PRODUCT MARKET COMPETITION AND AGENCY COSTS

Transcription

1 THE JOURNAL OF INDUSTRIAL ECONOMICS Volume LV June 2007 No. 2 PRODUCT MARKET COMPETITION AND AGENCY COSTS Jen Baggsw Jean-Etenne de Bettgnesz We model the effects of competton on manageral effcency and solate the agency effect of competton, present only n frms subject to agency costs, from the drect pressure effect of competton, whch s present n all frms. Usng a unque set of Canadan data that surveys both frms and ther employees, we then evaluate the emprcal sgnfcance of these two effects. We fnd that competton has a sgnfcant drect pressure effect as well as a sgnfcant agency effect. Both effects ncrease the mportance frms place on qualty mprovements and cost reductons as well as on contractual ncentves and employee effort. I. INTRODUCTION ECONOMISTS HAVE A VAGUE SUSPICION that competton s the enemy of sloth (Caves [1980] p. 88; cted n Nckell [1996]); yet the process through whch competton mproves manageral effort s stll not fully understood. There are two prmary ways to thnk about ths process. Competton may put drect pressure on frms to ncrease qualty (or decrease costs)ffor example by ncreasng the margnal mpact of such an ncrease on expected proftsfa pressure that s passed on to agents through hgher powered ncentves. But competton may also reduce agency costs, makng t cheaper for the prncpal to elct more effort from the agent. 1 The purpose of ths paper s We thank two anonymous referees and the edtor for very helpful comments. We are also grateful to Statstcs Canada, n partcular the BLMA dvson, for gvng us access to the data used n ths paper. We thank Rchard Arnott, Jm Brander, Murray Frank, Keth Head, Thomas Hellmann, John Res, Tom Ross, Johannes Van Besebroeck, Jm Vercammen and Ralph Wnter, as well as semnar partcpants at Queen s Unversty, the Unversty of Brtsh Columba, the Unversty of Florda, the Unversty of Guelph, the Unversty of Vctora, the CEA meetngs (Hamlton, 2005), the IIO conference (Atlanta, 2005), the FMA European meetngs (Sena, 2005), and the WFA meetngs (Portland, 2005) for ther suggestons and advce. We gratefully acknowledge fnancal support from Socal Scences and Humantes Research Councl (SSHRC) MCRI grant and (Bettgnes) from the Robert and Carol Fresen Research Fellowshp. All remanng errors are ours. wauthors afflatons: Faculty of Busness, Unversty of Vctora, PO Box 1700, STN CSC, Vctora, Brtsh Columba, V8W 2Y2, Canada. e-mal: jenbaggs@uvc.ca zsauder School of Busness, Unversty of Brtsh Columba, 2053 Man Mall, Vancouver, Brtsh Columba, V6T 1Z2, Canada. e-mal: bettgnes@sauder.ubc.ca 1 We thank an anonymous referee for suggestng ths motvaton. Publshed by Blackwell Publshng Ltd, 9600 Garsngton Road, Oxford OX4 2DQ, UK, and 350 Man Street, Malden, MA 02148, USA. 289

2 290 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES frst to solate theoretcally the drect pressure effect from the agency effect and then to measure the emprcal mpact of these effects on frms strategc choces, contractual ncentves and employee effort. To that end, we propose a smple duopoly model where two frms compete n qualty and prce. Wthn each frm, agency problems may arse from nonverfable efforts and manageral wealth constrants. Competton s measured by the degree of substtutablty between products and has two mpacts n our model. Frst, by makng demand more elastc, t ncreases the mpact of a qualty mprovement on the market share one can steal from a rval; we call ths the ncreased busness stealng effect. Second, t reduces prce-cost margns; we call ths the rent reducton effect. We show that the ncreased busness stealng effect of competton, by ncreasng the margnal mpact of a qualty ncrease on expected profts, puts drect pressure on frms to provde more ncentves and elct hgher agent effort n order to mprove qualty. Rent reducton, on the other hand, works the other way: t lowers the margnal product of qualty, and hence puts drect pressure on frms to reduce qualty. The combnaton of these two effects generates the drect pressure effect of competton (the ncreased busness stealng effect, net of rent reducton) and affects all frms. In frms where agency costs are present, the ncreased busness stealng effect and the rent reducton effect also work through an addtonal channel: they both reduce frms margnal cost of elctng effort from agents. Ths agency effect of competton has a postve mpact on frms equlbrum choce of product qualty, the power of ncentves, and employee effort. Our theoretcal analyss naturally calls for an emprcal assessment of the sgns of the drect pressure effect and the agency effect. To address these ssues, we explot a detaled set of lnked employer-employee data that allows us to observe smultaneously the presence (or absence) of agency costs n frms, the ntensty of competton frms face, the strateges they pursue, the types of contracts and ncentves offered to ther employees, as well as detaled nformaton about ndvdual employee effort. We solate the agency effect of competton from the drect pressure effect, and determne ther emprcal sgnfcance. We fnd that, frst, competton does have a postve drect pressure effect. Even n frms n whch agency costs are absent, competton ncreases the mportance frms place on qualty mprovements and cost reductons, the ntensty of contractual ncentves, and ndvdual employee effort, suggestng that ncreased busness stealng emprcally domnates rent reducton. Second, we fnd that competton also has an agency effect. Indeed, the postve mpact of competton on these varables s even larger for frms that are subject to agency costs. The theoretcal lterature on competton and ncentves can be dvded nto two broad categores dependng on how agency problems are assumed to arse. On the one hand, n hdden nformaton models, neffcences arse manly because the agent has superor nformaton, relatve to the prncpal,

