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

Transcription

1 Employee Barganng Power, Inter-Frm Competton, and Equty-Based Compensaton Abstract We develop a model to llustrate that employee compensaton and product market decsons are related. When the product market s compettve and employees have low barganng power, the unque equlbrum n our settng s for each frm to offer equtybased compensaton to ther employees. In ths settng, equty-based compensaton leads to a lower wage rate, whch makes each frm more compettve wth ts rval. However, ths unque equlbrum s a Prsoner s Dlemma for the frms orgnal owners. Our results are consstent wth several emprcal regulartes and provde predctons on when frms wll offer equty-based compensaton to ther employees.

2 1. Introducton Hölmstrom (1979) 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 the agent s compensaton contngent on the frm s profts. One practcal way to acheve ths outcome s for a frm s owners to grant an employee an equty stake n the company. However, as Hölmstrom (1982) notes, when too many employees are ncentvzed wth equty-based compensaton, a free-rder problem arses that may dmnsh an agent s desre to put n a greater effort. In such a settng, as Oyer (2004) eloquently suggests, equty ncentves may have no ncentve effect. Gven ths nsght, t s puzzlng that publcly-traded frms, whch usually have many employees, often adopt equty-based compensaton plans. To address ths puzzle, several papers have put forth alternate motvatons for offerng equty grants to employees. For example, Oyer (2004) suggests that a frm s owners mght compensate employees wth company stock n order to ndex employee compensaton to outsde optons. In ths respect, equty-based compensaton acts as a useful tool for employee retenton. Separately, Lazear (2004), Arya and Mttendorf (2005), and Bergman and Jenter (2007) post that a frm s owners mght use equty-based compensaton for sortng purposes, where employees reveal prvate nformaton about ether the frm or ther own abltes by puttng ther money where ther mouth s. 1 We propose a complementary and emprcally relevant motvaton. We post that a frm s owners may offer equty-based compensaton to ther employees n order to negotate low wage rates. A lower wage rate reduces the frm s margnal cost and makes the frm not 1 Whle there s evdence that frms provde equty grants for the purpose of ncentve algnment (e.g., Core and Guay, 1999), there s also support for the alternate motvatons. Oyer and Shaffer (2005) consder three economc justfcatons for provdng equty compensaton to employees ncentve algnment, sortng, and employee retenton and fnd evdence consstent wth the latter two motvatons. Core and Guay (2001), Ittner, Lambert, and Larker (2003), Rajgopal, Shevln, and Zamora (2006), and Balsam and Mharjo (2007) also fnd evdence consstent wth frms usng equty-based pay for employee retenton purposes. 1

3 only more proftable, but also more compettve when facng a rval. We generate these nferences from a model of employee barganng power and nter-frm competton. We mplement our dea n a three-perod model n whch two frms compete n a product market. In the frst perod, each frm s orgnal owners smultaneously make decsons on contract forms. Specfcally, each frm s non-employee owners decde whether to compensate ther respectve employees wth wages only (a wage-based contract) or wth wages and an equty stake n the company (an equty-based contract). In the second perod, the compensaton terms.e., the level of wages and, n cases where equty compensaton s offered n the frst perod, the percentage of the frm that wll be gven to employees of both frms are smultaneously determned va barganng games between each frm s respectve owners and employees. Note that, by ncorporatng a barganng framework, the model allows for an mperfectly compettve market for labor, where employees can extract varyng levels of above-market rents from the frm, contngent on ther barganng power. 2 In the thrd and fnal perod, frms make producton decsons and play a Cournot game n the product market. We fnd that two types of equlbra emerge n our economy: an employee ownershp equlbrum, n whch each frm s owners offer an equty-based contract; or a wage only equlbrum, n whch each frm s owners offer a wage-based contract. These two equlbra arse at the nexus of several competng forces. On the one hand, when barganng s over both wages and an equty stake, the total surplus of non-employee owners and employees s maxmzed, whch tends to make the employee ownershp equlbrum more favorable to non-employee owners. On the other hand, when negotatng over wages only, employees end up wth a smaller porton of the ensung total surplus, because they are aware that the 2 An mperfectly compettve market for labor s plausble n many ndustres. Many factors such as unonzaton, local unemployment rates, and frm-borne employee swtchng costs can lead to neff cences n the labor market that allow employees to extract rents above the compettve market wage (see Bova, Dou, and Hope, 2014; Lndbeck and Snower, 1986, 2001). 2

4 frm s producton s decreasng n the wage rate and thus do not demand overly exorbtant wages. Ths force tends to make the wage only equlbrum more favorable to non-employee owners. The relatve strength of the two competng forces depends on the product market s compettveness and employees barganng power. We fnd that when nter-frm competton s suff cently ntense and employees barganng power s suff cently low, the domnant strategy for each frm s non-employee owners s to offer ther employees an equty stake n the game s frst perod. In ths case, the employee ownershp equlbrum s the unque equlbrum. In contrast, when nter-frm compettveness s suff cently low and employees barganng power s suff cently hgh, the domnant strategy for each frm s non-employee owners s to offer ther employees wages only. In ths case, the wage only equlbrum prevals as the unque equlbrum. Our results contrbute to the lterature by provdng a novel, complementary, and emprcally relevant channel for the ncdence of employee ownershp. For example, alternatve exstng theores, such as agency models, retenton models, and sortng models, all feature uncertanty. By contrast, all parameters n our economy are commonly known, there s no unobservable effort on the part of the agent, and there are no stochastc returns. It s new, then, that equty-based compensaton can stll arse endogenously as an equlbrum outcome n our determnstc settng. Specfcally, ths result runs n contrast to the ntuton n prevous models, where n a frst-best scenaro wthout uncertanty, a prncpal would not compensate an agent wth equty n the company. 3 In a broad sense, our paper makes a basc pont that employee compensaton and product market decsons are related. In our settng, the structure of employee compensaton affects the product market equlbrum through ts effect on the wage rate, because the wage rate 3 For example, n the classc Hölmstrom (1979) model, when the agent s actons are observable, the optmal strategy of a self-nterested prncpal s to only pay the agent a fxed wage provded the agent supples the desred effort. 3

