Competition, Human Capital and Innovation Incentives

Transcription

1 Competton, Human Captal and Innovaton Incentves Competton, Human Captal and Innovaton Incentves Abstract Ths paper sheds lght on the changng nature of the frm and offers an explanaton for why nnovatve, human captal ntensve frms tend to operate n compettve envronments, as dscussed n Zngales (JF, 2000). We develop a model n whch employees ncentves to acqure human captal, a necessary nput for nnovaton, depend on the number of frms competng for employee human captal. A key nsght of our paper s that frms operatng n the same compettve ndustry have a hgher degree of relatedness, snce they nvest n smlar and more compatble technologes. Ths mples that employees n more compettve ndustres develop human captal that can be transferred more easly from one frm to another and, thus, can extract more rents (.e., greater wages) from ther frms. Antcpatng ther hgher rent extracton ablty, employees nvest more n human captal and nnovate more. Thus, competton n the market for nnovaton leads to competton for employee human captal and promotes nnovaton. We show that, under certan condtons, frms prefer to operate n a compettve product market n order to become more nnovatve. In ths way, greater competton emerges endogenously and leads to more nnovaton. Hence, our analyss obtans endogenously the emergence of today s human captal ntensve frms whch are hghly nnovatve n spte of operatng under greater competton than ever. We also show that horzontal mergers may be detrmental to nnovaton generaton, and that frms may prefer to preserve a compettve envronment n order to provde better ncentves for ther employees. Ths fndng mples that, whle nternal competton wthn a frm may be detrmental for nnovaton (as n Rotemberg and Saloner, 1994), external competton may promote effort and foster nnovaton. Fnally, our paper has mplcatons for the choce of ndustry standards, such as open source technologes, and the adopton of contractual measures that hnder employee moblty, such as no-compete clauses.

2 1 Introducton The last two decades have wtnessed three major changes on the nature of frms, as dscussed n Zngales (2000). The frst s that ownershp of physcal assets no longer represents a source of comparatve advantage for frms snce developments n fnancal markets and easer access to captal markets sgnfcantly ncreased ther ablty to nvest n physcal assets. As a result, frms value generatng ablty today depends much more on the human captal they employ rather than on the physcal captal they own. Thus, recrutng, retanng and motvatng employees becomes a crtcal step for value creaton. The second change s that shortened product lfe cycles and ncreased worldwde competton have made t more vtal for frms to contnuosly nnovate. Ths trend has rased even further the mportance and the prce of human captal, the most crtcal and expensve nput for nnovaton. The thrd major change s that employees now have a hgher ablty to move from one frm to another as a result of ncreased competton. The presence of a greater number of frms competng n smlar product markets has ncreased employee moblty, and hence the prce of human captal. Interestngly, n spte of beng exposed to greater competton than ever, today s frms are remarkably successful n generatng new products and technologes at an unprecedented pace. Our paper tes these trends together by establshng a new, postve lnk between competton and nnovaton ncentves n human captal ntensve frms. We argue that human captal ntensve frms may beneft from competton n the product market because t creates competton for employee human captal, ncreasng the prce of human captal and thus enhancng employees ncentves to nvest n ther own human captal. Hence, our model helps to explan the emergence of today s human captal ntensve frms as hghly nnovatve ventures, despte beng subject to ntense competton. Our paper also helps to explan why frms may beneft from employee moblty, and why human captal ntensve frms may choose not to mpose on ther employees no-compete clauses that would restrct employee moblty across frms n the same ndustry. Fnally, our paper examnes the effect of merger actvty on nnovaton ncentves. We show that, n order to preserve strong nnovaton ncentves, human captal ntensve frms may prefer to forego horzontal mergers, even when these mergers ncrease ther market power. The ntuton of our model s as follows. In our set-up, nnovaton arses as an outcome of costly nvestment n human captal by employees. Human captal orgnates from an nvestment n the knowledge and sklls necessary to generate an nnovaton. In our model, frms can operate n a protected envronment, facng no competton from other frms, or operatng n a compettve envronment n the presence of rval 2

3 frms. A key nsght of our paper s that frms competng n smlar product markets have a hgh degree of relatedness, snce they nvest n smlar technologes. Ths mples that employees n more compettve ndustres wll develop human captal that can be transferred more easly from one frm to another. Due to ther ablty to transfer ther human captal to competng frms, employees can extract hgher rents from ther employers and nternalze a greater part of the return from ther human captal nvestment. Thus, antcpatng ther hgher rent extracton ablty, employees nvest more n human captal and nnovate more. In ths way, our paper establshes a lnk between product market competton and the rate of nnovaton through the benefcal effect of competton on the accumulaton of human captal. An nterestng mplcaton of our paper s that not only employees, but frms as well can beneft from product market competton n spte of the fact that competton allows employees to extract hgher rents and reduces a frm s market share. We show that competton presents frms wth the followng tradeoff. On the one hand, t mproves employee ncentves to nnovate by creatng an nter-frm market n whch frms compete for employees. Snce frms proft from the nnovatons generated by ther employees, they wll also beneft from the compettve envronment that encourages nnovaton. On the other hand, competton hnders nnovaton ncentves and frm proftablty by reducng a frm s market share and ts ablty to proft from nnovaton. In our paper, we show that the postve effect of competton on ncentves may outwegh ts negatve effect, and that frms may ultmately beneft from competton. We show that the beneft of competton s stronger when nnovaton ncentves are low, whch happens when ether employees have low barganng power or when the cost of exertng nnovaton effort s large. We also suggest that a compettve envronment s more lkely to emerge n sectors characterzed by greater human captal ntensty. Projects wth greater human captal ntensty nvolve more costly human captal nvestments and therefore beneft most from the addtonal ncentves provded by a compettve envronment. Thus, our model helps to explan why today s human captal ntensve frms tend to operate n hghly compettve envronments (as dscussed n Zngales, 2000). Economsts have long dscussed whether nnovaton flourshes better n an open and compettve envronment (where nnovators threaten ncumbents wth new products), or n a protected envronment (where nnovators harvest the frut from ther effort whle shelded from potental mtators). For example, Schumpeter hmself evolved from hs earler entrepreneural theory of nnovaton (see Schumpeter, 1911) to hs later vew that a market structure nvolvng large frms wth a consderable degree of market power s the 3

