Endogenous managerial compensation contracts in experimental duopolies

Transcription

1 Endogenous manageral compensaton contracts n expermental duopoles Iván Barreda-Tarrazona Nkolaos Georgantzís Constantne Manasaks Evangelos Mtrokostas Emmanuel Petraks Abstract In a Cournot duopoly, we expermentally nvestgate whether frms owners compensate ther managers wth contracts combnng own profts and revenues or own profts and relatve performance. We also explore the effects of the selected contracts on the output levels set by managers. In lne wth the theory, Relatve Performance contracts are chosen more frequently than Proft Revenue contracts. Nevertheless, Proft-Revenue-compensatng owners put more weght on own profts than Relatve Performance-compensatng owners do. Ths s n lne wth the theory, but only for asymmetrc contract confguratons. Generally speakng, output reacts to the contract terms n the expected way although t tends to exceed the predcted levels. Keywords: Expermental economcs; Olgopoly theory; Manageral delegaton; Endogenous contracts JEL Classfcaton: D43; L21 Fnancal support by the Spansh Mnstry of Scence and Innovaton (ECO , ECO and ECO ), Junta de Andalucía (P07-SEJ-03155) and Bancaxa (P1-1B and P1-1A ) are gratefully acknowledged. Part of ths research was undertaken whle N. Georgantzís was vstng the Unversty of Cyprus whose hosptalty s gratefully acknowledged. Fnancal support (Proect INV ), whle E. Petraks was vstng the Economcs Department at Unverstat Jaume I, s gratefully acknowledged. We are grateful to Anhoa Jaramllo for help wth the data analyss. We would also lke to thank partcpants at the IO Workshop 2011, Otranto; EARIE 2008 Conference, Toulouse; the ASSET 2008 Meetngs, Florence; and the Semnars Seres at UADPhlEcon, Department of Economcs, Unversty of Athens, for ther helpful comments and suggestons. We are grateful to two anonymous referees of the ournal. The usual dsclamer apples. LEE & Economcs Dept., Unversty Jaume I of Castellón Span; e-mal: van.barreda@eco.u.es. LEE-UJI Castellón & GLOBE-Economcs Dept., Unversty of Granada, Span; e-mal: ngeorgantzs@ugr.es. Poltcal Scence Dept., Unversty of Crete, Greece; e-mal: manasaks@econ.soc.uoc.gr. Economcs Dept., Unversty of Portsmouth, UK; e-mal: evangelos.mtrokostas@port.ac.uk. Economcs Dept., Unversty of Crete, Greece; e-mal: petraks@econ.soc.uoc.gr.

2 1 Introducton It s well establshed that n modern frms, where ownershp and management are separated (Fama and Jensen, 1983), one of the key aspects of corporate governance relates to manageral compensaton (van Wtteloostun et al., 2007). In ths context, owners choose ther managers compensaton contracts so as to motvate them to gan a compettve advantage n the market (Murphy, 1999; Jensen et al., 2004). Several corporate performance measures have been assocated wth manageral compensaton. Early emprcal studes (Baker et al., 1988; Jensen and Murphy, 1990; Lambert et al., 1991) suggest that CEO compensaton s postvely assocated wth profts and revenues. Moreover, ndustry-level analyses suggest that contracts combnng own proft and revenues are wdely adopted n the CEO compensaton practce n US new economy frms (Nouray and Daroca, 2008), the US electrc ndustry (Duru and Iyengar, 1999) and the US gas utlty ndustry (Agrawal et al., 1991). 1 There s also evdence suggestng that top executves compensaton s based on ther relatve performance,.e., a manager s compensaton s a combnaton of own profts and the relatve performance aganst the rvals profts (Gbbons and Murphy, 1990; Barro and Barro, 1990; Janakraman et al., 1992). Aggarwal and Samwck (1999) and Joh (1999) fnd that contracts of ths type are wdely adopted both n the US and Japanese manufacturng sector. Regardng the UK, Keasy (2008) suggests that relatve shareholder return growth remans the most popular performance measure lnked wth executve compensaton. 2 Ths varety n manageral compensaton practces has lead researchers, practtoners and polcy makers to seek an explanaton for the emergence of the alternatve confguratons of manageral compensaton contracts. Ths paper presents expermental evdence, frstly, on whether frms owners compensate 1 The strategc use of manageral compensaton contracts combnng own profts and revenues has been ntroduced n the lterature by Vckers (1985), Fershtman (1985), Fershtman and Judd (1987) and Sklvas (1987). In ths lne of research, an owner has the opportunty to delegate the output decson to hs manager and by offerng hm an approprate compensaton contract, to drect the manager to a more aggressve behavor n the market. Ths forces rval frms to reduce ther output. In ths way, the owner has the opportunty to become a Stackelberg leader n the market, provded that the rval owners do not delegate output decsons to ther managers. In equlbrum however, all owners delegate output decsons to managers, endng up n a Stackelberg warfare stuaton wth relatvely low profts for all frms. 2 Mller and Pazgal (2001; 2002; 2005) formalze relatve performance contracts. In ths case too, frms end up n a Stackelberg warfare. However, frms profts are hgher than n the case of proft-revenue contracts. Note that moral hazard ssues arsng n a strategc delegaton context are usually gnored by the relevant lterature, whch focusses exclusvely on the use of delegaton of authorty from owners to managers as a credble commtment to non-strctly proft maxmzng strateges. 1