5 s the margnal producton cost n the product market. Gven that labor relatons can nfluence the product market equlbrum, a frm s owners have ncentves to desgn employee compensaton so as to nfluence the product market n ther favor. Our analyss also generates nsghts on the pros and cons of employee ownershp, both from a normatve and a postve perspectve. On the normatve sde, we fnd that total profts are hgher under equty-based compensaton than under wage-based compensaton, because of the lower wage rate negotated under equty-based compensaton. Ths lower wage rate and more eff cent producton addtonally beneft each frm s consumers n the product market. However, when the employee ownershp equlbrum prevals, t s a Prsoner s Dlemma for each frm s non-employee owners as each group would be better off, had they been able to commt to offerng ther respectve employees wages only n the game s frst perod. Moreover, when competton s suff cently ntense and employee barganng power s suff cently low, not only are non-employee owners worse off by not beng able to commt to offerng wages only, but so are each frm s employees. Ths result may help explan why equty-based compensaton seems to arse endogenously as an equlbrum outcome, even n stuatons where t appears to make both employees and non-employee owners worse off. From a postve perspectve, our analyss s useful for understandng a wde range of fnancal phenomena and suggestng new testable predctons. For nstance, our model provdes an explanaton for why (1) equty-based compensaton s less commonly observed n hghly unonzed settngs (McCarthy, Voos, Eaton, Kruse, and Blas, 2011); (2) equty grants often substtute, rather than complement, wages when employees are compensated wth larger equty stakes (Km and Oumet, 2014); and (3) frm and stakeholder outcomes vary wth the sze of employee equty stakes (Km and Oumet, 2014; Faleye, Mehrotra, and Morck, 2006). Our results are also consstent wth the observed outcomes of several recent con- 4

6 tract negotatons for example, the 2009 contract negotatons between the Unted Auto Workers and two major Amercan automoble manufacturers. Fnally, our model generates addtonal emprcal predctons regardng the ncdence of equty-based compensaton. Some of these predctons are consstent wth exstng emprcal fndngs, whle others offer new opportuntes to test our model. For example, our model would predct that equty-based compensaton should be more prevalent among frms whose product market s more compettve, whose employees have lower barganng power, and where labor s a more mportant factor of producton. The remander of the paper s organzed as follows. Secton 2 descrbes the model, and Secton 3 characterzes the equlbrum. In Secton 4, we conduct an eff cency analyss to examne the normatve mplcatons of equty-based compensaton. Secton 5 explores the emprcal mplcatons of our analyss and Secton 6 further dscusses several key features and assumptons of our model. Fnally, Secton 7 summarzes and concludes. The appendx ncludes all the proofs. 2. The Model We consder an economy wth three perods, t = 1, 2, and 3. The tmelne of the economy s descrbed n Fg. 1. Our analyss focuses on a monopolstc sector wth two frms, where each frm uses labor as a sole nput to produce a dfferentated good. Frms are orgnally owned by ther non-employee shareholders. In perod 1, each frm s orgnal owners decde whether to offer ther respectve employees wages only, or wages and an equty stake n the frm. In perod 2, each frm s non-employee 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). The negotated outcome wll 5

7 be set through Nash barganng and n ths respect, the model allows for an neff cent labor market where employees can extract varyng above-market rents from the frm, contngent on ther barganng power. In perod 3, each frm sets producton to maxmze ts profts, consumers purchase frms products, prces are realzed, and profts accrue to non-employee owners and employees, provded employees have an equty stake n the frm. [INSERT FIG. 1 HERE] 2.1. Producton and product markets The product market operates n perod 3, and the two frms play a Cournot game n ths market. As n Sngh and Vves (1984), the demand for each frm s products s generated by a representatve consumer who has a utlty functon as follows: U (q 1, q 2 ) = (1 k) [ 12 q21 + q 1 12 ] q22 + q 2 [ +k 1 ] 2 (q 1 + q 2 ) 2 + (q 1 + q 2 ) (P 1 q 1 + P 2 q 2 ), (1) where k (0, 1) s a constant, q s the amount of good, and P s ts prce. The frst two terms n equaton (1) represent the consumer s ntrnsc utlty from consumng the two goods, whle the thrd term captures the cost of purchasng these goods. The frst term s quadratc n q 1 and q 2, respectvely, whch reflects how good 1 and good 2 separately affects the consumer s utlty. By contrast, the second term s quadratc n (q 1 + q 2 ), and thus the two goods are perfectly substtutable when affectng the consumer s utlty through ths term. Hence, parameter k captures the degree of substtutablty of the two goods n the consumer s preference. The hgher the value for k, the more substtutable are the two goods, and the more compettve the two frms are n the product market. Thus, parameter k represents a measure of the ntensty of product market competton. The representatve consumer chooses quanttes q 1 and q 2 to maxmze her preference n 6

8 (1) takng prces P 1 and P 2 as gven. Ths utlty maxmzaton problem gves rse to the followng standard lnear nverse demand functon for frm : P = 1 q kq j, for, j = 1, 2, and j. (2) As k 0, equaton (2) degenerates to P = 1 q, whch s the nverse demand functon for a monopoly frm. As k becomes hgher, frm s product prce s affected more by frm j s producton quantty, and thus the product market becomes more compettve. The supply of products n the market arses from each frm s optmal producton decsons. The producton process utlzes only one nput, labor. Producton features constant returns to scale so that one unt of labor produces one unt of product. Frm s cost for one unt of labor s gven by a wage rate, w, whch s endogenously determned through a barganng game n perod 2 (whch wll be ntroduced shortly). Thus, frm s gross proft s Π = q P q w, and ts optmal producton q s determned by 4 Max q (q P q w ), (3) where P s gven by the nverse demand functon (2). In the proft maxmzaton problem, frm takes the wage rate w and ts rval s producton q j as gven. The frst-order condton of program (3) wll yeld the best response functon of frm. As per usual, the ntersecton of the two best response functons (for = 1, 2) determnes the equlbrum quantty produced by each frm Contracts and surplus At the begnnng of the economy, each frm s orgnally owned by a set of non-employee shareholders. In perod 1, the non-employee owners for each frm, consder offerng ther 4 Here, the frm s maxmzng total profts, whch means that the frm s management works on behalf of all shareholders n perod 3. Alternatvely, we can assume that the frm contnues to operate n the nterest of the orgnal non-employee owners n perod 3. Then, the optmal producton q s determned by Max q (1 z ) (q P q w ), whch wll yeld the same soluton as (3), provded the orgnal non-employee owners contnue to own a strctly postve share of the frm. 7