4 prce that socety must pay for rapd technologcal progress. 1 Most of the theoretcal work n Industral Organzaton has stressed the later Shumpeteran vew that competton, by decreasng the potental rents avalable to nnovators, s detrmental to nnovaton (see, for example, Salop, 1977, Spence, 1984, Aghon and Howtt, 1992). Ths predcted negatve relatonshp between competton and nnovaton ncentves, however, has been challenged by recent emprcal work, such as Nckell (1996), Blundell, Grffth, and Van Reenen (1999), and Knott and Posen (2003), whch document a postve relatonshp between product market competton and nnovaton. A remarkable excepton to ths lterature s provded by Aghon, Bloom, Blundell, Grffth, and Howtt (2002), whch develops a model predctng an nverted u-shaped relatonshp between nnovaton and competton. In ths model, moderate competton s benefcal for nnovaton because, by reducng prennovaton profts, t ncreases the ncremental benefts that an nnovator gans from leapfroggng ts rvals. A postve effect of competton on manageral ncentves (and thus on nnovaton) s also predcted by some agency-based models. For example, n Hart (1983) more competton n the product market allows a frm s owners to wrte better ncentve contracts for managers, strengthenng manageral ncentves and thus nducng more effort. In Schmdt (1997) and Aghon, Dewatrpont and Rey (1999) the threat of bankruptcy nduces managers to exert more effort as a way to avod lqudaton. More recently, n a model wth endogenous market entry, Rath (2003) shows that the mpact of competton on effort depends on the sources of varaton n the degree of competton. The paper fnds that greater competton ncreases effort f t s due to greater product substtutablty, whle t decreases effort f t s due to lower entry costs. Our paper presents a new explanaton for the relatonshp between nnovaton and competton. In our model, competton and nnovaton are both endogenous and nteract n essental ways. Our analyss shows that, under certan condtons, frms prefer to compete n the product market n order to become more nnovatve. Thus, greater competton emerges endogenously n the ndustry and leads to more nnovaton: the desre to nnovate spurs competton and competton leads to more nnovaton. An addtonal mplcaton of our model s that human captal-ntensve frms may beneft from promotng ther employees moblty. For example, frms may beneft from operatng n a legal envronment that does not put any restrctons on the moblty of employees. Ths mplcaton s consstent wth the dea that the presence of legal restrctons to nter-frm moblty, such as the ncluson of no-compete clauses n 1 Nelson and Wnter (1985), page 278. See, also, the dscusson n Schumpeter (1942), pages

5 employment contracts, may hnder nnovaton. In an extenson of our model, we show that n equlbrum frms choose not to mpose such clauses on ther employees n order to enhance employee ncentves. Thus, our model supports the vew dscussed n Glson (2004) suggestng that an mportant element accountng for the better relatve performance of Slcon Valley wth respect to Boston s Route 128 can be traced to the dfferences n ther legal envronments (snce Calforna does not enforce no-compete clauses, whle Massachusetts does). Our mode also sheds new nsghts on the choce of ndustry standards and on the locaton of frms. Snce employee moblty among frms can be promoted by the adopton of compatble technologes, our model shows that frms may beneft from the creaton of homogeneous ndustry standards that facltate the transferablty of employee human captal from one frm to another. In a smlar way, frms may beneft from creatng ndustry clusters or formng ndustral hubs. By locatng n the same geographcal area, frms ncrease employee moblty from one frm to another and facltate the creaton of an ntra-ndustry market for employee human captal, wth a postve spllover on employee ncentves and nnovaton. In ths way, our paper s related to a recent paper by Almazan, De Motta and Ttman (2004), whch studes the lnk between human captal nvestment and frm locaton. Snce geographcal proxmty promotes the development of a compettve labor market, ths paper shows that frms prefer to cluster when employees pay for ther own tranng, whle they locate apart when frms pay for ther employees human captal development. Our paper dffers from thers n an mportant way. Almazan, de Motta and Ttman (2004) focuses on the nteracton between locaton and the development of human captal, abstractng from the nteracton between locaton and product market competton. In our paper we focus precsely on the lnk between product market competton and ncentves to accumulate human captal. In our model competton n the product market for nnovaton leads to competton for employee human captal, promotng human captal formaton and ultmately fosterng nnovaton. Our model mples that frms may be wllng to cluster even f ths choce results n greater employee wages and competton n the product market. In our analyss, the benefcal effect of competton on ncentves s partcularly appealng for frms when employees have low barganng power n wage negotatons. When frms have a hgh level of barganng power, they can approprate a large share of the value from the nnovaton generated by ther employees, reducng employee ncentves to nnovate. The creaton of an nter-frm labor market through competton n the product market allows employees to retan a greater share of the value of the nnovaton they create, promotes nnovaton and ultmately benefts frms. In ths way, our work s related to the earler 5