3 ther managers wth contracts combnng own profts and revenues or own profts and relatve performance. Secondly, on how aggressvely owners drect ther manageers to behave as sellers n the market. And thrdly, on the effect of these contracts on output levels set by managers. Data are obtaned under two alternatve settngs, dependng on the ablty of frm owners to commt, or not, on contract types before choosng ther respectve contract terms. 3 Ths allows us to test the relatve mportance of strategc commtment on specfc contract types n a context for whch real world data are naturally unavalable. In the experment, we study a Cournot market where two ex-ante symmetrc frms produce a homogeneous good. Each frm has one owner and one manager. In the basc scenaro, frms owners commt ex-ante over the types of contracts they employ to compensate ther managers. Ths s formalzed n a three-stage treatment, where, n the frst stage, each frm s owner commts to one of two types of manageral compensaton contracts: Frst, the Proft-Revenue contract, P R, accordng to whch the manager s compensaton s a lnear combnaton of own profts and revenues. And second, the Relatve Performance contract, RP, accordng to whch, the manager s compensaton s a lnear combnaton of own profts and relatve performance. In the second stage, gven that the manageral contracts have become common knowledge and cannot be reset, each owner sets the manageral ncentve parameter,.e., the weght of own profts and revenues or own profts and relatve performance. In the thrd stage, managers smultaneously set output. The alternatve scenaro where frms owners do not commt over the types of contracts, before choosng ther respectve contract terms, s formalzed n a twostage treatment, where, n the frst stage, each owner chooses both the type of contract wth whch to compensate hs manager and ts respectve manageral ncentve parameter. In the second stage, managers set output. The predctons of the theoretcal model are the followng: Frst, n equlbrum, frms owners choose to compensate ther managers wth RP contracts. Ths equlbrum s unque n the three-stage scenaro. In the two-stage scenaro, multple equlbra exst, wth RP contracts emergng n the Pareto superor equlbrum. Ths allows us to test whether the prevalence of RP contracts s explaned by the frms owners ablty to commt to a specfc contract type, before choosng ts respectve terms, or by the owners selecton of the Pareto 3 A key assumpton n the strategc manageral delegaton lterature s that frms owners commt over the types of contracts that they choose to compensate ther managers. Yet, Manasaks et al. (2010) fnd that when there s no such commtment, each type of contract s an owner s best response to the rval owner s contract choce, leadng to multplcty of equlbra. 2

4 superor equlbrum contract types. Second, the manageral ncentve parameters set by RP - compensatng owners drect ther managers relatvely closer to proft-maxmzaton than the parameters set by P R-compensatng owners do. Ths holds for symmetrc confguratons, where both frms owners choose to compensate ther managers wth contracts of the same type. The opposte holds n asymmetrc confguratons where the types of contracts chosen dffer across rval frms. And thrd, frm-level output set under unversal adopton of RP contracts s lower than the output set under unversal adopton of P R contracts, whle n asymmetrc contract confguratons the above rankng s reversed. We tested the predctons of the theoretcal model n the laboratory mplementng the twostage and three-stage treatments of the model. A total of four 36-subect sessons were run, two under each scenaro. Eghteen owner-manager pars, labeled as frms, were randomly formed at the begnnng of each sesson. These pars were kept fxed throughout the 50 perods of the sesson n order to encourage the development of a cooperatve relatonshp between the agents who formed each frm. In each perod, frms were matched nto pars formng nne random duopoles n order to preserve the one-shot nature of the market game and avod any collusve outcomes (Huck et al., 2004; Holt, 1985). Our man fndng s that under both treatments, RP contracts were more frequently chosen by owners than P R contracts. Ths evdence s n lne wth the theory. We are also able to contrast the two alternatve motves offered by the theoretcal analyss for the prevalence of RP contracts. Our expermental evdence reveals that the adopton of RP contracts does not depend on whether frms owners can commt, or not, to contract types before ther respectve terms are chosen. Hence, the prevalence of RP contracts can be fully explaned by the frms owners selecton of the Pareto-superor equlbrum contract types. Ths, n turn, refutes the mportance of strategc commtment over contract types for explanng the prevalence of RP contracts. Regardng the manageral ncentve parameters, our results reveal that frms owners only rarely chose to compensate ther managers accordng to ther own profts alone. Ths s n lne wth the theory and n contrast to Huck et al. (2004). Moreover, we fnd that under both treatments, P R-compensatng owners set hgher ncentve parameters as compared to the RP - ones. For symmetrc contract confguratons, ths fndng s n contrast to the theoretcal predcton and mples that P R-compensatng owners drect ther managers relatvely closer to proft-maxmzaton than the RP -compensatng owners do. A possble explanaton for 3

5 ths reversal could be that P R-compensatng owners set relatvely hgh manageral ncentve parameters n order to mtgate the expected proft loss due to the Stackelberg warfare that ther contract choces would provoke. In contrast, n asymmetrc contract confguratons, ths fndng confrms the theoretcal predctons. Fnally, regardng the effects of contract types and manageral ncentve parameters on output levels, our expermental evdence mples the followng: Frst, the output levels are hgher than those predcted by the theory. Ths holds for all cases except for the output level set by RP -compensated managers n asymmetrc contract confguratons. Hence, our results suggest that contract types and manageral ncentve parameters chosen by the frms owners often lead to a Stackelberg warfare fercer than the theory predcts. However, under unversal RP -rewardng contracts, whch s the most frequent contract combnaton, ths devaton s slghtly more than 10% of the predcted theoretcal level. Ths s n lne wth other quantty settng expermental markets (Huck et al., 1999) and s contrast wth a sharp convergence to equlbrum usually reported n prce-settng experments (Garca-Gallego, 1998). Thrd, as the manageral ncentve parameters ncrease, nducng managers to focus more on own profts, managers output choces become less aggressve. That s, managers set lower output when ther ncentves depend more on ther frms profts and less on the alternatve obectves of revenue or relatve performance. Ths fndng s n lne wth the theory too. Our paper contrbutes to the lterature nvestgatng the corporate performance measures that owners choose to compensate ther managers. The most closely related paper to us s Huck et al. (2004) whch s the only prevous expermental study on strategc manageral compensaton contracts n olgopoly. The authors adopt a dscrete strategy space where owners choose among two dfferent contracts. The frst contract (No-Delegaton) gves managers ncentves for strct own proft-maxmzaton, whle the second contract (Delegaton) gves an addtonal sales bonus. Gven the owners choces regardng the types of contracts, managers choose output from a dscrete strategy space. Ther expermental evdence suggests that the Delegaton contract s only rarely chosen. More specfcally, owners drect ther managers towards mere proft-maxmzaton, wth a relatve frequency of more than 66% n all ther treatments. We depart from ths paper n four ways. Frst, n our experment, owners have a wder strategy space, regardng the types of contracts from whch they choose to compensate ther managers. Second, owners have an almost contnuous strategy space on the manageral ncentve parameter that weghs own profts aganst ether own revenues or relatve performance. 4