3 PRODUCT MARKET COMPETITION AND AGENCY COSTS 291 about an mportant parameter such as the frm s level of productvty. In these frameworks, the effects of competton depend on the type of contract desgned n equlbrum, whch n turn depends on manageral preferences. In Hart [1983], preferences are such that a target proft for the manager s optmal. Competton, by reducng the market prce, nduces managers to ncrease ther cost-reducng efforts, n an attempt stll to meet proft targets. In contrast, n Scharfsten [1988], manageral preferences requre a statecontngent contract, and the mpact of competton s shown to be negatve. On the other hand, n hdden acton models, neffcences arse because manageral effort s not verfable. In Hermaln [1992], the man mpact of competton s an ncome effect. Snce lesure s a normal good, hs argument suggests that competton, by reducng ncome, should lead the manager to consume less lesure and work more. In Schmdt [1997], the ncreased threat of lqudaton assocated wth competton s what motvates the manager to exert more effort. Fnally, n Rath [2003], the effect of competton on ncentves and effort takes place through a change n the equlbrum number of frms n the ndustry. Our theoretcal model makes two prmary contrbutons to the lterature. Frst, usng a Hotellng [1929] model of competton, we brng strategc nteractons between frms to the forefront of the model. Among other thngs, ths allows us to characterze the ncreased busness stealng effect of competton, whch plays a key role n the dervaton of our results. These strategc nteractons are absent n prevous work. 2 Indeed, Hart [1983] and Scharfsten [1988], for example, use models of perfect competton n whch (ncreased) busness stealng plays no role. In ther models, an ncrease n competton s measured by an ncrease n the proporton of effcent entrepreneural frms n the economy, whch n turn leads to ncreased aggregate supply and a fall n the market prce. Perhaps more mportantly, although the effects of competton prevously dentfed n the lterature emerge n the context of agency models, the lnk between these effects and agency costs remans fuzzy. Indeed t s unclear whether these effects are specfcally related to agency problems and present only n frms dealng wth such ssues, or whether they are unrelated to agency problems and thus take place n all frms. Thus, the second key contrbuton of our theoretcal model s to dsentangle these two types of effects: we dentfy a postve agency effect that s dstnct from the drect pressure effect of competton. In dong so, we shed lght on the precse channels through whch competton affects ncentves, effort, and effcency. The emprcal lterature does seem to confrm a postve mpact of competton, measured n a varety of ways, on effcency. Increased number 2 Rath [2003] s an excepton. See also Bettgnes [2006], whch studes the mpact of strategc nteractons on the boundares of the frm n an ncomplete contract framework.

4 292 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES of compettors and lower levels of rents (Nckell [1996]) as well as lower ndustry concentraton (Haskel [1991]), for example, are shown to sgnfcantly ncrease total factor productvty growth. Industry concentraton has also been shown to reduce techncal effcency (Caves and Barton [1990]; Green and Mayes [1991]; Caves et al. [1992]). As well, Syverson [2004a, 2004b] recently showed that substtutablty between products has a postve mpact on average productvty levels. Much less work has been done, however, to analyze emprcally howf.e., through whch processfcompetton affects effcency. Several papers have looked at peces of ths puzzle, ncludng Burgess and Metcalfe [2000], Santalo [2002], Cun at and Guadalupe [2005], who fnd evdence of a lnk between competton and manageral ncentves, and Grffth [2001], who shows that competton ncreases productvty and that ths effect s larger n frms where agency costs are present. Explotng a more recent verson of the survey data used by Santalo [2002] whch ncludes a rcher set of varables to choose from, we contrbute to the emprcal lterature by provdng a more accurate pcture of the precse channelsfdrect pressure and agency effectsf through whch competton affects not only effcency and contractual ncentves, but also effort. The paper s structured as follows. Secton II presents our theoretcal model and results. We dscuss the mplcatons of the model, and ther emprcal mplementaton, n secton III. We descrbe the data n secton IV and our emprcal results n secton V. Secton VI concludes. II(). Basc Structure II. THEORETICAL MODEL Two frms, 1 and 2, are postoned at each end of a Hotellng [1929] lne, wth locatons x and x 2 5 1, respectvely. The two frms sell mperfectly substtutable products and compete on qualty q and prce p. Margnal costs of producton for both frms are normalzed to zero. Each frm s composed of a prncpal and an agent, both of whom are rsk-neutral. The prncpalagent relatonshp could be nterpreted as the relatonshp between a board of drectors and the chef executve offcer (CEO) of the frm, or between a dvsonal manager and her subordnate, for example. For convenence, we refer to the prncpal as female and to the agent as male. A unque consumer, whose locaton s random and unformly dstrbuted along the lne, purchases one unt of the product from ether frm 1 or frm 2. Frms 1 and 2 know the locaton dstrbuton of the consumer, but they do not know the actual locaton on the lne. At locaton x, the consumer ncurs a transport cost tx for travellng to frm 1 and a cost t(1 x) to vst frm 2. The consumer enjoys condtonal ndrect utlty U 1 5 s þ q 1 p 1 tx from product 1 and U 2 5 s þ q 2 p 2 t(1 x) from product 2 (where s represents