6 lterature, started by Fama (1980) and Holmstrom (1982), whch emphaszes the postve role of the nterfrm manageral labor market as an ncentve devce. Fnally, our paper examnes the effects of horzontal mergers on employee ncentves to develop human captal, and shows that horzontal mergers may be detrmental for nnovaton ncentves. Horzontal mergers affect ncentves n three ways. The frst one s that, by consoldatng competng frms, horzontal mergers reduces competton for human captal whch affects ther ncentves adversely. The second way s that a horzontal merger ntroduces nternal competton between the employees n the merged frm, agan mpactng employee ncentves negatvely. Ths reducton n nnovaton ncentves (due to the nternal competton n the merged frm) s smlar to that dentfed n Rotemberg and Saloner (1994). The thrd effect of a merger on ncentves s postve, snce the merger elmnates competton between frms n the product market and ncreases ts market power. Our analyss shows that, under certan condtons, frms prefer to forego the ncreased market power provded by a horzontal merger n order to preserve the benefcal effect of a compettve envronment on ther employees ncentves. Ths mples that, whle nternal competton may be detrmental for nnovaton, external competton may promote t. Thus, frms wll beneft from belongng to a compettve ndustry, even f ths comes at the expense of competton n the product market. The paper s organzed as follows. In secton 2, we take the market structure under whch the two frms operate as gven and we present the basc results of the paper. In secton 3, we endogenze the choce of the market structure, that s, whether the frms choose to compete by enterng nto the same market or to have monopoly power by enterng nto dfferent markets. Secton 4 analyzes frms ncentves to nvest n nnovaton under competton and monopoly. In secton 5 we examne frms ncentves to lmt or enhance the ablty of ther employees to leverage ther human captal outsde the frm. Secton 6 studes the mpact of a horzontal merger on nnovaton ncentves. Secton 7 concludes. All proofs are n the Appendx. 2 The Basc Model We consder an economy endowed wth two frms and two employees. All agents are rsk-neutral and there s no dscountng. We assume that at the begnnng of the game each frm s already matched wth one of the two employees. The two frms are human captal ntensve n the sense that they create value by mplementng ther employees nnovatons. The nnovaton cycle nvolves two stages of a project. The 6

7 frst stage of the project s performed by the employee and, f successful, generates an nnovaton. 2 The second stage nvolves the development and commercalzaton of the nnovaton and s performed by the frm wth the collaboraton of the employee. We assume that the actve partcpaton and effort of the employee who ntally generated the nnovaton s necessary also n the second stage for ts development nto a fnal product. 3 The success probablty n the frst stage of the project depends on an unobservable effort exerted by the employee, whch s denoted by e, = 1, 2. Employee effort determnes the success probablty of the project: p (e ) = e [0, 1]. Exertng effort s costly: we assume that effort costs are convex and gven by k 2 e2. The parameter k measures the cost of exertng such effort. We nterpret employee effort broadly, as representng the costly nvestment made by the employee to acqure the knowledge and human captal necessary for the success of the project. 4 The human captal acqured by an employee n the frst stage of the project s essental for both the generaton and the development of an nnovaton. The key feature of our model s that employee ncentves to acqure human captal depend on the market structure n whch the two frms operate. If a frm operates as a monopolst, there are no rval frms n the product market and employee nnovatons can only be developed and commercalzed wthn the orgnal frm. Ths s because the human captal developed by the employee s frm-specfc and s valuable only f deployed wthn the orgnal frm. If the two frms operate n the same product market, they wll have technologes that are related to each other. In ths case, t wll be easer for employees wth an nnovaton to transfer (albet mperfectly) ther nnovaton and human captal from one frm to the other. Ths mples that the presence of other frms n the same product market enables employees to develop human captal that can be valued outsde the orgnal frm, allowng employee moblty. Thus, competton n the product market facltates the transfer of employee sklls and promotes the creaton of an external market for employee human captal. As we 2 Innovaton can be broadly nterpreted as any new dea, process or product whch mproves frm proftablty. 3 Ths assumpton mples that f an employee wth a successful nnovaton leaves hs frm at the end of the frst stage, the frm cannot mplement the nnovaton wthout the orgnal employee. Smlarly, we assume that f the employee leaves the frm, he cannot mplement the nnovaton by hmself but he must jon another frm wth the resources and capabltes necessary to mplement the nnovaton. We assume also that the employee needs the frm s resources durng both stages of the producton process, whch mples that he can generate an nnovaton only f he has joned a frm at the begnnng of the game. In secton 4, we model frms nvestment n nnovaton explctly. 4 As such, parameter k can be also nterpreted as measurng the degree of human captal ntensty of the project. Ths may be seen by notng that projects characterzed by greater human captal ntensty requre more knowledge and effort and therefore are nherently more costly, per unt of success probablty e, than projects wth lower human captal ntensty. 7