9 employees two possble forms of compensaton, ether wage-based compensaton or equtybased compensaton. Under a wage-based contract, the frm compensates ts employees wth wages only, whle under an equty-based contract, the frm compensates ts employees wth both wages and a porton z of the frm s gross profts Π. The welfare of non-employee owners s partcularly relevant n our analyss, snce they control whch form of contract s chosen n perod 1, and offerng an equty stake to employees dlutes ther stake n the frm. Once the contract form s set n perod 1, the terms of the contract are determned n perod 2 accordng to a Nash barganng game between non-employee owners and employees of each frm. Note that for the wage-based contract, only the wage rate w s negotable, whle for the equty-based contract, both the wage rate w and the equty stake proporton z are negotable. Intutvely, startng from a poston of non-ownershp for employees, offerng a wage-based contract suggests that equty ownershp s smply not on the barganng table n perod 2. By contrast, f non-employee shareholders do open the door for employee ownershp n perod 1, then employees can bargan over both wages and the sze of ther equty stake n perod 2. In the perod-2 barganng game, the equlbrum outcome depends on each party s utlty surplus resultng from reachng an agreement. If employees of frm decde to work for the frm, they wll receve an amount of q w + z Π (wth z = 0 n settngs where only the the wage-based contract s offered n perod 1). If they decde not to work for the frm, we assume that they can work at an exogenous, lower market wage rate c (0, 1); 5 that s, they can work at ther opportunty cost of c per unt of labor. Thus, the surplus of frm s employees s E q w + z Π q c = q (w c) + z Π. (4) 5 We mpose the constrant of c < 1, whch means that the compettve labor market rate c s lower than the maxmum product prce, 1, n equaton (2). 8

10 In the Onlne Appendx, we show that E s consstent wth the objectve functon of an employee base n varous barganng settngs as descrbed n McDonald and Solow (1981). Next we defne the surplus that accrues to frm s non-employee owners. The nonemployee owners for frm receve the resdual profts that do not accrue to employees, (1 z ) Π. Addtonally, the non-employee owners outsde opton s 0. Ths outcome arses because we assume that each frm faces swtchng costs (e.g., unonzaton, unque human captal amongst ther employee base) that preclude the owners from replacng current employees wth outsder workers. These swtchng costs create an mperfectly compettve market for labor wthn the frm whch, n turn, generates the barganng power for each frm s employees. As a result, when calculatng the surplus that accrues to frm s non-employee owners, the compettve wage rate c s rrelevant. Taken together, frm s non-employee owners receve a surplus of S (1 z ) Π. (5) To generate the equlbrum compensaton levels n perod 2, the non-employee owners and employees set the wage, w, and n cases where the equty-based contract was offered n perod 1, the porton of equty, z, to maxmze the generalzed Nash product below, E β S1 β, (6) where parameter β (0, 1) represents the strength of employee barganng power. As our analyss wll llustrate, when the frm and ts employees can negotate over the terms of partcular forms of compensaton (.e., wages or wages and equty), there exst mportant nteractons between employee compensaton and product market decsons, so that barganng n our settng has not only dstrbutonal consequences, but also allocatonal consequences. 9

11 3. The equlbrum An equlbrum n the economy s defned n a subgame perfect sense. Formally, we defne an equlbrum as producton quanttes q (w, w j, k) of each frm n perod 3, contract terms w (β, k) and z (β, k) between each frm and ther respectve employees n perod 2, and contract form choces of each frm s non-employee owners n perod 1, such that (1) the producton quanttes q (w, w j, k) form a Cournot duopoly equlbrum n the perod-3 product market, (2) the contract terms, w (β, k) and z (β, k) (n case where an equty stake s offered n the frst perod), for both frms are smultaneously determned as the outcomes of ther respectve Nash barganng games n perod 2, gven the Cournot outcome n perod 3, and (3) the contract form choces of each frm form a Nash equlbrum from the perspectve of the two groups of non-employee owners n perod 1, gven the perod-2 and perod-3 equlbrum outcomes. In ths secton, we frst work out the equlbrum usng backward nducton and then conduct comparatve statcs on the equlbrum outcomes Product market equlbrum n perod 3 In perod 3, each frm smultaneously chooses a producton quantty to maxmze ts profts n (3), gven the employee wages negotated n perod 2, the quantty choce of ts rval, and the nverse demand functon (2). Solvng the frst-order condton yelds the best response functon of frm as follows: q = 1 kq j w, for, j = 1, 2, and j. 2 Usng the two best response functons, we can compute the Cournot duopoly equlbrum n the perod-3 product market, whch s summarzed n the followng lemma. Lemma 1. For any gven employee wages (w 1, w 2 ) and product market compettveness k, the product market equlbrum s unque wth the producton quantty and proft of frm 10

12 beng gven respectvely by for, j = 1, 2, and j. q (w, w j, k) = 2 k 2w + kw j 4 k 2, (7) Π (w, w j, k) = (2 k 2w + kw j ) 2 (4 k 2 ) 2, (8) 3.2. Barganng game equlbrum n perod 2 In perod 2, each frm s non-employee owners and employees negotate over the terms of the compensaton.e., the wage rate w under a wage-based contract, and the wage rate w and equty porton z under an equty-based contract accordng to a generalzed Nash barganng game. Insertng the expressons of q and Π n Lemma 1 nto equatons (4) and (5), we can obtan the employees total compensaton E and non-employees resdual profts S as follows: S (z, w, w j, k) = (1 z ) (2 k 2w + kw j ) 2 (4 k 2 ) 2, (9) E (z, w, w j, k) = 2 k 2w + kw j 4 k 2 (w c) + z (2 k 2w + kw j ) 2 (4 k 2 ) 2, (10) for, j = 1, 2, and j. Under a wage-based contract, we have z = 0, and frm s wage rate w s determned by Max w [E (0, w, w j, k)] β [S (0, w, w j, k)] 1 β. (11) Under an equty-based contract, frm s wage rate w and the porton of employee equty z are determned by Max z,w [E (z, w, w j, k)] β [S (z, w, w j, k)] 1 β. (12) Note that n (11) and (12), frm s negotated compensaton terms hnge on ts rval s wage rate w j, whch n turn depends on frm j s contract choce n perod 1. Thus, there are three possble equlbrum paths n perod 2, dependng on each frm s contract choces n perod 11