6 Thrd, managers select output also from an almost contnuous strategy space. By dong so, we test not only whether owners drect ther managers away from strct own proft-maxmzaton, but also the effects of contracts chosen by owners on output levels set by managers. Fnally, the dstncton between the two-stage and the three-stage scenaro allows us, frst, to contrast the two alternatve motves offered by the theoretcal analyss for the prevalence of RP contracts, and second, to nvestgate the relatve mportance of the owners commtment over contracts types for ther managers, before settng ther respectve contract terms. The rest of the paper s organzed as follows: Secton 2 descrbes and brefly analyzes the theoretcal model that leads to a number of hypotheses that wll be tested expermentally. Secton 3 presents the expermental desgn. Secton 4 reports the results. Fnally, Secton 5 concludes. In the Appendx the expermental nstructons are ncluded. 2 The theoretcal framework We consder a homogeneous good ndustry where two frms, denoted by, = 1, 2,, compete n quanttes. The (nverse) demand functon for the fnal good s gven by P (Q) = A Q, where Q = q 1 + q 2 s the aggregate output. Frms are endowed wth constant returns to scale technologes and have the same constant margnal cost c, wth c < A. Hence frm s profts are: Π = (A q q c)q (1) In ths ndustry, each frm has an owner and a manager. Followng Fershtman and Judd (1987), owner s a decson maker whose obectve s to maxmze the profts of the frm. Ths could be the actual owner, a board of drectors, or a chef executve offcer. Managers are agents hred by owners to make real tme operatng decsons concernng output. Followng Straume (2006), we consder that each manager chooses the frm s output so as to maxmze hs compensaton whch s set accordng to a contract provded by the owner. Each owner compensates hs frm s manager accordng to one of the followng two types of contracts. The frst s the Proft-Revenue, P R, contract. Followng Fershtman and Judd (1987) and Sklvas (1987), under ths type of contract, the compensaton scheme takes a partcular form: manager s pad n proporton to a lnear combnaton of own profts and revenues. More formally, under ths type of contract, manager s compensaton s gven by: 5

7 C P R = α P R Π + (1 α P R )R (2) where Π and R are frm s profts and revenues respectvely, and α P R s the manageral ncentve parameter whch s chosen optmally by frm s owner so as to maxmze hs profts, wth 0 α P R 1. If α P R < 1, frm s owner drects hs manager away from strct proftmaxmzaton towards ncludng consderaton of revenues and thus, manager becomes a more aggressve seller n the market. The hgher the α P R puts on own profts. If α P R strct proft-maxmzaton. s, the hgher s the weght that owner = 1, manager s behavor concdes wth owner s obectve for The second type of contract s the Relatve Performance, RP, one. Followng Mller and Pazgal (2001; 2002; 2005), under ths type of contract, frm s owner compensates hs manager by puttng a weght α RP on own profts and a weght (1 α RP ) on the dfference between own profts and the profts of the rval frm, wth 0 α RP 1. Under ths type of contract, manager s compensaton s gven by: C RP = α RP Π + (1 α RP )(Π Π ) (3) The lower the α RP s, the hgher s the weght that owner puts on relatve performance, drectng, thus, hs manager to become a more aggressve seller n the market. If α RP manager s behavor concdes wth the owner s obectve for strct proft-maxmzaton. = 1, the To nvestgate the types of manageral compensaton contracts that arse n equlbrum, we consder a three-stage game wth observable actons, wth the followng tmng. In the frst stage, each frm s owner commts to one of the two types of contracts, D {P R, RP }. In the second stage, each owner sets the respectve manageral ncentve parameter α D stage, managers set output. 4. In the thrd An alternatve two stage game wth observable actons s also consdered, accordng to 4 At ths pont, t s useful to bear n mnd two alternatve nterpretatons of the game. Accordng to the frst one, followng Fershtman and Judd (1987) and Sklvas (1987), an owner hres a manager and drects hm va an approprate ncentve contract. The alternatve nterpretaton s the one presented by Mller and Pazgal (2002). In the latter, the problem faced by the owner of each frm s to choose the best type of manager among those that are avalable, whle each manager s commtted to behavng n a certan manner by vrtue of hs personalty type. More specfcally, n Mller and Pazgal (2002), potental managers take on a contnuum of atttudes toward relatve performance whch s captured by ther type, ϕ. However, the dfference between the above two approaches s only semantc, snce owners have, by assumpton, all the barganng power whle settng the contracts. 6

8 whch, n the frst stage, each owner chooses both the type of contract D and the respectve manageral ncentve parameter α D. In the second stage, managers set output. The latter captures a stuaton n whch there s no ex-ante commtment over the type of contract that each owner offers to hs manager. The crucal, yet reasonable, assumpton here s that the type of contract and the contract terms that owner sets are not observable by the rval owner before contract-settng s everywhere completed. Ths alternatve game helps us to evaluate the relatve mportance of strategc commtment on an owner s choce of contract type. The equlbrum concept employed to solve the above games s the subgame perfect equlbrum. Consder frst the Unversal Proft-Revenue, U P R, confguraton of contracts. In ths case, both frms owners commt to a P R contract wth whch they compensate ther managers. In the thrd stage, manager chooses q to maxmze hs utlty gven by eq. (2). Takng the frst order condtons and solvng the system of equatons, the output level that manager sets s: q P R (α P R, α P R ) = A c(2αp R 3 α P R ) q From (4), t can be checked that: P R < 0 and qp R α P R > 0. That s, the weght owner sets α P R on own profts affects negatvely the output level chosen by manager, whle owner s weght on own profts affects q postvely. In the second stage, each owner chooses α P R so as to maxmze profts gven by: (4) Π P R (α P R, α P R (A c(2αp R ) = α P R ))(A c(3 α P R α P R )) 9 (5) Solvng the system of the frst order condtons, we obtan equlbrum manageral ncentve parameters, output levels and profts: α P R = A + 6c ; q P R = 5c 2(A c) ; Π P R = 5 2(A c)2. (6) 25 Second, the Unversal Relatve Performance confguraton, U RP, of contracts s examned. In ths case, both frms owners commt to an RP contract wth whch they compensate ther managers. In the thrd stage, manager chooses q to maxmze hs utlty gven by eq. (3). Solvng the system of the frst order condtons, the output level that manager sets s: q RP (α RP, α RP (A c) (2 αrp ) = 4 α RP α RP ) (7) 7