8 wll dscuss below, the presence of an external market n whch frms compete for human captal allows employees to extract more rents (.e., hgher wages) from ther frms. In ths way, competton ncreases employee ncentves to nvest n human captal and promotes nnovaton. We assume that employee effort s not observable, exposng frms to moral hazard. Followng Stole and Zwebel (1996a and 1996b), and n the sprt of Grossman and Hart (1986) and Hart and Moore (1990), we also assume that frms and employees cannot wrte bndng contracts on the development of successful nnovatons and that they can wthdraw ther partcpaton from the project before the development phase. Ths mples that f an employee generates an nnovaton the allocaton of the surplus from the nnovaton s determned, as n Stole and Zwebel (1996a and 1996b), by ntra-frm barganng between the frm and the employee at the nterm date before the second stage of the project s performed. Ths also mples that contracts wrtten ex-ante between a frm and ts employee on how to share the fnal surplus, such as equty contracts (or optons, as n Noldeke and Schmdt, 1998), are neffectve snce both the frm and the employee can (unlaterally) wthdraw ther essental assets and partcpaton (human captal, n the case of the employee) from the development phase of the nnovaton. 5 The outcome of barganng process between the employee and the frm (that s, the dvson of the project s payoff between them) depends on ther relatve barganng power and on each party s outsde opton. We assume that each frm s outsde opton whle barganng wth ts employee s lmted by the fact that the frm cannot replace ts current employee wth a new one from the general labor market populaton, but t can only hre an employee from a rval frm n the same product market. Ths assumpton captures the noton that t s mpossble for the frm to contnue producton by replacng the orgnal employee wth a new one from the generc (unsklled) labor market pool. Ths assumpton s easy to justfy f employees need a tranng n the frst perod to produce n the second perod. The presence of an outsde opton for the employee depends on the employee s ablty to transfer hs human captal from one frm to the other. Ths wll be possble only f the employee can move from hs orgnal frm to a rval frm n the same product market, that s, f a rval frm exsts n the same product market. In ths case, competton between frms n the product market, by creatng competton for employee human captal, affects the allocaton of the surplus between the frm and the employee. Thus, product market competton nfluences employee effort and the overall effcency of the nnovaton generaton process. 5 For a further dscusson on the role of employment at wll and renegotaton on surplus allocaton, see Stole and Zwebel (1996a) and (1996b). 8

9 The market structure (that s, whether the frms operate under monopoly or competton) affects project payoffs as follows. If a frm s a monopolst n ts own market, and the frst stage of the project has been successful, then the project generates a payoff M. 6 If the two frms operate n the same product market, then the payoff from the project wll depend on whether one or both frms have been successful n the frst stage of ther projects. If both frms have been successful (that s, f employees at both frms obtan an nnovaton) the two frms wll compete n the commercalzaton of the nnovaton. We assume that n ths case the two frms wll engage n Bertrand competton, and each project s payoff wll be equal to 0. 7 If, nstead, one of the two frms fals, then the successful frm wll be a monopolst, and the payoff from the project wll be M C. Note that the two market structures may have product markets of dfferent sze, wth the compettve structure havng a greater (smaller) market sze than the monopolstc market structure f M C > (<)M. Fnally, f an employee fals to obtan an nnovaton, the payoff from the project s zero. In ths secton we take the market structure under whch the two frms operate as gven, and we compare the nnovaton ncentves under monopoly and competton. 8 The basc game unfolds as follows. At t = 0, after observng whether hs frm s operatng under monopoly or competton, each employee exerts effort, whch determnes the success probablty of hs project. Effort choces are made smultaneously by the two employees. At t = 1, the outcome of the frst stage of the project s known. If the frst stage s successful, then each employee bargans wth hs frm over the dvson of the surplus from the commercalzaton of the nnovaton. The share of the surplus earned by the employee may be nterpreted as the wage (or bonus) that the employee receves for hs contrbuton necessary for the further development and commercalzaton of the nnovaton. When barganng wth hs frm, the employee captures a share β [0, 1] of the net jont surplus that depends on hs barganng power. Thus, we wll refer to the parameter β as measurng the employee barganng power. The payoffs from barganng depend on the employee outsde optons, and on whether the two frms 6 We assume n ths secton that the sze of the product market, whch determnes the project payoff M, s gven. Ths assumpton s relaxed n Secton 4, where we allow frms to make at the outset of the game a costly nvestment that affects the sze of the product market. 7 We make ths assumpton for analytcal tractablty. The man results of our paper can be extended to nclude dfferent forms of product market competton between the two frms. 8 Ths assumpton s relaxed n Secton 3, where we allow frms to endogenously choose the market structure n whch they operate. 9

10 operate n the same product market, and therefore compete, or they operate n dfferent product markets, and therefore are monopolsts n ther respectve markets. If the two frms are monopolsts n ther own market, the employees cannot transfer ther frm-specfc sklls to the other frm. Thus, both employees and frms have zero outsde optons whle barganng. If the two frms operate n the same product market, employee human captal can be redeployed at the rval frm. The possblty of redeployng human captal at the competng frm gves the employee an outsde opton when barganng wth hs own frm. We assume that an employee can transfer hs nnovaton to the competng frm and commercalze t wth a potental payoff δ M C. We nterpret the parameter δ as measurng the degree of transferablty of employee human captal. 9 At t = 3, the payoff s realzed and the cash flow s dstrbuted. We frst consder the case n whch the frms do not compete, that s, each frm operates n ts own market and employee human captal s not transferable from one frm to another. We consder next the case n whch the two frms compete n the same product market, allowng employees to transfer ther human captal from one frm to another. 2.1 Innovaton Incentves under Monopoly If frms operate n a monopolstc envronment, employees develop frm-specfc human captal and nnovaton that they cannot transfer from one frm to another. Ths mples that both employees and frms have zero outsde optons when barganng at the nterm date over the dvson of the project s payoff, M. We model the barganng game between an employee and hs frm as a standard alternatng-offers game n whch the two partes make alternatng offers under the threat that barganng breaks down wth a certan exogenous probablty (see, for example, Bnmore, Rubnsten, and Wolnsk, 1986). If barganng breaks down, employees and frms obtan ther outsde optons, whch, n the case of monopoly, are equal to zero for both partes. One can show that, as the probablty that the barganng process breaks down tends to zero, the outcome of the subgame perfect equlbrum of the barganng game s such that the employee and the frm receve a fracton β and 1 β, respectvely, of the surplus that they jontly generate. As a result, employees obtan a payoff equal to βm, whle frms capture the remander, whch s equal to 9 We assume ntally that a frm cannot prevent ts employee from jonng the rval frm. We relax ths assumpton n Secton 5, where we assume that each frm can requre ts employee to sgn a no-compete agreement, effectvely preventng the employee from jonng the rval frm. 10

