yet in our signaling equilibrium, tne marqinal value product of the firm in the high productivity state exceeds the worker's reservation wage, in fact , this marginal value product even exc-eeds the efficiency wage' Thus, we demonstrate that the '*• biandard efficiency wage theory argues that monitoring intensity varies inversely with firm si^e For example see Katz (1936). This may indeed be the case. But such a negative correlation need not iniply a positive correlation between firm size and wages, when one allows that performance bonds ^rt viable In addition, there does not appear to be a compelling reason for assuming that small firois have a comparative advantage in monitoring Our explanation holds true under the assumotion that monitoring intensity is constant, regardless of firm size, and remains true under the assumption that miomtonng intensity varies inversely with firm size '^ See the exchange between Carniichael (1985) and Shapiro and Stiglitz(l985) cnarqinq of up ''rorit fe&:- is compatible with involuntary unenripinvrrient. Our result follows Decause tne f ir m musi convince us employees ihai 'here ^s no nsK of Dona expropr ;ation. This places The loilowinQ sionalinq constraint on the firm, wnen m me nign pr oductivity s'aie. The equi iibnum payoff to the firm when in the low productivity staie shoulo be at least as large as the payoff that ihe firm in the low productivity state would ootain were it to offer the equilibrium contract for the firm in the higti. proouctivity state followed oy it expropnaimq the performance bonds associated with this contract. This signaling constraint appears as an upward sloping curve in employment-wage space. That is, the firm in the high productivity state acts as if its supply of labor is not perfectly elastic, as long as the contract it offers calls for some degree of performance bonds. Furthermore, the firm in the hiqn productivity staie does not charge an entry fee to its employees, since ooing so would only tighten tne signal ir.g constrairii. These fees are charged to workers when the firm is in the low produc'ivi'v state. The higher the efficiency wage paid in The hign producnvity siaie, the higner the fee col lec'ed in the low productivity state However , sequential rationality imposes the restriction mat the firm ooes not internalize this benefit. This is the crucial insight of the paper. The rest of this paper is organizeo as loiiows, m section li we provice a sin":piified, one- per icd version of the moijel tc provide some intuition tor now efficiency wages work to signal firnri value, in section iil we provide the basic set up of the general , infinite horizon mocel in section IV we Discuss some of the main properties of separating equilibr lum. !n section V we characterize equilibrium. Finally, we offer a orief conclusion in section vl. II. A Diagrammatic Approach In this section we provide a simplified, one period version of our model to give an iaea of how efficiency wages are used to signal firm value and to suggest those cases where such a signal v/ill be utilized. Suppose a firm c^n be in one of two possible states, either m or A' where state m Is less favorable to the firm than state M. Assume that the realization of the state is private in'^oriTia* -on ^'leid tv '''e i^rTi , vp , wnr>-e:~s cannot oDse^ve the firm's stats. Let U oeriote the iitcti-ne v^iue 01 trie *irTn whep u (S in state u for u = m^M. L' < U ^.. Assume the tirTn'sooiv iT; I i input IS laDor ana thg: tr;e fir.T;s choice prot^iem is to select the profit maximizina employment contract from among inose contracTs vvhich workers will find acceptable. In this simplifiea version of our model , a amtract is a pair , ( vr\ i ) , where W is the contract wage and L is the voiume of employrnent. Workers can earn the reservation wage, W r,, t?y seeking employment elsewhere. Hence, W 1 W n is a necessary condition for contract acceptability. In addition, suppose that empla/mient with me firm neoessuaies thai 'workers post a performance bond of value P The other neces'sary ccncition which governs c-oniract acceptability is that workers must oelieve thai the firmi won t expropriate the performance ooncs mat ihey post. We elaborate on this condition he low Suppose that if the coniraci ( W .L ) if. accepted then the current period profit of the firm in state u isn( u, ^V,l ) and suppose that if, m addition, the firm expropriates the performance bones then its lifetime value is n( p , ^y,l )■*- r>"Z , for \!^-m,M. If workers were primiarily CJiincerned about expropriation by the firm, when its state is m , they would not accept a contr.x.t which satisfied: U ,, ■ n( m , W .l )+ /^Z . When this inequality is reversed workers should be 111 cwvinced that there is no risk of bond expropriation. We v^a^^ to the constraint: U 2 n( /?; , W\L ) as the signaling constraint, SC, because when it is violated workers beliefs will assign high prooability to tne firmi being in state m The firmi can only convince its workers thai It is m state M bv offering a contract which satisfies the SC Assume that n exhibits the rol lowing properties; n > 0, n ,., ^ 0, n , , '- 0, and n , > 0. M r/ LL U zl Let L ^^1 - - ^ n( M , li''r-,,l ) We focus on the oroblerri which determines the firnVs optimal contract when the firm is m state /V, since in ej:]uil!brium it is only in this state that efficiency wages are possible This problem is given by rriaxirrr.ze n( /Y, vt-', z ) subiect to ij > n( /?? , yV. I )^ pl in figure i we qraon the so'mtion to this problem under the assumotion that the SC does not Dind, Observe that the isoprofit curve is tangent to the horizontal line /■"/ = /f n at Z/s-^and the SC cuts tne horizontal line l^V = H'n at L. > l^f. This is necessary when the SC doesn't bind. In figures 2 and 3 we graph the solution to this problem when the SC binds. We identify two candidates as solutions of this problem. The appropriate choice depends on the respective slopes of the isoprofit curves for the firm in state A/ and the SC. In figure 2 , there is an interior solution This is the case where efficiency wages occur. The first oraer necessary condition in tnis case is n . ( //, i'V.., Z ^.J == n ,{ m, ff' .