Employee Bargaining Power, Inter-Firm Competition, and Equity-Based Compensation

Transcription

1 Employee Barganng Power, Inter-Frm Competton, and Equty-Based Compensaton Francesco Bova Joseph L. Rotman School of Management Unversty of Toronto January 4 th, 04 Abstract Prncpal-agent theory suggests that equty ncentves should lead to greater effort from employees when effort s both costly and unobservable. However, due to free rder problems, ths ncentve effect may be lmted when a frm employs a large number of workers. It s not clear then, why publcly-traded frms that employ many workers would choose to compensate ther employees wth company stock. I provde a possble explanaton that s consstent wth several emprcal fndngs. Utlzng a model of employee barganng power and nter-frm competton, I fnd a unque, pure strategy equlbrum where each competng frm offers an equty stake to ts employees provded employee barganng power s suffcently low and nterfrm competton s suffcently ntense. Ths outcome arses because offerng employees an equty stake mproves wage effcency and allows each frm to become more compettve wth ts rval. However, the equlbrum s a Prsoner s Dlemma for the frms owners as they, and n some cases ther employees, would be better off had the owners been able to commt to compensatng employees wth wages only. I thank Vktora Dser, Bjorn Jorgensen, Bran Mttendorf, N. V. Ramanan, and semnar partcpants at the 04 AAA Management Accountng md-year meetng, the 03 Beyster Symposum, and the Unversty of Toronto for helpful comments. I am grateful for fundng from the Unversty of Toronto and the Lous O. Kelso and Accurate Equty Fellowshps whch fund research on employee ownershp. All errors are my own.

2 . Introducton Hölmstrom (979) suggests that one way to elct a hgh level of effort from an agent when agent effort s both unobservable and costly, s to make her compensaton contngent on the frm s profts. However, as Hölmstrom (98), Huddart and Lang (005), and others note, when too many employees are ncentvzed wth contngent pay, a free-rder ssue arses that may cause the ncentve effect of contngent pay to be muted. Specfcally, as the number of employees ncreases, ndvdual workers may not exert extra effort because they can make only /N dfference to the frm s profts and /N becomes very small when N, the number of employees, becomes very large. In such a settng, as Oyer (004) eloquently suggests, equty ncentves may have no ncentve effect, and the best response for all employees may be to not exert effort. Gven ths nsght, t s perhaps puzzlng that publcly-traded frms, whch employ many workers, often compensate employees wth equty n the company. Several papers have put forth possble explanatons to ths puzzle. For example, Oyer (004) suggests that a frm s owners may compensate employees wth equty stakes n order to ndex ther compensaton to outsde optons. In ths respect, equty-based compensaton mght be useful as a tool for employee retenton. Separately, Lazear (004) and Arya and Mttendorf (005) post that a frm s owners may compensate ther employees wth equty-based compensaton for sortng purposes, where employees reveal nformaton about ether the frm or ther own abltes by, puttng ther money where ther mouth s. I propose an addtonal factor that may lead a frm s owners to compensate employees wth equty n the company. I suggest that a frm s owners may offer an equty stake to ther These alternate explanatons appear to be borne out emprcally. Oyer and Shaffer (005) consder three economc justfcatons for provdng equty compensaton to employees ncentve algnment, sortng, and employee retenton and fnd evdence consstent wth the latter two. Core and Guay (00) and Ittner, Lambert, and Larker (003) also fnd evdence consstent wth frms usng equty-based pay for employee retenton purposes.

3 employees n order to glean concessons on other facets of employee compensaton. These concessons lower the frm s cost base and make the frm not only more proftable, but also more compettve when facng a rval. I generate these nferences from a model of employee barganng power and nter-frm competton. In the frst stage of the model, a frm s owners decde whether to compensate ther employees wth wages only or wth wages and an equty stake n the company. In the second stage, rather than compensate employees only up to the pont where employee partcpaton s nduced (.e., the employees reservaton wage), the owners and employees negotate over the terms of the compensaton (.e., the level of wages and, n cases where equty compensaton s offered, the percentage of the frm that wll be gven to employees). In ths respect, the model allows for an neffcent labor market where employees extract above-market rents from the frm, contngent on ther barganng power. In the thrd and fnal stage, each frm makes producton decsons as a functon of negotated employee compensaton and the ntensty of nter-frm competton. I fnd that whenever a frm s owners offer both wages and an equty stake to ther employees, the frm s more proftable than f the owners offer employees wages only. Ths outcome arses because an equty stake n the company ntroduces a competng ncentve for employees to maxmze frm profts whch, n turn, are decreasng n employee wages. Whle the frm s profts are strctly hgher when equty compensaton s offered, the frm s owners may or may not be better off. Specfcally, whle the frm s more proftable (.e., the sze of the pe s bgger), the owners remanng share of the profts s lower (.e., the owner s slce of the pe s smaller), as offerng an equty stake to employees dlutes the owners poston n the frm. In a settng wth no competton, the costs to dlutng the owners holdngs n the company outwegh Many factors such as unonzaton, local unemployment rates, and frm-borne employee swtchng costs can lead to neffcences n the labor market that allow employees to extract rents above the compettve market wage (see Bova, Dou, and Hope 03, Lndbeck and Snower 986, 00).