11 (1 β)m. 10 In antcpaton of hs payoff from barganng, employee chooses hs effort level e M by maxmzng hs expected profts, π M E, gven by Correspondngly, frm s expected profts, π M F, are gven by max e π M E βme M k 2 (em ) 2 ; = 1, 2. (1) π M F (1 β)me M ; = 1, 2. (2) The optmal level of effort under monopoly, e M, and the correspondng level of expected profts for the employee, π M E, and the frm, πf M, and total profts, πt M, are characterzed n the followng lemma. 11 Lemma 1 The optmal level of effort under monopoly s e M = e M j = e M βm k. (3) The correspondng expected profts for employees and frms are π M E = β2 M 2 2k ; πm F = (1 β)βm 2 k ; π M T π M E + π M F = 2 (2 β)βm, = 1, 2. (4) 2k It s mmedate to see that the optmal level of effort, e M, and proft levels are ncreasng functons of the monopoly payoff, M, and decreasng functons of the cost of exertng effort, k. Ths mples that, all else equal, the probablty of obtanng an nnovaton s ncreasng n the project s market sze, and declnng n the cost of exertng effort. The effect of employee barganng power β, n contrast, s ambguous, and s characterzed n the followng lemma. Lemma 2 The optmal level of effort under monopoly (3) s an ncreasng functon of employee barganng power, β. Furthermore, the effect of employee barganng power, β, on the expected profts s as follows: πe M > 0; πf M 0 for β 1 2 ; πt M 0, = 1, 2. (5) A greater level of barganng power, β, allows the employee to extract more surplus from hs frm and leads to a greater nnovaton probablty, e M, and employee expected profts, πe M. The effect of 10 Note that ths dvson of the surplus corresponds to the Nash-barganng soluton n whch the employee s and the frm s barganng powers are, respectvely, β and 1 β, and nether party has an outsde opton. See Bnmore, Rubnsten, and Wolnsk (1986). 11 To ensure nteror solutons we assume that k βm. 11

12 employee barganng power on frm s expected profts, πf M, s ambguous and depends on the trade-off of two opposng effects. On the one hand, greater employee barganng power leads to a hgher level of effort and nnovaton probablty, whch always benefts the frm under monopoly. On the other hand, a greater barganng power allows the employee to extract more rents, whch s costly for the frm. The frm benefts from hgher employee barganng power when the postve ncentve effect domnates the negatve rent extracton effect. Ths happens when the employee barganng power, and therefore effort, s small, that s, when β 1 2. Frms expected profts are maxmzed when the ncentve and rent extracton effects balance each other out exactly, whch n our model occurs when the frm and the employee have the same barganng power, that s, when β = 1 2. Fnally, the total expected profts, πm T, are always an ncreasng functon of employee barganng power. Ths s an mplcaton of the fact that the rent extracted by the employee s just a transfer of surplus between the two barganng partes. Hence, the only effect of an ncrease n employee barganng power on total expected profts s ts postve effect on employee ncentves. 2.2 Innovaton Incentves under Competton If frms operate n a compettve envronment employees develop human captal and nnovaton that can be transferred from one frm to another, whch gves them an outsde opton whle barganng wth ther frms. The outcome of barganng between frms and employees, and thus the allocaton of the surplus, depends on whether only one, or both, employees generate an nnovaton. If only one employee, say employee, s successful n generatng an nnovaton, he wll bargan wth hs frm over the dvson of the payoff, M C. Note that ths case dffers from the monopoly case n that now employee has the opton to transfer hs nnovaton and human captal to the competng frm j, wth a payoff of δ where δ M C. 12 We model the barganng game between employee and frm agan as one n whch the two partes make alternatng offers under the threat that the barganng process breaks down wth a certan exogenous probablty. If barganng wth frm breaks down, employee has the opton to start a new round of barganng wth frm j. Thus, the payoff from barganng wth frm j represents employee s outsde opton when barganng wth frm. One can show that, as the probablty that the barganng process breaks down tends to zero, the outcome of the subgame perfect equlbrum of the 12 Note that n equlbrum employees wll never transfer ther human captal and nnovaton to the rval frm snce δ M C. It s straghtforward to extend our model to the case where (wth some exogenous probablty) employees may be more valuable when they redeploy ther human captal outsde ther orgnal frm. Ths case orgnates, for example, when δ > M C, and therefore employees move from one frm to another n equlbrum. 12