-^ a-)"^ ^- The noht hand s^de of tnis eauation is L I i I 1 L fill positive when the SC is rising. When n , is inierpreted as the difference between the margma! value product of labor and the wage and when the tangency point occurs on the rising pc^tion o^ the SC, the marginal value proauct of labor exceeds the efficiency wage, \V ^^\ in this sense our model predicts even grosser allocative inefficiency than the standard eff icienisy wage model . such as Shapiro and Stiglitz ( 1 9S4). In figure 3. there is a corner solution , ( KS.^.Z ,,) = ( V/n.Lr.). Efficiency wages hrb not utilized in this case, though there is evidently allocative inefficiency relative to the first oest solution where v/orkers can observe the firm's state. The first order necessary condition in this case, n , ( t1 , ^^V>,/q) 'LTi a m , r/^,Z,-,)+ B, indicates that the firm finds It too costly to utilize efficiency wages to expand its employment. in the subsequent sections we expand on this basic mcdel in order to endogenize those values which were taken parametrically in this simplified version. However, the m,ain message remains mt.act when going to the full model: Efficiency wages are utilized to signal the firm's state and tnereby to convince workers that there is no risk of bond expropriation This signaling distorts the laoor allocation relative to the first best solution Moreover , we are able to show that this distortion remains, even when the firm charges its employees up front fees, so that over the lifetim.e of employment workers only earn their reservation wage. M Figure 1 W SC Wk isoprofit curves M M Figure 2 W Wr isoprofit curves Figure 3 Hi. Preliminaries There are three commcidlties in the moaei a proauced qooa, labor -leisure, ana a stocK commodity which serves as numeraire. There are two types of agents, the firm and workers Workers are identical in every respect except employment status. Each worker is infinitely lived and endowed with both an indivisible unit of labor- leisure and enough of the numeraire stock to oe able to post the requisite bond, should the worker choose to do so. Worker preferences are specified by the rate of time preference, /", which coincides with the market interest rate, and a oer period von Neumann-Morgensiern utility function defined over leisure ana numeraire consumption. As is typical in this literature, we assume thai, workers are risk neuira! Workers who are employee by the firm ge; to cnoose their level of effort , £?s [ , 1 1 When ..-= an employed worker is t.aking leisure on ;he lob or .shirking When e= I the worker is oe.r.g productive or putting forth effort. Intermediate values of Assume < l? < if? '• 1 The firm 1-^ taken to maximize di'^coijnied exoect&c oroMTS, wnere the discount rate is tiie marKet interest rate, r Eocr, penoc ;hat the firm is iri operauon is oroken down into four stages of cecision, In the first staqe, the firm offers a contracl A contract in oenod / 1s an ordered 5-tuple, C,, C- ( W,.B ,S .,F ..f^ i). where rV , is the waae rate to be paid to each employed worker, d . is ((.if',.; 1 ' ( the pe!"formance Dond to oe oosted Py each employed worker , Z ^ is the volume of employment should the contract he acceoted, F ^ is the fee paid t^y workers who are in the firm's reserve pool , and R , is the size of the reserve pool. The pool of workers to whom the firm may offer a contract in penoc t. in order of priority, consists of first, thos* workers em.pia/ed by the firm in period /- / who are m qooa standina, second, those workers in the firm's reserve pool in period t- 1 ; ono tn:rd, "vOe outside wo^Kers who are unemployed in period / and seek employment frorri ^'j\t firrri ;n mat period, '/vithin each of the^-e priority ciasstfiication joos are alloc^ited on a pro rata Pasis In the second stage eacn worker who is offered the contract either accepts it or rejects it. The contract is null and void in the event that the firm cannot find L , v/orkers to accept it. In this case, me remaining Vvvn Mages are foregone and tne firm, necessarily continues operation into period '■+ i Any worker wno dia accept the contract is freed from this obligation and entitled to seek empiovment eisewnere ;n perioo / Similarly, each worker who is offered a slot m the reserve ooci eitne'' acceots !