13 1: each frm offers wage-based contracts; each frm offers equty-based contracts; and one frms offers a wage-based contract whle the other offers an equty-based contract. Below we use Proposton 1 to characterze the equlbrum contract terms determned n perod 2 for these three cases. 6 Proposton 1. (1) When both frms offer wages only to ther respectve employees n the frst perod, we have w ww 1 (β, k) = w ww 2 (β, k) = c + q ww 1 (β, k) = q ww 2 (β, k) = β (2 k) (1 c), 4 kβ 2 (2 β) (1 c) (4 kβ) (k + 2), S ww 1 (β, k) = S ww 2 (β, k) = Π ww 1 (β, k) = Π ww 2 (β, k) = 4 (2 β)2 (1 c) 2 (4 kβ) 2 (k + 2) 2, and E ww 1 (β, k) = E ww 2 (β, k) = 2β (2 β) (2 k) (1 c)2 (4 kβ) 2. (k + 2) (2) When both frms offer wages and equty stakes to ther respectve employees n the frst perod, we have z1 zz (β, k) = z2 zz (β, k) = β + k2 (1 β), 2 w1 zz (β, k) = w2 zz (β, k) = c k2 (1 c) 4 + 2k k, 2 q zz 1 (β, k) = q zz 2 (β, k) = 2 (1 c) 4 + 2k k 2, S zz 1 (β, k) = S zz 2 (β, k) = 2 (1 β) (2 k2 ) (1 c) 2 (4 + 2k k 2 ) 2, Π zz 1 (β, k) = Π zz 2 (β, k) = 4 (1 c)2 (4 + 2k k 2 ) 2, and E zz 1 (β, k) = E zz 2 (β, k) = 2β (2 k2 ) (1 c) 2 (4 + 2k k 2 ) 2. (3) When frm 1 offers wages and equty stakes and frm 2 offers wages only to ther respectve 6 For each case, we use the frst (second) superscrpt of each varable to ndcate frm 1 s (frm 2 s) contract choce. Letter w represents wage-based compensaton and letter z represents equty-based compensaton. For nstance, w1 zw (β, k) refers to the equlbrum wage rate of frm 1, when frm 1 adopts an equty-based contract and frm 2 adopts a wage-based contract. 12

14 employees n the frst perod, we have z1 zw (β, k) = β + k2 (1 β), wzw 1 (β, k) = c k2 (2 k) (4 + kβ) (1 c), k 2 + βk 4 w2 zw (β, k) = c + β (4 k2 ) (4 2k k 2 ) (1 c), 32 16k 2 + βk 4 q zw 1 (β, k) = 2 (2 k) (4 + kβ) (1 c) 32 16k 2 + βk 4, q zw 2 (β, k) = 2 (2 β) (4 2k k2 ) (1 c) 32 16k 2 + βk 4, S zw 1 (β, k) = 2 (1 β) (2 k2 ) (2 k) 2 (4 + kβ) 2 (1 c) 2 (32 16k 2 + βk 4 ) 2, Π zw 1 (β, k) = 4 (2 k)2 (4 + kβ) 2 (1 c) 2 (32 16k 2 + βk 4 ) 2, S zw 2 (β, k) = Π zw 2 (β, k) = 4 (2 β)2 (4 2k k 2 ) 2 (1 c) 2 (32 16k 2 + βk 4 ) 2, E zw 1 (β, k) = 2β (2 k2 ) (2 k) 2 (4 + βk) 2 (1 c) 2 (32 16k 2 + βk 4 ) 2, and E zw 2 (β, k) = 2β (2 β) (1 c)2 (4 k 2 ) (4 2k k 2 ) 2 (32 16k 2 + βk 4 ) 2. When frm 1 offers wages only and frm 2 offer wages and equty stakes to ther respectve employees n the frst perod, the varables w1 wz (β, k), w2 zw (β, k), z2 wz (β, k), q wz (β, k), Π wz (β, k), S wz (β, k), and E wz (β, k) are characterzed symmetrcally Contract choce equlbrum n perod Equlbrum characterzaton In perod 1, each frm s non-employee owners smultaneously choose the forms of compensaton contracts. The payoffs of non-employee owners are determned by the equlbrum outcomes of the barganng games n perod 2. For nstance, f both frms compensate ther respectve employees wth wages only, then the non-employee owners of both frms wll end up wth a payoff of S ww (β, k), whch s gven by Part (1) of Proposton 1. Usng the expressons of S ww (β, k), S zz (β, k), S zw 1 (β, k), and S zw 2 (β, k) n Proposton 1, we can construct the payoff matrx of the game played by frms n perod 1 and descrbe t n Fg. 2. Analyzng 13

15 ths payoff matrx, we can compute all the pure strategy equlbra n perod 1, whch are summarzed n the followng proposton. [INSERT FIG. 2 HERE] Proposton 2. For any k (0, 1), there exst two threshold values of β, ˆβ 1 (k) and ˆβ 2 (k) (wth 0 < ˆβ 1 (k) < ˆβ 2 (k) < 1), whch are functons of parameter k and respectvely defned by equatons (A11) and (A15) n the Appendx, such that the equlbrum s characterzed as follows: (1) If β (0, ˆβ 1 ), then there s a unque equlbrum, n whch both frms offer wages and equty stakes to ther respectve employees. (2) If β [ˆβ1, ˆβ ] 2, then there are two pure strategy equlbra. In one equlbrum, both frms offer wages and equty stakes to ther respectve employees. In the other equlbrum, both frms offer wages only to ther respectve employees. (3) If β (ˆβ2, 1), then there s a unque equlbrum, n whch both frms offer wages only to ther respectve employees. Examnng Proposton 2, we fnd that two types of equlbra are supported n perod 1: ether both frms offer an equty-based contract or both frms offer a wage-based contract. We refer to the frst type of equlbrum as the employee ownershp equlbrum and the second type as the wage only equlbrum. We use Fg. 3 to plot the regmes of equlbrum types n the parameter space of (k, β). Generally speakng, as k becomes hgher and β becomes lower, the employee ownershp equlbrum s more lkely to preval. [INSERT FIG. 3 HERE] Corollary 1. Frms are more lkely to provde equty based compensaton to ther respectve employees when the product market s more compettve and when employees have lower barganng power (.e., when k s hgher and when β s lower). 14