4 the benefts to more effcent wages and greater frm profts. As a result, n a monopoly settng, owners have a strct dsncentve to offer employees equty compensaton. In a compettve settng (.e., the frm competes aganst a rval), the owners optmal strategy depends on the barganng power of employees and the ntensty of nter-frm competton. Notably, I fnd a unque, pure strategy equlbrum where each competng frm offers a wage and an equty stake to ts employees (.e., the employee ownershp equlbrum) provded employee barganng power s suffcently low and nter-frm competton s suffcently ntense. Ths outcome arses because an equty stake generates more effcent wages whch, n turn, reduces each frm s cost base (as n the monopoly settng). Ths reduced cost base not only makes the frm more proftable, but also allows each frm to become more compettve wth ts rval. However, the equlbrum s a Prsoner s Dlemma for each frm s owners, as both frms owners would be better off had they been able to commt to offerng ther respectve employees wages only. Moreover, n settngs where competton s suffcently ntense, not only are the frm s owners worse off by offerng an equty stake, but so are the frm s employees. Importantly, the model s results are consstent wth several emprcal fndngs. Frst, there s a large emprcal lterature that fnds a postve correlaton between equty-based compensaton and frm productvty and proftablty (see for example, Conte et al. 996, Km and Oumet 03, Jones and Kato 995). A plausble explanaton for ths outcome s that equty compensaton leads to greater worker effort whch n turn drves greater frm producton and profts. An alternate explanaton however can be provded by the model. Specfcally, when equty compensaton s offered, employees also agree to more effcent wages. More effcent wages lead to a lower cost base for each frm, whch n turn leads to greater producton and 3

5 hgher profts. Thus, even absent an ncentve effect related to worker effort, compensatng employees wth equty n the company may lead to greater output and hgher profts. Second, there s mxed evdence regardng the frm and stakeholder benefts to adoptng employee ownershp plans n publcly-traded companes (e.g., Blas, Conte, and Kruse 996). In partcular, there have been several puzzlng fndngs related to the sze of employee equty stakes and varous stakeholder outcomes. For example, Km and Oumet (03) suggest that when a frm compensates employees wth small equty stakes n the company, not only s the frm more proftable, but employees extract more of the surplus generated followng the equty grant. Conversely, Km and Oumet (03) and Faleye et al. (006) fnd that, when employees are granted a large equty stake n the company, the effects of employee ownershp are muted and, often, all partes are worse off. Based on these emprcal observatons, a frst queston mght be to ask why frm and stakeholder outcomes vary wth the sze of employee equty stakes. A second queston mght be to ask how the decson to grant large equty stakes arses endogenously, f large equty stakes appear to make both owners and employees worse off. A possble explanaton arses by assessng two mportant comparatve statcs n the model. Specfcally, any tme the employee ownershp equlbrum s supported, the optmal equty stake (wage) for each frm s ncreasng (decreasng) n the compettveness of the market. So, when a frm has a near monopoly n ts ndustry, we can expect employees to be compensated wth a small equty stake and a hgher wage. Conversely, when the frm faces ntense competton from a rval, we can expect employees to be compensated wth a large equty stake and lower wages. When equty stakes are farly small (.e., settngs where competton s more muted), I fnd that employees are better off wth equty compensaton than wth wages only. Employees 4

6 are better off because ther wages are stll relatvely large and they enjoy a small share of the frm s profts when the frm s profts are also relatvely large due to less competton. Ths result s consstent wth the fndng that when employees own smaller equty stakes n the company, they often enjoy more of the ensung surplus (.e., Km and Oumet 03). Conversely, when equty stakes are large (.e., settngs where competton s more ntense), I fnd that, not only are the frm s owners worse off by offerng an equty stake, but so too are the frm s employees. Ths outcome ensues as wages are relatvely low and, although employees enjoy a larger share of the frm s profts va a larger equty stake, the frm s profts are also comparatvely low because compettve pressures are hgh. Interestngly, the model nevertheless suggests that we should expect large employee equty stakes to arse endogenously n hghly compettve settngs, despte owners and employees beng worse off than f owners offered wages only. Fnally, I provde the 009 contract negotatons between the Unted Auto Workers (UAW) and General Motors, Ford, and Chrysler, as a practcal example of the tensons descrbed n the model. It s mportant to note that the auto ndustry s characterzed by ntense nterndustry competton and that the UAW entered ths partcular contract negotaton wth reduced barganng power due to the Fnancal Crss. 3 Gven these ponts, several outcomes that followed the negotatons appear to be consstent wth the results generated by the model. Frst, employees made steep concessons to ther cash wages (e.g., entry poston hourly wages were reduced to $4/ hour) n return for large equty stakes n the company and proft sharng arrangements. 4 Second, all three frms, as opposed to only one frm, agreed to contracts wth 3 The reduced negotaton leverage was drven by the U.S. government s threat to push G.M. and Chrysler n to bankruptcy f the UAW dd not make concessons

7 lower wages and benefts but larger equty stakes and proft sharng. 5 Thrd, UAW members became some of the largest employee owners of publcly-traded stock n the U.S. 6 Fourth, the wage concessons appear to have ncreased both producton and profts at all three frms. The combned analyss hghlghts employee barganng power and nter-frm competton as two mportant factors that may drve both the exstence and the level of employee ownershp n a frm and, more broadly, an ndustry. The model s results also provde several nsghts that may explan that documented varaton n stakeholder outcomes arsng from owners compensatng ther employees wth equty, ncludng a potental explanaton for how employee ownershp arses endogenously even when both owners and employees would be better off had employees been compensated wth wages only. The paper proceeds as follows: Secton presents the model and results, Secton 3 provdes lmtatons and mplcatons, and Secton 4 concludes.. Model The analyss encompasses a sngle perod model set n three stages. To hghlght the mportance of competton n the equlbra, I present two settngs a benchmark settng wth no competton (.e., one frm has a monopoly) and a focal settng whch ncorporates competton (.e., two frms compete n a duopoly). For brevty, I descrbe the stages of the game for the duopoly settng, but note that they are dentcal to the monopoly settng, save that n the monopoly settng there s one frm nstead of two. 5 The model predcts that, n equlbrum, ether each frm offers wages and an equty stake or each frm offer wages only to ts employees. 6 Employees own roughly 7.5% of G.M. s shares, over 0% of Ford s shares, and 55% of Chrysler s shares 6

