Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Incentives and relative-wealth concerns: theory and evidence
(USC Thesis Other)
Incentives and relative-wealth concerns: theory and evidence
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
INCENTIVES AND RELA TIVE-WEAL TH CONCERNS: THEOR Y AND EVIDENCE by Salv atore Miglietta A Dissertation Presen ted to the F A CUL TY OF THE USC GRADUA TE SCHOOL UNIVERSITY OF SOUTHERN CALIF ORNIA In P artial F ulllmen t of the Requiremen ts for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRA TION) Ma y 2010 Cop yrigh t 2010 Salv atore Miglietta Acknowledgments I thank m y advisor Kevin Murph y , Ricardo Alonso, Mariagio v anna Baccara, Murillo Camp ello, Juan Carrillo, Daniel Carv alho, Man uel Castro Soares Pinho, T om Chang, Stefano Della Vigna, Ran Duc hin, W a yne F erson, Eleonora Granziera, Larry Harris, A dam Kaufman, An thon y Marino, John Matsusak a, Roger Mo on, Oguzhan Ozbas, Alessandro Previtero, Heikki Ran tak ari, Breno Sc hmidt, Josh ua Shemesh, Mark W est- ereld, F ernando Zapatero, seminar participan ts at Arizona State Univ ersit y , BI Nor- w egian Sc ho ol of Managemen t, Instituto de Empresa, Univ ersit y of Southern Cal- ifornia, and the FMA do ctoral studen t consortium for their helpful commen ts and suggestions. ii T able of Contents A c kno wledgmen ts ii List of T ables iv Abstract v Chapter 1: T esting for Preferences 1 1.1 Preferences with Relativ e-W ealth Concerns 6 1.2 The Exp erimen t 11 1.2.1 The First T reatmen t 11 1.2.2 The Second T reatmen t 14 1.2.3 The Exp erimen tal Design 16 1.3 The Hyp otheses 16 1.4 Exp erimen tal Results 20 1.4.1 First T reatmen t 21 1.4.2 Second T reatmen t 27 1.5 Conclusions 33 Chapter 2: The Optimal Con tract 36 2.1 The T w o Agen t Case with Indep enden t Pro ductions 39 2.2 The T w o Agen t Case with Correlated Pro ductions 45 2.3 The General Multi-Agen t Case 50 2.4 Conclusions 55 Chapter 3: The Imp ortance of Observ ation 58 3.1 Case 1: T w o Agen ts,Uncertain and Kno wn Reserv ation Utilit y 59 3.2 Case 2: T w o Agen ts, Both with Uncertain Reserv ation Utilit y 63 3.3 Case 1 vs. Case 2 65 3.4 A Short Discussion of the Utilit y F unction 67 3.5 Conclusions and F uture W ork 68 References 69 App endices: App endix A: Pro of of Prop osition 1 72 App endix B: Pro of of Prop osition 2 75 App endix C: Pro of of Prop osition 6 77 iii List of T ables T able 1: First T reatmen t - Agen t D F requencies 22 T able 2: First T reatmen t - Agen t D Regression Analysis 24 T able 3: First T reatmen t - Agen t C F requencies 26 T able 4: First T reatmen t - Agen t C Regression Analysis 27 T able 5: Second T reatmen t - Agen t D F requencies 29 T able 6: Second T reatmen t - Agen t D Regression Analysis 30 T able 7: Second T reatmen t - Agen t C F requencies 31 T able 8: Second T reatmen t - Agen t C Regression Analysis 32 iv A Abstract In this w ork I sho w that if risk-a v erse agen ts prefer b oth to b e ric her in absolute terms and to b e ric her than their p eers (relativ e-w ealth concerns), then 1) they will prefer p ositiv e correlation b et w een their pa y os and the pa y os of other agen ts, and 2) they will b e a v erse to negativ e correlation b et w een pa y os. I test these theoretical predictions in a lab oratory exp erimen t. I nd that sub jects prefer p ositiv ely corre- lated pa y os o v er risk-free and negativ ely correlated pa y os. F urthermore, sub jects who b y observing other participan ts’ pa y os signal stronger relativ e-w ealth concerns, also sho w stronger a v ersion to negativ ely correlated pa y os. W omen app ear to b e concerned ab out other agen ts’ pa y os more than men. This no v el evidence has im- plications that help explain wh y rms apparen tly use prot-sharing and broad-based incen tiv es con tracts to o extensiv ely , and wh y Relativ e P erformance Ev aluation (RPE) con tracts are scarcely used in common comp ensation practice. F urther, I sho w that in the presence of relativ e-w ealth concerns 1) it is optimal for a principal to oer a comp ensation sc hedule link ed to the o v erall rm or team p erformance, ev en when eac h agen t’s p erformance is observ able, con tractible and indep enden t on the actions tak en b y his/her colleagues, 2) Relativ e P erformance Ev aluation is less desirable for the principal. Finally I in v estigate under what conditions it is optimal for a self- concerned principal to enforce a w age secrecy p olicy within an organization. v Chapter 1 T esting for Preferences T w o puzzles ha v e b een put forth b y sev eral studies in the comp ensation literature: the extensiv e use b y rms of broad-based incen tiv e plans for lo w-lev el emplo y ees and the paucit y of Relativ e P erformance Ev aluation (RPE) con tracts, where agen ts are comp ensated for the p erformance they ac hiev e measured relativ e to the p erformance of their p eers. In this pap er I oer and then test in a lab oratory exp erimen t a preference-based h yp othesis that con tributes to the solution of b oth puzzles. I as- sume that agen ts prefer to b e b oth w ealthier in absolute terms and w ealthier than their p eers. Moreo v er, I assume agen ts to b e risk-a v erse in b oth absolute and relativ e w ealth. I dene an agen t for whom these t w o assumptions hold true as relativ e-w ealth concerned. I then sho w theoretically that relativ e-w ealth concerned agen ts prefer p os- itiv e correlation b et w een their pa y os as, for example, in the case of rm-wide sto c k option plans. Also, under these assumptions I sho w that agen ts are a v erse to negativ e correlation b et w een their comp ensations, as in the case of RPE con tracts where an agen t’s rem uneration is reduced as his colleagues earn more. The exp erimen tal results pro vide evidence in supp ort of the relativ e-w ealth concerns h yp othesis. In addition, I nd that w omen app ear to b e concerned ab out other agen ts’ pa y os more than men. The rst puzzle is that rms routinely tie comp ensation to the o v erall rm p er- formance for emplo y ees who cannot p ossibly inuence suc h p erformance, ev en when their individual outputs are observ able and con tractible. This practice conicts with 1 the w ell-kno wn results of Holmstrom (1979), who sho ws that p erformance-link ed con- tracts should b e used only when the p erformance measure con v eys a signal ab out the eort exerted b y emplo y ees. If emplo y ees cannot aect the p erformance measure, the rm cannot gain an y kno wledge ab out their eort. Moreo v er, risk-a v erse emplo y ees require a risk premium as a consequence of the v olatilit y of their p erformance-link ed pa y o. As a result, comp ensation sc hedules based on uninformativ e p erformance measures are more costly than a xed w age and do not pro vide emplo y ees with an y incen tiv e. There is no conclusiv e evidence of the reasons b ehind this puzzle. Oy er (2004) and Oy er and Sc haefer (2005) suggest that the rm-wide use of incen tiv e con tracts 1 is motiv ated b y the opp ortunit y to tie w ork er w ages to the uctuation of their reserv ation utilities, whic h a v oids costly w age renegotiation. Core and Gua y (2001) h yp othesize that sto c k option plans are a c hannel through whic h the compan y can b e nanced b y its o wn emplo y ees. 2 Kedia and Ra jgopal (2008) nd that so cial forces justify the geographical clustering of sto c k option plans. The second puzzle is the scarce use of RPE con tracts in comp ensation practice, whic h app ears surprising in the ligh t of the results of Holmstrom (1982). If emplo y- ees’ outputs are aected b y common random sho c ks, then pa ying based on relativ e p erformance nets out the common noise source and pro vides the rm with a more precise signal of the eort exerted b y eac h emplo y ee. Despite this argumen t, RPE con tracts are rarely used in practice. The literature has pro vided relativ ely little ev- idence on the reasons b ehind the paucit y of RPE use as a comp ensation instrumen t (Murph y (1999)). Hall and Murph y (2003) suggest that accoun ting rules ma y driv e comp ensation practice a w a y from RPE instrumen ts lik e mark et or industry indexed 1 By incen tiv e con tracts the authors mean comp ensation con tracts that link the emplo y ee pa y o to the o v erall rm p erformance. 2 This argumen t do es not pro vide an exhaustiv e explanation of wh y a compan y in need of nancial resources w ould resort to suc h an exp ensiv e source giv en the high risk premium required b y risk a v erse and undiv ersied agen ts (see Hall and Murph y (2003)). 2 options. 3 Aggarw al and Sam wic k (1999) justify the lac k of use of RPE con tracts as a consequence of strategic in teraction b et w een comp eting rms. Bandiera et al (2005) nd that the enforcemen t of collusiv e agreemen ts b et w een emplo y ees justies the scarce resort to RPE con tracts within a rm. In this pap er I oer and test a preference-based h yp othesis that reconciles eco- nomic theory with observ ed practice. Supp ose that individuals’ utilit y increases in b oth their absolute w ealth and their w ealth measured relativ e to their p eers. Sup- p ose further that, in addition to b eing risk a v erse in their absolute w ealth, agen ts are also risk a v erse in their relativ e w ealth. If b oth assumptions hold true for a group of agen ts, I dene them as relativ e-w ealth concerned. Since p ositiv e correlation b et w een pa y os reduces the v olatilit y of relativ e w ealth, while negativ e correlation increases it, the relativ e-w ealth concerned agen t will prefer p ositiv ely correlated pa y os to neg- ativ ely correlated ones. I also sho w that relativ e-w ealth concerned agen ts prefer a mo derately v olatile pa y o o v er a risk-free pa y o of comparable v alue, as long as the v olatile pa y o is p ositiv ely correlated with the pa y os of their p eers. In a companion pap er (Miglietta (2009)) I deriv e the optimal linear con tract that a principal oers to a b o dy of relativ e-w ealth concerned agen ts: they are comp ensated on the basis of b oth their individual p erformance and the o v erall rm p erformance. In the same pap er I sho w that, in the presence of relativ e-w ealth concerns, the informational ad- v an tages of RPE con tracts ma y b e out w eighed b y the additional comp ensation cost induced b y agen ts’ a v ersion to negativ e correlation. 4 3 Although more recen t accoun ting rules eliminated the disadv an tage in the use of these instru- men ts, in practice their use did not increase. 4 The optimal comp ensation in the presence of other-concerned preferences is studied b y F rank (1984a, 1984b). The author sho ws that if agen ts are concerned ab out their relativ e w age, then the w age distribution among w ork ers is less disp ersed than the distribution of their marginal pro ductivit y . More recen tly , F ersh tman et al (2003) study the impact of relativ e-w ealth concerns on the optimal con tract oered to an agen t, in a m ulti-principal/one-agen t con text. Bartling (2008) and Englmaier and W am bac h (2006) deriv e the optimal comp ensation con tracts in the presence of inequit y a v ersion (F eher and Sc hmidt (1999)). 3 The ab o v e theoretical results are a direct consequence of agen ts b eing relativ e- w ealth concerned. Hence, an y attempt to v alidate the theory m ust rst nd evi- dence of relativ e-w ealth concerns in agen ts’ preferences. Since arc hiv al data pro vide extremely noisy information on agen ts’ preferences, a lab oratory exp erimen t is the most promising w a y to in v estigate this sub ject fruitfully . I run sev en exp erimen tal sessions with college studen ts as participan ts. In the rst three sessions, half of the participan ts receiv e a random pa y o and they can c ho ose a lev el of costly eort 5 in order to mo dify the probabilit y distribution of their pa y os. The other half of the participan ts can c ho ose b et w een a risk-free pa y o and a risky pa y o but they do not c ho ose a lev el of eort. In the second part of the session, their pa y o c hoices are dieren t; they can c ho ose b et w een three p ossible pa y os: a risk-free pa y o and either one of t w o risky pa y os, one p ositiv ely correlated and the other negativ ely correlated with the pa y o of another agen t. Along with this c hange in the pa y o c hoices, par- ticipan ts are giv en the p ossibilit y to observ e other sub jects’ pa y os. The ob jectiv e of these initial sessions is to ascertain whether sub jects mo dify their c hoices once they mo v e from a non-so cial con text, where no correlation and no observ ation is allo w ed, to a so cial one, where correlation b et w een pa y os and observ ation of other agen ts’ pa y os are allo w ed. Should participan ts c ho ose dieren tly in a so cial con text, I further need to test whether this mo dication in their c hoices is indeed driv en b y relativ e-w ealth concerns. F or this reason, I run four additional exp erimen tal sessions. In these last sessions, I try to separate participan ts that are relativ e-w ealth concerned from those who are not, and v erify that the rst b eha v e consisten tly with m y theoretical predictions. The k ey to ac hieving this goal is to trac k whether sub jects observ e their p eers’ pa y os. The exp erimen tal design is suc h that the observ ation of other sub jects’ pa y os should 5 P articipan ts b y sp ending dieren t amoun ts of money can induce dieren t probabilit y distribu- tions o v er their pa y o. This is a simple w a y to replicate eort exertion in a lab oratory en vironmen t. 4 not con v ey economically relev an t information. Hence, b y c ho osing to observ e other sub jects’ pa y os a participan t signals that she is concerned ab out her relativ e pa y o. The exp erimen tal results sho w that in the so cial con text agen ts c ho ose a risky pa y o more frequen tly than in the non-so cial con text. In particular their most fre- quen t c hoice is the p ositiv ely correlated pa y o. Most imp ortan tly , participan ts who observ e the pa y os of other sub jects, signaling in this w a y stronger relativ e-w ealth concerns, sho w a signican tly stronger a v ersion to negativ ely correlated pa y os, con- sisten t with the relativ e-w ealth h yp othesis. A dditionally , I nd no signican t impact of relativ e-w ealth concerns on agen ts’ eort c hoices. The exp erimen tal approac h has b een frequen tly used in the analysis of b eha vioral theories in lab or economics and comp ensation. F ehr et al (1996) run a lab oratory exp erimen t and argue that fairness concerns induce emplo y ers to oer emplo y ees ren ts ab o v e their reserv ation utilit y (see also Ak erlof and Y ellen (1990)). Charness and Kuhn (2007) study exp erimen tally ho w the eort exerted b y an agen t is inuenced b y relativ e comp ensation, nding no signican t impact. My results con tribute to this literature b y adding evidence ab out agen ts’ correlation preferences. Another asp ect I examine is whether w omen’s eort and pa y o correlation c hoices dier from the c hoices made b y men. 6 My results suggest that w omen are more con- cerned ab out other agen ts’ pa y os than men. In fact w omen ha v e stronger preferences for p ositiv ely correlated pa y os than men. F urthermore, w omen c ho ose a higher lev el of eort when they mo v e from a non-so cial con text to a so cial one, while male par- ticipan ts do not sho w an y signican t c hange in their eort c hoices. The pap er pro ceeds as follo ws: in Section 2 I deriv e the theoretical predictions that will allo w me to test the presence of relativ e-w ealth concerns in a lab oratory setting. 