16 Specal case: k = 0 We now examne the specal case of k = 0, n whch case each frm becomes a monopolst n ts own product market. Ths analyss serves two purposes. Frst, t helps to develop the ntuton of Proposton 2 for the general case of k (0, 1). Second, t llustrates the mportance of competton n generatng the employee ownershp equlbrum, as the wage only equlbrum always prevals as the unque equlbrum n ths monopoly case. Corollary 2. Equty-based compensaton s never n the nterest of non-employee owners n the absence of competton. That s, f k = 0, the wage only equlbrum prevals as the unque equlbrum for any β (0, 1). We use Fg. 4 to llustrate the ntuton for Corollary 2. Here, we plot the perod-2 Nash barganng outcomes for frm under a wage-based contract (n blue) and an equtybased contract (n red), respectvely. In Fg. 4, we set the parameter values as follows: β = 0.5, c = 0.2, and k = 0. Under the wage-based contract, the barganng fronter s: E = (1 c) S 2S. (13) To obtan (13), we frst nsert z = k = 0 nto (9) and (10) to fnd the expressons of S and E (whch ndcate the surplus of both non-employee owners and employees for a specfc wage rate w ), and then cancel w n these two expressons to get a relaton between E and S (whch ndcates the possble combnatons of (E, S ) when w s vared under a wage-based contract). The Nash barganng outcome s determned by the tangency of the barganng fronter and the ndfference curve mpled by the objectve functon (6) n the barganng game. Ths outcome s depcted as pont N w n Fg. 4. [INSERT FIG. 4 HERE] 15

17 Under the equty-based contract, the barganng fronter s: S + E = (1 c)2. (14) 4 We obtan (14) as follows. Insertng k = 0 nto equatons (9) and (10), we have: S = (1 z ) (1 w ) 2 4 and E = (1 w ) 2 (1 w ) 2 (w c) + z. (15) 4 Usng (15), we can get all the achevable barganng outcomes (E, S ) by varyng w and z. For a gven w, we frst cancel z n (15) and lnk E and S as follows: S + E = (1 w ) 2 (w c) + (1 w ) 2, (16) 4 whch ndcates the total surplus that s avalable for non-employee owners and employees to dvde under a specfc wage rate w. We then choose w to maxmze ths total surplus n (16), whch yelds the barganng fronter (14). Drect computaton shows that the total-surplus-maxmzng wage rate s the market wage rate c. Ths result s ntutve, snce each frm s a monopolst n ts product market and the true margnal cost of labor s c. To understand ths result, we use the defnton of E, S, and Π, and compute the total producer surplus T for the case of k = 0 as follows: T S + E = q (w c) + Π = q (1 q c). The total surplus s maxmzed at q = 1 c, whch s exactly the product quantty mpled 2 by equaton (7) wth w = c and k = 0. Agan, the barganng outcome, depcted as pont N z n Fg. 4, s determned by the tangency of the barganng fronter and the ndfference curve. Comparng (13) wth (14), whch are depcted n Fg. 4, we have the followng two observatons. Frst, the fronter under the wage-based contract les nsde the fronter under the equty-based contract. Ths outcome arses because the wage rate w under the wagebased contract s generally dfferent from the market wage rate c, whch causes the product quantty to be dstorted from the value that maxmzes total surplus. The two fronters (13) 16

18 and (14) concde only at the S-ntercept, at whch pont non-employee owners get all of the surplus and employees get none (at ths pont, under the wage-based contract, the wage rate w s also set to be c and thus, the producton s total-surplus eff cent). Hence, by commttng to wage barganng, the non-employee owners commt to barganng over a set of neff cent producton quanttes. Ths consderaton tends to make equty-based compensaton more attractve. Second, wage barganng causes the fronter n (13) to pvot nward whle the fronter n (14) s lnear under the equty-based contract. The barganng fronter n (14) s lnear for equty-based compensaton, because the barganng s drectly over the maxmzed total surplus T. Gven the Cobb-Douglas preference (6), the resultng barganng outcome s that employees obtan a share β of the total surplus. In contrast, wth wage barganng, the surplus that employees can extract s lmted by the fact that every ncrease n the wage rate also reduces output and therefore the total surplus, and as a result, wage barganng causes the fronter n (13) to pvot nward. Ths nward pvot renders the ndfference curve to be steeper at the tangency pont N w than at the tangency pont N z, leadng to a Nash barganng outcome that s more favorable to non-employee shareholders, despte wage barganng leadng to less eff cent producton and lower total surplus. Taken together, n the perod- 1 equlbrum, self-nterested non-employee shareholders wll choose to offer a wage-based contract n the monopoly case General ntuton Havng presented the monopoly case, we now consder the compettve case wth k > 0. Proposton 2 shows that the equlbrum type depends on employees barganng power β. We use Fg. 5 to llustrate the ntuton. We frst conduct an analyss smlar to Fg. 4 and 17