■ or rejects it, .Acceptance requires payment of the fee, r ^, which is nonrefund-aPle Workers in the reserve pool c-an obtain emiployment elsewhere in period /, i.e. , they can earn rv ^ j'\ i-r) in the period indeed, our reason for including a reserve pool m tne model is that when -aPor contracts call for efficiency wages, workers earn rents and thus should be willing to pay for the rignt to emplioyment. ' '^ The firm could extract such a pa^/ment by hoarcing worKers. encouraging them to shirk , and capturing the performance bonds of those workers it caught shirking When the workers' reservation wage is positive, this is an '■^ See Carmirjtael (19851 1! ineiTicient mecnon'T.rr, for extracting such payments. The reserve pool mechanisrr, , wnsre vvorrers pav fcr trie right to be ottered employment when vacancies appear but may worK elsewhere m the meantime, is superior The contr-xt is operational when Z, workers accept it. Once the contract is operational ,. each ot the i , emolo^/ees receives the wage ^V. and posts the bond £^, . Thus the net pa^/ment made by the tirm to each emp!o^/ee at this juncture is ^'^r^/. which may be positive or negative. In the th'rd stage, each worker chooses i?.. This choice is not observed by the firm. Instead, the firm has a chance of detecting the worker taking leisure on the job The detection probability is ( /-e,)B, where e is a parameter reflecting the firm's monitoring intensity, <8 < 1. In the conclu(^inq section we briefly cxinsider the firm's problem when it is iree to cnoose tne magnitude of 8 . Once the tnirc' stage has occurred, production occurs and output is publicly observed Both the firm and its workers are able to impute the effective labor input m per loa t, C\, via observation of fi^m output and their knowledge of the production function, f. We assume that there is a determ mistic relationship between Z^, Z^ , and. the number of workers detected d d -= shirkina in period /, Z.. This relationship is Given bv Z/=(Z,-Z'J8. The reason tor makino L ■'■III this assumption is that when there are layoffs, Z . , < Z ,-^^f . ^'"'e retention probability is nonlinear in Z . , Hence, the value of future employment to workers currently under contract could depend on noise in the detection of worker shirking, i.e., if L. were a random variable then the value of future employment would depend on the distribution of this random variable. This effect could conceivably offset our argument against labor hoarding. Given Z . , the firm decides in the fourth stage to either coniinue operation into period /+ 1 or cease ooeration at the end of period t When the firm has decided to continue operation, all the workers wnn are detected shirking are fired and made to forfeit their performance bonds to the firm. .All of the other L ri* workers are considered employees in good standing. At the start 12 of Dennd /+ 1 such emD!o\'ees aet bact, ( 1 + /■) d ^ from the firm. When the firm decides lo cease ODeraticn at the end oi 'jenoQ t , observation of l ^ is imrnater lal. in this case, ttie firm keeps tne performance bonds of all its workers, regardless of whether they nave been detected shirking. The game ends once the firm has decided to cease ooeraticn. Our goal is to construct sequential equilibria m strategies where the history of pi3\' can be completely summarized by workers" current beliefs about the firm's internal price. This restriction on strategies appears natural given the Markovian structure of the underlying uncertainty. • 5 !n order to construct such equilibria, we must first specify wha^ strategies and beliefs are and then impose seauential rationality, on strategies, and consistency with Payes' Law and with eauilibrium strategies, en beliefs. V/e shall do so in a 'ather informal manner , to save on notation and thereby to enhance readability. At the star t of oeriod /, workers will have genuine uncertainty as <.o the curreO' va'ue o'' the firm's internal price. Let a ^ represent the beliefs of workers that tne firm is in tne low productivity state in period /, before the contract in period / is offered but after the play of the game through period /- 1 has been completed, a ^ = Pr{u = m] The contract offer serves as a signal of the firm's internal price. Letp^ represent these revised beliefs. Tnenp . = |3 (a ..^^), I.e. , the initial beliefs and contract offer map into revised beliefs. The consistenD/ reouirernent restricts p via Bayes' Law for the equilibrium values of C.. but imposes no restriction on p for out of equilibrium values of C. If the contract offer is not accepted by Z , workers, then Bayes' Law requires that a ^_^ .=«./:''+( 1 -« J <^ If the contract in period / is operational , then c-ontinuation of firm operation into period /+ 1 may also signal the firm's internal price in period / and hence provide information that is relevant in predicting the firm's internal price m oenod t^\. Ttien Bayes' Law requires: a - ^ — ' - /^i- P,//,,,^ (i-P,)/^; //-/ •-^ Note, however, that this restriction on strategies is not innocuous The restriction has the effect of taking away all the workers" bargaining power, in particular, under the restriction workers can't play trigger strategies where they punish the firm, by not accepting the contract offer, unless tfie contract provides employees with sufficient rents. wnere H, denotes trie proDabilitv ^*iat the firm honors tne contr act qwen I u ^= u ■ , < u - .: ■ I'or u = m, M. A strateg/ for a worker Is an orderec inole of functions. The firs* function maos initial beliefs and contract offers into acceptance or rejection decisions This function governs the employment decision. The se^xind function also maps initial beliefs and contract offers into acceptances or rejections, Put this one governs the decision concerning entry into the reserve pool. The third function maps revised beliefs and contract offers into effort levels. Thus the first two functions govern play m stage two, while the third function governs play in stage three In what follows we assume that all workers pursue tne same strategy/ A strategy for the firm is an orderec pair of functions. The first function maps tne firn-i's internal price and wor, O'^i \- ti) 0'J\/{ 1 -»■ r), individual rationality require; that n „i 0. Similarly, individual rationality requires n ., 2 0. Thus, either n „ = n ^_, = and conseQuentlv U,, = U^. = 0, in which case the equilibrium is trivial witr i-i I ; ' III I ■ the frrn never m operation, or max sn _ , n ,....) > 0, in which case 0' , 0'^^ > 0, In fact, since n ( /V, ^„ ■ 1 n i rn ,C), with strict inequality when Z _> , and since n ., > n ( //, ^„ ) , /77 ^ ,7i ri m pecause ^.