8 In the frst stage of the game, each frm s owners decde whether to offer ther respectve employees wages only or wages and an equty stake n the company. In the second stage of the game, each frm s owners and employees negotate over the terms of the compensaton (.e., the level of wages and, n cases where equty compensaton s offered, the percentage of the frm that wll be gven to employees) wth the negotated outcome drven by the degree to whch employees have barganng power over ther respectve owners. In ths respect, the model allows for an neffcent labor market where employees can extract above-market rents from the frm, contngent on ther barganng power. In the fnal stage of the game, each frm sets producton to maxmze profts, prces are realzed, and profts accrue to owners and employees provded employees have an equty stake n the frm. The game s three stages are represented n Fgure. Fgure Tmelne Each frm s owners smultaneously chooses whether to compensate ther employees wth wages only or wages and an equty stake. Each frm s owners and employees smultaneously negotate over the level of wages, and n cases where an equty stake s offered, the level of equty gven to employees. Quanttes are smultaneously chosen by each frm, consumers purchase, and each frm realzes ts profts a porton, z, of whch accrue to employees.. Monopoly Settng To provde a benchmark settng, I frst assess a model wthout competton. In ths settng, the tmelne s dentcal to the one descrbed n Fgure, but the focal frm faces no rval compettor. Consumer demand for the frm s product s represented by the followng lnear (nverse) demand functon, P q, where P s the frm s product prce and q s the quantty 7

9 produced by the frm. 7 I assume that the frm has one nput to producton, labor, and that there are constant returns to scale so that one unt of labor s used to produce one unt of product. 8 The frm pays a wage, w, where w 0, for one unt of labor and the compettve market wage per unt s, c. Fnally, c <, where represents the demand ntercept. To generate the subgame perfect equlbrum, I work backward n the game. In the thrd stage of the game, gven the negotated employee wage, w, the frm s chooses q to maxmze ts proft functon 9 : Max q[ q] q[ w] () q The frst order condton n () wth respect to q yelds qw, ( ) the optmal quantty as a functon of employee wages: w qw ( ) () Pluggng () nto () yelds frm profts as a functon of the employee wage, ( w). In the second stage, the frm s owners and ts employees negotate over the level of wage, w, and n cases where the owners offer an equty stake n the frm, the level of equty stake, z, gven ( w). The frm s owners seek to maxmze, Swz (, ), the resdual profts that do not accrue to employees: 7 Ths type of demand functon arses when consumers maxmze a quadratc utlty functon subject to a budget constrant as n Sngh and Vves (984) 8 Ths modellng assumpton maps n to the UAW example descrbed n the Introducton. Specfcally, UAW employees are pad an hourly wage, w, of $4/hour for drect labor, and drect labor hours are sgnfcant nputs n to producton at GM, Ford, and Chrysler. 9 When an equty stake s offered to employees, employees are compensated wth cash wages based on the pece rate wage, w, that s set before producton, and ther share of company profts, z, that s garnered after quantty s set and profts are realzed. Thus employee equty stakes, f they are offered, do not mpact the cost of producton. 8

10 Swz (, ) ( z) ( w) (3) The frm s employees seek to maxmze, E( wz, ), the sum of ther wage and equty-based compensaton: E( wz, ) qw ( )[ wc] z[ ( w)] (4) The employee partcpaton constrant s Ewz (, ) 0. 0 To generate the optmal compensaton levels n the second stage, the owners and employees set the wage, w, and n cases where the owners offer an equty stake n the frm, the level of equty stake, z, to maxmze the generalzed Nash product below: [ Ewz (, )] [ Swz (, )] (5) represents the employees negotaton leverage and (0,). As, employees glean next to all of the negotaton leverage and are effectvely the monopolst suppler of labor. As 0 Whle I assume w 0, I do not assume w c. Thus, I allow for w c. w c may arse provded employees are compensated wth a large enough equty stake n the company, such that Ewz (, ) 0. Such a contract would be an example of fnancal bootstrappng (.e., a contract where employees forgo cash wages n return for an equty stake n the company). In (5), employees negotate to maxmze the sum of aggregate wages and equty stakes across all employees. Ths modellng choce s consstent wth evdence that barganng often takes place between owners and employee representatves that negotate on behalf of a group of employees. Addtonally, as the model assumes an neffcent labor market, I note that the market for labor s often neffcent n precsely those settngs where representatves negotate on behalf of a group of employees (e.g., collectve barganng groups). 9

11 0, employees glean next to none of the negotaton leverage and the market for labor approaches perfect competton. The outcome n the game s second stage depends on whether the frm s owners offer wages only or wages and an equty stake to ther employees n the frst stage. As a result, I derve the optmal outcomes negotated n the second stage condtonal on the type of compensaton offered n the frst stage... The frm s owners offer wages only If the frm s owners offer to compensate employees wth wages only, I set z 0 n (5) and both partes choose w to maxmze the generalzed Nash product n (5). The frst order condton of (5) wth respect to w yelds w( ). Substtutng w( ) and the frm s optmal quantty from () nto (), (3), and (4) yelds the frm s equlbrum profts, w ( ), the owners share of w w the profts, S ( ), and employee compensaton, E ( ), respectvely. The equlbrum outcomes when owners offer to compensate ther employees wth wages only are summarzed below: w c( c) w ( )( c) w ( )( c) w, q ( ), E ( ) 4 8 S ( ) ( c ) w w ( ) ( ) 6 (6) As expected, n a model wthout equty ownershp, wages (frm profts) are ncreasng (decreasng) n the employees negotaton leverage. I denote any settng where a frm s owners compensate ther employees wth wages only wth the superscrpt, w. 0

12 .. The frm s owners offer wages and an equty stake n the frm If the frm s owners offer to compensate employees wth wages and an equty stake n the frm n the frst stage, the contract that arses as a result of the barganng process s gven by the parameter values w and z that maxmze the generalzed Nash product n (5). 3 Solvng the frst order condtons of (5) wth respect to w and z yelds the employees wage, w, and the employees equty stake, z( ). Substtutng the wage, w, and optmal quantty from (), nto (), (3), and (4) and the equty stake, z( ), nto (3) and (4) yelds the frm s equlbrum profts, z z owners share of the profts, S ( ), and employee compensaton, E ( ), respectvely. The equlbrum outcomes when the frm s owners offer to compensate employees wth both a wage and an equty stake are summarzed below: z, z z ( ), w z c, q z c, z ( )( c) S ( ), 4 E z ( c) z ( c), 4 4 (7) Note that the wage s strctly lower (.e., employees are pad the compettve wage rrespectve of barganng power) when a frm s owners offer to gve employees an equty stake n the company. Ths outcome arses as an equty stake ncents employees to focus on maxmzng frm profts, and frm profts are decreasng n employee wages. Note also, that the 3 I denote any settng where a frm s owners compensate ther employees wth wages and an equty stake wth the superscrpt, z.