13 barganng game between frm and employee s such that the employee and the frm receve the value of ther outsde optons (the value that they can obtan n the case of a breakdown n barganng), plus the fractons β and 1 β, respectvely, of the surplus that they jontly generate net of the sum of ther outsde optons. 13 We can determne the payoffs from barganng between frm and employee by proceedng backwards. If barganng between employee and frm breaks down, employee has the opportunty to bargan wth frm j. In ths second barganng game, both employee and frm j have zero outsde optons. The employee and the frm wll therefore dvde the jont surplus, δ, accordng to ther barganng power obtanng bδ and (1 b)δ respectvely, where b represents employee s barganng power when barganng wth frm j. 14 The payoff that employee obtans when barganng wth frm j, whch we denote as bδ, wth 0 M C, represents the value of employee s outsde opton whle barganng wth frm. Snce employee j has faled to obtan an nnovaton, frm has an outsde opton wth value zero. Ths mples that employee s payoff from barganng wth frm s equal to + β(m C ) = βm C + (1 β). Correspondngly, frm s payoff s gven by (1 β)(m C ). If both employees have been successful, the frms compete n the product market and both frms and employees earn zero profts. In antcpaton of hs payoff from barganng, employee chooses hs effort level, e C, by maxmzng hs expected profts, πe C, gven by max e π C E e C (1 e C j )(βm C + (1 β) ) k 2 (ec ) 2 ; = 1, 2; j. (6) Correspondngly, frm s expected profts, π C F, are gven by π C F e C (1 e C j )(1 β)(m C ); = 1, 2; j. (7) The frst-order condton of (6) provdes employee s optmal response, gven employee j s choce of effort, and s as follows: e C (e C j ) = (1 ec j )(βm C + (1 β) ) k = βm C e C j βm C + (1 e C j )(1 β) ; = 1, 2; j. (8) k 13 Note that ths dvson of the surplus corresponds to the Nash-barganng soluton wth outsde optons, n whch the employee s and the frm s barganng powers are, respectvely, β and 1 β. See agan Bnmore, Rubnsten, and Wolnsk (1986). 14 Note that ths specfcaton allows employee s barganng power whle barganng wth frm j, gven by b, to dffer from hs barganng power whle barganng wth frm, gven by β. 13

14 From the frst-order condton (8), t can mmedately be seen that employee s effort s a decreasng functon of employee j s effort, whch mples that effort choces by the two employees are strategc substtutes, due to competton. Furthermore, employee s effort s an ncreasng functon of project payoff, M C, and of the value of hs outsde opton,, and a decreasng functon of the cost of exertng effort, k. A comparson of the frst-order condtons under monopoly (3) and under competton (8) allows us to dentfy the mpact of competton on employee ncentves to exert effort. Competton affects employee ncentves n three ways. The frst effect, measured n the RHS of (8) by the term βm C, s of ambguous sgn and depends on the sze of the compettve market relatve to the monopolstc market (that s, whether M C > M or M C < M). The second effect, measured by the term e C j βm C, s negatve and reflects the reducton n profts due to competton n the product market. If the rval frm successfully obtans an nnovaton, whch occurs wth probablty e C j, competton between the two frms reduces employee payoff to zero (from βm C ) wth a negatve mpact on employee effort. The thrd effect, measured by the term (1 e C j )(1 β), s postve and orgnates from the benefcal mpact of competton on employee ncentves to acqure human captal. If frms compete n the same product market, employee s human captal can be redeployed at the competng frm (although ths wll never happen n equlbrum). The presence of ths outsde opton enables the employee to extract more rents from hs frm, enhancng hs ncentves to exert effort. Note that ths effect arses only when the employee of the rval frm has faled, whch happens wth probablty 1 e C j. We now characterze the Nash-equlbrum of the effort subgame. Lemma 3 The unque (symmetrc) Nash-equlbrum of the effort subgame s gven by: e C = e C j = e C βm C + (1 β) k + βm C + (1 β). (9) The correspondng expected profts for frms, employees and total profts are πe C k (βm C + (1 β) ) 2 = 2 ; = 1, 2, 2 (k + βm C + (1 β) ) (10) πf C = k(1 β) (βm C + (1 β) ) (M C ) (k + βm C + (1 β) ) 2 ; = 1, 2, (11) πt C πe M + πf M = k (βm C + (1 β) ) (M C + (1 β)(m C )) 2 (k + βm C + (1 β) ) 2 ; = 1, 2. (12) We now establsh some prelmnary results that wll be useful n our subsequent analyss. Note frst that an mportant dfference between the monopoly case and the compettve case s that a greater (equlbrum) 14

15 level of effort s not always desrable for the two frms when they compete n the product market whle t always benefts them under monopoly. Ths property reflects the fact that under competton a greater level of effort by both employees ncreases the probablty that both frms successfully develop the nnovaton and thus compete n the product market, obtanng a zero payoff. The net effect of employee effort on frms expected profts wll then depend on the balance between the beneft of a hgher probablty of nnovaton and the reducton n proftablty due to competton. Ths s establshed n the followng lemma. Lemma 4 The expected profts of the frms as a functon of the Nash-equlbrum effort level, e C, have the followng property: or, from (9), f and only f k βm C + (1 β). π C F e C 0 ff ec 1 2 ; (13) The followng lemmas establsh the propertes of the Nash-equlbrum level of effort and expected profts under competton. Lemma 5 The Nash-equlbrum level of effort of under competton, e C, s an ncreasng functon of the project payoff, M C, of the degree of transferablty of human captal, δ (and, thus, the value of the outsde opton, ), and of the employee s barganng power, β, and s a decreasng functon of the cost of exertng effort, k. Lemma 6 Expected profts of frms and employees under competton are ncreasng functons of the project payoff, M C. The effect of the employee outsde opton,, barganng power, β, and the cost of exertng effort, k, on ndvdual profts are, n contrast, ambguous and are examned n the followng lemmas. Lemma 7 Employee expected profts are ncreasng n the value of ther outsde opton,. Frm expected profts and total expected profts are ncreasng n only f employees have low barganng power: wth β F < β T. πe C > 0; = 1, 2, (14) πf C 0 ff β β F km C (M C + 2k) ; = 1, 2, (M C + 2k)(M C ) (15) πt C 0 ff β β T km C (M C + k) ; = 1, 2, (16) (M C + k)(m C ) 15