^ is a Pest response for the firm wnen its internal price is /7, it miust be that max {n ,^. .ji .,,: = n ^.. hence, in a nontrivial equilibrium , i'. > L' > 0. This is the case we mil'! 1 1 ffl focus on below C^r.-nsider the farm's stage four decision given that an arbitrary contract has been offered and accented m period / and that the internal price is m. Were it to cease operation at the end of period /. the firm would expropriate the performance bonds of all its workers who would otherwise oe m good standing. The value of this expropriated bond is d X I.- Z .) = •^ fhis IS shewn to be d necessary property of eqijilibrium m lemnna 1 ' ' This 15 3I50 shown to t>e a necessary properly of equilibrium in ienima 1 L X ^ ~( ' ~ i-'M]- Were the firm to continue operai.ion, the firm's lifetime, expected, ( ( discounted value equals [ fi 0'„^-^{ ]-/?) ifA.J/', l -^ r). Tnus, the v,rrr\ honors the contract only if (2) cU/^- {]-/)) C/^^ 1 (l^r)/^^Z^[!-( i-.^je]. ( 2) is termed the no expropriation condition for the firm in state m , NEC , where the subscript refers to the current internal price of the firm. NEC^ is defined similarly for the firm with current internal price equal to A/. Since d< z??. the NEC is more restrictive than the NECk.. The model was constructed so that this would he the case. Mote that the expropriation decision is maeoendent of '4'., f,, and /?,, since these vanaDles are "sunf- " oy the third stage and have no impact on either the effort decision or on the future profits of the firm. For a contract such that me NtC^, is violatea out the NEC^ is satisfied, worker oeliefs are critical m determinina the mil extent of e.^.oropnation risk , and hence, the value of acceotinq the contract C. . This ma^/ provide a motive for the firm to signal Us workers wnen its internal price is /i. It is this motive which explains why the firm might be willing to pay efficiency wages. Frorri the workers' point of view, the effort decision in stage three depends on the current disutility of effort, worker beliefs abcui the productivity of the firm , and the expected gains from being in good standing at the eno of period / Let the equilibrium lifetimeexpectedutility of a worker employed with the firm be y and /.,, when tfie current internal price of the firm is r/? and //, respectively. Also, let the eouilibnum employment levels of the firm be L and L.. in states /77 and A/, respectively. Then the lifetime, discounted expected value of an employee under the contract C^ who has chosen the effort level e, is given by V KZ)v{e^. C^)= >'/.-^^-[e(i-^^)ni-e(i-.-^,)]/?.^^^,^}[y^-^^]-[i-8(i -^^)][i-/^^^^^^ 16 v/n.pre ■'^ IS tri<^ DroDeDiiuv inai the iirrr rerieaes on the contra'"t vis exLToonritiC'ri . r - P .( 1 - .V. )+ ( 1 -p Jv 1 - /V,,,,) , 5.,^ IS the proDaDihty that d wortcer in Qood stancnna st^.er penod / IS retained by the firm Qiven |u , ,=rp].s.= min (Z ,,,■'[ l-e( 1 - i=,)j Z ., '1, aria ; "^ 1 (/77 'ill t i s.^. is defined simildrly given (u ,_^ ,=/'/) Note that the individual employee takes 5.^ and 5,^,^, as parameters. The effort level used to evaluate tnese parameters is the common effort of the employee's coworkers. To better understand (3), consider the expression term by term, The first term is the wage minus the disutility of effort. The second term is the product of the probability of losing the oerformance bond, both through detec:ion of shirking and throijgh expropriation by the firm , and the difference between the value of being employee elsewhere m the subseguent period and i\\e value of the lost bond. The third term is the pi^oduci of tne probability that the worker is in gocc standing in period /+ i given that tne firm operates in that period, the probaoility that tne firm operates in period ^+ I . and the expected value 'o a wori er who is in good standing when the firm, operates in period <'+ 1 . Each employee under contract chooses e. to maximize ( 3.). Obsei" ve that ( 3) is linear m t\ so that the-^e is alwa\'s a corner oot-mum The condition that e,- 1 yields a maximum is termed the No Shirking Condition, NSC, and is given oy The first com.ponent of a worner's st^atei^ is governed by the empliT/men* accep' condition . EAC. This condition is g;ven by (5) max[ /(0,^J, y\ 1,^/;] ^ V Workers will not accept an employment offer when ( 5) is violated. The .:.econi3 comporieni of a worker's siraieijy is Qoverneo rjy tne reserve pool accepiance conduion, RAC S^rice There iS no exproprtatiori risK for those -workers who are ofiereo a Dosition in ine firms reserve dooi, tnis concition is Qiven by lb) \\-p..