6 The dierences b et w een men and w omen in their attitudes to w ard other agen ts is the sub ject of a n um b er of exp erimen tal studies. Ec k el and Grossman (1998) nd that w omen are more generous (seless) than men. On the other hand, Bolton and Katok (1995), do not nd an y gender-related dierence in the b eha vior of participan ts. Andreoni and V esterlund (2001), nd that w omen tend to b e more equalitarian in their c hoices (that is, they tend to equally share), while men seem to p olarize around either a completely seless or selsh b eha vior. 5 Section 3 describ es the exp erimen tal approac h. Section 4 dev elops the h yp othesis tested within the exp erimen tal framew ork, and Section 5 analyzes the results of the exp erimen t. Section 6 concludes the pap er. 1.1 Preferences with Relative-W ealth Concerns Throughout this w ork I con trast t w o alternativ e assumptions for agen ts’ preferences. The rst one is that agen ts are self concerned, that is, they are only in terested in their w ealth. Therefore, the preferences of a generic agen t i are represen ted b y: U i (t i ;e i ) =E [u (t i )c (e i )] (1) In this case agen t i’s utilit y function is additiv ely separable in the (p ossibly ran- dom) monetary pa ymen t t i and in the costly eort e i 2fe l g l=1;2:::N . The functionu() is increasing (u 0 > 0) and conca v e (u 00 < 0), and the cost function c() is increasing in its argumen t. The second h yp othesis is that agen ts are relativ e-w ealth concerned. Under this h yp othesis, the preferences of the generic agen t i are represen ted b y the follo wing exp ected utilit y function: U i (t i ;e i ;t j ) =E [u (t i ) + i g (t i t j )c (e i )] (2) In this case, agen ti’s utilit y function is additiv ely separable in monetary pa ymen ts t i , eort e i and, assuming that agen t i is assigned to a group of t w o p eople, his relativ e pa y o (t i t j ) (wherej indicates the individual with whom agen t i is matc hed). The function u() is increasing and conca v e. F unction g() is increasing (g 0 > 0) and conca v e (g 00 < 0) as w ell. These assumptions imply that agen ts are risk a v erse not 6 only in their absolute w ealth but also in their relativ e w ealth. 7 The co ecien t i 0 measures ho w concerned an agen t is ab out his w ealth measured relativ e to his p eer’s w ealth. Finally , notice that (1) is a particular case of (2), when i = 0. I will indicate agen ts whose utilit y is giv en b y (2) and with i > 0 as relativ e-w ealth concerned. The wider class of preferences that are impacted b y the c hoices or the pa y o of other agen ts, ev en without an y impact on the agen t’s w ealth, will b e indicated as other- lo oking or other-concerned preferences. The ob jectiv e of this study is to in v estigate ho w relativ e-w ealth concerns migh t induce risk-a v erse agen ts to prefer v olatile pa y os, and to understand the impact of relativ e-w ealth concerns on the eort exerted b y agen ts. F or this reason I will consider t w o t yp es of agen ts. The rst t yp e of agen ts receiv es incen tiv es, in that b y exerting more or less eort they can induce a dieren t probabilit y distribution o v er their pa y o outcomes. Since they can induce a dieren t probabilit y Distribution o v er their pa y o, the rst t yp e of agen ts will b e indicated as Agen t D. Agen ts of the second t yp e do not receiv e an y incen tiv e and they can just c ho ose to exert a xed eort. Also, they can c ho ose whether to receiv e a xed pa ymen t or a pa ymen t that is p ositiv ely or negativ ely correlated with the pa ymen t of agen t D. Since the agen ts of the second t yp e can c ho ose the Corr elation of their pa y os they will b e indicated as agen ts C. Within this simplied framew ork, I deriv e some testable implications of the presence of relativ e-w ealth concerns and con trast them with the implications of the alternativ e preferences h yp othesis, namely , the self-concerned preferences. Assume that all agen ts are assigned to a group of t w o p eople where ev ery agen t C is matc hed with one agen t D. Also, assume that eac h agen t D mak es his eort 7 A similar concept is inequit y a v ersion, in this case, though g 0 can b e b oth p ositiv e ore negativ e. Also, in the form ulation of the mo del b y F ehr and Sc hmidt (1999), if an agen t will alw a ys b e ric her or p o orer than his p eers, then he will b e risk neutral b oth in his absolute w ealth and his relativ e w ealth. In this case, agen ts C should not displa y an y particular preference for p ositiv e or negativ e correlation. 7 decision and that the agen t C rationally exp ects it. Giv en the eort agen t D exerted, he can receiv e a random monetary transfer t D t D = 8 > > < > > : t H D with probability p t L D with probability (1p) (3) where t L D <t H D . Then w e ha v e the follo wing: Pr op osition 1. If agent C’s pr efer enc es ar e r epr esente d by (2), and she is matche d with an agent D whose p ayo is given by (3), then 1. A gent C wil l pr efer a mo der ately volatile p ayo t C with exp e cte d value t over a risk-fr e e p ayo of t, if t C is p ositively c orr elate d with agent D’s p ayo. 2. A gent C wil l b e mor e averse than a self-c onc erne d agent to mo der ate volatile p ayos that ar e ne gatively c orr elate d with agent D’s p ayo. 3. Ther e exists a unique r andom p ayo t C = t H C ;t L C , p ositively c orr elate d with the p ayo of agent D, that minimizes the exp e cte d value of agent C’s p ayo and do es not violate her p articip ation c onstr aint. Mor e over, t C is such that u 0 t H C u 0 t L C [g 0 (t L C t L D )g 0 (t H C t H D )] = C (4) Pr o of of Pr op osition 1 . Se e App endix Prop osition 1 tells us that, if agen t C is relativ e-w ealth concerned, she will alw a ys prefer a sligh tly v olatile pa y o that is correlated with the pa y o of her D coun terpart rather than a risk-free pa y o with the same exp ected v alue. P oin t 2 of Prop osition 8 1 follo ws from the fact that the conca vit y of function g() amplies the a v ersion of agen t C b ey ond the risk a v ersion implied b y the conca vit y of u(). Finally , the last p oin t of the prop osition tells us that if agen t D is receiving a sp ecic random pa y o, a h yp othetical principal has a unique pa y o to oer agen t C, and the pa y os of the t w o agen ts will b e p ositiv ely correlated. The rationale b ehind this result is fairly simple: when agen t C receiv es a risk-free pa y o and her D coun terpart receiv es a risky one, this will induce v olatilit y in her relativ e w ealth. Giv en the conca vit y of agen t C’s utilit y function in her relativ e w ealth, she will b e willing to pa y a premium in order to reduce the v olatilit y of her relativ e w ealth. Of course, b y stabilizing agen t C’s relativ e pa y o a principal induces v olatilit y in her absolute w ealth. Hence in order not to in tro duce to o m uc h v olatilit y in agen t C’s absolute w ealth her pa y o will b e mo derately v olatile. The optimalit y condition in (4) implies that as C increases the agen t will b e less concerned ab out the v olatilit y in tro duced in her absolute pa y o and more concerned ab out stabilizing her relativ e w ealth. Last, notice that the optimalit y condition in (4), includes the self-concerned solution. By setting C = 0, the optimalit y condition w ould imply u 0 t H C u 0 t L C = 0, that is t H C =t L C , consisten t with the assumption of risk a v ersion of agen t C in her absolute w ealth. T urning atten tion to agen t D, his eort c hoice is driv en b y t w o motiv ations, the rst one is to incremen t the exp ected utilit y originating from his absolute w ealth and the second is to incremen t the exp ected utilit y originating from his relativ e w ealth. Therefore if agen t D mo v es from a stand-alone status (where he is not matc hed with an y other agen t) to a matc hed status (where he is matc hed with another agen t), his eort decision migh t c hange giv en his concerns ab out relativ e w ealth. In addition, the correlation c hoice of his C coun terpart in the matc hed status ma y impact the incen tiv es originating from relativ e-w ealth concerns. F or this reason, dieren t pa y o correlation c hoices b y agen ts C ma y induce agen ts D to exert dieren t lev els of eort. This argumen t is formalized in the follo wing: 9 Pr op osition 2. Assume that agent D is r elative-we alth c onc erne d and risk averse as in (2). Also, he c an exert a level of eort chosen fr om the nite set fe l g l=1;2:::N wher e e i < e j if i < j . Assume further that the eort choic e e i induc es a c ost e qual to c i , such that c i < c j if i < j . Final ly, the eort choic e e i induc es a pr ob ability p i to r e c eive the high p ayo t H D , and 0<p i <p j < 1 if i<j . Then, 1. Moving fr om a stand-alone status to a matche d status, if t H D t H C >t L D t L C , the eort exerte d by agent D incr e ases or stays the same. 2. In the matche d status, when his C c ounterp art cho oses a risk fr e e p ayo t, the eort exerte d by agent D is the same or higher than the eort exerte d by D when his C c ounterp art cho oses a p ositively c orr elate d p ayo t C = t H C ;t L C , wher e t H C > t>t L C . 3. In the matche d status, when his C c ounterp art cho oses a risk fr e e p ayo t, the eort exerte d by agent D is the same or lower than the eort exerte d by D when his C c ounterp art cho oses a ne gatively c orr elate d p ayo t C = t H C ;t L C , wher e t H C > t>t L C . Pr o of of Pr op osition 2 . Se e App endix P oin t 1 of Prop osition 2 tells us that mo ving from a stand-alone case to a matc hed case, the incen tiv es to exert eort are strengthened b y the fact that agen ts can no w also b ecome ric her than their p eers. P oin t 2, tells us that when in a matc hed status agen ts C c ho ose p ositiv ely correlated pa y os, the incen tiv es for agen t D to exert eort in order to b ecome ric her than his p eers b ecome w eak er. If they b ecome w eak enough, then he migh t c ho ose to exert a lo w er eort than in the case of uncorrelated pa y os. P oin t 3, just in v erts the logic of P oin t 2. 10 The empirical implications of Prop osition 2 are someho w more am biguous than the implications of Prop osition 1. Agen ts D will c hange their eort decisions only if the c hanges in the incen tiv es originating from relativ e-w ealth motiv ations are large enough. If the IC conditions where slac k to b egin with (ha ving a nite n um b er of eort c hoices) the c hange in the relativ e-w ealth motiv ations migh t not b e large enough to induce a dieren t eort c hoice. Therefore, in the empirical test of this theory , w e m ust exp ect to observ e stronger results in the case of agen ts C than in the case of agen ts D. 1.2 The Experiment The exp erimen tal results presen ted in this pap er are obtained from sev en exp eri- men tal sessions. The rst three sessions aim at v erifying the existence of other-lo oking preferences. The ob jectiv e of the last four is to understand whether there are relativ e- w ealth concerns in agen ts’ preferences. I will indicate the rst three sessions as the First T reatmen t and the last four sessions as the Second T reatmen t. 1.2.1 The First T reatment Eac h session of the First T reatmen ts is divided in t w o parts, eac h formed b y sev en decision rounds. Hence, participan ts to ok part in 14 decision rounds. Before starting the rst round, agen ts w ere assigned to one of t w o p ossible roles: D or C and w ere endo w ed with 500 P oin ts. P articipan ts assigned to role D will realize either 1000 P oin ts or 500 P oin ts and can mo dify the probabilit y distribution of their pa y o b y in v esting more of their endo wmen t. 8 Belo w it is indicated ho w the outcome 8 In the exp erimen tal con text eort exertion is mimic k ed b y a P oin t exp enditure. 