5 ncome) and smply chooses the product whch gves the hghest utlty. The tmng of the game s as follows: At date 0, prncpal, 5 1,2, makes a take-t-or-leave-t contractual offer to agent, who s wealth constraned wth zero ntal wealth and has a reservaton wage of zero. Offer s only observable to agent (and not to agent j), a necessary assumpton for the exstence of equlbrum n our model. Ths assumpton s consstent wth the fact that managers and employees typcally do not know the exact condtons stpulated n the employment contract for the equvalent poston n rval frms. At date 1, agent exerts effort e at cost Kðe Þ¼ 1 2 e2. Effort determnes the level of nnovaton undertaken by frm and the product qualty q that results from t. For smplcty we set q 5 e ; hereafter, we refer to q usng agent effort or product qualty nterchangeably. Note that all of the theoretcal results of the paper stll hold f we assume that effort reduces the margnal cost of producton nstead of ncreasng qualty or that t affects both cost and qualty. Ths s confrmed emprcally below, where we show that the results are smlar for qualty-enhancng and cost-reducng nvestments. At date 2, after observng qualtes, prncpal chooses prce p. The same results apply f the prcng decson s gven to the agent: ths assumpton s made for clarty purposes and s wthout loss of generalty. At date 3, the consumer chooses one of the products and demands are realzed. Frm realzes profts P whch are splt between the agent, who receves payoff W accordng to the contract sgned at date 0, and the prncpal, who keeps P W. Transport cost t, whch measures the degree of horzontal product dfferentaton, s an deal parameter to represent toughness of competton (or rather lack thereof ) n the ndustry, to use Sutton s [1992, p. 9] termnology. Throughout the paper, an ncrease n product market compettons represented by a decrease n t. We restrct our attenton to values of, whch ensures strct concavty of all maxmzaton programs throughout the paper and non-negatve effort levels n both frms. We assume that total revenues and hence profts are contractble. In contrast, demands and prces are not verfable and cannot be contracted upon (although they are observable). Ths assumpton, whch helps us keep the analyss smple by generatng second-best equlbrum contracts that are contngent only on profts, s not unreasonable. Indeed, n order for sales and prce of a product to be verfable n a court of law, the nature of that product must be descrbed ex ante n a way that allows a judge to match products wth sales and prces. In practce, frms sell not one but a varety of products, the nature of whch changes enormously over tme dependng on contngences such as technologcal nnovatons or market condtons. We argue that these products cannot be unambguously descrbed ex ante, and hence contracts cannot be made contngent on assocated sales or prces. t 2 4=3 9 ; 2 9 PRODUCT MARKET COMPETITION AND AGENCY COSTS 293

6 294 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES For smlar reasons, product qualty (effort), though observable, may or may not be verfable: the multdmensonalty of qualty mght make t dffcult to descrbe precsely n a contract ex ante (Hart and Holmstro m [1987], p. 134). We analyze both possbltes. In subsectons II() and II(), we characterze the subgame-perfect Nash equlbrum of the game (snce n our duopoly settng there are smultaneous moves at every stage by the two rval frms) when qualty s verfable and not verfable, respectvely. Dependng on the verfablty of qualty, the optmal contract may be contngent on realzed profts and/or product qualty: W 5 W (P, q ). Three condtons must hold for any contract to be feasble: a) Incentve compatblty constrant: agent exerts effort bq, whch maxmzes hs expected gross payoff w whch s a functon of expected profts p (q ) and/or qualty mnus hs cost of effort: ð1þ bq 2 argmax½w ðp ðq Þ; q Þ K ðq ÞŠ: b) Partcpaton constrant: for the agent to partcpate, hs expected net payoff must be weakly larger than hs (zero) reservaton wage: ð2þ w ðp ðbq Þ; bq Þ K ðbq Þ*0: c) Wealth constrant: the agent s wealth constraned wth zero ntal wealth, and thus hs realzed payoff must be non-negatve n all states of the world: ð3þ W ðp ; bq Þ*0 for all realzed values of profts P : II(). Equlbrum wth Verfable Qualty (Frst-Best) In ths subsecton, we consder the case of frms that have verfable qualtes. We determne the subgame-perfect Nash equlbrum and verfy that the frst-best (FB) level of effortf.e., the level that would be exerted f the prncpal and the agent were one and the same personfcan be acheved. 3 We then analyze how the equlbrum s affected by competton. When qualty s verfable, prncpal can elct effort q from agent by offerng hm the followng contract at date 0: the agent s to receve wage W q ¼ K q ¼ 1 2 q2 at date 3 f qualty s verfed to be q ¼ q and W 5 0 otherwse. Note that the ncentve compatblty constrant (1), the partcpaton constrant (2), and the wealth constrant (3) all hold under the condtons of ths offer. Therefore, the contract wll be accepted by the 3 Note that the analyss n ths secton s not just a theoretcal benchmark as n other papers: t hghlghts equlbrum condtons for the subset of frms n whch agency costs are ether absent (e.g., n cases where the owner and the employee are the same person), or can be crcumvented (e.g., when the agent s effort can be verfed). As shown n the emprcal analyss below, ths subset represents a non-trval fracton of the populaton of frms.

7 PRODUCT MARKET COMPETITION AND AGENCY COSTS 295 agent and wll nduce hm to exert the equlbrum effort q chosen by the prncpal. The equlbrum of the game can be determned by backward nducton as follows: At date 3, prncpal receves realzed payoff P (q, p, q j, p j, t) W (q ). At date 2, prncpal chooses p to maxmze her expected payoff, takng qualtes as gven: ð4þ max p p ðq ; p ; q j ; p j ; tþ W ðq Þ; where expected profts p (q, p, q j, p j, t) 5 p d (q, p, q j, p j, t) are the product of prce and expected demand. 4 Takng the frst-order condtons wth respect to prce for 5 1,2 and solvng the resultng system of two equatons yelds the followng equlbrum prce: ð5þ p ¼ t þ q q j : 3 Substtutng equlbrum prces back nto the expected demand, we obtan an expresson for expected profts as a functon of qualtes: h ð6þ p ðq ; q j ; tþ ¼p ðq ; q j ; tþd ðq ; q j ; tþ ¼ t þ q q j þ q q j ; 6t where d ¼ 1 2 þ q q j 6t s the expected demand for frm. At date 1, agent exerts the effort level q ¼ q stpulated n the ncentve compatble ntal contract. At date 0, prncpal smply chooses the level of effort q to elct from the agent. Ths equlbrum level of effort maxmzes the prncpal s expected net beneft, p (q, q j, t) w (q ), whch smplfes to NB FB ¼ p ðq ; q j ; tþ Kðq Þ. Unsurprsngly, NB FB corresponds to the frst-best objectve functon, whch would be maxmzed f the prncpal and the agent were one and the same person and there were no agency costs. In other words, when qualty s verfable, prncpal can perfectly crcumvent agency costs by contractng drectly on qualty. Takng the frst-order condton, she chooses q ¼ q such ð7þ ; j; t ¼ q ;.e., such that the margnal product of effort equals the agent s margnal cost of effort, as n the frst-best. The frst-order condtons for prncpals 4 A consumer located at x s ndfferent between store 1 and 2 f and only f U 1 5 U 2,or q 1 p 1 tx ¼ q 2 p 2 tð1 xþ. Solvng for x, we easly derve the expected demand (purchase probablty) for frm : d q ; p ; q j ; p j ; t ¼ 1 ð Þþ ð q qj Þ : 2 þ pj p 2t