9 From (7), note that qrp < 0 and qrp α RP > 0. That s, the hgher the weght owner sets on α RP own profts, the lower the output level chosen by manager, whle the hgher owner s weght on own profts, the hgher the output chosen by manager. In the second stage, each owner chooses α RP Π RP (α RP, α RP ) = (A c) 2 ( 2 α RP ( so as to maxmze profts gven by: ) ( α RP 4 α RP ( ) ) 1 α RP + α RP ) 2 (8) Solvng the system of frst order condtons, we obtan the equlbrum manageral ncentve parameters, output levels and profts: α RP α RP = 2 3 ; qrp = 3(A c) ; Π RP = 8 3(A c)2. (9) 32 Fnally, the Coexstence confguraton of contracts s nvestgated. Wthout loss of generalty, owner commts to compensate hs manager wth a P R contract, whle owner commts to an RP contract. In the thrd stage, manager () chooses q (q ) to maxmze hs utlty gven by eq. (2) ((3)). Solvng the system of the frst order condtons, output levels are: ) q pr (α pr, α rp A + c(1 2αpr ) = 4 α rp (10) q rp (αpr, α rp A(2 αrp ) c(2 αpr ) = 4 α rp α rp ) As above, the weght an owner sets on own profts affects negatvely the output level chosen by hs manager, whle the rval owner weght on own profts affects t postvely (t can be checked that qpr α pr > 0). In the second stage, owners set the ncentve parameters so as to maxmze profts gven by: < 0, qrp α pr > 0, and qrp α rp < 0, qpr α rp [ ( )] [A c(2α pr Π pr (α pr, a rp ) = 1)] A c 3 2α pr α rp + α pr α rp ( ) 2 (12) 4 α rp (11) 8

10 Π rp (αpr, α rp ) = [ ( A 2 α rp ) ( c 2 α pr α rp )] [ ( )] A c 3 2α pr α rp + α pr α rp ( ) 2 (13) 4 α rp Solvng the system of the frst order condtons, we obtan the equlbrum manageral ncentve parameters, output levels and profts: α pr = 1; q pr = A c ; Π pr (A c)2 = 4 16 (14) α rp = 0; q rp = A c ; Π rp (A c)2 = 2 8 (15) Usng the equlbrum profts expressons under the U P R, U RP and coexstence of both contracts confguratons, t s easy to check that, n the frst stage, each frm s owner wll opt for a RP contract. Hence, the Unversal Relatve Performance contract confguraton emerges n the unque subgame perfect equlbrum of the three-stage game. 5,6 On the other hand, n the two stage game where owners are unable to commt to a specfc contract type, before settng ts respectve contract terms, multple equlbra arse regardng the type (and the terms) of contract that each owner chooses. 7 Usng the Pareto crteron for equlbrum selecton, owners would realze that t s n ther mutual nterest to move towards the equlbrum that ensures them the hghest profts, that s, the U RP contract confguraton equlbrum. Thus, t s expected that n the two stage game too, each owner wll choose to compensate hs manager wth an RP contract. 5 For further detals see Manasaks et al. (2010). The ntuton behnd ths result goes as follows: An RP contract makes a manager s behavor less susceptble to strategc manpulaton by rval managers. Less scope for strategc manpulaton gves to the rval owner less reason to provde ncentves for aggressve behavor to hs manager. Ths mples that the owner who chooses the RP contract for hs manager obtans compettve advantage n the market, for any contract choce of the rval owner. Ths, n turn, makes the selecton of an RP contract each owner s best response to whatever the rval owner s choce s. 6 Note that f both owners set the manageral ncentve parameters equal to 1, equlbrum output level and profts are q N = (A c) and Π N 3 = (A c)2, respectvely. In the strategy space of Huck et al. (2004), ths s 9 equvalent to the No-Delegaton case where owners themselves decde over the output levels. It s easy to check that output (profts) set under any of the manageral compensaton contracts dscussed above s hgher (lower) than that set n the No-Delegaton case. Intutvely, owner, by usng a manageral compensaton contract strategcally, drects hs manager to a more aggressve behavor n order to force the rval manager to reduce output. Because both owners act n the same way at the game s contract stage, frms end up n a prsoners dlemma stuaton. Naturally, the ncreased market supply leads to lower profts. 7 For a formal proof see Manasaks et al. (2010). 9