11 probabilit y , the exp ected v alue and the standard deviation of the net pa y o for a sub ject D v ary as a consequence of his exp enditure decision. D Exp enditur e 250 300 500 Pr[1000] 0.3 0.5 0.7 Pr[500] 0.7 0.5 0.3 Exp ected P a y o D 400 450 350 Std Dev P a y o D 230 250 230 The in v estmen t that maximizes the exp ected pa y o is 300 P oin ts (yielding an exp ected net pa y out of 450 P oin ts), while the in v estmen t with the lo w est exp ected pa y o is 500 P oin ts (yielding an exp ected net pa y out of 350). In v esting the lo w est amoun t (250 p oin ts) yields an exp ected pa y out of 400 p oin ts). In terms of the riski- ness of the pa y outs, the standard deviation from the lo w est and highest in v estmen ts are 230, while the standard deviation from the 300-P oin t in v estmen t (yielding the highest exp ected net pa y out) is 250. Therefore, a risk-neutral agen t concerned only ab out his o wn w ealth will in v est 300, while a risk-a v erse agen t concerned only ab out the exp ected utilit y of his o wn w ealth will in v est either 250 or 300, but should not in v est 500. P articipan ts assigned to role C can tak e part to a decision round b y sp ending 100 P oin ts. If a participan t C decides to participate to the round, she can c ho ose b et w een t w o dieren t pa y os: the rst is a xed pa ymen t of 475 P oin ts, the second is a random pa y o. The random pa y o consists of a pa ymen t of 500 p oin ts with probabilit y 0.5 and a pa ymen t of 450 with probabilit y 0.5. Therefore, the random pa y o has the same exp ected v alue as the risk-free pa ymen t (475 P oin ts) and a v olatilit y of 25 P oin ts. So a risk-a v erse participan t should c ho ose the risk-free pa ymen t while risk- neutral participan ts should b e indieren t b et w een the t w o pa y os. The sequence of actions in a giv en round is the follo wing: 12 1. P articipan ts C mak e their pa y o c hoice: receiv e a risk-free pa y o or a risky pa y o. 2. P articipan ts D mak e their exp enditure c hoice. 3. P a y os are realized After the rst sev en decision rounds, agen ts w ere randomly re-assigned to role C or D. 9 Once participan ts are assigned to their new roles, they will tak e part to sev en additional decision rounds. A t the b eginning of eac h round agen ts are randomly assigned to a group of t w o p eople, where one has role D and one has role C. The random re-assignmen t is suc h that participan ts w ere nev er matc hed with the same coun terpart more than once. The exp enditure decisions and the probabilit y distri- bution of the pa y o receiv ed b y participan ts D are the same. On the other hand, participan ts assigned to role C can no w decide to receiv e three alternativ e pa y o: a risk-free pa ymen t of 475 P oin ts, a random pa y o p ositiv ely correlated with the pa y o of the participan t D they w ere matc hed with, or a random pa y o negativ ely correlated with the pa y o of the participan t D they w ere matc hed with. The exp ected v alue and the v olatilit y of the pa y o receiv ed b y a participan t C in a giv en round are the follo wing: 10 Exp ected P a y o C D Exp enditur e 250 300 500 Fixe d 375 375 375 Positive Corr. 365 375 385 Ne gative Corr. 385 375 365 Std Dev P a y o C D Exp enditur e 250 300 500 Fixe d - - - Positive Corr. 23 25 23 Ne gative Corr. 23 25 23 9 The random re-assignmen t to role C or D, serv es the purp ose to a v oid the use of heuristic decision rules. If agen ts are assigned to the same role, ev en if a v ariation is in tro duced in the exp erimen t, they will rep eat their c hoices mainly guided b y the decisions tak en in the rst part of the exp erimen t, without considering the new setting. 10 Of course, the exp ected v alue dep ends on the exp enditure c hoice made b y the D coun terpart. 13 Supp ose that C c ho oses to b e p ositiv ely correlated with participan t D, then if participan t D receiv es a pa y o of 500 P oin ts at the end of the round, C will receiv e a pa y o of 450 P oin ts, or if agen t D receiv es a pa y o 1000 P oin ts at the end of the round, C will receiv e a pa y o of 500 P oin ts. If C c ho oses the risk-free pa y o, she will receiv e 475 P oin ts at the end of the round, indep enden tly on participan t D’s pa y o. Finally , in the second part of the treatmen t I in tro duce an observ ation option for b oth participan ts in a giv en group: participan ts D can decide to observ e whether their C coun terpart c hose an uncorrelated, p ositiv ely correlated or negativ ely correlated pa y o, b efore they mak e their exp enditure decisions. Agen ts C, at the end of the round, can decide whether to observ e the pa y o receiv ed b y their D coun terpart. Hence the sequence of c hoices in a giv en round for the second part of the exp erimen t is the follo wing: 1. P articipan ts are randomly assigned to a group of t w o p eople. 2. P articipan ts C mak e their pa y o c hoice: a pa y o uncorrelated (risk-free), p osi- tiv ely or negativ ely correlated with their D coun terpart’s pa y o. 3. P articipan ts D decide to observ e or not the c hoice of their C coun terparts. 4. P articipan ts D mak e their exp enditure c hoice. 5. P a y os are realized. 6. P articipan ts C decide to observ e or not the pa y o of their D coun terparts. 1.2.2 The Second T reatment In the second treatmen t participan ts are still assigned to one of t w o p ossible roles: C or D. Eac h exp erimen tal session, as in the previous treatmen t, is divided in t w o 14 parts, and eac h part is, in turn, divided in to sev en decision rounds. In the rst part of the exp erimen t, agen ts are randomly assigned to a group of t w o p eople: one with role C and one with role D. The exp enditure and pa y o c hoices are the same as in the second part of the rst treatmen t. The only dierence is that participan ts cannot observ e an ything ab out their coun terpart, therefore the sequence of actions is the follo wing: 1. P articipan ts are randomly assigned to a group of t w o p eople. 2. P articipan ts C mak e their pa y o c hoice: a pa y o uncorrelated, p ositiv ely or negativ ely correlated with their D coun terpart’s pa y o. 3. P articipan ts D mak e their exp enditure c hoice. 4. P a y os are realized The last sev en decision rounds of the Second T reatmen t, are the same as the last sev en decision rounds of the First T reatmen t: 1. P articipan ts are randomly assigned to a group of t w o p eople. 2. P articipan ts C mak e their pa y o c hoice: a pa y o uncorrelated (risk-free), p osi- tiv ely or negativ ely correlated with their D coun terpart’s pa y o. 3. P articipan ts D decide to observ e or not the c hoice of their C coun terparts. 4. P articipan ts D mak e their exp enditure c hoice. 5. P a y os are realized. 6. P articipan ts C decide to observ e or not the pa y o of their D coun terparts. 15 1.2.3 The Experimental Design The exp erimen tal sessions w ere run at the California So cial Science Exp erimen tal Lab oratory (CASSEL) at UCLA. P articipan ts are UCLA studen ts of age 18 or older. P articipan ts w ere recruited through email and p ostings on the CASSEL w ebsite. No sub ject to ok part to more than one session. The in teractions in a session w ere com- puterized, using the op en-source soft w are pac k age Multistage Games. The n um b er of participan ts to a giv en exp erimen tal session ranged from 14 to 18 sub jects. A t the b eginning of eac h session participan ts w ere giv en an endo wmen t of $1.25 (500 P oin ts, eac h P oin t b eing v alued $0.0025). P articipan ts’ earnings t ypically range from $18 to $28 for eac h session. A t the b eginning of eac h session, instructions w ere read from a stage to partici- pan ts. The instructions co v ered the rules of the game and describ ed the functioning of the computer Graphic User In terface (GUI). A sample cop y of the instructions is in the online app endix. 11 After the instructions w ere read, participan ts pla y ed one practice round for whic h they receiv ed no pa ymen t. After the rst sev en decision rounds, another set of instructions w as read to the participan ts, and then sub jects completed the last sev en decision rounds. Three sessions of the First T reatmen t and four sessions of the Second T reatmen t w ere run. The n um b er of sub jects participating in the First T reatmen t sessions w as 50 (30 men and 20 w omen), and 68 sub jects (39 men and 29 w omen) to ok part in the Second T reatmen t sessions, for a total of 118 sub jects. 1.3 The Hypotheses The main ob jectiv es of the exp erimen t are: 1) test if agen ts are concerned ab out the w ealth of their p eers, 2) if they are, whether relativ e-w ealth concerns induce 11 h ttp://www-scf.usc.edu/~migliett/researc h.h tml 16 agen ts’ preferences for p ositiv e correlation and an a v ersion for negativ e correlation b et w een pa y os, 3) observ e what impact relativ e-w ealth concerns migh t ha v e on the incen tiv es of agen ts to exert eort, and 4) examine the existence of gender-related dierences in relativ e-w ealth concerns. The First T reatmen t aims at detecting whether agen ts c hange their b eha vior when they mo v e from a stand-alone status to a matc hed status. In particular, it is imp ortan t to observ e if c hanges in agen ts’ c hoices are consisten t with concerns regarding other agen ts. Considering separately agen ts C and agen ts D, if there are other-lo oking concerns, I should b e able to refute the follo wing: Hyp othesis 1 If agents D ar e self c onc erne d they wil l sp end 300 Points (or 250 Points if they ar e risk-averse) and wil l not change their exp enditur e de cision moving fr om the rst p art of the exp eriment (wher e p articip ants ar e in a stand-alone situation) to the se c ond (wher e p articip ants ar e matche d in gr oups of two). If agents C ar e self c onc erne d, in the rst p art of the session their choic e should b e driven by risk-aversion in absolute we alth. The same should b e true for the se c ond p art. That is the r atio b etwe en agents cho osing the risk-fr e e p ayo and the risky p ayo should b e left unchange d b etwe en the two p arts. Considering the First T reatmen t, in order for the agen ts’ c hoices to b e consisten t with relativ e-w ealth concerns I should observ e the c hoice of p ositiv ely correlated pa y os b y agen ts C with a higher frequency (p oin t 1 Prop osition 1). In addition, I should observ e agen ts D either main taining their previous exp enditure c hoice or increasing it (p oin t 1 Prop osition 2). Nev ertheless, ev en if the results from the First T reatmen t are consisten t with the presence of relativ e-w ealth concerns, they are susceptible to m ultiple alternativ e in terpretations. Mo ving from the rst to the second part of the 17 session, agen ts migh t c hange their actions for an altruistic reasons or biased b elief ab out other agen ts’ t yp e. In fact, agen ts ma y decide to in v est more P oin ts assuming that follo wing a p ositiv e correlation c hoice b y their C coun terparts (altruism). On the other hand, participan ts C ma y c ho ose the p ositiv ely correlated pa y o b ecause they exp ect their coun terpart to in v est 500 P oin ts. Therefore the driving force b ehind agen ts C c hoice migh t b e a prot maximizing motiv ation rather than the presence of relativ e-w ealth concerns. Hence, I further need to test whether the other-lo oking preferences originate from relativ e-w ealth concerns as opp osed to other b eha vioral reasons. The purp ose of the Second T reatmen t is to address this issue. In particular, follo wing from the rst p oin t in Prop osition 1 and the last t w o p oin ts of Prop osition 2, I will test the follo wing h yp othesis: Hyp othesis 2 If agents D ar e r elative-we alth c onc erne d, and in the se c ond p art of the ses- sion they observe the choic e of p ositive c orr elation by agent C, their investment should b e either the same or lower (p oint 2, Pr op osition 1). If they observe the choic e of ne gative c orr elation, their investment should b e either the same or higher (p oint 3, Pr op osition 1). If agents C ar e r elative-we alth c onc erne d, then they wil l pr efer a p ayo p osi- tively c orr elate d over a p ayo that is xe d or ne gatively c orr elate d with their p e ers (p oint 1 Pr op osition 1). In p articular, if p articip ants C observe the p ay- o r e c eive d by their c ounterp arts, they should show a higher pr op ensity towar ds p ositive c orr elation (p oint 1 Pr op osition 1) and a str onger aversion towar ds ne gative c orr elation (p oint 2 Pr op osition 1). 18 Agen ts C ma y b e heterogeneous in their relativ e w ealth concerns: some of them ma y b e in terested in the relativ e w ealth of their p eers ( C > 0) some other ma y b e self concerned ( C = 0). The fact that an agen t C observ es her coun terpart’s pa y o signals that she is relativ e-w ealth concerned. In fact the Second T reatmen t is designed so that the observ ation do es not con v ey an y economically-relev an t information. Hence, I assume that the agen ts C who observ e ha v e C > 0. F or this reason the exp ected utilit y of an observing agen t increases when her pa y o is mo derately v ariable and p ositiv ely correlated with the pa y os of her D coun terpart. Also, compared to a self- concerned agen t, she exp eriences a sharp er decrease in her exp ected utilit y when her pa y o is negativ ely correlated with the pa y os of her D coun terparts. 