^.j ■■ T—. where g ^ ^ is tne orohability that a worker who is in the reserve pool in penod / gains empla/ment from the firm which is in state u in period /+ 1 . for u =/7?. n . g,^^ = mm n . max [0, ( Z - Z . + Z v)/ /? J) Let a^ and a^^. denote the equilibrium effort levels and le* A'^ and H^^^ denote the eauiiiDnum proPaoilities that the firm honors the contract m states m and /7, respectively. As we nave air^eaci/ noted, ^^j^t^^f ^^\,-'^k^ = ' Selow we demonstrate why this is necessarily the case It IS simple to see that .H ,H^, *0 For were this not the case, then from ( 6) it is apparent that no worker would he willing to pa-v to enter the reserve pool. Moreover , from (4) it is just as apparent that all emiployed workers would shirk Hence, the EAC reduces to Vy'- B . i rV ■{ I -^ r) > m this rase But sinre firm prnfi^ per employee would De 8 - w, and firm operation would cease after perioa ^ the firm would be oetter off oifenn.g an unacceptable contract in period t so that it could continue operation into per ioq ''+ 1 . In lemma 1 we show that intermediate values of H and .^^.can beruledout a? well- The imuition for this result is that were such ranaomizirig optimal . the firm would necessarily be indifferent between continuing operation and expropriating the bonds. But when the firm randomizes over its decision to expropriate the performance bonds or honor the contract, Us employees face some expropriation risk. As a result, a compensating differential must be embedded in the contract wage, to induce the employees to accept the expropriation risk The firm could offer an alternate contract, by reducing the size of the bonds posted by its workers, thereby eliminating ttie expropriation risk and, consequently, lowering the wage which workers find 16 occeptabie. When ine aitHmate oontrcict nas the prooerty thai it is less orofitaDie to the firm , vs-ere it m trie oiner jT^t.:;, :.riar, tne HQuiiibrium contract offered by the firm when in the other st.aie, workers' revised beliefs should be the sam,e whether the original contract or the alternate contract IS offered- Tnis is precisely tne requirement that the intuitive criterion imposes. '^ We demonsirate That an alternate contract with this property exists Therefore, by invoicing the intuitive criterion, an equilibrium with partial bond expropriation and an associated compensating differential would be undermined through the offering of such an alternate contract. Since the firm tionors the equilibrium contract and since the NEC_ is more restrictive m than the NEC..., , workers will not perceive expropriation risk at the contract C , regardless of their beliefs, if / > '-' , tnen the firm should be able to lower ,if' while Keeping the coniract in stale ,r, accepiaole, as long as workers' revised beliefs were unaffected We show that this car; be oone, acair; by invo^ioQ the intuitive criterion. Therefore, an equilibrium with ,i'„ > )>\_ rn u would be underminec. Note that this argument is not applicable to rule out ihe possibility that V^, > •'■' .when worker s would perceive expropriation risk at the contract ^' were it offered by the firm vvhen its internal price equals /?? Lemma 1 Suppose the separating equilibrium satisfies the intuitive criterion. Then ( i) //^, = //„ = 1 , ( ii ) /^ = '/ , and ( iii) if K > 0, then ^v = e.,= 1 . /?.' .' / -V? U III I i PrrjQV We first show ihat H - 1 and that if V > 0, then e = 1 . Suppose not. Consider an rri u m alternate contracUonstructed from ^ , call it ^ , where /'>'' ^W ,5 ^H d +c,for m m rn m rn rn m .^„. = P- ... + ( \- e^)L ^. !n essence, the contract C has a slightly larqer effective bond than h'f.. , the eftective bond resultmq from C , wittiout the expropriation risk. It also places ni III ' fn f- r- '* C^o snd Kreos explain the intuilive criterion as follows i am sendiog niessacie m which ought lo convince you thai I know /' For I would never wish lo send rr/ ;f ! know t . while if i know /" . and it" sending this nnessaqe so convinces you. then as you can see, it is in my interest to send it Ihe y^or>-ers who shirk under C into the reserve nool , alonq with those workers alreacN- in the m Tfit'c^'f;. dog! under C , and then averages the fee tne firm is colleciing from the former m ^B ->•'-_, with A . Note that when ^ isacceptabieand when workers emoloyed under ^ m m m m m put forth effort, the effective labor input and the wage rate under both contracts are the same. In this case the firm has the same lifetime discounted value when it offers C as when it offers m C , regardless of its internal price. Since either H < 1 or min(Z ^^n^^^M- minfZ /[l-e(l-(? )]Z ,1) = 5 , for u = /77, A/, since andp(a ,,C ) = 1 , the NSC is satisfied as a strict ineguality under C and, therefore, employees necessarily put forth effort under this contract. Since C.^ IS ootimal when the firm's internal price is N , it must be that ^'" V/^^K''^^^)-'^'^^^-';.^^' When ( 7) holds as a strict ineguality, which we assume for now, the intuitive criterion requires thatpla "^fr}^~ ^- Thecase where (7) holds as an equality is considered later in the proof. When 6>_ > 0, the E.AC for the contract C can be written as m m (6) ;^- -1 -(]-// )Z? ^ ^ , "^ '-^- ^ m mm 1 ^- /• Vr// - 'u ' mint M rV u \^-i^-e^)o]L^ r When 6' 1 , the EAC for the contract C can be written as m m 20 (9) -(i-9)(i-.^,j/?^ ^ ^^TT^ ^^ Similarly, the RAC for the contract C^ can be written as t>H [\-e )L {V -y ) ^^^' FTTT71 ^ n't ( I - ^ ) //t; rrnn{/?^ .max[0,Z^ -[ l -(1 - e^^ )ej z,^^ ]'K />; - /'^. ) _ ^ /? ( 1 + r "i /?? We will now show that (6)-( 10) irnoiy contract acceptarjiiitv for C Since th^rf- 1-, nn m shirking and no expropriation under ^ and since f l-( l-r' )9!Z le L , (3) implies the m IV m iTi iTi EACfor^ indeed, this condition holds as a strict inequalitv when ,V < ! Similarly, in m ^ multiplying(9)by(l-^ )Z^/[^_,^(!