13 optmal compensaton structure when a frm and ts employees negotate over both an equty stake and wages s a two-part tarff, where the employees are pad the reservaton wage and the ensung profts are dvded proportonally dependng on whch party has more barganng power. 4 PROPOSITION. In a market wth no competton:.) owners never offer ther employees an equty stake n the frm..) the frm s more proftable and employees are strctly better off when owners compensate employees wth both wages and an equty stake than when owners compensate employees wth wages only. As wages are strctly lower n a model where employees have an equty stake, t s ntutve to see that the frm s more proftable due to a lower cost base. The same however s not true for the share of profts that accrue to the frm s owners. On the one hand, provdng employees wth an equty stake n the company reduces employee wages to the reservaton wage and leads to greater frm profts than f the frm s owners compensated employees wth wages only. On the other hand, compensatng employees wth an equty stake dlutes the owners equty poston, meanng that they accrue a smaller porton of frm profts. When the frm has a monopoly, ths latter force domnates for all 0,, and owners are worse off f they offer an equty stake. Thus, despte the frm beng more proftable and the employees beng better off when compensated wth an equty stake, the owners wll never opt to offer equty compensaton 4 For another example of generalzed Nash barganng over a two-part tarff, see Arya and Mttendorf (03).

14 to ther employees n a settng wth no competton. 5 A natural concluson from ths result s that we should not expect a frm to compensate ts employees wth equty n order to make ther wage bll more effcent. In the next secton, I reassess ths concluson n a compettve settng.. Compettve Settng In the compettve settng, two frms compete n a duopoly. Consumer demand for each frm s product s represented by a lnear (nverse) demand functon P q kq where P s j frm s product prce, q s the quantty produced by frm, and, j,, j. k s the substtutablty parameter and k (0,]. When k, the frms produce perfect substtutes. As k 0, each frm has a near monopoly for ts product. Thus, competton ntensty s ncreasng n k. As n the monopoly settng, I assume that each frm has one nput, labor, and that there are constant returns to scale so that one unt of labor s used to produce one unt of product. 6 The cost to each frm for one unt of labor s the wage, w, where w 0 and the compettve market wage per unt s c. I also assume that k cc * ( k), as ths assumpton guarantees w 0 4 k rrespectve of the type of compensaton offered by each frm s owners n the game s frst stage. Fnally, c <, where represents the sze of the market. 5 Although an equty stake should not be granted to employees n order to glean wage concessons n a monopoly settng, ths does not preclude the possblty that owners of a monopoly mght provde equty-based compensaton for other reasons. 6 As employees are nput supplers, the analyss also contrbutes to the lterature that assesses the effects of competton on supply chan contracts (see for example, Arya and Mttendorf 007 and Arya, Mttendorf, and Yoon 03). 3

15 To generate the subgame perfect equlbrum, I work backward n the game. In the thrd stage of the game, frm chooses q to maxmze ts profts n (8), gven ts negotated employee wage, w, and q j : Max q [ q kq ] q[ w ],, j,, j (8) q j Solvng the two frst order condtons n (8) yelds the symmetrc equlbrum quanttes as a functon of each frm s employee wages and product substtutablty: kw kwj q( w, wj, k), j,, j 4 k (9) Substtutng the quanttes from (9) nto (8), yelds frm profts as a functon of each frm s employee wages and product substtutablty, ( w, w, k). j In the second stage, as n the monopoly settng, each frm s owners and ther respectve employees negotate over the level of wage, w, and n cases where the owners offer an equty stake n the frm, the level of equty stake, z, gven expected ( w, w, k). Each frm s owners j seek to maxmze, S( z, w, wj, k ), the resdual profts that do not accrue to ther employees: S ( z, w, w, k) ( z ) ( w, w, k), j,, j (0) j j 4

16 Each frm s employees seek to maxmze the sum of ther wages and equty stakes, E( z, w, wj, k ) : E ( z, w, w, k) q ( w, w, k)[ w c] z ( w, w, k), j,, j () j j j To generate optmal compensaton levels n the second stage, each frm s owners and employees set the wage, w, and n cases where the owners offer an equty stake n the frm, equty stake, z, to maxmze the generalzed Nash product below: [ (,,, )] [ (,,, )] j j,,, E z w w k S z w w k j j () represents the employees negotaton leverage and (0,). As n the monopoly settng, each frm s optmal compensaton structure generated n the second stage s drven by the type of compensaton offered by the owners n the frst stage. However, unlke the monopoly settng, each frm s optmal compensaton structure also hnges on the type of compensaton offered by the rval frm s owners. Thus, there are three possble strategy sets n the frst stage: each frm s owners offer wages only; each frm s owners offer both wages and an equty stake; and one frm s owners offer wages only and one frm s owners offer both wages and an equty stake. I assess the optmal outcomes negotated n the second stage condtonal on each of the possble strategy sets n the frst stage... Both frms owners offer wages only 5