11 We concentrate now on the hypotheses whch wll be tested wth our expermental desgn. We begn by consderng the owners contract type choces wth whch they wll compensate ther managers. Our theoretcal analyss predcts unversal adopton of RP contracts n both the 2-stage and 3-stage games. However, coordnaton on the Pareto superor equlbrum (whch s one out of an nfnte number of equlbra n the 2-stage game) may requre too much n terms of subects ratonalty. If so, the unqueness of the equlbrum predcted n the 3-stage game, due to the strategc commtment motve, could provde a more favorable envronment for the emergence of RP contracts. Therefore, f coordnaton on one of multple equlbra s a dffcult task, we would expect a hgher frequency of RP contracts n the 3-stage game. Otherwse, RP contracts should be adopted n both games wth smlar frequences and thus, commttng to a contract type before choosng ts respectve terms should not be an mportant factor explang the emergence of RP contracts. Thus, from a practcal pont of vew, comparng the 2-stage and 3-stage games allows us to evaluate the role of strategc commtment to a contract type before choosng ts respectve terms. The above lead to the followng hypothess that wll be tested expermentally: HYPOTHESIS 1: (H1.1) Relatve Performance contracts wll always be preferred by owners over Proft-Revenue ones and (H1.2) The frequency of Relatve Performance contracts wll be lower n the absence of owners commtment over the contract type before choosng ts respectve contract terms. Gven the above arguments, t s straghtforward that the equlbrum contracts manageral ncentve parameters should be set at a level such that RP -compensatng owners gan hgher profts than the P R-ones. Ths can be formalzed n the followng hypothess: HYPOTHESIS 2: (H2.1) Under unversal adopton of each type of contract, Relatve Performance-compensatng owners set manageral ncentve parameters at a level hgher than that set by Proft-Revenue-compensatng owners. (H2.2) In asymmetrc contract confguratons, the aforementoned rankng s expected to be reversed. (H2.3) No dfference s expected between the two stage and three stage games. Frms output s expected to be hgher under UP R contracts than under URP contracts. The opposte rankng holds for frms profts. Ths explans why the latter equlbrum s more proftable for frms owners than the former. In asymmetrc contract confguratons, an RP -compensated manager sets output at a level hgher than that set by hs P R-compensated rval manager. Furthermore, accordng to expressons (4), (7), (10) and (11), and the follow 10

12 up dscusson, own output should react negatvely to ncreases n a frm s own manageral ncentve parameter and postvely to the rval frm s ncentve parameter, under all contract confguratons. The above can be summarzed n the followng hypothess: HYPOTHESIS 3: (H3.1)Compared to the case of Unversal Relatve Performance contracts, output wll be hgher under Unversal Proft-Revenue contracts. Whenever the two contract types coexst, an RP -compensated manager s predcted to set output at a level hgher than that set by hs P R-compensated rval. (H3.2) A frm s output wll be hgher the lower the frm s own manageral ncentve parameter and the hgher the rval frm s ncentve parameter. 3 Expermental desgn We have tested the predctons of the theoretcal model outlned above n a laboratory experment. A total of 144 subects partcpated n the sessons. They were volunteers recruted among 2nd and 3rd year students enrolled n the Busness and Human Resources degrees at the Unverstat Jaume I (Castellón, Span) accordng to standard protocols used n the Laborator d Economa Expermental (LEE). Each sesson lasted approxmately 100 mnutes. The experment was organzed under two treatments. A total of four 36-subect sessons were run, two under each treatment. In the frst treatment, labeled as 3-stage game, the choce of contract type precedes the choce of the manageral ncentve parameter. Then, managers set output. In the second treatment, labeled as 2-stage game, owners choose smultaneously both the type of contract wth whch to compensate ther managers and the respectve manageral ncentve parameter, before managers decde on ther frms output. Incentve parameters were chosen between 0 and 1 (nclusve) usng up to two decmal dgts, whereas output was chosen among the ntegers n the range between 0 and 500. The experment was programmed usng the z-tree toolbox (Fschbacher, 2007). At the begnnng of each sesson wrtten nstructons were gven to the subects and each of them was randomly assgned the role of an owner or a manager. Eghteen owner-manager pars, labeled as frms, were randomly formed at the begnnng of each sesson. These pars were kept fxed throughout the 50 perods of the sesson n order to encourage the development of a cooperatve relaton between the agents who formed each frm. Nne duopoles were randomly formed n each perod n order to preserve the one-shot nature of the market game. In order 11

13 to ncrease the number of completely ndependent observatons per sesson, matchng occurred wthn three groups of 6 owner-manager pars (frms), that s, three ndependent matchng groups of 12 subects each. However, ths precse detal was not known by the subects who had an addtonal dffculty to guess the total group sze and assess the lkelhood of beng rematched wth the same frm n two dfferent perods, gven that the computer network of the LEE s nstalled n two dstant rooms between whch there s no possblty of vsual contact. No sgnfcant dfference was found across matchng groups wthn each treatment and, thus, data from the same treatment were pooled together. Followng ths desgn, a total of three totally ndependent observatons per sesson s guaranteed by the fact that strateges and the hstory experenced by each subect were never contamnated nor dd they contamnate decson makng wthn the other two matchng groups. Therefore, n a very strct statstcal sense, our conclusons are based on behavor wthn sx totally ndependent groups per treatment. In order to facltate learnng n the quantty-settng stage, owners could change ther managers compensaton contract every 3 perods, durng the frst 30 perods and n every perod, durng the last 20 perods. 8 Before subects made ther decsons n the second and thrd stages of the game they were nformed on prevous stage actons by other players n the same market. At the end of each perod, each subect s feedback ncluded full nformaton on strateges and outcomes of all players n the same market. No other decson makng ad was avalable to them. The four sessons were run on two dates. The order between the 2-stage and the 3-stage sesson was changed across the two dates to mnmze the probablty that a subect could antcpate the treatment that would be mplemented should any nformaton have been transmtted from one sesson to another. Each subect partcpated n one sesson only. Therefore, sessons 1 and 4 correspond to the 3-stage treatment, whle sessons 2 and 3 belong to the 2-stage treatment. The total amount spent on subect payoffs was 2, 739 euros whch mples slghtly above 19 euros per subect earnngs, rangng between 7.3 and 29.6 euros (an owner subect n a 3-stage treatment and an owner-subect n a 2-stage treatment respectvely). Subects n the 3-stage treatment receved slghtly lower payments than n the 2-stage one (18.7 and 19.3 euros 8 Prevously, ths format has been effcently mplemented as a learnng facltatng devce n several experments on multstage olgopoles such as n Barreda-Tarrazona et al. (2011), Camacho-Cuena et al. (2005) and Fatás-Juberías et al. (2013). 12