16 Lemma 8 Employee expected profts are ncreasng n the value of ther barganng power, β. Frm expected profts and total expected profts are ncreasng n β only f the value of the employee outsde opton s low: πe C πf C π C T > 0; = 1, 2, (17) 0 ff F M C (k(1 2β) βm C ) ; = 1, 2, (18) (1 β)(2k + M C ) 0 ff T M C (k(1 β) βm C ) ; = 1, 2, (19) (1 β)(k + M C ) wth F < T. The presence of the employee outsde opton s, as expected, always benefcal for the employee. As the value of hs outsde opton,, ncreases, the employee can extract more rents from the frm. Ths always ncreases the level of employee effort and employee expected profts. The mpact of the outsde opton on the frm s expected profts, n contrast, s ambguous and depends on the balance of two opposng effects. On the one hand, the avalablty of the outsde opton allows the employee to extract more rents from the frm, whch, all else equal, has a negatve effect on the frm s expected profts. On the other hand, a greater value of ncreases the probablty of an nnovaton by nducng more effort. The postve effect on employee ncentves domnates the negatve effect on rents when employee effort s low, whch happens when the employee has a low barganng power (.e., when β β F ). 15 By a smlar argument, total expected profts are ncreasng n the value of the outsde opton when effort s suffcently low, whch agan happens when the employee has lmted barganng power (.e., when β β T ). 16 The effect of employee barganng power on expected profts mrrors the effect of the outsde opton. As expected, employees always beneft from havng greater barganng power when negotatng wth ther frms. The mpact of employee barganng power on the frm s expected profts, s agan ambguous, reflectng the dual role of the barganng power dscussed n Lemma 2. On the one hand, greater barganng power allows the employee to extract more rents, whch s always detrmental to the frm at the negotatng stage. On the other hand, greater barganng power gves the employee better ncentves and leads to a greater probablty of nnovaton. The postve ncentve effect domnates the negatve rent extracton effect 15 From the defnton of β F n (15), note also that β F > 0 f and only f k > M C, that s, when the cost of exertng M C 2 effort s hgh (and, therefore, the level of equlbrum effort s low). 16 Note agan that, from (16), β T > 0 f and only f k > M C, that s, when the cost of exertng effort s hgh and M C therefore the level of equlbrum effort s low. 16

17 when employee effort s suffcently low. Ths happens when the value of the employee outsde opton s lmted,.e., when F. In a smlar way, total expected profts, πt C, are an ncreasng functon of employee barganng power when the value of the outsde opton s low,.e., when T. 17 Lemma 9 Employee and frm expected profts under competton are decreasng n the cost of exertng effort, k, f and only f k > βm C + (1 β). An ncrease n k affects employee and frm expected profts n two dfferent ways: frst, t makes employee effort more costly, whch leads the employee to reduce hs own effort level; second, t reduces employee effort at the rval frm. By the envelope theorem, the frst effect s always negatve on employee profts, whle the second s always postve, snce each employee s better off when the rval employee exerts lower effort. Lemma 9 mples that the frst (negatve) effect domnates the second (postve) effect only when the equlbrum level of effort s low, that s, when the cost of exertng effort s suffcently hgh, gvng k > βm C +(1 β). Smlarly, frms suffer when ther own employee decreases effort and beneft when the rval frm s employee lowers effort. Lemma 9 shows that the frst (negatve) effect domnates the second (postve) effect agan when the equlbrum level of effort s low, that s, when k > βm C + (1 β) Competton and Innovaton We now present the frst two man results of our paper. Frst, we show that the probablty of obtanng an nnovaton can be greater under competton than under monopoly. Next, we show that frm profts can be greater under competton than monopoly, whch mples that frms themselves may beneft from operatng n a compettve rather than n a monopolstc envronment. Proposton 1 The probablty of obtanng an nnovaton under competton (9) s strctly greater than that under monopoly (3) f and only f ( ) k βm 1 (1 β) βm C + k( M C 1) > 0. (20) M Competton nfluences employee effort and the probablty of nnovaton through three separate channels, whch are represented by the three terms n (20). The frst channel s the postve mpact of the 17 Note that F and β F, and T and β T are related to each other as follows: F = M C(k(1 2β F ) βm C) M C(k(1 β T ) βm C) (1 β T )(k+m C ). (1 β F )(2k+M C ) and T = 18 Note that ths s result s an mplcaton of Lemma 4, whch states that frms suffer from a decrease n the level of effort only when equlbrum effort s low (and, therefore, when the cost of effort k s large). 17