8 296 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES and j form a system of two equatons n two unknowns, whch can be readly solved. The unque soluton s the symmetrc frst-best equlbrum n whch prncpals and j elct effort level q ¼ q j ¼ 1 3 ¼ q from ther agent. Thus: Lemma 1. Wth verfable qualty, the subgame-perfect Nash equlbrum s the followng. At date 0, both prncpals propose to pay ther agents Wq ð Þ ¼ 1 2 q2 at date 3 f frst-best qualty q ¼ 1 3 s verfed and zero otherwse. At date 1, agents exert frst-best effort q. At date 2, prces are chosen followng (5), whch yelds p ¼ p j ¼ t; and expected demands equal d ¼ dj ¼ 1 2. Fnally, demands and profts are realzed, and the ntal contract s honored. Proof. Follows drectly from above. Effects of Product Market Competton. Competton affects equlbrum effort to the extent that t affects prncpal s margnal beneft from elctng effort by her agent, net of her margnal cost of dong so. Indeed, startng from an equlbrum stuaton where condton (7) holds, f for example an ncrease n competton rases prncpal s margnal beneft from an effort ncrease above the margnal cost, then her optmal response s to ncrease q (by strct concavty of her maxmzaton program) untl condton (7) holds agan. Prncpal j reacts n the same way, and a new equlbrum s reached. As shown above, wth verfable qualty, the prncpal s margnal cost of elctng effort s smply the agent s margnal cost of ð Þ ¼ q, whch s ndependent of t and unaffected by competton. In contrast, the prncpal s margnal beneft from nducng effort, whch corresponds to the margnal product of s affected by competton. To see ths, note frst that frm s margnal product of effort, gven effort levels q and q j, can be obtaned from (6) by dfferentatng expected profts wth respect to q ðq ; q j ; tþ d ðq ; q j ; ðtþp ðq ; q j ; tþ. In equlbrum (when frms choose dentcal strateges), ths smplfes to: q ; q j ; t d ðtþp ðtþ: The margnal product of effort can thus be expressed as the sum of two factors. Frst, ncreasng effort/qualty enables the frm to charge a hgher prce to reflect the hgher product >0; and the mpact on expected profts s the margnal change n prce tmes equlbrum expected d. Second, ncreasng effort/qualty also allows frm to gan a qualty advantage over ts rval, and to steal market share as a ðþ>0. t We call ths the busness stealng mpact of an effort/qualty ncrease; and ts

9 PRODUCT MARKET COMPETITION AND AGENCY COSTS 297 mpact on expected profts s the margnal change n expected demand tmes the equlbrum ðtþp ðtþ. It s easly shown that competton does not affect the frst factor. Indeed, nether the margnal change n ¼ 1 3, nor equlbrum expected demand d ¼ 1 2, are functons of t, d =@t ¼ 0. Therefore the mpact of competton on the margnal product of effort can be obtaned by dfferentatng the second factor wth respect to t: 2 @d : An ncrease n product market compettonfor, equvalently, a fall n t affects the margnal product of effort n two conflctng ways. Frst, by makng demand more elastc, competton ncreases the busness stealng mpact of a qualty ¼ 1 <0. We call ths the ncreased 6t 2 busness stealng effect of competton. Ths effect of competton has postve mpact on the margnal product of effort: 2 p <0. Second, competton makes consumers more senstve to prces and qualtes, thus forcng frms to compete more fercely and to lower ¼ 1>0. We call ths the rent reducton effect of competton (n contrast to the rent ncrease effect of n equaton [8]). Snce, as dscussed >0, rent reducton has a negatve mpact on the margnal product @t >0. These results yeld the followng proposton: Proposton 1: In the frst-best, competton, through ts ncreased busness stealng effect, rases the margnal product of effort. Ths has a postve mpact on prncpals net margnal beneft from an effort/qualty ncrease, and hence puts drect pressure on frms to elct hgher agent effort. However, competton also has a rent reducton effect, whch reduces the margnal product of effort and hence works the other way. We defne the drect pressure effect of competton as the ncreased busness stealng effect, net of rent reducton. Proof. Follows drectly from above. The key mplcaton of proposton 1 s that the sgn of the drect pressure effect of competton could n prncple be postve or negatve. If (and only f ) ncreased busness stealng domnates rent reducton, competton has a postve mpact on the prncpal s (net) margnal beneft from an ncrease n effort and puts drect pressure on frms to elct hgher effort/qualty from