17 If both sets of owners offer wages only n the frst stage, then nether frm s owners offer an equty stake to ther employees and z z 0 n (). In ths settng, each owner/employee parng smultaneously solves the frst order condton of () wth respect to w, yeldng each employee group s optmal wage, w, k and wage, w, k. Substtutng each frm s optmal quantty from (9) ww, nto (8), (0), and () yelds each frm s profts, (, k), owners share ww ww of profts, S ( ), and employee compensaton E ( ), respectvely. The equlbrum outcomes when both sets of owners offer wages only to ther employees are summarzed below: ww ww 4c ck w (, k) w (, k) 4 k ( )( ) ( k)(4 k), q ww (, k) q ww (, k) c ( )( ) ( ) (, ) (, ) k E ww k E c ww k ( k) (4 k), 4( ) ( ) ww (, ) ww (, ) ww (, ) ww (, ) c S k S k k k ( k) (4 k). (3) As n the one frm case, t s easy to see that employee wages (frm profts) are ncreasng (decreasng) n employee barganng power when owners offer wages only to ther employees... Both frms owners offer wages and an equty stake If both sets of owners offer wages and an equty stake n the frm to ther employees, each owner/employee parng smultaneously solves the frst order condtons of () wth respect to w, and equty share, z, yeldng the optmal wage, w, k, and optmal equty stake, z, k 6

18 for each frm. Substtutng each frm s optmal quantty from (9) and wage w, k (0), and (), and each frm s equty stake z, k nto (8), nto (0) and () yelds each frm s zz zz optmal profts, (, k), owner s share of the profts, S ( ), and employee zz compensaton, E ( ), respectvely. The equlbrum outcomes when both frms owners offer wages and equty stakes are summarzed below: ( ) z zz (, k) z zz (, k) k, (, ) (, ) c k w zz k w k zz k 4 k k ( ) (, ) (, ) c ( c) k q zz k q zz zz zz k, E (, k) E (, k) 4 k k (4 kk ) ( )( c) k zz zz (, ) (, ) S k S k (4 kk ),,, 4( ) zz (, k) zz (, k) c (4 kk ). (4) LEMMA. When both frms owners offer wages and equty stakes to employees, equty stakes and wages are ncreasng and decreasng n product substtutablty, respectvely. The outcomes n Lemma are drven by two forces. Frst, the more compettve the settng, the more mportant t s for the focal frm to glean a compettve advantage over ts compettor. Second, the larger the equty stake, the more employees focus on maxmzng frm profts whch are decreasng n wages. Thus, t s perhaps unsurprsng that n hghly compettve settngs, we observe employees wth the hghest equty stakes and the lowest wages. Fnally, 7

19 note that an mplct takeaway from the analyss s that whenever both frms owners offer equty stakes to ther employees, equty stakes substtute, as opposed to complement, wages. Ths substtuton effect s at ts largest when competton s at ts most ntense and n turn, equty stakes (wages) are at ther hghest (lowest). Ths outcome maps n to the Km and Oumet (03) fndng that wages decreases when employees are compensated wth large equty stakes a result drven, n part, by the substtuton of cash wages wth company stock...3 One frm s owners offer wages only, one frm s owners offer both wages and an equty stake. Fnally, I assess a settng where one frm s owners compensate employees wth wages only and the other frm s owners compensate employees wth wages and an equty stake. Wthout loss of generalty, I assume that the owners of frm offer ther employees both wages and an equty stake and the owners of frm offer ther employees wages only. Thus, I set z 0 for frm n (). Smultaneously, frm s owner/employee parng solves the frst order condtons of () wth respect to wage, w, and equty share, z, and frm s owner/employees parng solves the frst order condton of () wth respect to wage, w. Ths yelds optmal wages, w kand w k and optmal equty stake, z k,,, optmal quanttes from (9) and each frm s optmal wages w k and w k and () along wth frm s optmal equty stake z k,,. Substtutng each frm s nto (8), (0),, nto frm s (0) and (), yelds zw zw each frm s profts, (, k), each owners share of the profts, S ( ), and each employee zw group s compensaton, E ( ), respectvely. The equlbrum outcomes when frm s owners 8

20 offer wages and an equty stake to ts employees and frm s owners offer wages only to ts employees are summarzed below: z zw ( ) k 3 8( ) ( )( ) (, k), (, ) c c k c k w k zw k 4 3 6k k 3 4, w 3 6 ( ) (( )( )(4 ) (8 4 4 )) (, ) c k k k k k c k k k zw k 4 3 6k k, ( )( )(4 ) (, ) c k k ( )( )(4 ) q zw k, 4 (, ) c k q zw k k, 4 3 6k k 3 6k k E ( c) k (4 k) k zw (, k) 4 (3 6 k k ) ( )( c) (4 kk ) 4k zw E (, k) 4 (3 6 k k ) S ( )( c) k (4 k) k zw (, k) 4 (3 6 k k ),,, 4( ) (4 ) (, ) c k zw k k 4 (3 6 k k ), 4( c) 4 kk ( ) zw zw S (, k) (, k) 4 (3 6 k k ). (5) Havng defned the optmal outcomes contngent on the type of compensaton chosen by the owners n the frst stage, I next defne the parameter space over whch both frms owners offer a wage and an equty stake to ther respectve employees. 9