14 respectvely). An exchange rate of 1 euro per 80, 000 EXCUs was used. Followng closely the contracts studed n the theoretcal model, the contract schemes for the experment were desgned after a seres of plot sessons n order to guarantee that subects wth dfferent roles could earn smlar expected rewards. In partcular, the P R contract took the followng formula: EXCUs as a fxed salary plus a half of a lnear combnaton between the profts and the revenues of the frm. The respectve formula for the RP contract was: EXCUs as a fxed salary plus a half of a lnear combnaton between the frm s profts and the dfference between the frm s profts and the profts of the rval frm. 9 The model s parameter values mplemented n the experment were A = 1000 and c = 200. Under ths set of parameters, n the Unversal P R equlbrum, both owners should set α P R = 0.2 and managers should set the correspondng equlbrum output levels at q P R = 320. The respectve values n the Unversal RP equlbrum are α RP = and q RP = 300. The equlbrum contract terms and output levels when owner chooses the P R contract whle [ ] chooses the RP one are: α P R, α RP, q P R, q RP = [1, 0, 200, 400]. A strct test of the theoretcal model should am at comparng the observed data on contract types, contract terms and outputs to the aforementoned theoretcal predctons. However, any expermentalst would mmedately recognze the dffcultes assocated wth such a strct test of the theory, gven that, unlke the usual theoretcal assumpton of perfectly nformed human decson makers wth unlmted calculus capacty and perfect foresght, real human agents learn from tral-and-error strateges and may make systematc mstakes due to a number of reasons. 10 Thus, we wll focus on the test of the predctons provded n a qualtatve form by the hypotheses H1 H3 stated n the prevous secton. 9 For the nstructons gven to subects, see the Appendx. 10 A vast lterature has been dedcated to varous factors that may be responsble for observed shortcomngs of human behavor n complex envronments, such as ms-percepton of feedback (Pach and Sterman, 1993; Sterman, 1994), lmtatons n subects learnng when exposed to strategc complexty (Rchards and Hays, 1998), or mult-task decson makng (Kelly, 1995). A number of factors that favor subects mprovement of performance have, also, been dentfed. For example, tral-and-error algorthms have been shown to facltate convergence of the strateges played by unnformed subects toward symmetrc, full-nformaton equlbrum predctons, as shown n Garca-Gallego (1998) for the case of a prce-settng olgopoly. Whle full convergence near the theoretcal benchmark s obtaned n the symmetrc sngle-product settng of Garca-Gallego (1998), the ntroducton of multproduct frms n Garca-Gallego and Georgantzs (2001) or the asymmetry n Garca- Gallego et al. (2004) provde suffcently unfavorable envronments for the hypothess of convergence to the theoretcal predcton to be reected. 13

15 4 Expermental results Let us now proceed wth the presentaton of the expermental results. overall descrptve statstcs of our experment. We begn wth the 4.1 Overall descrptve statstcs Table 1 provdes aggregate adopton frequences for the two contract types. The aggregaton of data does not allow us to test any specfc hypothess. We wll do ths n the followng subsectons. However, the overall pcture ndcates that RP contracts were adopted n over 70% of the cases n both treatments. We proceed now wth a more detaled analyss of the data takng nto account the dfferent possble contract confguratons arsng from the choces of both owners. Table 1: Contract adopton frequences Treatment 2-Stage 3-Stage Both Contract Type* RP P R RP P R RP P R Relatve Frequency 73.3% 26.7% 70.9% 29.1% % * Proft-Revenue Contract =P R, Relatve Performace Contract =RP 4.2 Types of contracts and contract confguratons Regardng the total number of occasons n whch each contract type was adopted, we fnd that, n both treatments, the frequency of RP adopton was sgnfcantly hgher than that of P R. More specfcally, RP vs. P R contracts were chosen 1320 vs. 480 tmes n the 2- stage treatment and 1277 vs. 523 tmes n the 3-stage treatment. However, the predcton of unversal adopton of RP contracts s confrmed less frequently than these numbers may suggest. To see ths, we refer to Table 2. What we are really nterested n s to nvestgate whether the combnaton of owners contract choces s as predcted by the equlbra of the theoretcal model. As shown n Table 2, more than half of our expermental duopoles took place under Unversal RP contracts. Ths holds for both the 2-stage (988/1800 = 54.89%) and the 3-stage (932/1800 = 51.78%) 14

16 treatments. Contrary to ths, the Unversal P R confguraton receved scarce support (8.22% for the 2-stage and 9, 89% for the 3-stage). In fact, the frequency of Unversal P R s approxmately one fourth of the frequency of Coexstence of the two contract types, P RRP and RP P R, n the same market Table 2: Owners choces of contract types Treatment UP R URP P RRP & RP P R 2-stage 8.22% 54.89% 36.89% 3-stage 9.89% 51.78% 38.33% Total 9.06% 53.33% 37.61% Note also that frms owners only rarely chose to compensate ther managers n a way drectng them to strct own proft maxmzaton. More specfcally, only n 4% (6%) of the contracts n the 3-stage (2-stage) treatment, owners set the manageral ncentve parameter equal to one. Ths result comes n sharp contrast to the expermental evdence of Huck et al. (2004). They fnd that the No-Delegaton strategy s chosen wth a relatve frequency of more than 66% n all ther treatments. These results clearly confrm Hypothess H1.1. Furthermore, the fact that U RP and the overall frequency of RP contracts reman almost nvarant across treatments leads us to reect the commtment motve as a reason for selectng RP contracts, reectng H1.2. Therefore, we can state the followng result: RESULT 1: 1. Under both treatments, Relatve Performance contracts are sgnfcantly more frequent than Proft-Revenue ones (confrmng H1.1). 2. The adopton frequency of Relatve Performance contracts does not vary across the 2-stage and 3-stage treatments (reectng H1.2). Ths result ndcates that the prevalence of the Unversal RP confguraton over the Unversal P R alternatve one can be fully explaned by the subects selecton of the Pareto-superor 11 Hereafter, P RRP ndcates the confguraton where owner 1 chooses the P R contract and owner 2 chooses the RP contract. The opposte holds for RP P R. 12 A χ 2 test (p < 0.001) has been used to confrm the sgnfcance of the dfference between the aforementoned observed frequences and a random dstrbuton of strategy pars unformly across the correspondng outcomes of the game n the contract stage. 15