-r^)Z^],(iO}L)y Pl{R^-{ l-^^)/^i,ana addinq the results implies the RAC (or ^ In this case the condition holes as a sir ict mequal iiv tn when e^ < 1 and either H < 1 or A' , > 0, When the EAC holds as a strict inequality the firm can offer an alternative contract which yields higher profits by offering a slightly lower wage than W When the RAC holds as a strict inequality the firm can offer an alternative contract whh:> yields hioher profits by charqinq a slightly hiqher fee than F Moreover , from tne intuitive criterion workers should be certain that the internal price of the firm is m when they observe this alternate contract . since (7) holds as a strict inequality This shows that H = 1 and r' = i when K > 0, Similar reasoning rules out ^' > v . since were this the case (S) would hold as a strict inequality and the firm would have an incentive to upset the equilibrium by lowering its wage offer. 21 We turn to the Ccise where ( ?'■ holds '-s an eoualUv. Alter the contract C Vj ihe contract m C . were the two contracts differ onlv tr; me^r waae rates a^d '^noiovrnent leve^. L ~L~ m - ' ' n' m di ,^\)^^ dL )s small out Dosnive, and W ,^ - W ^^{k m^^ fDXK i J)i2- Wjx^iL^. Then Tx's m,C ) >U(/n,C ) and III /V, C ) < ri'' /"/, C^ ). Thus, the same araumem. as civen above mm m m can be applied to the contract C^ m A Similar construction can be given to generate the contract Cj^ Observe that if H.^ < 1 , then fi^^l^^^[]-si\-e^)] = [ dO'^H ]- d) l/^^]/{ \ ^ r) ^ [ dO'^^^i ]~ d) l^^^j/i \ ^ r). Thus, when /A. < 1 the firm prefers C^ to C^^ , given that its internal price is /?? , since C^ involves less bonds to exprooriate than C^ When i=., < 1 , either the firm prefers C^ to C^, t1 i1 ' t1 t1 Qiven that its internal once is m , aqam because C ^ involves less bonds ^o exorooriate than Cm , or an alternate contract, C ^ , can be constructed so thai m m , C ^ ' - ri' -' . C .. ) enc n( /V, Cm) > n( df ,Cm) The construction is the same as the one Qtven in the Daraci'aDh above n n except that in th^s case Z ^, ^ Z ^, is 'equired SS Let W r, denote the workers' reservation waqe inclusive of the disutility '^^i effort, W n - A " n 1 + rK /( 1 + r). Since ^ = K i K^., it must be that W\ i ,'■?-„ ^ ''^'m- indeed, by taMnq u u ni 1 1 111 h 1 1 account of the properties of equilibrium given in lemma i , one can solve for tne rent per worKer resulting from being employed when the firnVs internal price is dl M u r *d :r ?r -r Let L^ be implicitly de.tined '^i m\\ z^^ ) = W r,. Note that L < L^, even when H^ < H'. '^ It follows that L^'^L.,\ for if not , n ^, ^ n( dl ,C^ ) From ( 11 ) and the fact that ( I - A III// / / m 19 Were Z >Z ,. the firm could do oetler by iowerinq its employment to Z„, .putting Z -Z„ workers into the reserve pool when L ^ '> Z_. or cuttinq its waqe by ( I-Zj )Z^ ( 1^^,- ''' )/*! + /•)( 1/Z_-1/ Z 1^ m :) -i I M N u mm 22 t-) IS trie tranj'.tion prob.^tul'ity from stale '?/ to state A/, the expected aiscounted rent per worKer wnen tne t^rrn s iriterna! price is ■?',' cind tne tirrn's employment is i is mini i,,// ,1 -i :-/.'•■ '''n i',.- /■' ,\i' + ,^') *^^ By invokinq an araumerit similar to the one Given ■ / /■ • > t/ m trie proot oi iemma 1 , rnere is no ioss in assuming that the firm extracts ail future rents accruing to its worKers wnen its interna! price is m . Then from (11). lemma 1 , and assuming there are no redundant workers in the reserve pooi we nave (12) V^Z) = min(-^,li ,;, ^ ■ ^y/)=/'^^-^-^(/). ^^, -^--^^^^^ and /?Jl) =max(Z^,- Z,Oi Note -Pa' ^!"'- v/e-r ioecuality restnctino ^ necessarily nolds as and equality only v/nen the NcC hiOGs In essence, all tnat is left for tne firm to choose when its internal or ice is m is its level of employn^itint Thus the problem which determines the firm's optimal contract when its internal p'" 'ce equals /?? can he written as : f , ^ .J ■ , ,- , r i ,. L r ' r- I , \^ , III / ' (13) , _.^" m\{L)-iy^l^r^^L^ Subject to [— /^(Z)]Z i '" , , ^ ^^, Since Z is the solution to ( 13), it is evident that either Z = Z ^ or the N£C_ binds in .?;• /77 /77 m eauilihni.irn Note that in ( 1 3) .-'^Z ,., is the value of the rents which the firm can extract from Its workers, both from its empia/ees, m the form of v/age reductions, and from the workers in its reserve pool , directly in the form of entry fees. Observe that this amount is fixed, regardless of the choice of emiplcr/ment level. ''vhen / '^ /. Thai suct^i an alternative contract would be acceplaMe follows tiy a similar arqument to the one given m tt"ie proof of lemma 1 T A "" It 15 appropriate to compule these rents from the point of viev/ of play in stage three, after acceptance of the current contract has already occurred. Tnere i:> no reason for the firm to taKe any costly action in oraer lo convince its wor r.force that its internal price is /// , both because workers don't earn any rents and because workers view oond ex'propriation to be more likely in this state. When the firm's internal price is A'', {t]e situoiion is reversed. There may very well be a reason for the firm to pay a cost in order to convince its employees of its true internal price. For workers to be so convinced, the wage- employment pair , ( i^^U ), must satisfy the following signaling constraint, SC ( 14) i/^ > /77i ( £ )- f^Z ^max ( ^^^-JT^ — .^,^./ on. where f.,{ Z ) - 1/e - f^,{ L ) and FA L )= min{Z .,/Z ,i)( l- kV.