21 PROPOSITION..) If * ( k), there s a unque, pure strategy equlbrum where both sets of owners offer wages and equty stakes to ther employees..) The equlbrum n.) s a Prsoner s Dlemma for each frm s owners, as both sets of owners would be better off had they both been able to commt to offerng wages only..) Frm profts are strctly hgher when both frms owners offer wages and equty stakes to ther employees than when both frms owners offer wages only. If * ( k) and both frms owners offer employees wages only, the best response for the focal frm s owners s to devate from offerng wages only to offerng wages and an equty stake. By dong so, the focal frm gleans concessons n the pece rate wage, w, from ts employees and reduces ts cost base. Ths reduced cost base gves the focal frm a compettve cost advantage over ts rval whch makes the focal frm more proftable and, mportantly, ts owners better off despte dlutng ther holdngs. However, when * ( k), the competng frm s owners best response to the focal frm s owners offerng ther employees an addtonal equty stake s to also offer ther employees an addtonal equty stake. Dong so leads to party n wages across both frms, resultng n nether frm havng a compettve cost advantage over the other. Taken together, when * ( k), there s a unque, pure strategy equlbrum where each frm s owners offer ther employees wages and an equty stake n the company. 7 The shaded 7 When β > β * (k), there s porton of the parameter space where two pure strategy equlbra are supported: One pure strategy equlbrum where both frm s owners offer wages only, and one pure strategy equlbrum where both frm s owners offer wages and an equty stake. However, as Proposton, clam 3 llustrates, the wages only equlbrum Pareto domnates the wages and equty stake equlbrum. As a result, when β > β * (k), I assume that both owners wll choose the wages only equlbrum as t s ether a unque, pure strategy equlbrum or a Pareto domnant, pure strategy equlbrum. 0

22 area n Fgure llustrates the parameter space over whch both frm s owners offer wages and an equty stake to ther employees and employee wages are non-negatve. I denote ths parameter space, the employee ownershp equlbrum. Both frms are strctly more proftable when the employee ownershp equlbrum s supported because equty stakes drve lower nput costs. The lower costs, n turn, reduce double margnalzaton across the channel, and lead to greater profts. However, both frms owners are strctly worse off by offerng equty stakes than had they both offered wages only. As n the monopoly benchmark case, although profts are greater when owners compensate employees wth equty n the company, the owners share of those profts are smaller, and t s ths latter force that domnates. Ths leads to the nterestng result that both sets of owners offer ther respectve employees an equty stake n the frm, despte the owners beng better off had they been able to commt to offerng employees wages only. Fgure Parameter space over whch wages are strctly postve and both frms owners offer equty compensaton b b * k c * k k

23 Proposton provdes nsght n to not only the types of frms where employee ownershp should be more promnent, but also the types of frms where equty compensaton should not be offered. For example, n frms where employees have greater barganng power (.e., * ( k) ), a focal frm s owners best response to a competng frm s owners offerng wages only s to also offer wages only. To understand why ths s a best response, we can assess an extreme settng where employees have nearly all of the negotaton power (.e., ). In ths settng, offerng an equty stake leads to a much lower cost base, but also means that nearly all of the frm s profts wll accrue to employees because employees wll be compensated wth nearly all of the frm s equty. In such a settng, both frms owners would be better off offerng wages only, havng a hgher cost base, and retanng 00% of (albet smaller) profts. Interestngly, ths nsght provdes a potental explanaton for why we do not commonly observe equty-based compensaton n hghly unonzed settngs. 8 Unonzed frms tend to have more negotaton leverage over the frm than ther non-unonzed counterparts, n part, because ther ablty to strke and bargan collectvely allows them to hold up the frm (see Bova 03). In such a settng, the model suggests that owners are better off offerng employees wages only, lvng wth hgher neffcent wages, but also retanng some profts, than offerng employees an equty stake n the company, negotatng very effcent wages, but retanng none of the profts. compensaton. I next assess the mpact of equty compensaton on producton and employee 8 For example, Bova et al. (03) fnd a negatve correlaton between unon densty and the sze of equty stakes held by employees and McCarthy et al. (009) fnd a monotoncally decreasng relatonshp between unonzaton and employee ownershp.

24 COROLLARY. When the employee ownershp equlbrum s supported:.) frm producton s strctly hgher than when both frms owners offer wages only..) employee compensaton for each group of employees s hgher provded ** Max 0, ( k), otherwse each group of employees s better off wth wages only. 3.) both sets of owners and both sets of employees are worse off than f both sets of owners ** * offered wages only, provded Mn Max 0, ( k), ( k). The nferences from Corollary are consstent wth several fndngs. Frst, the emprcal lterature fnds a correlaton between a frm offerng equty ncentves to ts employees and both greater frm producton (see for example, Hochberg and Lndsay 00, Km and Oumet 03, Jones and Kato 995). A frequently cted explanaton for ths correlaton s that equty ncentves drve greater worker effort whch, n turn, leads to ncreased frm producton and frm profts. However, Corollary provdes another explanaton for these fndngs. Greater producton may also arse because workers agree to more effcent wages. More effcent wages lead to a lower cost base for each frm, whch n turn lead to greater producton. 9 Second, the model s outcomes are consstent wth several puzzlng fndngs related to the sze of employee equty stakes. Specfcally, n a publcly-traded settng, when employees have smaller equty stakes, they tend to enjoy more of the ensung surplus (.e., Km and Oumet 03). Conversely, all stakeholders appear to be worse off when employees have larger equty stakes (Km and Oumet 03, Faleye et al. 006). When ** Max 0, ( k), compettve 9 Ths fndng bulds on the lterature that documents a lnk between compensaton and producton n a Cournot olgopoly. For example, Vckers (985) and Fershtman and Judd (987) fnd that compensatng employees based on revenues as opposed to profts encourages greater producton. Also, Brander and Lews (986) fnd that when a frm faces hgher fxed costs (e.g., a frm fnances wth debt nstead of equty), mangers may have an ncentve to overproduce. In contrast, the model presented n ths paper fnds that the frm can generate hgher producton by lnkng employee compensaton to profts when costs are varable (.e., total labor costs ncrease wth producton). 3

25 pressures are low and equty stakes are farly small. In ths settng, I fnd that consstent wth the emprcal evdence, employees are better off wth wages and equty compensaton than wth wages only. Ths regon s represented by the lghtly shaded parameter space to the left of the dashed lne n Fgure 3. The employees are better off because wages are stll relatvely large and they enjoy a small share of the frm s profts when the frm s profts are also relatvely larger due to less competton. Conversely, when ** Max 0, ( k), compettve pressures are hgh and equty stakes are farly large, and I fnd that not only are the frm s owners worse off wth the employee ownershp equlbrum, but so are the frm s employees. Ths regon s represented by the dark shaded parameter space to the rght of the dashed lne n Fgure 3. The employees are worse off because ther wages are relatvely low and although they enjoy a larger share of the frm s profts, the frm s profts are also comparatvely low because compettve pressures are hgh. Fgure 3 Parameter space over whch wages are strctly postve and both frms owners offer equty compensaton b b ** k b * k 0. c * k k 4