19 plot the perod-2 Nash barganng outcomes for frm, when β takes a low value of 0.1 (n Panel a1 of Fg. 5) or when β takes a hgh value of 0.9 (n Panel a2 of Fg. 5). In both panels, the other parameters are set at k = 0.8 and c = 0.2, and we assume that frm j offers an equty-based contract to ts employees. We then use Panel b of Fg. 5 to present the best response functons of each frm and the resultng Nash equlbrum n perod 1. [INSERT FIG. 5 HERE] Smlar to obtanng equaton (13), we can use equatons (9) and (10) to compute the fronter under the wage-based contract as follows: E = [ 1 c k 2 (1 w j)] S ) (2 k2 S. (17) 2 We can also compute the followng barganng fronter under the equty-based contract: E + S = (2 2c k + kw j) 2, (18) 8 (2 k 2 ) whch, as n the monopoly case, s obtaned by choosng the wage rate w to maxmze the total surplus, T (w, w j, k, c) E (z, w, w j, k) + S (z, w, w j, k) = 2 k 2w ( ) 2 + kw j 2 k 2w + kw j (w 4 k 2 c) +, (19) 4 k 2 where the second equalty follows from the expressons of S (z, w, w j, k) and E (z, w, w j, k) n equatons (9) and (10). Equatons (17) and (18) respectvely extend equatons (13) and (14) to the general case of k 0. In equatons (17) and (18), w j s fxed at ther correspondng perod-2 barganng game equlbrum values specfed by Proposton 1. For nstance, f both frms offer an equty-based contract (e.g., the red lne n Panels a1 and a2 of Fg. 5), then w j takes the value of w zz j (β, k) = c k2 (1 c) 4+2k k 2 by Part (2) of Proposton 1. In the top panels of Fg. 5, the barganng fronter s stll lnear under the equty-based contract, whle t pvots nward under the wage-based contract, for the same reason as n Fg. 18

20 4. However, unlke Fg. 4, the two fronters no longer concde on the S-axs where the nonemployee owners get all the surplus. For nstance, n Panel a1 of Fg. 5, the fronter (18) now has a hgher total surplus than the fronter (17). Ths s because wth wage compensaton, the wage rate w s equal to c at the S-ntercept of equaton (17), whle at the S-ntercept of equaton (18), the wage rate w s smaller than c, whch makes frm more compettve n the perod-3 product market and leads to a hgher total surplus, takng the rval s contract as gven. The more compettve s the product market, the larger the gap between the two fronters, because frm can obtan a larger market share from the product market by commttng to a lower wage rate and hence a lower margnal producton cost. The outward shft of the barganng fronter under the equty-based contract resembles somethng lke an ncome effect. Ths ncome effect favors the choce of the equty-based contract, as t ncreases the total surplus T and hence the non-employee owners payoff S (recall that S = (1 β) T at pont N z whch depcts the Nash barganng outcomes for the equty-based compensaton). By contrast, as we dscussed for the monopoly case, the nward bendng fronter under the wage-based contracts makes the ndfference curve steeper at the tangency pont N w than at the tangency pont N z. Ths effect resembles a substtuton effect, and t favors the choce of the wage-based contract. In Panel a1 of Fg. 5, where β s low, the ncome effect domnates so that frm chooses to offer an equty-based contract. In Panel a2 of Fg. 5, where β s hgh, the opposte s true. The dfference between Panels a1 and a2 can also be understood from the expresson of S n Proposton 1, the varable determnng the contract choce of non-employee owners of frm. Under equty-based compensaton, non-employee owners payoff S lnearly decreases wth β, whle S s convex n β under wage-based compensaton. Intutvely, under the equty-based contract, employees smply negotate a share β of the total surplus T. Under 19

21 the wage-based contract, however, an ncrease n β not only rases employees share of the pe but also reduces the pe tself by drvng up the wage and hence drvng down the total surplus. The latter effect mtgates the negatve effect of an ncrease n β on the negotated payoff S. Thus, as we ncrease β from 0.1 n Panel a1 of Fg. 5 to 0.9 n Panel a2 of Fg. 5, S decreases less under the wage-based contract than under the equty-based contract, whch explans why non-employee owners start to favor wage-based compensaton once β becomes suff cently hgh. Panel b of Fg. 5 presents the best response functons of each frm and the resultng perod-1 equlbrum. Specfcally, when employees barganng power β s suff cently low, offerng the equty-based contract s a domnant strategy for each frm, and thus the employee ownershp equlbrum prevals as the unque equlbrum n perod 1. By contrast, when β s suff cently hgh, offerng the wage-based contract becomes the domnant strategy for each frm, whch makes the wage only equlbrum the unque equlbrum n perod 1. When β takes an ntermedate value, each frm s best response depends on the choces of ts rval. If frm j adopts an equty-based contract (a wage-based contract, respectvely), t s n frm s nterest to adopt an equty-based contract (a wage-based contract, respectvely) as well. As a result, both the employee ownershp equlbrum and the wage only equlbrum can be supported as a pure strategy equlbrum n perod 1. Note that under the employee ownershp equlbrum, the negotated wage rate w s below the market wage rate c,.e., w zz (β, k) = c k2 (1 c) 4+2k k 2 < c as long as k > 0. As we mentoned above, ths outcome arses because under equty-based compensaton, each frm maxmzes the total surplus n (19) and chooses a lower wage rate, n order to generate a lower margnal producton cost and thus become more compettve n the product market. As a result of the lower negotated wage rate, the negotated share z exceeds β (.e., z zz (β, k) = 20

22 β + k2 (1 β) > β for k > 0), because employees want not only ther share β of profts but 2 also need to be rembursed for acceptng a below-market wage rate w zz. Ths nsght s comparable to an nsght generated from the top-dog strategy (Fudenberg and Trole, 1984), where a frm commts to be tough n the product market n order to get a rval frm to retreat. Brander and Lews (1986) and Fershtman and Judd (1987) also propose related deas. In Brander and Lews (1986), shareholders strategcally take on debt to become more aggressve n the product market. Hgher debt levels force equty holders to restrct attenton on hgher margnal proft states, whch leads to more aggressve producton decsons. In Fershtman and Judd (1987), shareholders wrte contracts rewardng managers for maxmzng revenues nstead of profts, whch encourages managers to make more aggressve decsons n the product market Comparatve statcs Comparatve statcs wth respect to β By Proposton 2, ether an employee ownershp equlbrum or a wage only equlbrum prevals n perod 1. Thus, we frst conduct comparatve statcs wth respect to parameter β on these two equlbra respectvely, and then make predctons on the perod-1 outcomes that take nto account equlbrum swtches. Proposton 3. (1) In the wage only equlbrum, f the employees barganng power β ncreases, then: the employee wage w ww (β, k) ncrease; and the frm producton q ww (β, k) and the employee compensaton E ww (β, k), the frm profts Π ww (β, k), and the non-employee owners resdual proft S ww (β, k) decrease. That s, www (β,k) β > 0, qww (β,k) β < 0, Sww (β,k) < β 0, Πww (β,k) β (β,k) < 0, and Eww > 0, for = 1, 2. β (2) In the employee ownershp equlbrum, f the employees barganng power β ncreases, 21