17 equlbrum contract types and refutes the mportance of strategc commttment over contract types for expanng the prevalence of RP contracts. It s also nterestng to see the dynamcs of contract adopton frequences. Fgure 1 presents the evoluton of RP contract adopton n the two treatments, startng from below 40% n perod 1, and reachng frequences close to 90% n perod 50. Fgure 2 presents the same data broken down by contract combnaton. Fgure 2 shows that n both treatments, Unversal P R adopton represents a small and rather stable proporton of choces. The coexstence of both contracts decreases over tme whle Unversal adopton of RP contracts ncreases up to around 3/4 of the cases. Fgure 1: Evoluton of ndvdual RP contract adopton. 16

18 Fgure 2: Evoluton of Contract Combnatons. 4.3 Manageral ncentve parameters Let us now present our fndngs regardng owners choces of manageral ncentve parameters. We present our evdence n Table 3 and Fgure 3. Table 3: Owners choces of manageral ncentve parameters Confguraton 2-stage 3-stage UPR U RP P RRP RP P R Predcted α Mean α St. dev Mean α St. dev

19 Fgure 3: Evoluton of ncentve parameter by contract combnaton. Recall that our theoretcal analyss predcts αp R = 0.2 and αrp = Regardng the symmetrc confguratons of contracts, our expermental evdence leads to the followng observatons. Frst, under unversal contract adopton n both treatments, the average ncentve parameter set by P R-compensatng (RP -compensatng) owners was hgher (lower) than the predcted one. Ths mples that P R-compensatng (RP -compensatng) owners ntenton towards proft-maxmzaton was stronger (weaker) than predcted. Fgure 3 shows a dynamc pcture of these observatons, depctng observed ncentve parameters aganst ther respectve theoretcal values (plotted as an horzontal lne). No systematc trend s observed n any of these parameter seres, whereas fluctuatons n the case of unversal P R contracts are due to the small and nosy sample under ths confguraton. In absolute values, the devaton of observed ncentve parameters from the respectve predcted equlbrum values for P R contracts was twce the devaton for RP contracts. Interestngly enough, wthn each treatment, P R-compensatng owners set, on average, ncentve parameters hgher than those set by the RP -compensatng ones.13 Ths s n contrast to the theory s predctons and mples that P R-compensated managers were drected relatvely closer to proft-maxmzaton than RP -compensated ones. Note also that for both contract types, the dfference n ncentve parameters across treatments (2-stage vs 3-stage) s not statstcally sgnfcant Wthn each treatment, the dfference n ncentve parameters across contract types s sgnfcant, as shown by a Mann-Whtney test comparng medans of ndependent groups (p = for the 2-stage treatment and p = for the 3-stage treatment). 14 Gven a P R contract, the statstcal sgnfcance of the dfference n ncentve parameters across treatments (2-stage vs 3-stage) s reected by a Mann-Whtney test comparng the medans of ndependent groups (p = 18

20 The evdence regardng the relatvely hgher manageral ncentve parameters set by P R- compensatng owners can be ratonalzed as follows: P R-compensatng owners, antcpatng the ferce market competton that ther contract choces would gve rse to, mght realze that t s n ther mutual nterest to drect ther managers towards a relatvely less aggressve behavor (hgher α P R ), so as to ncrease ther profts. Thus, n order to mtgate ths Stackelberg warfare, they set relatvely hgh manageral ncentve parameters, drectng ther managers to a less aggressve behavor than RP -compensatng owners dd. α P R In asymmetrc confguratons, our theory predcts that the P R-compensatng owner sets = 1 and the RP - one sets α RP = 0. Regardng the asymmetrc contract confguratons, our emprcal evdence leads to the followng three observatons. Frst, under both treatments, the average ncentve parameter set by P R-compensatng (RP -compensatng) owners was lower (hgher) than the predcted one. Second, as n the symmetrc contract confguratons, n mxed contract schemes too, P R-compensatng owners set, on average, ncentve parameters hgher than those set by the RP -compensatng ones. 15 Ths holds for both treatments, t s n lne wth the theoretcal model s predcton, and mples that RP -compensated managers were drected relatvely closer to proft-maxmzaton than P R-compensated ones. Thrd, for both contract types, the dfference n ncentve parameters across treatments (2-stage vs. 3-stage) s not statstcally sgnfcant. In fact, the ncentve parameters n the asymmetrc contract structures are strkngly close to those reported n the symmetrc contract confguratons. 16 The most strkng pattern observed n the evdence reported so far s that gven a contract type, owners set very smlar ncentve parameters across treatments. More specfcally, P R- compensatng owners fx α P R around , whle RP -compensatng owners fx α RP around In fact, these values do not depend on the contract type used by the rval owner or on the rval owner s contract observablty (3-stage treatment vs. 2-stage treatment). Whle the observed ncentve parameters devate from ther correspondng theoretcal values 17, 0.25). The respectve test for an RP contract reects the statstcal sgnfcance of ncentve parameters across treatments too (p = 0.48). 15 Wthn each treatment, the dfference n ncentve parameters across contract types s sgnfcant, as shown by a Mann-Whtney test comparng medans of ndependent groups (p = for the 2-stage treatment and p = for the 3-stage treatment). 16 The sgnfcance of the correspondng dfferences s reected by the respectve Mann-Whtney tests obtanng p values such that p > 0.5 n all cases. 17 For both symmetrc confguratons, there s a systematc devaton of observed ncentve parameters from the respectve predcted equlbrum values, upwards for Proft-Revenue contracts and downwards for Relatve Performance contracts. For asymmetrc confguratons, there s a systematc devaton of observed ncentve parameters from the respectve predcted equlbrum values, downwards for Proft-Revenue contracts and upwards 19