26 The collectve fndngs provde a possble explanaton for the mxed evdence wth respect to the effect of employee ownershp on varous stakeholders, ncludng a possble nsght n to how large equty stakes arse endogenously despte both the frm s owners and employees potentally beng worse off when employees are compensated wth equty (.e., the parameter space encompassed by ** * Mn Max 0, ( k), ( k) ). Fnally, ths result also supports the Km and Oumet (03) fndng of a negatve relatonshp between employee surplus and the sze of employee equty stakes n the company. 3. Lmtatons and Implcatons A possble lmtaton of the analyss s that the model does not ncorporate uncertanty wth respect to any of the model s parameters. On the one hand, not havng any uncertanty n the model hghlghts the potental robustness of the result, as equty compensaton contnues to arse endogenously despte the lack of uncertanty. 0 Ths result runs n contrast to many models where, n a frst-best settng wth no uncertanty, a prncpal would not compensate employees wth equty n the company. For example, n the classc Hölmstrom (979) result, n a frst-best world where the agent s actons are observable, the optmal strategy s to pay the agent a fxed wage provded the agent supples the desred effort. On the other hand, n a model wthout uncertanty, the rsk preferences of the employees play no role n the equlbrum. Specfcally, absent uncertanty, the value of one dollar of wages s equvalent to one dollar of frm proft, and employees wll negotate the same contracts rrespectve of whether they are rsk neutral, rsk averse, or rsk seekng. In practce, however, 0 Ths modellng approach follows n the sprt of Ray (007) where the analyss s presented n a frst-best world to show the man forces at work and hghlght the key economc ntuton. 5

27 because there s varaton around the expected payoff of an equty stake, a rsk averse employee should value $ of expected equty returns less than $ of guaranteed wages. To address ths concern, I assess whether the model s results stll hold when employees mpose a dscount on company profts (.e., the returns on ther equty stakes) relatve to ther wages by replacng the employees objectve functon n () wth (6) below: E ( z, w, w, k, ) q ( w, w, k)[ w c] z ( w, w, k), j,, j (6) j j j represents the dscount that a rsk averse employee would place on an expected dollar of equty returns relatve to a guaranteed dollar of wages and (0,). I rerun the optmzaton program n Secton., alternately usng values of 3/ 4, /, and /4, and I fnd that the general tenor of the results stll holds. Specfcally, below some threshold, * ( k), both frms owners offer an equty stake to ther employees. The results mply that owners wll stll offer company stock endogenously, even when employees place a dscount on equty-based compensaton, provded employee barganng power s suffcently low. Another lmtaton of the result s that a cooperatve soluton to the Prsoner s Dlemma may be acheved f the game s played n an nfntely repeated settng. In other words, both frms owners may commt to the cooperatve equlbra of offerng wages only f negotatons occur nfntely many tmes. However, a repeated game may not be approprate for ths settng, as the decson to offer an equty stake n one perod has the potental to lmt compensaton choces n future perods. Specfcally, offerng an equty stake n one perod means that, unless the employees decde to dvest themselves of company stock, employees wll have equty ownershp n subsequent perods by constructon. Ths outcome may potentally make moot the 6

28 owners decson on whether to offer employees wages only or wages and an equty stake n a subsequent perod, and n turn prevent the game from beng played n a repeated manner. Fnally, a soluton to reducng a frm s cost base when an neffcent suppler sets prces above the compettve market prce s for the downstream frm to vertcally ntegrate ts rentextractng suppler. In ths way, the downstream frm can acqure ts nputs at margnal cost, reduce double margnalzaton, and boost profts across the channel. Whle employees cannot be vertcally ntegrated n to the frm, one way to potentally make wages more effcent mght be to replace a prce-settng employee base (.e., an neffcent suppler of labor) wth an employee base that can be pad the compettve market wage. Ths soluton would lower the frm s cost base and possbly preclude the need to offer employees an equty stake n the company. However, ths soluton may be mpractcal for several reasons. Frst, Lndebeck and Snower (986, 00) suggest that neffcences n the labor market often arse when employee swtchng costs are hgh. By constructon, when swtchng costs are hgh, replacng exstng employees may be unfeasble. Second, due to ther ablty to hold up the frm, neffcent wages also arse n hghly unonzed settngs. However, n many jursdctons t s llegal to threaten to replace unonzed employees wth non-unonzed counterparts (who typcally accept more effcent wages than ther unonzed peers). Taken together, replacng a prce-settng employee base wth a more wage-effcent one may not be a practcal alternatve to offerng exstng employees equty-based compensaton. The model also provdes some nsghts on when we mght expect frms owners to offer ther employees company stock. For example, we mght expect to see the employee ownershp equlbrum arse followng negatve shocks to employee barganng power (.e., negatve shocks to that lead to * ( k) ). An example of a negatve shock to employee barganng power 7