23 then: the equlbrum porton z zz (β, k) of equty stakes and the employee compensaton E zz (β, k) ncrease; the employee wage w zz frm profts Π zz (β, k), the frm producton q zz (β, k), and the (β, k) do not change; and the non-employee owners resdual proft S zz (β, k) decreases. That s, zzz (β,k) β > 0, wzz (β,k) β = qzz (β,k) β = Πzz (β,k) β = 0, Szz (β,k) β < 0, and E zz (β,k) β > 0, for = 1, 2. The ntuton for Proposton 3 s as follows. In the wage only equlbrum, employees can bargan over ther wages only. Thus, when ther barganng power ncreases, they end up wth a hgher wage rate n equlbrum. Ths ncreased wage rate n turn ncreases the producton cost of the frm, and n response, the frm produces less and has a lower proft. Hgher barganng power also makes employees better off whle makng non-employee owners worse off. In the employee ownershp equlbrum, the equlbrum wage rate s not affected by employee barganng power. Recall that under equty-based compensaton, the wage rate s set such that the total surplus s maxmzed, and thus the equlbrum wage rate s ndependent of barganng power. The resultng total surplus s dvded proportonally dependng on whch party has more barganng power. As a result, the employees equty share ncreases wth employee barganng power. Because the wage rate, and hence the frm s cost structure, are ndependent of the employees barganng power, so are the producton levels and profts of the frm. As before, t s ntutve that when employees have more barganng power, they wll be better off overall, whle the non-employee owners are worse off. Usng Proposton 3, we have the followng corollary on the perod-1 equlbrum outcomes z and w that takes nto account equlbrum swtches as k changes: Corollary 3. For any k (0, 1), as the employees barganng power β monotoncally ncreases from 0 to 1, the equlbrum porton z of equty stakes frst monotoncally ncreases 22

24 and then jumps down to 0, whle the equlbrum wage rate w frst keeps at a constant and then jumps upward and monotoncally ncreases Comparatve statcs wth respect to parameter k Proposton 4. (1) In the wage only equlbrum, an ncrease n the product market competton parameter k wll decrease the employee wage w ww the frm profts Π ww (β, k), the frm producton q ww (β, k), the non-employee owners resdual proft S ww (β, k), (β, k), and the employee compensaton E ww (β, k). That s, www (β,k) k < 0, qww (β,k) k < 0, Πww (β,k) k < 0, Sww (β,k) < k (β,k) 0, and Eww < 0, for = 1, 2. k (2) In the employee ownershp equlbrum, an ncrease n the product market competton parameter k wll ncrease the equlbrum porton z zz employee wage w zz (β, k), the frm producton q zz (β, k), the nonemployee owners resdual proft S zz (β, k) of equty stakes, but decrease the (β, k), the frm profts Π zz (β, k), and the employee compensaton E zz (β, k). That s, zzz (β,k) k > 0, wzz (β,k) k < 0, qzz (β,k) k < 0, Πzz (β,k) k < 0, Szz (β,k) k < 0, and Ezz (β,k) k < 0, for = 1, 2. In Proposton 4, all varables except z decreases wth product market competton k n both types of equlbrum. The ntuton s as follows. It s natural that compettve pressure tends to reduce frms profts Π and hence non-employee owners welfare S. As a result, n a more compettve product market, frms can only afford to pay lower wage rates w. Employees are worse off because of the lower total wages and n case of equty compensaton, lower profts. In the employee ownershp equlbrum, as the product market becomes more compettve, frms have a greater ncentve to lower ther wage rates by offerng larger equty stakes to ther employees, whch explans why the equlbrum equty stake z zz wth k. (β, k) ncreases 23

25 Proposton 4 mples the followng corollary on the perod-1 equlbrum outcomes z and w that takes nto account equlbrum swtches as β changes: Corollary 4. When β s hgh, as the product market competton parameter k monotoncally ncreases from 0 to 1, the equlbrum porton z of equty stakes s kept constant at 0, whle the equlbrum wage rate w monotoncally decreases. When β s low, as k monotoncally ncreases from 0 to 1, z frst stays constant at 0 and then jumps upward and monotoncally ncreases, whle w frst monotoncally decreases and then jumps downward and monotoncally decreases. 4. Eff cency analyss In ths secton, we explore the normatve mplcatons of offerng employees an equty stake. Gven that our focus s on the choce of compensaton contracts, whch occurs n perod 1, we wll keep the perod-2 and perod-3 subgames at ther equlbra, respectvely. Ths approach s standard n the lterature. For nstance, n the eff cency analyss of Goldsten, Ozdenoren, and Yuan (2013), the authors vary the level of coordnaton n nvestors tradng decsons, whch s the focus of ther paper, whle keepng all the other equlbrum features of the economy. We compare settngs where ether both sets of owners choose a wage-based contract or both sets of owners choose an equty-based contract. Ths treatment s also appealng n the sense that these two optons are the only possble equlbrum outcomes characterzed n Proposton 2. The varables of nterest are: q, the producton of each frm; Π, the profts of each frm; S, the resdual profts of the non-employee owners; and E, the compensaton of employees. It s clear that varables S and E capture the welfare of non-employee owners and employees, respectvely. Varables q and Π serve two purposes. Frst, they measure the producton 24

26 eff cency assocated wth each frm. Note that by Lemma 1, we have Π = q 2 n equlbrum (whch s mpled by the frst-order condton of each frm s producton decsons n perod 3), and so these two producton eff cency measures are essentally the same. Second, Π and q also measure consumers welfare. Specfcally, by nsertng the consumers demand functon (2) nto ther objectve functon (1) and by notng q 1 = q 2, we can compute the consumers utlty evaluated at the perod-3 product market equlbrum as follows: U (q 1, q 2 ) = (1 + k) Π = (1 + k) q 2. (20) Therefore, more eff cent producton ultmately mproves consumers welfare. Usng Proposton 1, we can characterze the eff cency mplcatons of offerng equty compensaton as follows. Proposton 5. Relatve to both frms offerng the wage-based contract, when both frms offer the equty-based contract, we have: (1) Frm producton and profts that are hgher,.e., q zz Π ww (β, w) for = 1, 2; (β, w) > q ww (β, w) and Π zz (β, w) > (2) Consumers that are better off,.e., U (q zz 1 (β, w), q zz 2 (β, w)) > U (q ww 1 (β, w), q ww 2 (β, w)) ; (3) Non-employee owners that are worse off,.e., S zz (β, w) < S ww (β, w) for = 1, 2; and (4) Employees that are better off f and only f ther barganng power s suff cently hgh,.e., E zz (β, w) > E ww where ˆβ 3 (k) 2( k3 +6k 2 +4k 8) k 2 (2+k). { (β, w) (for = 1, 2) β > Max 0, ˆβ } 3 (k), As we dscuss above, equty-based contracts enable frms to lower ther negotated wage rates. These lower wage rates lead to a lower margnal cost of producton, a greater volume of producton, and more profts for each frm. From equaton (20), consumers also beneft from the resultng greater producton. Ths explans Parts (1) and (2) of Proposton 5. 25