12 Lastly , I also study the impact of gender on relativ e w ealth concerns. In the exp erimen tal literature there are indications of w omen b eing more seless than men (Ec k el and Grossman (1998)) or of w omen ha ving a more pronounced tendency to share than men (Andreoni and V esterlund (2001)). F or this reason, an in teresting extension of this w ork is to examine whether w omen dier in their eort and pa y o c hoices from men, and if this dierence can b e traced bac k to stronger relativ e-w ealth concerns. 12 T o see this more formally , assume that agen t D can receiv e t H D or t L D b oth with probabilit y 1 2 , and t H D > t L D . Assume that agen t C can receiv e either a non random pa y o t or a random pa y o where she receiv es t + 2 if agen t D receiv es t H D or t 2 if agen t D receiv es t L D . Hence, if > 0, agen t C’s random pa y o is p ositiv ely correlated with agen t D’s pa y o, if < 0, agen t C’s random pa y o is negativ ely correlated with agen t D. It can b e sho wn (see pro of of Prop osition 1) that the rst order appro ximation of the dierence b et w een the exp ected utilit y of agen t C when she receiv es a random pa y o and the exp ected utilit y when she receiv e a risk-free pa y o is giv en b y U Random U RiskFree C g 0 tt H D g 0 tt L D . Therefore the larger C , the stronger the incen tiv e for a relativ e w ealth concerned agen t C to c ho ose a p ositiv ely correlated (and mo derately v ariable) pa y o ( > 0) and to refuse a negativ ely correlated pa y o ( < 0). 19 1.4 Experimental Results In this section I separately analyze the results from the t w o treatmen ts. F or eac h treatmen t, I will rst study the distribution of frequencies o v er the p ossible c hoices made b y sub jects. The c hoice frequencies, though, are susceptible to b e driv en b y the b eha vior of a small group of participan ts rather than represen ting the b eha vior of the p opulation. Therefore, it is imp ortan t to conduct an analysis of the results that con trols for individual eects. In this w ork I will con trol for individual random eects. 13 In order to ev aluate ho w individual and c hoice c haracteristics inuence the lik eliho o d of a participan t to mak e a c hoice, I estimate a linear-probabilit y mo del. In particular, I will regress the indicator function of agen ts making a particular c hoice on a n um b er of indep enden t v ariables. 14 I also run a logit regression with random eects (unrep orted) and the results are consisten t with the linear-probabilit y regressions. The main dra wbac k of the linear approac h is that the co ecien ts migh t b e suc h that the tted probabilit y can b ecome negativ e or bigger than 1, for a subset of v alues tak en b y the indep enden t v ariables. Nev ertheless, in the linear probabilit y mo del the magnitude of the estimated co ecien t giv es a more in tuitiv e understanding of the impact of the regressors on the probabilit y of the agen t making a sp ecic c hoice. 13 The c hoice to rely on random eects rather than xed eect, is due to the fact that the high n um b er of dumm y v ariables the matrix of the observ ations of the indep enden t v ariables b ecomes nearly singular. Random eects, allo w me to o v ercome this problem b y assuming a normal distri- bution of the random eects, whic h requires the estimation of t w o parameters of the distribution rather than the estimation of N individual xed eects. Also, I test for the presence of xed eects and I can reject this h yp othesis in fa v or of the presence of random eect at 1% signicance, through a Lagrange m ultiplier test. 14 I will run unrelated regressions. Nonetheless, the probabilit y of an agen t making a giv en c hoice should b e consisten t with the probabilities of making the other, since the sequence of c hoices b y an agen t could b e though t as a trinomial distribution. Hence, the unrelated regression will not accoun t for this consistency . On the other hand, the linear probabilit y mo del, allo ws me to join tly con trol for individual random eect and errors clustered at an individual lev el. 20 1.4.1 First T reatment The First T reatmen t directly addresses Hyp othesis 1. The main ob jectiv e of the treatmen t is to v erify if agen ts ha v e other-lo oking preferences, that is, if agen ts mo dify their b eha vior mo ving from a stand-alone status (where they are not matc hed with an y other participan t), to a matc hed status (where they are matc hed with another participan t). In fact, in this treatmen t if participan ts D are self-concerned, they ha v e no reason to c hange their in v estmen t decision mo ving from the rst to the second part, since there is no c hange in the w a y they can aect their pa y os through their in v estmen ts. R esult 1 Moving fr om the stand-alone status to the matche d status, male p articip ants as- signe d to r ole D do not change their investment choic e, while female p articip ants incr e ase their investment. The results for agen ts D in the First T reatmen t are summarized in T able 1. The most frequen t c hoice is the 300-P oin t in v estmen t. This is not surprising since the 300-P oin t in v estmen t is the c hoice that guaran tees the highest exp ected net pa y o. What is not in line with the exp ected pa y o maximizing b eha vior is that agen ts seem to prefer the 500-P oin t in v estmen t c hoice o v er the 250-P oin t in v estmen t, although the lo w er in v estmen t oers a higher exp ected pa y o at the same risk. The bias to w ards the 500-P oin ts in v estmen t ma y b e justied b y b eha vioral asp ects suc h as optimism of the agen ts when they ev aluate their exp ected pa y o or a probabilit y w eigh ting that o v er- w eigh ts the lik eliho o d of p ositiv e outcomes. The fact that participan ts c ho ose to in v est 500 P oin t rather than 250 P oin t seems not to dep end on other-lo oking preferences: in P anel A of T able 1, ev en if the frequency of the 250 in v estmen t in the rst part is t wice the frequency in the second part, the c hi-square and F-exact test statistics sho w that the dierence b et w een the c hoice frequencies in the t w o parts is not signican t. 21 T able 1 First T reatmen t - Agen t D F requencies . This table rep orts the relativ e (absolute) frequencies with whic h P articipan ts D c ho ose an in v estmen t of 250, 300, 500 p oin ts in the First T reatmen t. P anel A rep orts the in v estmen t c hoices for the rst and second part of the session. P anel B rep orts the in v estmen t c hoices brok en do wn b y gender in the rst part of the session. P anel C rep orts the in v estmen t c hoices brok en do wn b y gender in the second part of the session. The Chi-square and the F exact statistics P-v alues are rep orted. P anel A In v estmen t T ot 250 10:00% (35) 300 53:71% (188) 500 36:29% (127) T otal 100% (350) PanelA First P art Second P art 13:14% (23) 6:86% (12) 53:14% (93) 54:29% (95) 33:71% (59) 38:86% (68) 100% (175) 100% (175) 2 Exact Pr = 0:13 Pr = 0:13 PanelB FirstPart F emale Male 13:10% (11) 13:19% (12) 52:38% (44) 53:85% (49) 34:52% (29) 32:97% (30) 100% (84) 100% (91) 2 Exact Pr = 0:97 Pr = 0:97 PanelC SecondPart F emale Male 7:14% (5) 6:67% (7) 37:14% (26) 65:71% (69) 55:71% (39) 27:62% (29) 100% (70) 100% (105) 2 Exact Pr< 0:01 Pr< 0:01 Nev ertheless, P anel B and P anel C of T able 1 sho w that mo ving from a stand-alone to a matc hed status in tro duces a signican t c hange in participan ts’ c hoices once the results are separated b y gender, while the frequency distributions o v er in v estmen ts are not signican tly dieren t for men and w omen in the rst part of the session (stand- alone), they div erge the second part (matc hed). In particular, the frequency with whic h w omen c ho ose the 500-P oin t in v estmen t increases b y more than 20% in the matc hed case, and it is accompanied b y a decrease of around 15% in the 300-P oin t in v estmen t. The c hange in female participan ts’ c hoices are inconsisten t with the h yp othesis of self-concerned preferences: w omen c ho ose the in v estmen t option with the w orst exp ected net pa y o (500 P oin ts) and they do so b y reducing the frequency with whic h they c ho ose the option with the highest exp ected net pa y o (300 P oin ts). Ov erall, b y this rst analysis, w e can dra w a rst conclusion that female participan ts, when assigned to role D, seem to b e more other-concerned than male participan ts, who, in turn, app ear to act more in accordance with self-concerned preferences. Considering the linear probabilit y mo del in the case of sub jects D, the explanatory v ariables of in terest are: 22 Gender of the participan t: female (0) male (1). The fact that the c hoice is made in the rst part (0) or the second part (1) of the session. Whether the participan t D observ ed a p ositiv ely correlated c hoice b y his C coun terpart (1) or not (0). Whether the participan t D observ ed a negativ ely correlated c hoice b y his C coun terpart (1) or not (0). Whether the participan t w as assigned to role D in b oth parts of the session(1) or not (0). P anel A of T able 2 rep orts the estimate of three regressions estimating the impact of the ab o v e v ariables on the probabilit y of c ho osing one in v estmen t lev el o v er the other t w o. The gender of participan ts stands out as an explanatory v ariable, in particular female sub jects are signican tly more lik ely to c ho ose a 500 P oin t in v estmen t and less lik ely to c ho ose a 300 P oin t in v estmen t. P anel B and P anel C of T able 2 rep orts ho w the lik eliho o d to c ho ose the 500-P oin t in v estmen t or the 250-P oin t in v estmen t o v er the 300-P oin t in v estmen t is impacted b y the ab o v e indep enden t v ariables. In particular, P anel B rep orts the results obtained with observ ations from b oth parts of the sessions, while P anel C rep orts the results obtained with observ ations from the second part of the sessions. The regressions sho w that w omen are more lik ely to c ho ose the 500 P oin ts in v estmen t and less lik ely to c ho ose the 300-P oin t in v estmen t. Moreo v er, it app ears that this gender-driv en eect is mostly due to c hoices made in the second part of the session. 23 T able 2 First T reatmen t - Agen t D Regression Analysis . P anel A rep orts three separate linear probabilit y regressions. The rst one rep orts the impact of gender (Male=1 F emale=0), the fact that participan ts where pla ying the rst 7 or the last 7 rounds (First P art=0 Second P art=1), the fact that a participan t observ ed the pa y o correlation c hoice of her coun terpart (P ositiv e or Negativ e), and the fact that they where assigned to role D for b oth parts of the session (Same Role) on the probabilit y of D c ho osing a 500-P oin t in v estmen t decision. The second regression rep orts the impact of the same v ariables on the probabilit y of D c ho osing a 300 P oin t in v estmen t decision, while the third regression rep orts the impact of the same v ariables on the probabilit y of D c ho osing a 250 P oin t in v estmen t decision. P anel B rep orts t w o linear probabilit y regressions estimates of the impact of the indep enden t v ariables on the probabilit y of participan ts c ho osing the 500 P oin t in v estmen t o v er the 300 P oin t in v estmen t, and on the probabilit y of participan ts c ho osing the 250 P oin t in v estmen t o v er the 300 P oin t in v estmen t. P anel C rep orts the same estimates as in P anel B, using observ ations from the second part of the sessions. T-statistics are rep orted in paren thesis. Pr (Investment) = i + 1 Male + 2 Second + 3 ObsPos + 4 ObsNeg + 5 SameRole PanelA 500 vs. Rest 300 vs. Rest 250 vs. Rest Male 0:181 (1:96) 0:165 (1:95) 0:014 (0:30) Se c ond Part 0:028 (0:36) 0:014 (0:19) 0:056 (1:80) Obs Positive 0:010 (0:13) 0:004 (0:05) 0:005 (0:16) Obs Ne gative 0:078 (0:78) 0:156 (1:71) 0:093 (1:34) Same Role 0:126 (1:31) 0:175 (1:87) 0:050 (1:13) Individual RE Y es Y es Y es Cluster e d Err ors Y es Y es Y es R-sq 3.89% 5.36% 2.13% PanelB 500 vs. 300 250 vs. 300 0:182 (1:93) 0:030 (0:44) 0:016 (0:21) 0:074 (1:43) 0:008 (0:10) 0:010 (0:18) 0:118 (1:12) 0:162 (1:52) 0:145 (1:46) 0:098 (1:50) Y es Y es Y es Y es 5.04% 5.05% PanelC SecondPart 500 vs. 300 250 vs. 300 0:295 (2:27) 0:044 (0:50) 0:001 (0:01) 0:003 (0:04) 0:097 (0:98) 0:156 (1:51) 0:175 (1:35) 0:024 (0:28) Y es Y es Y es Y es 11.97% 4.39% 24 R esult 2 Moving fr om a stand-alone status to a matche d status, p articip ants assigne d to r ole C change their p ayo choic e. Mor e p articip ants cho ose a variable p ayo inste ad of a risk-fr e e p ayo. Also, female p articip ants cho ose a p ositively c orr elate d p ayo mor e fr e quently than male p articip ants. The results for agen ts C in the First T reatmen t hin t in a stronger w a y at the existence of other-lo oking preferences. P anel A of T able 3 sho ws that in the rst part of the sessions 38.29% of the participan ts c ho ose the risk-free pa y o while 61.71% c ho ose the risky pa y o. Mo ving from the rst part of the session to the second part, where agen ts C ha v e the p ossibilit y to decide to b e correlated, the p ercen tage of participan ts c ho osing the v olatile pa y o increases b y 20%. P anel B and P anel C of T able 3 sho w that male and female participan ts C app ear to b eha v e similarly b oth in the rst and the second part of the session when w e just consider the c hoice b et w een a xed pa y o and a v ariable pa y o. Ho w ev er, P anel C of T able 3 sho ws that w omen c ho ose the p ositiv ely correlated pa y o more frequen tly than men (72.86% for w omen and 48.57% for men). Considering no w the c hoices of participan ts C, I regress the indicator function of them c ho osing risky pa y o o v er a risk-free pa y o on the follo wing v ariables: 15 Gender of the participan t: female (0) male (1). The fact that the c hoice is made in the rst part (0) or the second part (1) of the session. The fact that the participan t observ es the pa y o receiv ed b y her D coun terpart (1) or not (0). 