18 competton on employee ncentves to acqure human captal, and s captured by the frst term n (20). As dscussed n the prevous secton, by enablng the employees to develop human captal that s transferable across frms, competton creates an outsde opton for the employees when they bargan wth ther frms. The presence of ths outsde opton allows the employees to extract (1 β) addtonal surplus from ther frms, whch always has a benefcal effect on employee ncentves to exert effort. The second channel, represented by the second term n (20), s gven by the reducton n expected profts due to competton when both employees obtan an nnovaton. Ths effect always has a negatve mpact on employee effort, and s captured by the loss n the employee s share of the payoff, βm C. The thrd channel arses from the potental dfference n market sze under competton and under monopoly and, s measured by the term M C M 1 n (20). Ths effect s of ambguous sgn: t s postve when the market sze under competton s greater than that under monopoly, and negatve otherwse. Note that condton (20) s more lkely to be satsfed when ether employee barganng power s low, that s, when β s low, and when the cost of exertng effort s large, that s, when k s hgh. In ether case, the employee exerts too lttle effort under monopoly. A compettve envronment, on the contrary, allows the employee to extract more surplus from the frm, wth a benefcal effect on hs ncentves to exert effort. An nterestng mplcaton of Proposton 1 s that frms characterzed by greater human captal ntensty are more lkely to beneft from competton. Ths property reflects the fact that projects wth greater human captal ntensty requre more costly human captal nvestment (that s, a greater value of k) and hence they beneft most from the better ncentves provded by a compettve envronment. Proposton 1 shows that employee effort, and thus the probablty of generatng an nnovaton, can be greater under competton than monopoly. Snce frms create value by developng ther employee nnovatons, they may be better off operatng n a compettve envronment, even f ths exposes them to a possble loss n profts and to greater employee rents. Proposton 2 Let M C (M 0, M 1 ), wth M 0 < M = 1 < M 1. Then, there s a threshold level β F (M C,, k) (defned n appendx) such that frm expected profts under competton (11) are strctly greater than those (4) under monopoly f and only f β β F (M C,, k). Furthermore β F (M C,,k) k > 0. Proposton 2 shows that when product markets have smlar szes under competton and monopoly (that s, when M C s close to M), frm profts under competton can be greater than those under monopoly when employee barganng power s suffcently low, that s, when β β F (M C,, k). Competton s partcularly desrable when employees exert too lttle effort under monopoly, whch happens ether when 18

19 employee barganng power s low (.e., a low value of β), or when the cost of exertng effort s hgh (.e., a hgh value of k). Under these condtons, competton n the product market facltates competton for employee human captal, whch promotes the formaton of human captal and mproves effort ncentves. Smlarly, an ncrease n the cost of effort, k, makes competton relatvely more desrable for frms: An ncrease n the cost of effort reduces employee ncentves under monopoly and makes competton relatvely more desrable due to ts postve mpact on effort. In contrast, when employee barganng power s suffcently hgh (that s, when β > β F ), employees already have suffcent ncentves under monopoly. In ths case, from the frm s perspectve, the addtonal ncentves provded by competton do not justfy the hgher rents extracted by employees and the expected losses due to competton. Hence, for hgh values of β (and low values of k) frm profts are lower under competton than under monopoly. 3 Endogenous Competton In ths secton we endogenzed the market structure and we allow frms to choose the market structure under whch they operate. Specfcally, we extend our basc model by allowng the two frms to choose whether to compete wth each other by enterng nto the same product market, or not to compete by enterng nto dfferent product markets where each frm has monopoly power. We wll show that, under certan condtons, the two frms prefer to forgo the benefts of monopoly and, rather, to engage n drect competton for ts benefcal effect on nnovaton ncentves. Thus, greater competton emerges endogenously and leads to more nnovaton: the desre to nnovate spurs competton and competton leads to more nnovaton. We modfy our model as follows. Each frm can choose one of the two possble types of technologes. The frst type of technology s frm-specfc. If a frm chooses ths technology, t produces a dfferentated product whch effectvely nsulates the frm from (the other frm s) competton n the product market. The second type of technology s compettve n that f both frms choose that technology, they produce smlar products and therefore are exposed to competton n the product market. Note that the technology selecton decson can also be nterpreted as geographcal locaton selecton, as n the lterature on frm clusterng. If frms choose the compettve technology, ths would be equvalent to clusterng. If they choose a frm specfc technology, ths would be analogous to solatng from each other by locatng at dstnct geographcal places. Alternatvely, the choce of technology may be nterpreted as the selecton of market 19

20 wde product specfcatons. In ths context, the choce of the frm-specfc technology would be equvalent to the selecton of propretary standards requrng the development of frm-specfc human captal that cannot be transferred across frms. The choce of the compettve technology would be equvalent to the selecton of common standards, such as open sourcng, that allows employees to develop human captal that can be easly transferred across frms. 19 We model the choce of technology, and thus competton between the two frms, as follows. Frms make ther technology selecton decson n a sequental manner. Frm 1 moves frst and chooses whether to protect tself from future competton by choosng ts frm-specfc technology or to be exposed to competton by choosng the compettve technology. After observng the choce made by frm 1, frm 2 moves next and decdes whether to stay protected from competton by choosng ts own frm-specfc technology, or to challenge frm 1 by undertakng the compettve technology f frm 1 has chosen the compettve technology as well. If frm 1 has chosen ts frm-specfc technology, both frms wll be monopolsts n ther respectve product markets regardless of the technology chosen by frm After that, the game unfolds as before. We now characterze the equlbrum of the game. Proposton 3 Let M C (M 0, M 1 ), wth M 0 < M = 1 < M 1. Then, there s a threshold level β F (M C,, k) (defned n appendx) such that ) f β β F (M C,, k), then the frms choose the compettve technology; ) f β > β F (M C,, k), then frm 1 chooses the compettve technology f M C 1 and t chooses ts frm-specfc technology f M C < 1; frm 2 always chooses ts frm-specfc technology. The equlbrum choce for the two frms wll be the compettve technology when the beneft of competton on employee effort outweghs ts cost through hgher employee rents (.e., greater wages) and the potental losses n the product market. The compettve technology s partcularly desrable when employees exert too lttle effort under monopoly. As dscussed n Propostons 1 and 2, ths happens ether when employee barganng power s low (.e., a low value of β), or when the cost of exertng effort s hgh (.e., a hgh value of k). Proposton 3 shows that the compettve technology s chosen when employee barganng power s lower than a certan threshold β F. In ths case, the choce of the compettve technology, by 19 We thank Jm Brander for the suggeston of ths nterpretaton. 20 Note that the sequental nature of the game allows us to avod the possblty of mxed strategy equlbra and does not affect our analyss n any substantal way. 20