27 Part (3) of Proposton 5 shows that both groups of non-employee owners are strctly worse off under equty-based contracts than under wage-based contracts. Ths welfare result has two mplcatons for the propertes of the equlbrum characterzed by Proposton 2. Frst, accordng to Part (1) of Proposton 2, when β (0, ˆβ ) 1, each frm s non-employee owners offerng equty compensaton s a domnant strategy and thus, the employee ownershp equlbrum consttutes the unque equlbrum n perod 1. However, by Part (3) of Proposton 5, both sets of non-employee owners would be better off had they been able to commt to compensatng employees wth wages only. Thus, whle the prevalng employee ownershp equlbrum s a unque pure strategy equlbrum when β < ˆβ 1, t s also a Prsoner s Dlemma for each set of non-employee owners. The ntuton for ths result s as follows. Although the focal frm can negotate a lower wage rate w and make tself more proftable by adoptng the equty-based contract, the competng frm s best response to ths decson s to also offer equty-based compensaton when β < ˆβ 1. When both frms adopt the equty-based contract, there s party n wages across both frms, ex post, resultng n nether frm havng a compettve cost advantage over the other. However, each frm s non-employee owners stll retan a dluted poston n the frm as a result of provdng an equty stake to ther employees. Taken together, each frm s owners would have been better off, had they both been able to commt to provdng wages only n the game s frst perod. 7 Second, by Part (2) of Proposton 2, when β [ˆβ1, ˆβ 2 ], both the employee ownershp equlbrum and the wage only equlbrum are supported. Nonetheless, accordng to Part (3) of Proposton 5, the latter equlbrum Pareto domnates the former n terms of non- 7 Frms can also end up wth a Prsoner s Dlemma n the settngs derved n Brander and Lews (1986) and Fershtman and Judd (1987), where each frm tres to become more aggressve n the product market by commttng to takng on more debt or by rewardng managers wth revenues more than profts. The commtment seems to be more credble n our settng, because wages and employee ownershp are more vsble and recontractng s more costly than t s when dealng wth ndvdual credtors or managers. 26

28 employee owners payoff. Corollary 5. (1) When β (0, ˆβ 1 ), the employee ownershp equlbrum prevals as the unque equlbrum n perod 1 and t s a Prsoner s Dlemma from non-employee owners perspectve. (2) When β [ˆβ1, ˆβ 2 ], among the two pure strategy equlbra n perod 1, the wage only equlbrum Pareto domnates the employee ownershp equlbrum, n terms of non-employee owners welfare. Part (4) of Proposton 5 examnes the welfare of employees for each frm. Relatve to wage-based contracts, offerng equty-based contracts makes employees face a trade-off. Frst, under equty-based contracts, ther wage rate s lower, and so they suffer n terms of total wages. Second, equty-based compensaton provdes employees wth a beneft by allowng them to get a porton of the frm s profts. When employee barganng power β s relatvely hgh, employees can bargan for a larger equty stake, and thus ther beneft from proft sharng s larger than the cost to reduced wages. Ths outcome makes employees better off overall. By contrast, when β s suff cently low, employees are gven a smaller equty stake, ex post, and n ths case lower wages outwegh the proft sharng benefts, so that employees of each frm are worse off than f ther respectve owners had offered them wages only. [INSERT FIG. 6 HERE] Ths result, together wth Part (1) of Corollary 5, mples that when the employee ownershp equlbrum s the unque supported equlbrum n perod 1, all the supply-sde stakeholders of each frm.e., employees and non-employee owners can be worse off than f both frms non-employee owners could commt to offerng wages only. When ths outcome happens, we label the prevalng equlbrum as a frm neff cent equlbrum, snce the welfare of all stakeholders wthn the frm could be mproved. We use Fg. 6 to plot the regon 27

29 of parameters (k, β) that supports frm neff cent equlbra. The formal characterzaton of ths regon s provded n the followng corollary. Corollary 6. When β < Mn {ˆβ1, Max {0, ˆβ }} 3, the employee ownershp equlbrum s the unque pure strategy equlbrum and t s frm neff cent. Notably, nsghts from Km, and Oumet (2014) and Faleye, Mehrotra, and Morck (2006) suggest that, when employees are granted large equty stakes n the company, t s possble that all partes become worse off. It seems puzzlng that a decson to grant large equty stakes could arse endogenously f those equty stakes make both non-employee owners and employees worse off. Corollary 6 provdes a potental explanaton for ths puzzle. That s, when β < Mn {ˆβ1, Max {0, ˆβ }} 3, the frm neff cent equlbrum arses endogenously as the unque equlbrum. In ths equlbrum, each frm s owners offer ther employees equty stakes and, at the same tme, both non-employee owners and employees are worse off than f each frm s owners had offered ther employees wages only. 5. Emprcal mplcatons In ths secton, we frst use our analyss to explan several exstng emprcal fndngs n the lterature and then make testable predctons on the ncdence of equty compensaton The UAW example We use the analyss n Secton to generate nsghts regardng the 2009 contract negotatons between the Unted Auto Workers (UAW) and General Motors and Chrysler. The auto ndustry s characterzed by ntense nter-ndustry competton and drect labor hours are a sgnfcant nput n the producton process for the ndustry. These two features ft well wth our model settng. As Cody (2015) ponted out, the UAW entered ths partcular contract 28