10 298 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES ther agents. 5 To elct ths ncrease n effort, frms provde more ncentve to ther agents; n the context of our frst-best contract, ths s acheved by ncreasng the threshold level of qualty q requred to get postve compensaton, and the amount of that compensaton W q : But does the ncreased busness stealng effect domnate the rent reducton effect? In the specfc Hotellng framework consdered here, the mpact of ncreased busness stealng on the margnal product of effort, whch smplfes p ¼ 1 t ¼ 1 6t 2 6t, s exactly offset by the mpact of @t ¼ 1 1 6t ¼ 1 6t, and as a result, the drect pressure effect s null. Vves [2004], on the other hand, shows that the drect pressure effect could be postve or negatve dependng on the demand specfcaton. 6 The absence of theoretcal consensus on the drect pressure effect naturally calls for an emprcal assessment of sgn of ths effect. We address ths queston, and other emprcal mplcatons of the model, n sectons III-V. II(). Equlbrum wth Non-Verfable Qualty (Second-Best) If qualty, though observable, s non-verfable, t cannot be contracted upon and contracts must be made contngent on profts. 7 We focus on lnear contracts of the form W 5 ap þ b. In ths subsecton, we frst characterze the subgame-perfect Nash equlbrum, show that agency costs cannot be crcumvented, and then analyze the effects of competton on equlbrum ncentves and effort. At date 3, prncpal receves the followng payoff: (1 a )P (q, p, q j, p j, t) b. At date 2, prncpal chooses p to maxmze her expected payoff: (1 a )p (q, p, q j, p j, t) b, takng qualtes as gven. Ths maxmzaton yelds the same equlbrum prces as the maxmzaton descrbed n (4), and hence expected profts as a functon of product qualtes correspond to (6). At date 1, agent chooses q so as to maxmze hs expected payoff a p (q, q j, t) þ b K (q ), takng q j as gven. The agent chooses q ¼ bq such 5 The offsettng mpacts of ncreased busness stealng and rent reducton are not specfc to our Hotellng specfcaton, and prevous references to these effects can be found, for example, n Anderson et al. [1992], p. 230, and n Rath [2003], n the context of logt framework, and Salop [1979] crcle, respectvely. 6 To be precse, Vves [2004] fnds a postve mpact of competton wth Shapley/Shubk lnear demands as well as n CES and constant expendture models, but a negatve mpact wth Bowley lnear demands. He does not explctly solate ncreased busness stealng from rent reducton. 7 Ths assumpton of observable but non-verfable qualty s necessary for exstence of equlbrum. In Hermaln and Katz s [1991] agency model wth a rsk-averse agent, ths assumpton enables the prncpal to acheve the frst-best through renegotaton after effort exerton. Ths s not feasble n our model where both the prncpal and the agent are rsk neutral and there s no scope for renegotaton.

11 that the ncentve compatblty constrant holds: ð10þ bq ; q j ; t ðbq Þ: PRODUCT MARKET COMPETITION AND AGENCY COSTS 299 At date 0, prncpal offers contract (a, b ) to agent. To determne the optmal contract, the prncpal maxmzes the followng program: ð11þ max p ðbq ; q j ; tþ ða p ðbq ; q j ; tþþb Þ; ^q ;a ;b subject to constrants ð2þ; ð3þ; and ð10þ: Ths optmzaton can be smplfed as follows. Frst, a must be strctly postve, otherwse the agent, solvng (10), would choose zero effort. And b must be non-negatve: the wealth constrant (3)Fwhch can be expressed here as a P þ b X0 for all P smplfes to b X0 snce t must hold even when the consumer does not buy the product and realzed profts P are zero. Second, wth a 4 0 and b X0, the agent s equlbrum expected payoff s strctly postve snce t can be no smaller than what he would get wth zero effort (otherwse he would choose zero effort), whch tself s strctly postve: a p bq ; q j ; t þ b K ðbq Þ*a p ð0; q j ; tþþb >0. Therefore, the partcpaton constrant (2) s never bndng and can be gnored. Note that ths also mples that the agent earns rents over and above hs cost of effort; these rents are the expresson of the agency costs for the prncpal. Thrd, snce b has a negatve effect on the prncpal s objectve functon and does not affect ncentve compatblty, t s optmal to set t as low as possble,.e., such that the wealth constrant bnds: b 5 0. The wealth constrant can thus be replaced by b 5 0 n the maxmzaton program. Fnally, the ncentve compatblty constrant (10) can be expressed n terms of a bq ; q j ; t ðbq bq ; q j ; t ¼ bq = 1 3 þ ð ^q q j Þ of a necessary to elct an effort bq from the agent. Substtutng a nto the objectve functon, the program smplfes to: 8 9t ;.e., the value bq ; q j ; t ð12þ max NB SB wth NB SB ^q ¼ p ðbq ; q j ; tþ a ðbq ; q j ; tþp ðbq ; q j ; tþ: Takng the frst-order condton, the prncpal chooses effort level bq ¼ q such that her margnal beneft from elctng an ncrease n effort 8 Another way of solvng ths program s to solve (10) for bq ða ; q j Þ, to substtute bq ða ; q j Þ nto the objectve functon, and to maxmze wth respect to a. Whle the two methods are formally equvalent, here we use the former because t presents the second-best problem n terms of optmal effort to be elcted from the agent, whch can more easly be compared wth the optmal effort elcted n the frst-best. In contrast, presentng the equlbrum results n terms of optmal share of profts to be allocated to the agent s not conducve to comparsons between frst-best and second-best snce n the frst-best there are no a s (the prncpal s contract drectly on effort).

12 300 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES by the agent exactly equals her margnal cost of nducng such an ncrease: ðq ; q j ; @bq p ðq ; q j ; tþ: It can be shown NB SB NB 2 j <0 for all t 2 4=3 9 ; 2 9, whch ensures exstence of a unque Nash equlbrum n effort (Vves [1999] pp ). The symmetrc equlbrum, provded t exsts, therefore must be the unque equlbrum of ths game. Substtutng q ¼ q ¼ q nto (13), we obtan second-best effort level q ¼ 2 3 3t, whch s elcted by offerng q ; q j ; t ¼ 3q to the agent. Thus: a Lemma 2. In the second-best, the subgame-perfect Nash equlbrum s as follows. Both prncpals offer a fracton a ¼ 3q ¼ 2 9t of profts to ther respectve agent. As a result, both agents choose effort q ¼ 2 3 3t. Prces are chosen followng (5), whch yelds p ¼ p j ¼ t; and expected demands equal d ¼ dj ¼ 1 2. Fnally, demands and profts are realzed, and the ntal contract s honored. j Proof. Follows drectly from above. Second-Best Versus Frst-Best Effort. A drect mplcaton of lemmas 1 and 2 s that equlbrum effort s lower n the second-best than n the frstbest: q <q for all t 2 4=3 9 ; 2 9. The ntuton for ths result s as follows. When the prncpal can contract drectly on effort/qualty, her cost of elctng effort s smply the agent s personal cost of effort, K ðq Þ. In contrast, when qualty s not contractble, the only way the prncpal can provde ncentves s by gvng up a fracton of profts to the agent; and because of the agent s wealth constrant, she cannot recoup ths relnqushed share of profts through transfers. As a result, to the prncpal, the latter s a more costly way of provdng ncentves. She must pay the agent not only hs cost of effort but also, as noted above, some addtonal rents, namely the costs of agency. These agency costs translate nto a hgher margnal cost of elctng effort n the second best (everythng else equal), leadng to lower effort n equlbrum. To see ths more formally, consder agan equaton (13), the prncpal s frst-order condton n the second-best, whch can be expressed as a functon of q, q j, and t, as follows: 9 a 9 Condton (13) can be expressed ¼ a p. To see why a Substtutng ths nto gves the recall that