21 some of the predctons contaned n Hypothess 2 are confrmed. More specfcally: RESULT 2: 1. The predcton of the theory (H2.1) concernng the relatvely hgher ncentve parameters (.e., lower aggressveness) set by Relatve Performance-compensatng owners, over Proft-Revenue compensatng owners, s not confrmed, whereas the predcton (H2.2) concernng the relatvely lower ncentve parameters (.e., hgher aggressveness) set by Relatve Performance-compensatng owners, over ther Proft-Revenue rvals, s confrmed. 2. The manageral ncentve parameter set by an owner s ndependent of the contract used by the rval owner and of whether the rval owner s contract was observed or not before the contract terms were chosen (confrmng H2.3). 4.4 Output levels Fnally, we focus on the effects of contract types and manageral ncentve parameters on output levels. Table 4 presents descrptve statstcs. Recall that our theoretcal results predct q RP = 300 and q P R = 320 n the two symmetrc confguratons, whle when owner chooses the P R contract and chooses the RP one, the predcton s: q P R = 200 and q RP = 400. As shown n Table 4, for both symmetrc contract confguratons, the output levels set n the experment exceed our equlbra predctons, whereas, for asymmetrc confguratons, ths s true only for P R-compensated managers. In fact, n asymmetrc confguratons, RP -compensated managers set quanttes well below the correspondng equlbrum level. Therefore, the devatons of output from equlbrum cannot be unformly attrbuted to some subect-specfc bas or the framng of our setup as a compettve market envronment. 18 Furthermore, comparng overall output levels wth output correspondng to the subgame perfect equlbra may be msleadng because t gnores that condtonal optmalty of output choces must be vewed wth respect to the actual decsons n the precedng stages. for Relatve Performance contracts. 18 As ponted out by a referee, ths could have been the effect of usng the word rval when referrng to the other frm or the explct encouragement to maxmze own proft n the nstructons. 20

22 Table 4: Managers choces on output levels Confguraton UP R URP P RRP RP P R Predcted q stage Mean q St. dev stage Mean q St. dev In Table 5 we present the average devaton of the ncentve parameter from ts equlbrum predcton, as well as the absolute and relatve devatons of output and proft from the correspondng equlbra condtonal on the observed ncentve parameters. Contrary to Harrson s (1989) flat max crtque, accordng to whch obectve functons may be too flat near the optmum to gve an nformatve feedback to subects, we observe that even moderate devatons from equlbrum output have caused sgnfcant devatons from the correspondng equlbrum profts. Even n the most frequently observed confguraton of U RP, a relatvely hgh proft loss of 59% s observed under both treatments, despte the fact that the relatve devaton of quantty s the lowest (13-14%) among all contract confguratons. Ths mples that managers may have attrbuted some exceptonally low earnngs to the contracts they had been offered rather than to ther own wrong decsons or to ther nteracton wth other managers n the market. Subsequently, the owners decsons have also dverged from the correspondng equlbrum ncentve parameters due to the nosy choces of managers and the lttle number of observatons under some contract confguratons. We consder as evdence n favor of ths conecture the fact that devatons of the ncentve parameter from the correspondng equlbrum values have been smaller n the case of URP, whch has occurred more frequently, gvng owners more feedback from past actons. 21

23 Table 5: Average devaton from equlbrum choces condtonal on alpha 2-Stage 3-Stage Devaton UPR U RP P RRP RP P R UPR U RP P RRP RP P R alpha* (α) quantty (q) relatve devaton 25% 13% 31% 14% 21% 14% 28% 20% Frm Π (n 000 s) relatve devaton -77% -59% -50% -61% -56% -59% -51% -55% * The observed devaton n alpha s wth respect to the SPNE alpha. Fgure 4 depcts output dynamcs wthn each contract combnaton. Apart from the aforementoned dvergence from theoretcal predctons, we observe that output levels exhbt persstent oscllatons over the 50 perods of the experment. In other words, output levels do not seem to converge due to learnng, whch also occurs n other quantty settng expermental markets.19 Fgure 4: Evoluton of quantty by contract combnaton. A remanng queston concerns the response of output to a gven contract and a specfc ncentve parameter. Panel data analyss s a useful tool for dealng wth the temporal and 19 See, for example, the sharp dfference n the results obtaned by Garca-Gallego (1998) on learnng n Bertrand olgopoles and those reported by Huck et al. (1999) on learnng n expermental Cournot markets. 22

24 ndvdual dmensons of our expermental data. We report here the results of a Pras and Wnsten correlated panel regresson for quantty. A Hausman χ 2 (11) test value of 5.78 does not allow us to reect that the dfference n the coeffcents s not systematc, hence we use a random effects model. Usng a test for seral correlaton, we reect the null of no autocorrelaton: χ 2 (1)= Moreover, due to the fact that we grouped the frms nto matchng groups where they play aganst each other, there wll be contemporaneous correlaton effects. The presence of heterogenety, autocorrelaton, and contemporaneous correlaton n our data drves us to choose a panel corrected standard errors estmaton method wth a panel specfc AR(1) structure of the form: where ε t = ρ ε t 1. quantty t = β 0 + β 1 alpha t + β 2 other_alpha t + ε t, (16) Coef. Std. Err. z P>z 95% Conf. Interval constant [361.80, ] upr [-66.97, 1.72] prrp [-29.15, 20.26] rppr [-46.45, -5.75] alpha [-44.98, ] alpha upr [-0.52, 93.19] alpha prrp [-36.23, 30.25] alpha rppr [-10.14, 43.77] oth alpha [-26.41, -1.34] oth alpha upr [-29.60, 56.42] oth alpha prrp [12.36, 44.36] oth alpha rppr [-7.22, 45.11] Table 6: Pras-Wnsten regresson, correlated panels corrected standard errors (PCSEs) for Quantty. Group varable: frmd; Tme varable: perod; Number of obs = 3,600; Number of groups = 72; Panels: correlated (balanced); Autocorrelaton: panel-specfc AR(1); Obs. per group: 50; Estmated 23