15 In this case the logit approac h mo del can not b e used giv e the violation of the indep endence of irrelev an t alternativ es condition. 25 T able 3 First T reatmen t - Agen t C F requencies . This table rep orts the relativ e (absolute) frequencies of agen ts C c ho osing xed or v ariable pa y os in the First T reatmen t. P anel A rep orts the pa y o c hoices for the rst and second part of the session. P anel B rep orts the pa y o c hoices brok en do wn b y gender in the rst part of the session. P anel C rep orts the pa y o c hoices brok en do wn b y gender in the second part of the session, also the c hoices are further brok en do wn in p ositiv e or negativ e correlation pa y o c hoices. The Chi-square and the F exact statistics P-v alues are rep orted. P anel A P a y o T ot Fixe d 28:57% (100) V ariable 71:43% (250) Corr. + Corr. - T otal 100% (350) PanelA First P art Second P art 38:29% (67) 18:86% (33) 61:71% (108) 81:14% (142) 100% (175) 100% (175) 2 Exact Pr< 0:01 Pr< 0:01 PanelB FirstPart F emale Male 30:36% (17) 42:02% (50) 69:64% (39) 57:98% (69) 100% (56) 100% (119) 2 Exact Pr = 0:13 Pr = 0:18 PanelC SecondPart F emale Male 15:71% (11) 20:95% (22) 84:29% (59) 79:05% (83) 72:86% (51) 48:57% (51) 11:43% (8) 30:48% (32) 100% (70) 100% (105) 2 Exact Pr = 0:38 Pr = 0:44 Whether the participan t w as assigned to role C in b oth parts of the session (1) or not (0). The second regression in T able 4 16 , sho ws that mo ving from the rst to the second part of the sessions, increases the frequency of the c hoice of v ariable pa y os. Ov erall, the strongest evidence for the existence of other-lo oking preferences comes from the observ ation of agen ts C c hoices. This results is exp ected if the c hanges in b eha vior originate from relativ e-w ealth concerns. F rom Prop osition 1 it follo ws that whenev er agen t C is relativ e-w ealth concerned, she should always c ho ose a p ositiv ely correlated pa y o with her coun terpart. On the other hand, giv en the results of Prop o- sition 2, agen ts D migh t not c hange their actions once they are matc hed to another agen t ev en if they are relativ e-w ealth concerned. 16 In the second regression the Observ ation v ariable is dropp ed due to collinearit y with the v ariable indicating the second part of the treatmen t. In fact, b y dropping the observ ation v ariable the signicance of the co ecien t increases, without inducing a signican t c hange in the R squared. 26 T able 4 First T reatmen t - Agen t C Regression Analysis . This table rep orts t w o linear probabilit y regressions. The regression estimates the impact of gender (Male=1 F emale=0), the fact that participan ts w ere pla ying the rst 7 or the last 7 rounds (First=0 Second=1), the fact that a participan ts observ ed the pa y o of their coun terpart (Observ ation=1 No-Observ ation=0), and the fact that they where assigned to role C for b oth parts of the session (Same Role) on the probabilit y of C c ho osing a v ariable pa y o o v er a risk-free one. T-statistics are rep orted in paren thesis. Pr (Payoff) = i + 1 Male + 2 Second + 3 Observation + 4 SameRole V ariable vs Fix Male 0:073 (0:88) 0:074 (0:90) Se c ond Part 0:192 (1:93) 0:204 (2:83) Observation 0:016 (0:20) Same Role 0:027 (0:29) 0:028 (0:29) Individual RE Y es Y es Cluster e d Err ors Y es Y es R-sq 5.43% 5.47% 1.4.2 Second T reatment The First T reatmen t, in particular in the case of participan ts C, pro vides us with evidence that participan ts are not self-concerned. Nonetheless, it do es not allo w us to discern whether this result follo ws from relativ e-w ealth concerns as in (2) or other b eha vioral features of preferences. The design of the Second T reatmen t is suc h that the pa y o structure is the same in the rst part of the session (the rst sev en decision rounds) and the second part of the session (the last sev en decision rounds). The dierence b et w een the t w o parts is that, while in the rst sev en decision rounds participan ts cannot observ e an ything ab out their coun terparts, in the last sev en decision rounds: 1) participan ts D can observ e the pa y o correlation c hoice made b y the agen t C they are matc hed with, and 2) participan ts C can observ e the pa y o receiv ed b y their D coun terpart, after the pa y os are realized. Notice that the observ ation of their coun terpart’s pa y o b y participan ts C should not con v ey an y relev an t information for t w o reasons: 1) the pa y o ha v e b een already realized and 2) participan ts C will not b e matc hed with 27 the same participan t D more than once. F rom the discussion of Hyp othesis 2, if b y c ho osing to observ e participan ts signal their (higher) relativ e w ealth concerns, then w e can exp ect agen ts who observ e to c ho ose p ositiv e correlated pa y os more frequen tly . Also, they should b e more a v erse to negativ ely correlated pa y os. As b efore, I start b y analyzing the results for participan ts D and conclude with the analysis of the results for participan ts C. R esult 3 The intr o duction of observability do es not induc e any statistic al ly signic ant dif- fer enc e in the over al l fr e quency distribution of the investment choic es for p articip ants D. Nonetheless, c onsidering only female p articip ants, they cho ose the 500-Point in- vestment mor e fr e quently than male p articip ants. The results in T able 5 sho w that ab out 60% of the participan ts c hose the 300- P oin t in v estmen t, that is, the exp ected pa y o maximizing c hoice. Nonetheless, the frequency of the 500-P oin t in v estmen t is almost 10% higher than the frequency of the 250-P oin t in v estmen t, sho wing a sligh t bias to w ards o v er-in v estmen t as in the First T reatmen t. The in tro duction of observ abilit y has no signican t impact on the o v erall in v estmen t c hoices made b y participan ts as it is sho wn in P anel A of T able 5. Nev ertheless, P anel C of T able 5 sho ws that female participan ts c ho ose the 500-P oin t in v estmen t more frequen tly than male participan ts, but only in the second part of the sessions. This result is similar to the one observ ed in the First T reatmen t. Finally the regression analysis in T able 6 conrms the eect of gender on the probabilit y for a participan t to c ho ose the 500 P oin t in v estmen t. 17 Nev ertheless, participan ts D do not c hange their in v estmen t decisions up on observing a p ositiv ely or negativ ely correlation c hoice b y their C coun terparts. This circumstance suggests that the increase in the 17 I do not include the regression for the 300 and 250 c hoices, since there is no signican t eect of the indep enden t v ariables I consider on the in v estmen t c hoice. 28 T able 5 Second T reatmen t - Agen t D F requencies . This table rep orts the relativ e (absolute) frequencies with whic h participan ts D c ho ose an in v estmen t of 250, 300, 500 p oin ts in the Second T reatmen t. P anel A rep orts the in v estmen t c hoices for the rst and second part of the session. P anel B rep orts the in v estmen t c hoices brok en do wn b y gender in the rst part of the session. P anel C rep orts the in v estmen t c hoices brok en do wn b y gender in the second part of the session. The Chi-square and the F exact statistics P-v alues are rep orted. P ane l A in v estmen t T ot 250 15:13% (72) 300 60:50% (288) 500 24:37% (116) T otal 100% (476) PanelA First P art Second P art 16:39% (39) 13:87% (33) 61:76% (147) 59:24% (141) 21:85% (52) 26:89% (64) 100% (238) 100% (238) 2 Exact Pr = 0:39 Pr = 0:39 PanelB FirstPart F emale Male 12:24% (12) 19:29% (27) 63:27% (62) 60:71% (85) 24:49% (24) 20:00% (28) 100% (98) 100% (140) 2 Exact Pr = 0:31 Pr = 0:30 PanelC SecondPart F emale Male 7:14% (6) 17:53% (27) 52:38% (44) 62:99% (97) 40:48% (34) 19:48% (30) 100% (84) 100% (154) 2 Exact Pr< 0:01 Pr< 0:01 P oin t in v estmen t b y female participan ts is due to other lo oking features in their preferences, other than relativ e w ealth concerns 18 , suc h as altruism. R esult 4 If a p articip ant C observes the p ayo of her D c ounterp art, the likeliho o d that she chose the ne gatively c orr elate d p ayo de cr e ase. Also, female p articip ants ar e mor e likely than male p articip ants to cho ose a r andom p ayo as opp ose d to the risk-fr e e p ayo. In p articular, women cho ose mor e fr e quently the p ositively c orr elate d p ayo. F rom an insp ection of P anel A of T able 7, it seems that there is no signican t dierence in agen ts’ c hoices b et w een the rst and the second part of the session. Once I break do wn the frequencies b y gender in P anel C of T able 7, it is apparen t that female participan ts c hange their b eha vior in the second part of the session. They abandon the risk-free pa y o c hoice and incremen t their c hoice of p ositiv ely and negativ ely correlated pa y o, b eing the p ositiv ely correlated pa y o the one they c ho ose more frequen tly (56%). Male participan ts do not c hange their b eha vior b et w een the 18 In fact if the eect w as induced b y relativ e w ealth concerns, then the in teraction b et w een the observ ation of either p ositiv e or negativ e correlation c hoices b y agen t C with the gender v ariable (unrep orted) should ha v e some explanatory p o w er. This is not the case. 29 T able 6 Second T reatmen t - Agen t D Regression Analysis . This table rep orts a linear probabilit y regression relating to sessions of the Second T reatmen t. The regressions estimates the impact of gender (Male=1 F emale=0), the fact that participan ts w ere pla ying the rst 7 or the last 7 rounds (First P art=0 Second P art=1), the fact that a participan t observ ed the pa y o correlation c hoice of his coun terpart (P ositiv e or Negativ e correlation), and the fact that they w ere assigned to role D for b oth parts of the session (Same Role) on the probabilit y of D c ho osing a 500 P oin t in v estmen t decision. T-statistics are rep orted in paren thesis. Pr (Investment) = i + 1 Male + 2 Second + 3 ObsPos + 4 ObsNeg + 5 SameRole 500 vs. Rest Male 0:145 (1:85) Se c ond Part 0:035 (0:52) Obs Positive 0:037 (0:59) Obs Ne gative 0:021 (0:29) Same Role 0:087 (1:18) Individual RE Y es Cluster e d Err ors Y es R-sq 3.44% t w o parts of the session. Once again, it seems that there is a strong gender eect and that female participan ts ha v e more other-concerned preferences. Nonetheless, there is the concern of a small group of individuals driving the results, therefore a complete analysis requires to con trol for individual eects. The most relev an t result is rep orted in T able 8. First, male participan ts c ho ose a risk-free c hoice more frequen tly than w omen, whic h is consisten t with men b eing more self-concerned. Moreo v er, w omen c ho ose the p ositiv ely correlated pa y o more frequen tly than man, sho wing a higher degree of other lo oking concerns than men. Somewhat surprising is the fact that w omen also c ho ose the negativ ely correlated pa y o more frequen tly than male participan ts. Nev ertheless, the most frequen t pa y o c hoice made b y w omen is b y far the p ositiv ely correlated pa y o. The most in teresting result of this w ork comes from the consideration of the ob- serv ation activit y of participan ts C. P anel A of table 8 sho ws that the observ ation of the pa y o b y agen ts C impacts on their probabilit y to c ho ose a p ositiv ely correlated pa y o (whic h signican tly increases if they observ e), and the probabilit y of partici- 30 T able 7 Second T reatmen t - Agen t C F requencies . This table rep orts the relativ e (absolute) frequencies of agen ts C c ho osing a riskless pa y o or a pa y o p ositiv ely or negativ ely correlated with his D coun terpart, in the Second T reatmen t. P anel A rep orts the pa y o c hoices for the rst and second part of the session. P anel B rep orts the pa y o c hoices brok en do wn b y gender in the rst part of the session. P anel C rep orts the pa y o c hoices brok en do wn b y gender in the second part of the session.The Chi-square and the F exact statistics P-v alues are rep orted. P anel A P a y o T ot Fixe d 26:00% (123) Corr. + 45:24% (214) Corr. - 28:75% (136) T otal 100% (473) PanelA First P art Second P art 27:97% (66) 24:05% (57) 41:95% (99) 48:52% (115) 30:08% (71) 27:43% (65) 100% (236) 100% (237) 2 Exact Pr = 0:35 Pr = 0:35 PanelB FirstPart F emale Male 21:90% (23) 32:82% (43) 44:76% (47) 39:69% (52) 33:33% (35) 27:48% (36) 100% (105) 100% (131) 2 Exact Pr = 0:17 Pr = 0:18 PanelC SecondPart F emale Male 12:71% (15) 35:29% (42) 55:93% (66) 41:18% (49) 31:36% (37) 23:53% (28) 100% (118) 100% (119) 2 Exact Pr< 0:01 Pr< 0:01 pan ts C to c ho ose the negativ ely correlated one (whic h signican tly decreases when they observ e). A further analysis sho ws that the result is mainly driv en b y the a v er- sion of observing participan ts to negativ ely correlated pa y os. In particular P anel C of T able 8 sho ws that the lik eliho o d of the c hoice of a negativ e correlation pa y o is de- creased b y the fact that the agen t observ es the pa y o of their coun terparts. The fact that an agen t observ es her coun terpart’s pa y o seems not