13 PRODUCT MARKET COMPETITION AND AGENCY COSTS 301 ðq ; q j ; tþ ðq ðq ; q j ; tþp ðq ; q j ; tþ: The prncpal s margnal beneft from elctng an ncrease n effort s the margnal product of q ; q j ; t, as n the frst-best. But the margnal cost of elctng an ncrease n effort s dfferent n the second-best: t the sum of the frst-best margnal cost ðq Þ, and another ðq ; q j ; tþp ðq ; q j ; tþ. Ths second factor s the agency margnal cost of nducng effort: t measures the ncrease n the fracton of profts that must be pad out to the agent to nduce hm to ncrease effort. To understand the dfference between frst and second best, consder the behavour of frms subject to agency costs, at the frst-best equlbrum where q ¼ q j ¼ q. The agency margnal p, whch s strctly postve n equlbrum, mples that prncpal s margnal cost of elctng an ncrease n effort must be strctly larger than the margnal beneft at that pont. 10 Prncpal therefore optmally responds by lowerng q down to the pont where (14) holds, takng rval effort as gven. Prncpal j reacts n the same way, and the second-best equlbrum s reached where the two prncpals elct lower agent efforts q ¼ q j ¼ q. Proposton 2. The presence of an agency margnal cost makes the prncpal s net margnal beneft from elctng an ncrease n effort lower n the second-best than n the frst-best, everythng else equal. As a result, n equlbrum both prncpals elct lower agent effort n the second-best. Proof. Follows drectly from above. Ths proposton verfes n a duopoly settng a result poneered by Sappngton [1983] n a sngle frm model: agency costs assocated wth nonverfable effort cannot be crcumvented when the (rsk-neutral) agent s wealth constraned. Note that the lower levels of effort n the second best are nextrcably assocated wth lower-powered ncentves. Dfferences n compensaton schemes n the frst and second best render dffcult a comparson of ncentves across regmes. However, a frst approxmaton of ths dfference 10 It s easy to show p smplfes to 3t q j =2. At the frst-best outcome where q ¼ q j ¼ q, we p ¼ 3t 1 3 =2, whch s strctly postve for all t 2 4=3 9 ; 2 9. Snce the frst-best equlbrum condton (7) q ; q j ; t q, ths mples p when q ¼ q j ¼ q. One can also verfy that n the second-best equlbrum where q ¼ q j ¼ q, the agency margnal cost smplfes to 3t 1 3 >0.

14 302 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES can be obtaned by comparng the power of ncentves n second best, a ¼ 2 9t, to the power that would have to be offered n the second best to elct the frst best level of effort. Unsurprsngly ths s a ¼ 1, whch s strctly superor to a for all t 2 4=3 9 ; 2 9. Effects of Product Market Competton. It s mmedately clear from lemma 2 that n the second-best equlbrum, competton ncreases the power of ncentves a, and agent effort q. We now provde an ntuton for ths result. From expresson (14) we see that the drect pressure effect of competton on the prncpal s margnal beneft from elctng effort Þ must stll be present here. However, competton also works through an addtonal channel n the second best, by reducng the agency margnal p. The agency margnal cost s the product of two factorsfthe ncrease n ncentves necessary to elct hgher agent and expected profts p F both of whch are negatvely affected by competton. The mpact of competton on expected profts s smply that >0, puts downward pressure on prces, whch n turn reduces expected profts. More formally, lookng back at (6), we see that n equlbrum when frms choose @t d ¼ 1 2 >0. To understand how competton affects the ncrease n ncentves necessary to elct hgher agent two ponts should be noted. Frst, the sze of ths ncrease n ncentves depends tself on the agent s responsveness For example, f the agent s responsveness to ncentves s hgh, then only a small ncrease n a s necessary to generate a gven ncrease n effort. Wth lower responsveness, a relatvely larger ncrease n ncentves s necessary to acheve the same ncrease n effort. Second, as shown n the appendx, responsveness to ncentves s a strctly ncreasng functon the busness stealng assocated wth hgher effort. When respondng to hgher-powered ncentves wth hgher effort, the agent nternalzes the mpact of hs response on the market share he can steal from rvals: the larger ths mpact, the more responsve he s to ncentves. Competton, va ts ncreased busness stealng <0, ncreases the market share the agent can steal wth a margnal ncrease n effort. Ths makes the agent more responsve to ncentves, and n turn reduces the ncrease n ncentves necessary to elct hgher agent Together these results yelds the followng proposton: Proposton 3. In the second-best, the drect pressure effect of competton on the prncpal s margnal beneft from elctng s stll present. However, competton also works through an addtonal channel: ncreased busness stealng and rent reducton renforce each other and jontly reduce the agency margnal p, thus ncreasng the prncpal s net beneft from elctng effort. We call ths second factor the agency effect of competton.