29 mght be the Fnancal Crss reducng the UAW s negotaton leverage wth the Bg 3 automakers durng ther 009 contract negotatons. Gven the model s predctons, t s possble that ths negatve shock was a factor that led to UAW employees beng compensated wth large equty stakes n ther frms. Addtonally, we mght expect to see the employee ownershp equlbrum arse followng postve shocks to ndustry compettveness (.e., postve shocks to k that lead to * ( k) ), such as ndustry deregulaton. For example, the adopton of the Arlne Deregulaton Act n 978 led to more heated prce competton amongst arlnes over the followng two decades (Cappell 985). Interestngly, and consstent wth the model s predctons, by the md-90s at least major arlne carrers compensated employees wth sgnfcant equty stakes n ther respectve companes, wth Unted Arlnes becomng the frst majorty employee-owned, publcly traded Amercan arlne n Concluson Whle equty compensaton s frequently lauded as a means to algn ncentves between owners and employees, t s not clear whether the ncentve effect remans when the frm employs a large number of workers. Gven ths pont, t s nterestng to note that numerous publcly-traded frms, whch employ many workers, offer equty-based compensaton to ther employees. The lterature has posted several explanatons, such as retenton and sortng, for ths outcome. The precedng analyss provdes another factor. Specfcally, n settngs where employee barganng power s suffcently low and nter-frm competton s suffcently ntense, we may expect employee ownershp to arse not only n specfc frms, but also across entre ndustres. 8

30 The analyss also provdes a possble explanaton for the vared outcomes that arse when employees n publcly-traded companes are compensated wth company stock. In partcular, comparatve statcs related to the sze of equty stakes provde nsghts n to why, n some cases, employees extract more of the surplus, and n other cases, no stakeholder s better off when an equty stake s offered to employees. The model also provdes a possble explanaton for several other emprcal regulartes, such as the postve correlaton between employee equty stakes and frm producton and the substtutonary relatonshp between employee ownershp and unonzaton. Fnally, the model provdes a set of testable predctons regardng the tmng of frms adopton of equty-based compensaton plans. For example, we mght expect negatve shocks to employee barganng power or postve shocks to competton ntensty to precede the adopton of employee ownershp plans for not only specfc frms, but also across entre ndustres. 9

31 Appendx Proof of Proposton For (0,) : ( c ) w z S ( ) S ( ) 0 (clam ). 6 w z (4 )( c) ( ) ( ) 0(clam ). 6 ( ) E w ( ) E z ( ) c 0 (clam 3). 8 Ths proves Proposton. Proof of Lemma For k (0,] and (0,) : zz zz z ( k, ) z ( k, ) ( ) k 0. k k zz zz w ( k, ) w ( k, ) ( c) k(4 k) 0 k k (4 kk ) Ths proves Lemma.. Proof of Proposton For k (0,] and (0,) : zz ww 4( ( ) k )( 8 ( 4 k) k ( k)) (, k) (, k) 4( c) 0 ( k) (4 k) (4 kk ) (clam 3). ( ) ( ( ) ) (, ) (, ) c zw k A ww 4 S k S k Where: ( k) (4 k) (3 6 k k ) A k k k k (04 5( ) 6(6 ( 6 (0 ( ) ))) 8 (3 ) ) 30

32 S (, k) S (, k) s concave n for (0,) and k (0,]. Solvng for so that zw ww zw ww * S (, k) S (, k) 0 produces several roots. However, only one root, k * * k (0,]. Moreover, k (0,) for k (0,]. I defne k as follows:, s postve for C k k k k k k ( k 4470 k ( k k k k k k k k k k k k k k 36 / / k ) ) 4 6 C 8(64k 40k 3 k ) / ( k (4 k ) ) 3(6k 8 k k ) D F * / (64( (4864k 6656k 338k 70k 57 k ))) 4 (3 k (4 k ) C) 4 8( ) k k (4 k ) k 8 64 D F 4 (4 k ) (4 k ) k 8 8( k )( k 60k 98k 53k 4k DF 4 (4 k ) k (4 k ) DF 4 (4 k ) Fnally, zw ww 4 zw ww ( c) k S (, k) S (, k) 0 0 8( k) ( k ) S (, k) S (, k) s concave n for (0,) zw ww *, and k for k (0,]. Gven ths pont, and (0,) for k (0,], then S (, k) S (, k) 0provded * ( k). Thus, when * ( k), the best response for frm s owners when frm s owners offer wages only s to offer employees wages and an equty stake n the frm. zw ww From the prevous pont, we know that, S (, k) S (, k) 0provded * ( k). Thus, f ( S zz (, k) S zw (, k)) ( S zw (, k) S ww (, k)) 0, frm s owners best response to frm s owners offerng both wages and an equty stake s to also offer both wages and an equty stake provded * ( k), as ths would mply that ( zz zw S (, k) S (, k)) 0. 3

33 zz zw zw ww GH ( I J) ( S (, k) S (, k)) ( S (, k) S (, k)) K Let: Where, for k (0,] and (0,) : G c k k 6( ) ( ( ) ) H k k k k k k k k k ( ) (4 ) 6 (3 (6 ( 4 ( ) ))) 0 I k k k k k k (3 (3 ( )( 4 3 ( )))) 0 J k k k k k 8 (64 ( )( 40 (0 (8 )))) 0 K k k kk k k 4 ( ) (4 ) (4 ) (3 6 ) 0 For k (0,], I J s concave n wth two roots. The frst root equals zero. The second root (64 80k 36k 0 k k ) equals k (0,] k(3 3k8k 8k k 3 k ) Thus, I J 0 (0,) and k (0,]. It follows that, ( S zz (, k) S zw (, k)) ( S zw (, k) S ww (, k)) 0 for k (0,) and (0,). Thus, when t s more proftable for frm s owners to offer wages and an equty stake as a best response to frm s owners offerng wages only (.e., * ( k) ), frm s owners wll also be better off n offerng a wage and an equty stake as a best response to frm s owners offerng a wage and an equty stake. Ths outcome results n a unque, pure strategy equlbrum where both frms offer wages and equty stakes to ther employees provded * ( k) (clam ). Let: ww zz ( c) ( ( ) k ) L (, ) (, ) 3 S k S k 4 k (88 k k ) Where for k (0,] and (0,) : L k k k k k k k ( ) 8 (43 ) 8 ( ( (4 ))) 0 ww zz Thus, S (, k) S (, k) 0 for k (0,] and (0,) (clam ). Ths proves Proposton. Proof of Corollary For k (0,] and (0,) : 3