-., that is, the firm utilizes efficiency wages, then 6\., < Z^_ , i.e. , there is less reliance A/ A' ' ^ /Y ,^ on performance bonds when the firm's internal price is A* than when the firm's internal price is /T/ . as one's intuition would suggest. Note however, that Z? < 1 /e in this case. The problem which determines the firm's optimal contract when its internal price is A/ is given by maximize (15) ; .A M- M/ r ( / \ F/\il)- WL Subject to :. ( 1 4), the SC, and 3^^{L)L < ( 1 + /' ) Note that the lower Poured constraint on W in ( 1 5) Is just the EAC Observe that when the 50 binds, the lower bound constraint on ^V may not bind This is the case where efficiency wages are 24 i.it.-il-ize L then aiong the SC we (iW m f( L )-W ^\lt I When Ihisocturs it must r.ie that ,",,, = and >'/,_,= >f'',-,. !p this case i>' ,i^\. _!/e We refer tosucn an eGuiiibnurr; as a fail DonGinrjequiiibnurrK since aii of theeiTi:i:ovi?BS' mCenTive to put forth eitort is provided via pertormance ponas. In a full Ponding eGuiiipriurn , / .^^ = y' ^, - V . Thus, one would not associate such a con'ractuai eauilibnum wiih involuntary u unemployment, however , a full bonding equilibrium may be inefficient, relative to the first oest, because the NEC may bind, yielding a corner solution in ( 13), because the SC may just bind, yielding a corner solution in ( 15), or the NEC., may bind, also yielding a corner solution in ( 15). Let Z/y be implicitly defined by //]'( Z/y) = Wr,. Then full bonding equilibrium can be characterized as follows. Proposition 1 : In a full Donamg equi Ivoc uim which satisfies the miuiti ve enter ion ana assumption 1 >■ *■ ( i) either Z^, = L^ or L ^ ' Z^, , the NEC^ is binding, and 3^^ = 1 /e, 5nd ( ii) either L^ = Zyy or Z .. < L^^ in which case 5 ^^. = 1 Z6. In the latter case either 'he SC bindsand( A/-/7?)f'(Z;^) i IZeor the NEC., binds. // 1 1 Proof : ( i) follows immediately from e.Kamination o^' ( 1 3), From examnnation of ( 1 5) 't follows that when its internal price is M the firm chooses its single per lod profit rriaxim.izing employment level , if both the SC and the NEC^ do not bind. When either the SC or the NEC,, binds, the firm I i i i does not utilize redundant bonas, i.e., B .. = 1 ze. When the SC binds, it must be thai an increase in r/ employment, accompanied by the required wage increase to satisfy the SC. does not raise firm profit. This yields the c-ondition, ( /Z-/77)f'( Z..) < ize. SS Proposition 1 says that deviations from the single period profit ma.^imizing solution occur because there is risk of bond expropriation, either by thefirmi when its interna! price is m . directly through its own contract offer or indirectly through the SC by masquerading as if its i.^J inierna' pr:ce '^vere '", v Dy "se mt- v^hen it? intemai orice 13 /Y direoily through Us own cor^:r3Cv offer v/r;pr 5 fu; : oonding equ^^triurn exisT? where the SC binds, ^.Jx^. conaition that the firm ^'inds w o;::t;rr;a; to oav workers lust tneir reservation wage when its internal price is M i.T.pnes That 11 rr,;jst be too oostiy i\\T tne firm to signal its type so that it can expand Us employment Noie that m a separating equilibrium , deviations from single period profit miaxim ization cannoi occur in both states. However , it is possible to have a full bonding, pooling equiiiDnum where Z^, = z .,. the NEC is binding, the SC is binding, and it is too costly for the firm 10 signal its type so that it can raise employment when its internal price is M. iV.!i Efficiency V/dge EGuilibriurr! When the ^C Dinos in ( ' 5 j jna >4v, '* >'^''o- F ^^ ^•''- ''1^'^' oavs Us worKers above tneir / / hit reservation v.age :.: :V,gnai tha: ".:.:'. miernai \:)T\z^ is M . 'We refer to such an equilibrium as an efficiency waae ecurMurium. Ooiv.rve that this is miore likely to occur the qreaier is the difference, n- m , anc the qreaier is the quotient, /7/m . We characterize efficiency v/age equ ; 1 1 u r 1 u m as f \ I ov^ s. P'rooosition 2 : in an e:ficient7 wage equiiiDnum which satisfies the intuitive enter ion and assumption \ (0 either / „^, = L ^^ or Z^^. < Z^^ , the NEC^ bmds, ano B = 1 /e-/" , and (11) L^^L^,, rn^-.i^^)- ^r^y. z^^,= i/e-/-/,^,and/77l-(Z/^)^z?,.^i M'(Z/.^) if the NEC^, doesn't bmc tnen A/f'( Z ^) < m{'{ Z ^)+ 1 /e II / / // Proof ( i) fo'lows ;rimed)atelv from examination of (13), Since the SC binds, it follows from ( 14) and (15) that 5,, = I /e - f.. V/hen the NEC^ doesn't bind the first order condition for the optimal emp!i>/ment level m ( 15) is 27 As-iurriDticn i oar' De rRwrnteri as f,^. > ^-'^a /V- /t? )/ A^ Sut'StUutina in.? into the Tirst v-eauelitv IP ( * ) ana suDtracting .^i'^, f rem both sides yieids if It fellows that riyi l^.) > >v'^^, Irom which Z .. < Z/y also follows When the NEC., does bind the first orcer condition for the optimal employment level in ( 1 5) is lust the first inequality in (*). The remaining argument is similar to the one just given. SS When efficiency wage equi iihnum exists and the NECr.., doesn't bind, which we assume in the following discussion, there will be a continuum of such equilibria. See figure 4 for C'cp ificat ion on this coint. We focus on the particular member in this class which yields the highest vclu.e o'' the firm , where the firm's isoprofit curve in state M is tangent to the 50 from the ioVi 2^ -i'V 'his member is depicted as point A in figure 4. From proposition 2 it follows that there i; underempVjymen* m such an equilibrium. We can now reconcile this underemployment