to explain wh y she prefers a p ositiv e correlated pa y o o v er a risk-free pa y o. One p ossible explanation is that for a relativ e w ealth concerned agen t, the w orst c hoice is the negativ ely correlated pa y o, therefore this is the c hoice agen ts will a v oid more strongly . An alternativ e explanation is a risk-a v ersion argumen t: b y selecting a p ositiv ely correlated pa y o, relativ e w ealth concerned participan ts C increase their exp ected utilit y on the one hand, but on the other they increase the v olatilit y of their pa y o. Hence these t w o eects ma y oset eac h other and mak e the estimator of the co ecien t more noisy . The negativ ely correlated pa y o, though, decreases the exp ected utilit y of a relativ e- w ealth concerned agen t in a more sharply than in the case of a simply risk-a v erse agen t (p oin t 2 of Prop osition 1), therefore a relativ e w ealth-concerned agen t will b e more a v erse to negativ e correlation than an agen t who is simply risk a v erse. 31 T able 8 Second T reatmen t - Agen t C Regression Analysis . P anel A rep orts three separate linear probabilit y regressions. The rst one rep orts the impact of gender (Male=1 F emale=0), the fact that participan ts where pla ying the rst 7 or the last 7 rounds (First=0 Second=1), and the fact that a participan t observ ed the pa y o of his coun terpart (Non observ ation= 0 Observ ation=1), on the probabilit y of C c ho osing a negativ ely correlated pa y o vs. the other pa y os. The second regression rep orts the impact of the same indep enden t v ariables on the probabilit y of C c ho osing a p ositiv ely correlated pa y o vs. all others, while the third regression rep orts the impact of the same indep enden t v ariables on the probabilit y of C c ho osing a xed pa y o vs. all others. P anel B rep orts t w o linear probabilit y regressions. The rst regression rep orts the impact of the same indep enden t v ariables on the probabilit y of C c ho osing a negativ ely correlated pa y o vs. a xed pa y o, the second regression rep orts the impact of the same indep enden t v ariables on the probabilit y of C c ho osing a p ositiv ely correlated pa y o vs. a xed pa y o. P anel C rep orts t w o linear probabilit y regressions considering observ ation from the second part of eac h exp erimen tal session. The rst regression rep orts the impact of three v ariables on the probabilit y of C c ho osing a negativ ely correlated pa y o vs. a xed pa y o, the second regression rep orts the impact of the same three v ariables on the probabilit y of C c ho osing a p ositiv ely correlated pa y o vs. a xed pa y o. T-statistics are rep orted in paren thesis. Pr(Payoff) = i + 1 Male+ 2 Second+ 3 Observation+ 4 SameRole PanelA Negativ e vs. Rest P ositiv e vs. Rest Fix vs. Rest Male 0:089 (1:50) 0:070 (0:93) 0:160 (1:75) Se c ond Part 0:153 (1:89) 0:110 (1:11) 0:017 (0:42) Observation 0:257 (4:03) 0:174 (2:36) 0:070 (1:46) Same Role 0:092 (1:43) 0:054 (0:75) 0:037 (0:39) Individual RE Y es Y es Y es Cluster e d Err ors Y es Y es Y es R-sq 5.04% 2.04% 4.15% PanelB Negativ e vs. Fix P ositiv e vs. Fix 0:172 (1:59) 0:151 (1:52) 0:081 (1:42) 0:020 (0:24) 0:192 (2:47) 0:005 (0:09) 0:094 (0:89) 0:012 (0:12) Y es Y es Y es Y es 10.26% 4.01% PanelC SecondPart Negativ e vs. Fix P ositiv e vs. Fix 0:370 (2:84) 0:301 (2:44) 0:231 (2:68) 0:008 (0:20) 0:041 (0:33) 0:148 (1:19) Y es Y es Y es Y es 21.16% 10.65% 32 Once again, w e should not b e surprised that the results are stronger for partic- ipan ts C than for participan ts D. In fact a relativ e w ealth concerned agen t C, and more precisely an agen t who is risk a v erse in his relativ e w ealth, is always b etter o b y b eing p ositiv ely correlated with his p eer’s pa y o. Agen ts D, on the other hand, migh t not b e resp onsiv e to correlation c hoice ev en though they are relativ e w ealth concerned, if their incen tiv e compatibilit y condition is not binding or near-binding. 1.5 Conclusions In this pap er I in v estigate the impact of relativ e-w ealth concerns on the prefer- ences of agen ts for p ositiv e correlation and a v ersion to negativ e correlation b et w een agen ts’ pa y os. In particular, I assume that agen ts’ utilit y functions are increasing in their absolute w ealth as w ell as in their relativ e w ealth. In addition I assume that agen ts are risk a v erse in b oth absolute and relativ e w ealth. Under these assump- tions I sho w that agen ts prefer p ositiv e correlation b et w een pa y os and are a v erse to negativ e correlation b et w een pa y os. I then test this prediction in a lab oratory ex- p erimen t and nd that agen ts indeed prefer p ositiv ely correlated pa y os. Moreo v er, agen ts who observ e their p eers’ pa y o, sho wing concerns for their relativ e pa y o, are signican tly less lik ely to c ho ose negativ ely correlated pa y os. These ndings sup- p ort the h yp othesis that relativ e-w ealth concerns pla y a signican t role in explaining wh y rms use extensiv ely prot-sharing and broad-based incen tiv es (since they in- duce p ositiv e correlation b et w een pa y os) and rarely emplo y Relativ e P erformance Ev aluation con tracts (whic h induce negativ e correlation b et w een pa y os). This w ork also con tributes to the exp erimen tal literature on comp ensation b y di- rectly addressing the question of agen ts’ preferences for correlation b et w een pa y os. Previous w orks mainly fo cuses on ho w fairness concerns and recipro cit y shap e the re- lationship b et w een a principal and an agen t: F eher and F alk (1998) nd that agen ts 33 recipro cate a generous oer b y a principal b y exerting a higher than minimal eort. F eher et al (1996) sho w that emplo y ees ma y refuse w ages higher than their reserv ation utilit y if they deem the oer to b e unfair. Charness (2004), addresses the question of whether agen ts attitude to w ards a giv en pa y o ma y b e inuenced b y the fact that it is oered b y a p erson rather than b y a random pro cess. The author nds that agen ts recipro cate more an oer receiv ed b y an individual rather than an oer receiv ed b y an external pro cess. More related to this w ork is Charness and Kuhn (2007) that studies the impact of so cial forces b et w een emplo y ees rather than a v ertical relation b et w een emplo y ees and emplo y ers. In this pap er the authors nd that relativ e comp ensation has no impact on the lev el of eort exerted b y agen ts. These con tributions are based on theoretical grounds similar to the h yp othesis of relativ e-w ealth concerns, nev er- theless they do not directly test preferences of agen ts for correlation b et w een their pa y os and the pa y os of their p eers. The exp erimen tal approac h also allo ws me to o v ercome a problem that comp en- sation studies encoun tered when addressing the sub ject of RPE comp ensation. The fact that RPE con tracts are scarcely used in practice, strongly limits the p ossibil- it y to in v estigate this issue through arc hiv al data. In an exp erimen tal setting I can exogenously oer negativ ely correlated pa y os to the agen ts and study under what conditions they will refuse them. One more asp ect I in v estigate is ho w gender inuences agen ts’ preferences for pa y o correlation and their eort exertion. I nd that w omen c hange their b eha vior more sharply than men when they mo v e from a non-so cial con text to a so cial one. In particular they increase their eort and c ho ose more frequen tly a v olatile pa y o, in particular if p ositiv ely correlated with the pa y os of their p eers. These results suggest that in organizations where the presence of w omen is higher, w e should ob- serv e a wider use of rm-wide incen tiv e con tracts and a higher lev el of eort exerted. These predictions ha v e in teresting analogies with the ndings of A dams and F erreira 34 (2008) ab out gender-div erse b oards of directors. The authors nd that w omen ha v e higher attendance rates to b oard meetings than men, and they are more in v olv ed in committee activities than their male colleagues. Moreo v er, the authors nd that the prop ortion of female directors is asso ciated with more equit y-based pa y for directors. This evidence, far from b eing conclusiv e, op ens promising p ersp ectiv es for the study of the relation b et w een gender and comp ensation p olicies. 35 A Chapter 2 The Optimal Contract In this pap er I will assume that not only do agen ts obtain utilit y from their absolute w ealth but also from ho w ric h they are compared to their p eers (status concern 19 ). In this w ork, I will sho w ho w the optimal rem uneration con tract will c hange when w e mo v e a w a y from the self-in terest h yp othesis to a status concern setting in a hidden action problem. In particular, I will argue that team-p erformance based rem uneration is optimal ev en in situations where, according to most of the traditional principal- agen t theory , it should not b e optimal. In the last three decades, the economics literature has dev elop ed n umerous the- ories and do cumen ted empirically the existence of status concerns in the preferences of agen ts. Easteriln(1995) nds that although coun tries are b ecoming ric her, the satisfaction (happiness) of the p opulation seems not to b e increasing accordingly as a consequence of the rise in the so cial norms regarding w ell-b eing standards. More recen tly Alpizar et al. (2005) conducted an exp erimen t on a group of 325 studen ts, sho wing that they w ould rather b e p o orer in absolute terms in a so ciet y where they are relativ ely ric her, than ric her in absolute terms in a so ciet y where they are rel- ativ ely p o orer. F or what concerns the theory , Clark and Osw ald (1998) prop ose a mo del where agen ts are status concerned and they ha v e a constan t relativ e risk a v er- sion. F ehr and Sc hmidt (1998) in tro duced the concept of inequit y a v ersion: agen ts utilit y is decreased not only b y b eing p o orer than their p eers but also b y b eing ric her 19 This and other so cial norms are discussed in Camerer and F ehr (2003) 36 than them. F rank (1984a, 1984b) addresses more directly the problem of emplo y ee comp ensation and status concerns. The author sho ws that the presence of status concerns w ork ers migh t not b e paid according to their marginal pro ductivities. Ak- erlof and Y ellen (1990) in tro duced the idea of fair w age: emplo y ees ha v e a reference w age that they consider fair. If their comp ensation is b elo w this reference p oin t, they w ould resp ond b y exerting a lo w er eort. More sp ecically , this w ork will addresses t w o issues that receiv ed a go o d deal of atten tion in recen t researc h. The rst problem is wh y in the t ypical comp ensation practice w e observ e little use of Relativ e P erformance Ev aluation (RPE) con tracts (see Murph y (1999)). The optimalit y of this class of con tracts follo ws from Holmstrom (1982) informativ eness principle requiring eac h emplo y ee comp ensation to b e based on the p erformance ac hiev ed in exc ess of their colleagues, in order to net out an y random disturbance term that the agen ts share in their pro duction functions. Status concerns can also help to shed ligh t on a second puzzle emerged in recen t w orks: wh y do rms a w ard rm-wide incen tiv e con tracts ev en to those emplo y ees that do not seem to need an y incen tiv e. This sub ject has b een co v ered in a n um b er of recen t articles: Oy er (2004) and Oy er and Sc haefer (2005) suggest that the rm-wide use of incen tiv e con tracts 20 is motiv ated b y the p ossibilit y to trac k agen ts’ v ariation in their reserv ation utilit y without resorting to costly con tract renegotiation. Core and Gua y (2001) prop ose the idea that a compan y can b e nanced b y its o wn emplo y ees through option gran ts. This last argumen t, though, do es not pro vide an exhaustiv e explanation of wh y a compan y in need of nancial resources w ould resort to suc h an exp ensiv e source giv en the high risk premium required b y risk a v erse and undiv ersied agen ts (see Hall and Murph y (2003)). Status concerns join tly with risk a v ersion help address b oth puzzles: b eing agen ts risk a v erse with resp ect to b oth their absolute w ealth and their relativ e w ealth, they 20 By incen tiv e con tracts the authors mean comp ensation con tracts that link the emplo y ee pa y o to the o v erall rm p erformance. 37 will b e willing to giv e up part of their exp ected comp ensation in order to b e hedged against a wider div arication b et w een their rem uneration and the one of their p eers. Firm-wide incen tiv e con tracts, hence, are b enecial since they allo w an agen t’s w ealth to b e alw a ys aligned with the w ealth of her colleagues. Relativ e P erformance Ev aluation con tracts, on the other hand, increase the v olatilit y of relativ e comp en- sation. F or this reason the principal has to pa y an additional risk premium to the agen t that can oset the informational b enets of this category of con tracts. 