15 PRODUCT MARKET COMPETITION AND AGENCY COSTS 303 Proof. See appendx 1. Ths proposton characterzes an effect of competton that s present only n frms subject to agency costs. In such frms, the prncpal s margnal cost of elctng an ncrease n effort from the agent depends on the agent s personal margnal costs of exertng effort, and the agency margnal cost. Competton reduces ths agency margnal cost and hence makes t cheaper for the prncpal to elct a qualty ncrease. Ths has a postve mpact on prncpals net margnal beneft from an effort/qualty ncrease, and hence puts addtonal pressure on frms to elct hgher agent effort wth hgher-powered ncentves. To obtan an expresson for the mpact of ths agency effect on equlbrum effort and on ncentves, note that snce the drect pressure effect s null n our specfc model, the agency effect equals the total effect of competton and therefore can be obtaned by dfferentatng equlbrum effort and ncentves wth respect ¼ ¼ 9<0for all t 2 4=3 9 ; 2 9. To our knowledge, our model s novel n dentfyng ths agency effect of competton. To hghlght ths effect, we explctly dsentangle the effects of competton that are present n all frms from those that are present only n frms subject to agency costs, unlke prevous work that has focused on the aggregate effect of competton n models of agency. Indeed, although one may conjecture that the effects dentfed by Hermaln [1992], Schmdt [1997], and Rath [2003] (see ntroducton) all belong to the drect pressure category snce they are lkely to be present even n the absence of agency costs, one cannot be sure whether the effect observed n the second best s a drect pressure effect only, or n combnaton wth some form of agency effect. Conversely, the mpact of competton n Hart [1983] may resemble an agency effect, but t s unclear whether t would vansh n the frst best. We also depart from the prevous work n two other ways. Frst, wth our Hotellng model of competton, we brng strategc nteracton to the forefront of the our analyss, and hghlght the mportance of the relatonshp between ncreased busness stealng and rent reducton. Second, we use a smple model where agency arses due to the rsk-neutral agent s wealth constrant (rather than rsk averson, as n the classc prncpalagent model). The tractablty of our agency model, together wth a proftcontngent compensaton scheme for the agent, play an mportant role n dervng the agency effect and other results. Indeed, ths may explan why our agency effect s absent from Rath s [2003] model, despte a competton frameworkfa Salop [1979] crclefsmlar to ours. Unlke us he uses the classc agency model wth cost-reducng agent effort, and assumes that agent compensaton s cost-contngent rather than proft-contngent. Our agency effect of competton s also absent n Schmdt s [1997] model, even though he uses an agency model wth a rsk-neutral but wealth-constraned agent. Ths could be explaned by the dfferences n modelng competton

16 304 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES mentoned above and by the fact that n hs bnomal framework, the agent s compensaton s contngent on the state of the world (good or bad) rather than on realzed profts. III. EMPIRICAL IMPLICATIONS AND IMPLEMENTATION Our model yelds three key emprcal mplcatons. Frst, recall that our dscusson of proposton 1 led us to wonder about the emprcal sgn of the drect pressure effect of competton on frms net beneft from a qualty ncrease, contractual ncentves, and employee effort. If we observe emprcally that, n frms that are free of agency costs, competton ncreases these varables, ths wll ndcate that the drect pressure effect of competton s postve,.e. that ncreased busness stealng domnates rent reducton. Conversely a negatve mpact of competton wll ndcate that rent reducton domnates ncreased busness stealng. The second key emprcal mplcaton results from proposton 3, whch states that n frms that are plagued by agency costs, there s, n addton to the drect pressure effect, a postve agency effect of competton. Ths agency effect of competton should have a postve mpact on frms net margnal beneft from a qualty ncrease, and hence should put addtonal pressure on frms to ncrease the power of ncentves and employee effort. These two key mplcatons suggest that competton should have a dfferental mpact across frms. If the drect pressure effect of competton s postve, then the agency effect should renforce t, and the aggregate mpact of competton should be even more postve n frms subject to agency costs than n frms that are not. On the other hand, f the drect pressure effect s negatve, then the agency effect should mtgate t, and the aggregate effect of competton should be less negatve n frms subject to agency costs. Fnally, the thrd emprcal mplcaton of our model, whch results from proposton 2, s the followng. Agency costs should have a negatve mpact on the net margnal beneft from a qualty ncrease, and should put pressure on frms to reduce the power of ncentves and employee effort. Our model descrbes a logcal chan of events followng a change n exogenous varables such as competton or agency costs. For example, an ncrease n the degree of competton rases frms net margnal beneft from an ncrease n qualty, and hence ther qualty target choce; to acheve ths, frms ncrease the power of ncentves, and n turn, employee effort. Ideally, we would be able to observe these events as they occur, recordng a change n competton at tme t, the frms choce of qualty n response to that change at t þ 1, the contractual offer made to employees at t þ 2, and the effort those employees exert n response to ther new contract at tme t þ 3. In practce, however, t, t þ 1, t þ 2, and t þ 3 occur n rapd successon and, wthout daly or weekly data, we are unable to observe these events n sequence, and cannot model emprcally the sequence of decsons mpled by our theory.

17 PRODUCT MARKET COMPETITION AND AGENCY COSTS 305 We do expect, however, that competton wll have an mpact on each varable, namely the net margnal beneft from a qualty ncrease, the power of ncentves, and employee effort; and we can test for that wth annual data. Naturally, we expect our emprcal results to be consstent across regressons. To test our theory, we propose the followng emprcal specfcatons. III(). Importance of Qualty Improvements We start by examnng frms net margnal beneft from a qualty ncrease. Ths theoretcal concept can be nterpreted as frms atttude towards a qualty ncrease, as a measure of the mportance frms place on qualty mprovements. Indeed, one would expect a frm s long-term qualty target to be such that the net margnal beneft from a qualty ncrease s zero. In the short-term however, the net margnal beneft may be dfferent from zero, and the larger the net margnal beneft, the larger the qualty ncrease necessary to acheve the long-term goal (by strct concavty of the maxmzaton program). Consder the followng lnear regresson: ð15þ QUAL ¼ l 0 þ l 1 COMP þ l 2 AGENCY þ l 3 COMP AGENCY þ l 4 CONTROL þ e; where QUAL represents the mportance a frm places on qualty mprovements; COMP represents the degree of product market competton n terms product substtutablty (as n our theoretcal model); AGENCY measures agency costs and equals 1 when they are present n the frm, and to 0 otherwse; CONTROL s a vector of frm level control varables; and e s an error term. Equaton (15) allows us to estmate the drect pressure effect of competton, and the agency effect of competton, on frms atttudes towards qualty mprovements. To see ths, let us dfferentate QUAL wth respect to COMP, ¼ l 1 þ l 3 AGENCY. An mportant mplcaton of proposton 1 s that n frms that are not subject to agency costs, the only mpact of competton s the drect pressure effect. Ths allows us to dentfy the drect pressure effect n our emprcal specfcaton (15), snce the mpact of competton when AGENCY 5 0 ¼ l 1. Indeed, l 1 therefore econometrcally captures the drect pressure effect of competton on the mportance frms place on qualty mprovements. Our theoretcal analyss suggests that the sgn of l 1 s an open emprcal queston, snce the drect pressure effect s the net of two offsettng forces, ncreased busness stealng and rent reducton. A sgnfcantly postve l 1 reflects ncreased busness stealng domnance, whle a sgnfcantly negatve l 1 suggests rent reducton domnance.