result with the charging of up front fees when the firm is m the low productivity state. First, note that ttic firm cannot charge the up front fees in the high productivity state, because doing so would violate the oC Thus, the best the firm can do to recoup the rents it pays its employees m the pr.ocess of signaling is to chacige fees in the low productivity state Observe that all the rents are, m fact, recovered by the firm but the outcome is not as good as it would be were the firm able to charge the fees in the high productivity state. The difficulty is that the firm cannot credibly precommit to a higher employment level when in the high productivity state When the firm pays efficiency wages m the high prcductivity state it, in effect, creates a positive externality for the firm in the low productivity state, because the entry fees are collected m the low productivitv -^ Observe thai B ^, il)l i5 not differentiable at Z - Z „. Thus, there will be a kink in the SC al this entploynient levt^ti Because of the kink in the SC there need not be a tangency betv/een the SC and the relevant isoprofit curve ;ri equilibriunv "^ Since this tangency occurs at the kink in the SC, what we n-iean is that the isoprofit curve is tangent to the curve generated by the constraint (14), as written, ignoring the possibility of job rationing. isoprofit curves in state M ^^ L^ Lt L^ ^M Figure ^ state and the magnitijce oi the enirv tee cepends on the size of the eft iciencv waoe Sequent ia i ratinnaiitv necessitates that ihe firm rnaxim^ze current Denoo protit when deciding whicn contract to offer . ruling out tne possioilitv that the firm internalizes this apparent externality This IS why the equilibrium is inefficient. This view of firm equiiibrium differs fronri the standard efficiency wage equiiionum. The signaling aspect of equilibrium offers some very interesting hypotheses concerning wage determination. For example, larger scale firms, those with higher values of //, should pay higher wages, as should firms v/hich have greater volatility in their value. Thus, this signaling approach provides an explanation for industry-vviae v^age differentials which does not require assuming that fTioniioring intensity vanes across firms, the standard explanation of wage differentials proviced by eff icienc/ wage theory. -^ iV.l!; Ruiinq Out Comoerisatinc Differentials in Poolino Equilibrium The signaling equilibrium whicn v/e have demonstrated is not contingent on workers' initial beliefs, as long as workers are noi certain that the firm's internal pric^ is A/. This result may appear puzzling if workers are almosi certain that the firm's internal price is A/, why should the firm engage in costly signaling'-' That is, shouldn't a pooling equilibrium prevail in this case'i^ In such a pooling equilibrium p , =a .and there will be a small amount of expropriation risk. The expected capita! loss that a worker faces in such a pooling equilibrium isp ./^. and the effective performance bond, i.e. , the value of the performance bond net of the expected capital loss, is ( 1 -p .)f. Let Alp ,) denote the expected future rents per worker in such a pooling equilibrium. ( 1 8) n^^) = ( 1 -p p( 1 - d)( W,^- w^)i{r^d). -6 25seeKatz(l986). -^ Again, this assumes thai employment in the pooling equilibrium does not exceed L n' 29 Trier; r?, = l/ie ( i-p .)]-.'^(B ,)/M-|3 ..'and >■>',= >/>-/"(? J +P ,r.. Note that ine cont^acT wage contains a term whict^ eauais the exDec'ec caDital loss due to Dond exoroDr^ct^on in the i'oiiowing proDOsition we show tha; sucn pooiing equilioria are inconsistent with ihe mtuitive criterion. Proposition 3 : if the equilibnuni satisfies tne intuitive criterion ana « ^ > , then tnere Goes not exist a pooling equilibrium where the firm pays a compensating differentia: Proof : Were such an eouilibnum to exist, then fi,- yV, = I /e - V/'r,, independent of p .. Thus, as tin ;■ long as employment stays constant, the firm has no iricentive to affect p _. when its internal pr-ice eauals /77. However, ;H-' is increasing in p ,, so the firm has incentive to signal its internal p"'C? wnen ihis price equals A'. In particular, if ine firm were to offer an aUema'econtraci wnere the bond was reduced by d^^, the wage was reduced bv p . d^^; and emoloyment was slightly lowered, then the intuitive criterion implies that workers snouid be certain that the firm s iniernai price is A/ upon observing this alternate contract Indeed, as long as workers are certain tnat the firm is in state A/ upon ooserving the alternate contract, it follows that the alternate contr.act has ootn a larger effective bond and a larger effective wage tnan the original coniraci, Tnus. worker:, should both accept the alternate contract and put forth effon. once ine contraci is accepted. Tne availability of such an alternate contract undermines the pooling equilibrium, .S.S Notel : When a , = the araument in the proof of proposition 3 breaks down, since 'nere is no need to pay a compensating differentia! m this case. Indeed, C* is discontinuous at a . = 0. Note 2 : It might appear that there exists pooling equilibrium wher e there is no risk of oond expropriation but where the waoe paid is less than 'fVr,. In such an eduilibnum, , the firm fines r. that signaling to expand its employment is too costly, wnen in state A/, and the i''(^T^ fines it ad^'/antageous to pool to avoid paying a nigher w.age, when in state m. By essentially the sam,p orgiiiTient 3; Ine cne a^ven in :r