21 The impact of status concerns on the optimal linear con tract oered b y the prin- cipal to her agen ts has b een in v estigated b y a few authors: F ersh tman et al (2003) consider the case of t w o separate principals, eac h relating to one agen t, and sho w the optimalit y of implemen ting con tracts where eac h agen t receiv es a pa y o link ed to the other agen t’s p erformance. More in line with the spirit of what follo ws is Bartling (2008). In this w ork the author considers a m ulti-agen t setting, where eac h agen t has a utilit y function incorp orating status concerns, although in this case agen ts are risk a v erse with resp ect to their absolute w ealth, but are inequalit y a v erse and risk neutral, not risk a v erse, when it comes to their relativ e w ealth. The pap er will pro ceed as follo ws: the rst section in tro duces a mo del with one principal and t w o agen ts and indep enden t pro duction functions. In the second section I will consider a mo del with t w o agen ts whose pro duction functions are correlated while the third section generalizes the mo del to N > 2 agen ts. The fourth and nal section briey discusses the results and concludes the pap er. 21 Bandiera et al (2005) found that so cial forces justify the scarce resort to RPE con tracts. In their case, though, the main reason is the enforcemen t of collusiv e agreemen ts: emplo y ees slac k not to exercise a negativ e externalit y on their p eers. This equilibrium will b e ac hiev ed only if the agen ts can monitor eac h other in order to enforce a system of punishmen t if an y one deviates fro the agreed strategy . Kedia and Ra jgopal (2008) nd that so cial forces explain wh y option gran ting is geographically clustered. 38 2.1 The T wo Agent Case with Independent Productions I will rst consider the simple case of t w o risk a v erse, status-concerned agen ts and one risk neutral self-concerned principal. Dieren tly from the standard principal- agen t setting, in this case the agen t and the principal preferences will dier on t w o dieren t lev els: the rst one is the usual risk a v ersion of the agen ts con trasted with the risk neutralit y of the principal (Holmstrom (1979) Sha v ell (1979)). The second, and no v el, dierence is that the principal is self-concerned while the agen ts care ab out their relativ e standings with resp ect to their colleagues. This assumption seems to fairly realistic, in particular if w e consider the case of a corp oration w e can think of the shareholders as the principal (p ossibly represen ted b y a b oard of directors). Being the shareholders (or at least their ma jorit y) outsiders with resp ect to the corp oration (in the sense that they are not in v olv ed in the compan y’s op erations and therefore do not p erceiv e the w ealth of the emplo y ees as their b enc hmark) w e can assume them to b e self concerned. The preferences of the agen ts are represen ted b y the follo wing utilit y function: U i (t i ;t j ) = exp t i + (t i t j ) 1 2 e 2 i (5) The ab o v e is a negativ e exp onen tial utilit y function with Absolute Risk A v ersion (ARA) co ecien t equal to whose argumen t consists of three terms: the rst one is the the monetary transfer the agen t receiv es from the principal (t i ), the second is prop ortional to the dierence b et w een the agen t’s monetary transfer and his p eer’s (t i t j ), and the third term is the monetary-equiv alen t cost of eort giv en b y a quadratic function. The co ecien t measures the agen t’s concern ab out his relativ e 39 w ealth and it is assumed to b e constan t across agen ts. 22 In addition I assume that 0 < 1, that is, the agen t will alw a ys prefer to b e one dollar ric her in terms of absolute w ealth than one dollar ric her in terms of relativ e w ealth. Eac h agen t’s output (y i ) is observ able, con tractible and it is giv en b y the linear pro duction function y i =e i + i (6) Wheree i is the eort exerted b y agen t i and i is an additiv e noise term normally distributed with zero exp ected v alue and v ariance equal to 2 i . T w o further assump- tions are that the t w o noise terms ( 1 and 2 ) are indep enden t and that the eort exerted b y one agen t do es not aect the pro duction of the other agen t (no pro ductiv e in teraction). 23 I will assume that the comp ensation con tracts oered b y the principal are linear in the agen t’s o wn output as w ell as in his colleague’s output: 8 > > < > > : t 1 =w 1 +h 11 y 1 +h 12 y 2 t 2 =w 2 +h 22 y 2 +h 21 y 2 (7) The monetary transfer to agen t i will b e formed b y a xed salary w i and t w o v ariable terms: one giv en b y a p ortion h ii of the agen t’s o wn pro duction and the other giv en b y a p ortion h ij of the other agen t pro duction. Dieren tly from a principal-agen t problem with self-concerned agen ts, in (5) w e can observ e the presence of t w o sources of v ariation: the v olatilit y link ed to agen t’s 22 See F ersh tman et al (2005) for a mo del with risk neutral agen ts and heterogeneous status con- cerns. 23 The existence of pro ductiv e in teractions w ould easily justify the use of team-p erformance based con tracts, in this regard see for example Bushman et al (1995). 40 absolute w ealth (t i ) and the v olatilit y of agen t’s relativ e w ealth (t i t j ). This is easier to observ e if w e apply the usual monotonic transformation to the exp ected utilit y . Substituting (7) in to (5) w e obtain the follo wing expression for the (transformed) exp ected utilit y: E [U i ] =w i +h ii e i +h ij e j + [(w i w j ) +e i (h ii h ji ) +e j (h ij h jj )] | {z } A + 1 2 (h ii (1 +)h ji ) 2 2 i + (h ij (1 +)h jj ) 2 j | {z } B 1 2 e 2 i |{z} C (8) In (8) term A giv es us the exp ected v alue v alue of agen t i’s comp ensation to whic h w e need to (algebraically) add the exp ected v alue of his exp ected relativ e comp ensation w eighed b y the co ecien t . T erm B is the one accoun ting for the v olatilit y of the argumen t of the agen t’s utilit y , where w e can iden tify the t w o sources of v olatilit y: the idiosyncratic comp onen t of agen t i’s pro duction and the idiosyncratic comp onen t of agen t j pro duction. Dieren tly from the self-concerned case, it is not sucien t to link the agen t w age only to his o wn output to insulate him from the v olatilit y of his colleague’s pro duction. T o see this consider a con tract where agen t i only obtains a p ortion h ii of his output (h 12 =h 21 = 0), (8) b ecomes: E [U i ] =w i (1 +)w i +e i (h ii (1 +))e j (h jj ) + 1 2 (h ii (1 +)) 2 2 i + (h jj ) 2 2 j 1 2 e 2 i (9) As it is apparen t from (9) ev en when the monetary transfer to agen t i is inde- p enden t of agen t j pro duction, his exp ected utilit y is still aected b y the v olatilit y of j ’s output. The reason b ehind it can b e easily found b y lo oking at (5): if one agen t comp ensation dep ends only on his output there will still b e v olatilit y in his rel- ativ e comp ensation induced b y t j . Therefore the principal has to face one additional trade-o when agen ts are status concerned: b y p ositiv ely linking one emplo y ee com- 41 p ensation to the other emplo y ee p erformance, she will in tro duce additional v olatilit y in the emplo y ees absolute comp ensation but reduce the v olatilit y of their relativ e comp ensation. Therefore in equilibrium w e migh t exp ect to observ e h ij > 0, but there is one more asp ect to tak e in to consideration b efore dra wing this conclusion: from (8) w e obtain the follo wing eort c hoice for the agen t: e i =h ii + (h ii h ji ) (10) The equalit y in (10) is the the incen tiv e compatibilit y condition [IC] for agen t i, whic h tells us that the eort c hosen b y the emplo y ee will b e inuenced not only b y the piece rate with resp ect to his o wn output, but also b y the piece rate of agen t j with resp ect to i’s output. The rationale is that the agen t, b y increasing his eort of one unit, obtains h ii units of his output and this increases his exp ected absolute comp ensation. Moreo v er, b y increasing his absolute comp ensation the agen t also increases his relativ e w ealth whic h is w eighed b y the co ecien t . On the other hand, if agen t j receiv es a slice h ji > 0 of i’s output, ev ery additional unit of eort exerted b y i will mak e j ric her and this will reduce the incen tiv e for agen t i to exert eort. Ov erall the principal will face the follo wing trade-o: if she increases h ij she will insure agen ts against w age misalignmen t and sa v e on the exp ected cost of their w age, on the other side, increasing h ij will reduce the incen tiv e for the agen t to exert eort, and this will reduce the exp ected pro duction of the emplo y ees. In order to understand whic h eect will out w eigh the other 24 it is necessary to solv e the optimization problem of the principal. Calling the reserv ation utilities of the t w o agen ts u 1 and u 2 , the optimization problem will b e giv en b y: 24 This feature mak es this mo del dieren t from F ehr and Sc hmidt (1998), in their case the only relev an t eect w ould b e the insurance against the v olatilit y of w age misalignmen t. 42 8 > > > > > > > > > > < > > > > > > > > > > : max fw i ;h ii ;h ij g i;j2f1;2g; i6=j P i;j2f1;2g; i6=j e i w i h ii e i h ij e j s:t: e i =h ii + (h ii h ji ) i;j2f1; 2g; i6=j [IC] E [U i ]u i i2f1; 2g [PC] (11) The agen ts will b e k ept optimally to a utilit y lev el that matc hes their reserv ation utilit y , therefore the participation constrain t [PC] will b e binding. Solving the ab o v e problem w e obtain Pr op osition 3. In a mor al hazar d pr oblem with one self-c onc erne d, risk neutr al princip al and two agents with utility functions given by (5) wher e the te chnolo gy is given by the pr o duction function (6), the optimal line ar c ontr act of the form (7) has the fol lowing pie c e r ates: h ii = 1 + (1 + 2) (1 + 2 i ) (12) h ij = (1 + 2) 1 + 2 j (13) Pr o of of Pr op osition 3. F ollo ws from the solution of problem (11) v erifying the rst and second order conditions Prop osition 1 tells us that for the principal it is optimal to giv e to eac h agen t a slice of his colleague’s output. Therefore the p ossibilit y for the principal to sa v e on the exp ected comp ensation b y insuring the agen ts against the v ariabilit y of w age misalignmen t out w eighs the cost of in tro ducing w eak er incen tiv es. Moreo v er, consid- ering (10) and substituting in to it (12) and (13), w e observ e that at the optim um 43 the eort exerted b y agen t i will b e e i = 1 1+ 2 i , hence the in tro duction of the sta- tus concerns h yp othesis has no impact on the on the second-b est eort c hoice when compared to the self-concerned case. Nonetheless, setting the t w o piece rates to a p ositiv e lev el is piv otal for the principal in order to shift part of the exp ected pro- duction in to her hands. T o ha v e an idea of the amoun t of exp ected pro duction that the principal can div ert from agen ts (without c hanging their lev el of exp ected util- it y) b y setting h ij > 0, consider the case of a compan y oering the follo wing piece rates: ^ h ii = 1 (1+ 2 i )(1+) and ^ h ij = 0. F or the sak e of simplicit y , assume further that 1 = 2 = and u 1 = u 2 = u. It easy to v erify that ^ h ii and ^ h ij will induce the same eort as h ii and h ij . The prot ( ) of the principal is giv en b y the follo wing: = X i;j2f1;2g; i6=j e i w i h ii e i h ij e j (14) Finally call ^ the prot for the compan y under ^ h ii and ^ h ij , and indicate with the prot under the piece rates (12) and (13). It is immediate to v erify that ^ = 2 2 (1 + 2 ) 2 (1 +) 2 > 0 (15) Where the p ositiv e v alue (15) is exactly the amoun t of money giv en up b y the emplo y ees follo wing the v olatilit y reduction in the argumen t of their utilit y function. T urning our atten tion to the comparativ e statics results, from (12) and (13) it follo ws that @h ii @ i < 0 and @h ij @ > 0. This t w o results are fairly in tuitiv e: as the v olatilit y of agen t i’s o wn pro duction increases the piece rate relativ e to suc h output will b e reduced accordingly as it is implied b y the w ell kno wn trade o b et w een incen tiv e inducemen t and the premium required b y the agen t to b ear the risk of a random w age. The second comparativ e statics result tells us that, as the agen t b ecomes more concerned ab out his relativ e w ealth, the piece rate h ij will increase. Also this result is quite in tuitiv e, in fact if an emplo y ee is more concerned ab out ho w 44 ric her he is relativ e to his colleague, he will b e willing to giv e up more of his exp ected comp ensation in order to b e hedged against the v olatilit y of w age misalignmen t. T w o additional results are the follo wing: @h ij @ j < 0, linking agen t i’s comp ensation to j ’s output, w e are on the one hand pro viding i with insurance against w age misalignmen t, but on the other hand w e are in tro ducing another noise source in his absolute w ealth, and as suc h v olatilit y increases the piece rate paid to agen t i and relativ e to agen t j ’s p erformance (h ij ) will decrease. Finally @h ii @ < 0 follo ws from the fact that as the agen ts b ecome more concerned with their relativ e w ealth, it will b e necessary to reduce the piece rate relativ e to their o wn output in order to reduce the v olatilit y of relativ e w ealth. 2.2 The T wo Agent Case with Correlated Productions The optimal linear con tract deriv ed in the case of t w o status-concerned agen ts with indep enden t pro duction functions pro vides us with a motiv ation of wh y a compan y migh t pa y emplo y ees based on the o v erall p erformance (or team p erformance) ev en in cases in whic h this w ould not seem to b e necessary . 