18 306 JENBAGGSANDJEAN-ETIENNEDE BETTIGNIES In frms that are subject to agency costs, as suggested n proposton 3, competton has both a drect pressure and an agency effect. In our specfcaton, ths s ¼ l 1 þ l 3 when AGENCY 5 1. Snce l 1 captures the drect pressure effect, we can dentfy l 3 as the agency effect of competton, whch s predcted to be postve. The mpact of agency costs n equaton (15) can be ¼ l 2 þ l 3 COMP. It depends on l 2, whch can be nterpreted as the gross mpact of agency costs on frms atttudes towards qualty mprovements; and s also related to the agency effect of competton, l 3 (f the mpact of competton s larger n frms subject to agency costs, then the mpact of agency costs s larger n more compettve mplcaton of proposton 2 s that ought to be negatve. Snce l 3 COMP s expected to be postve, we should fnd l 2 to be negatve; suffcently negatve n fact for the net mpact of agency costs l 2 þ l 3 COMP to be negatve. III(). Incentves and Effort Our model suggests that compettton affects the mportance frms place on qualty mprovements, contractual ncentves, and employee effort n a smlar way, through a drect pressure effect and an agency effect. Thus, to emprcally examne the mpact of competton on contractual ncentves, we propose a specfcaton smlar to (15): ð16þ INCEN ¼ g 0 þ g 1 COMP þ g 2 AGENCY þ g 3 COMP AGENCY þ g 4 CONTROL Emp þ e; where INCEN measures ndvdual employee contractual ncentves, and CONTROL Emp s a vector of control varables whch ncludes both frmlevel and employee level controls. In later specfcatons, our dependent varable INCEN s replaced wth EFFORT, a measure of ndvdual employee effort. We defne the constant and the coeffcents of COMP, AGENCY, COMP AGENCY, and CONTROL Emp n the EFFORT regresson as y 0, y 1, y 2, y 3, and y 4, respectvely. Wth arguments smlar to the ones used n our descrpton of the coeffcents n the QUAL regresson, t can easly be shown that g 1 and y 1 dentfy the drect pressure effect of competton on ncentves and effort, respectvely. They should be of the same sgn as l 1, whch could be postve or negatve. Coeffcents g 3 and y 3 dentfy the agency effect of competton and are predcted to be postve. Fnally, g 2 and y 2 dentfy the mpact of agency costs on ncentves and effort, and are expected to be sgnfcantly negatve. To test these emprcal predctons, we have access to a unque dataset that ncludes several measures of product market competton and of agency costs, ndcatons of frm atttudes towards qualty mprovements, the

19 PRODUCT MARKET COMPETITION AND AGENCY COSTS 307 structure of employee contracts, and employee level measures of effort. We now descrbe these varables n more detal. IV. DATA The Workplace and Employee Survey (WES)Fconducted by Statstcs Canada wth the support of Human Resources Development Canada s a very rch longtudnal data set that conssts of two components: 1) The workplace survey of approxmately 6,300 frms provdes nformaton on work organzaton and organzatonal change, compettve envronment, busness strategy, nnovaton, and frm performance; and 2) The employee survey of approxmately 25,000 employees n the same workplaces, whch contans nformaton on compensaton, human captal, tranng, work hours and arrangements, and promotons. Taken together, these two components generate approxmately 1,000 frm and employee specfc varables and an unprecedented opportunty to examne the connecton between competton, contractual ncentves and effort. To the best of our knowledge, a comparable data set does not exst anywhere else. The WES data s relatvely new and to date has been predomnantly used wthn Statstcs Canada and by a small group of labour economsts, though ts potental for other applcatons s tremendous. WES was frst conducted n 1999 and has been readmnstered annually to the selected cohort of frms over the followng sx years. WES s a lnked employer-employee fle. Employers are sampled by physcal locatons, and employees are then sampled from employer-provded lsts wthn each locaton. The survey covers all ndustres except farmng, fshng, trappng, and publc admnstraton and all regons of Canada wth the excepton of the Arctc terrtores (the Yukon, Northwest Terrtores, and Nunavut). Currently, data for 1999, 2000, and 2001 are avalable for analyss, and the response rate for workplaces n each of these years s more than 95%. The questons about frm strategy, whch are used to construct our measures of the emphass frms place on qualty mprovements, were asked n 1999 and 2001 but not n In addton, our emprcal model ncorporates control varables from t 1, elmnatng the use of strategy responses from 1999 as dependent varables. As a result, our man set of dependent varables s derved from the 2001 WES, wth ndependent varables drawn from both 2001 and The process of sample selecton for WES stratfed busnesses n Canada nto relatvely homogeneous groups that were then used for sample allocaton and selecton. Busnesses were classfed by fourteen ndustry classfcatons, sx regonal classfcatons, and three employment sze categores, resultng n 252 possble strata. The strata were constructed so as to maxmze varaton between strata and mnmze varaton wthn strata. Frms are sampled usng Neyman allocaton, meanng frms are