25 Considering no w the issue of Relativ e P erformance Ev aluation and wh y w e do not observ e this feature frequen tly in practice, Holmstrom (1982) informativ eness principle w ould require the use of these con tracts an y time the p erformance of one agen t can pro vide information ab out the realization of the same random term in the p erformance of another agen t. There are a n um b er of pap ers addressing this puzzle: Aggrw al and Sam wik (1999) justify the lac k of RPE con tracts utilization as a consequence of strategic in teraction among comp et- ing rms. More recen tly , Bandiera et al (2005) do cumen t that so cial forces can induce 25 Remem b er that in this basic setting the output of the t w o agen ts w as observ able and con tractible. Moreo v er there is no pro ductiv e in teraction b et w een agen ts and the random terms in their pro duction functions are indep enden t. If the agen t w ere self-in terested and risk a v erse, there w ould b e no reason to link the w age to the o v erall rm p erformance. 45 a lo w er emplo y ees p erformance once RPE con tract are implemen ted while F ersh tman et al (2003) use a ARA utilit y function with status concerns to justify the lac k of RPE incen tiv es in a m ulti-principal/m ulti-agen t setting. The follo wing argumen ts are in line with this last w ork but address the dieren t con text of one principal/m ulti-agen t con text. In order to ha v e a b etter grasp of ho w status seeking agen ts migh t increase the cost of RPE-t yp e comp ensation, w e no w consider a dieren t tec hnology: y i =e i + + i (16) Dieren tly from (6), I in tro duce in (16) a random term normally distributed with exp ected v alue equal to 0 and v ariance equal to 2 . This additional term is shared b y b oth agen ts, therefore their pro duction functions are no w correlated. Moreo v er, for exp ository simplicit y , consider the case of 1 = 2 = . Solving the same optimization problem as in (11) with this new pro duction functions, w e obtain: Pr op osition 4. In a mor al hazar d pr oblem with one self-c onc erne d, risk neutr al princip al and two status-c onc erne d agents with utility function given by (5), wher e the te chnolo gy is given by the pr o duction function (16) the optimal line ar c ontr act of the form (7) has the fol lowing pie c e r ates: h ii = 2 + 2 (1 +) [ 2 (1 + 2 + 2 2 ) + 2 ] (1 + 2) (17) h ij = 2 + 2 [ 2 (1 + 2 + 2 2 ) + 2 ] (1 + 2) (18) Pr o of of Pr op osition 4. F ollo ws from the solution of problem (11) v erifying the rst and second order conditions 46 The piece rates (17) and (18) are a generalization of (12) and (13), in fact if w e set = 0, h ii and h ij b ecome resp ectiv ely equal to h ii and h ij . Moreo v er if = 0 (17) and (18) reduce to h RPE ii = 2 + 2 2 (1 + 2 + 2 2 ) + 2 (19) h RPE ij = 2 2 (1 + 2 + 2 2 ) + 2 (20) It can b e easily v eried that (19) and (20) are the piece rate implied b y Holm- strom (1982) informativ eness principle, therefore this mo del encompasses this theory and generalizes it to the case of agen ts with status concerns. As predicted b y the in- formativ eness principle, if agen ts are self concerned, the piece rate of one agen t with resp ect to his p eer’s output will b e negativ e, in order to net out the noise term im- pact on their p erformance and ha v e a cleaner signal ab out the agen t eort. But, once w e allo w > 0, this migh t not b e the case an ymore: when the agen ts are concerned ab out their relativ e w ealth, RPE con tracts will increase the v olatilit y of this quan tit y , therefore the agen ts will require the principal to comp ensate them for this additional risk. As a result the principal will b e facing the trade-o b et w een the b enets of the information gathered through RPE con tracts and the higher risk premium she has to pa y the agen ts. In this case w e can iden tify a condition on in order for h ij to b e p ositiv e, in particular there exists a threshold suc h that if > then h ij > 0 and if if < then h ij < 0. The v alue can b e easily deriv ed from (18) and it is giv en b y the follo wing: = 2 2 (21) If the v olatilit y of the systematic noise term ( ) con tributes the most to the o v erall v ariabilit y of the pro duction function (or, in other w ords, when the pro duction 47 function are highly correlated), the b enets of an RPE-t yp e comp ensation sc hedule are high and therefore the agen t should displa y a v ery high concern in relativ e w ealth in order forh ij to b e optimally set at a p ositiv e v alue. Ov erall, condition (21) suggests that as 2 increases or decreases, h ij should decrease and mo v e from p ositiv e to negativ e. As exp ected when the v olatilit y of the common noise term decreases h ij mo v es from p ositiv e v alues (the w age misalignmen t hedging b enets out w eigh the informa- tiv eness b enets) to negativ e v alues (the informativ eness b enets out w eigh the w age misalignmen t hedging b enets). Also, the w age misalignmen t hedging will not b e v aluable to the principal (in the sense that it will not allo w her to sa v e enough in terms of exp ected comp ensation) as the agen ts b ecome less concerned with their relativ e comp ensation. These in tuitions are conrmed b y the follo wing results: @h ij @ = 2 2 (1 + + 2 (1 + 2)) [ 2 (1 + 2 ) + 2 (1 + 2 2 )] 2 (1 + 2) < 0 (22) @h ij @ = 2 + 2 2 [ 2 (1 + 2 ) + 2 (1 + 2 2 )] 2 (1 + 2) > 0 (23) Dieren tiating h ii with resp ect to and deliv ers the follo wing: @h ii @ < 0 and @h ii @ < 0. The rationale b ehind these results is the same as b efore, as the v olatilit y of the systematic noise term increases also the o v erall v olatilit y of the agen t’s o wn output increases and this will lead to a decrease in the piece rate relativ e to suc h p erformance. As for , when it decreases, the agen t is less concerned with his relativ e w age therefore the principal has the p ossibilit y to set a higher v alue for h ii without running in to high costs for the risk of w age misalignmen t. A more in teresting result follo wing from (18) is the non-monotonic b eha vior of h ij as v aries whic h is detailed in the follo wing: 48 Cor ol lary. Given the pie c e r ate in (18) the fol lowing r esults hold: (i) if 4 2 < 1 then @h ij @ > 0 (24) (ii) if 4 2 > 1 and < 2 ( 2 + 2 ) + 1 4 2 1 then @h ij @ > 0 (25) (iii) if 4 2 > 1 and > 2 ( 2 + 2 ) + 1 4 2 1 then @h ij @ < 0 (26) Pr o of of Cor ol lary. Imme diate fr om (18) The results in (24) and (25) are consisten t with the same comparativ e statics of a situation in whic h the RPE-t yp e con tract is optimal: as the v olatilit y of the idiosyncratic random comp onen ts increases, the b enets from netting out the sys- tematic noise thorough RPE b ecome w eak er and, as a consequence, h ij (whic h in the RPE case is negativ e) will increase (decrease in absolute v alue). On the other side the result in (26) is consisten t with the case of t w o non correlated pro duction functions with status concerned agen ts: as it has b een discussed ab o v e, when the v olatilit y of the idiosyncratic comp onen t increases, the exp osure of one agen t to his colleague’s p erformance will decrease. These t w o coun terv ailing forces are w orking sim ultaneously , hence as the parameters of the pro duction and the utilit y functions mak e the problem closer to the pure RPE setting either (24) or (25) will hold true, if the problem approac hes more closely (11) then (26) will hold true. T o b etter see this, consider (24): if 4 2 < 1 the v olatilit y of the common noise term comp onen t is relativ ely larger than the v olatilit y of the idiosyncratic noise terms and if in addi- tion the ARA co ecien t is relativ ely small, this is the con text in whic h an RPE-t yp e con tract w ould pro vide the most b enets (relativ ely large 2 ) at a lo w er cost (lo w ARA co ecien t). A comparable situation is obtained in the case of (25), in fact the 49 condition < 2 ( 2 + 2 )+1 4 2 1 will b e more lik ely met if w e ha v e a relativ ely high v alue of 2 (that is the case in whic h an RPE-t yp e con tract is more v aluable) and a lo w v alue of (that is the the cost of the risk of w age misalignmen t is relativ ely lo w). Once again these t w o circumstances mak e the problem closer to an pure RPE setting therefore the resp onse of h ij to v ariations in will ha v e the same sign of the resp onse ofh RPE ij to the same v ariation. Finally , if the conditions under whic h (26) holds true, the problem for the principal Will b e closer to problem (11), and the b eha vior h ij will b e closer to the b eha vior of h ij as the v olatilit y of the idiosyncratic term v aries. 2.3 The General Multi-Agent Case In this section I will generalize the results obtained ab o v e to a setting with N 2 agen ts. Also in this case, I will assume the agen ts to ha v e preferences regarding b oth their absolute and relativ e w ealth that are represen ted b y the follo wing utilit y function: U i t i ;ft j g j6=i = exp 8 > < > : 2 6 4 t i + 0 B @ t i P t j j6=i N 1 1 C A 1 2 e 2 i 3 7 5 9 > = > ; (27) The ab o v e is just a generalization of (5), in fact it is straigh tforw ard to v erify that if N = 2, w e obtain the utilit y function of the t w o agen t case. With N agen ts, though, the reference p oin t for a giv en emplo y ee b ecomes the a v erage w age paid to all the other p eople w orking within the organization. 26 With resp ect to the tec hnology , let us rst consider the case of n indep enden t pro duction functions giv en b y (6). F or simplicit y I will assume the v ariance of i is constan t across agen ts and equal to 26 F or a discussion on ho w agen ts set their reference p oin t see K oszegi and Rabin (2006). 50 . The class of linear con tract o v er whic h the principal will solv e her optimization problem is giv en b y the follo wing: t i =w +h 1 y i +h 2 P y j j6=i N 1 (28) The transfer to agen t i as b efore is formed b y three terms: one xed salary w , one v ariable term dep enden t on the p erformance of agen t i and a second v ariable term prop ortional to the a v erage output of the other N 1 agen ts. Notice that the salary and b oth piece rates do not b ear an y indication of the agen t iden tit y since all agen ts ha v e a the same pro duction and utilit y functions and consequen tly they will b e rew arded according to the same linear con tract. Last, after plugging (28) in to (27), w e can apply the usual transformation to the exp ected utilit y and obtain: E h U i t i ;ft j g j6=i i =w +e i h 1 (1 +) N 1 h 2 +e j h 2 (1 +) h 2 (N 2) (N 1) | {z } A + 1 2 2 4 2 h 1 (1 +) N 1 h 2 2 + 2 N 1 h 2 N 1 (1 +) N 1 h 2 (N 2) (N 1) 2 ! 2 3 5 | {z } B 1 2 e 2 i |{z} C (29) As in the t w o agen t case, the exp ected utilit y in (29) is formed b y three terms: the rst one is the exp ectation of the argumen t of (27), the second accoun ts for the disutilit y of the v olatilit y of b oth absolute and relativ e w ealth. The last term is simply the cost b orn b y the agen t for the eort exerted. Giv en a comp ensation con tract of the form (28) the agen t will c ho ose an eort lev el e N i giv en b y: e N i =h 1 (1 +) N 1 h 2 (30) Dieren tly from the t w o agen t case, as the n um b er of agen ts within an organization increases, the disincen tiv e eect of h 2 decreases. Recall that when agen ts receiv e a 51 p ositiv e slice of their colleagues output, ev ery additional unit of eort they exert will mak e their p eers ric her and therefore mak e them w orse o in terms of relativ e w ealth. But with N agen ts, eac h of additional eort exerted b y an agen t will only con tribute N1 h 2 to the w ealth of other agen ts and this quan tit y is ob viously decreasing in N . Assuming that all agen ts ha v e the same reserv ation utilit y and that is is equal to u the principal will b e solving the follo wing problem: 8 > > > > > > > > > > < > > > > > > > > > > : max fw;h 1 ;h 2 g n P i=1 e i wh 1 e i h 2 P j6=i e j N1 s:t: e i =h 1 (1 +) N1 h 2 i = 1:::N [IC] E [U i ]u i = 1:::N [PC] (31) Solving the problem in (31) w e obtain: Pr op osition 5. In a mor al hazar d pr oblem with one self-c onc erne d, risk neutr al princip al and N agents with utility function given by (27) wher e the te chnolo gy is given by the pr o duction function (6), the optimal line ar c ontr act of the form (28) has the fol lowing pie c e r ates: h N 1 = +N 1 (N (1 +) 1) (1 + 2 i ) (32) h N 2 = (N 1) (N (1 +) 1) (1 + 2 i ) (33) Pr o of of Pr op osition 5. F ollo ws from the solution of problem (31) v erifying the rst and second order conditions The comparativ e statics results that applied to the t w o agen ts case also w ork in the case of N agen ts, in particular @h N 1 @ < 0 and @h N 2 @ < 0. Also the impact of 52 parameter on the piece rates is the same as in the case of t w o agen ts: @h N 1 @ < 0 and @h N 2 @ > 0. Consisten t with what w e observ ed in the previous sections, w e nd that as the agen ts b ecome more concerned in their status, the optimal exp osure of their w age to their o wn output decreases while the exp osure with resp ect to the p erformances of the other agen ts increases, in order to reduce the v olatilit y of the relativ e w ealth. The new insigh t w e can gain b y generalizing the mo del to N agen ts is ho w the size of the organization can impact the comp ensation sc hedule when the agen ts ha v e status concerns. In particular, dieren tiating (12) and (13), w e obtain the follo wing @h N 1 @N = 2 [N (1 +) 1] 2 (1 + 2 ) < 0 (34) @h N 2 @N = 2 [N (1 +) 1] 2 (1 + 2 ) > 0 (35) T o understand the ab o v e results, consider term B of (29). Within this term w e can distinguish t w o other: the rst, 2 h 1 (1 +) N1 h 2 2 , is the v olatilit y term relativ e to the agen t’s o wn output, and as N increases the co ecien t of 2 increases as w ell, consequen tly h N 1 will b e reduced. The second term of B, that is 2 N1 h 2 N1 (1 +) N1 h 2 (N2) (N1) 2 2 , relates to the v olatilit y of the a v erage w ealth of emplo y ees and as N increases suc h v olatilit y ( 2 N1 ) decreases, as a result h N 2 will increase. As in the t w o agen t case, also in presence of N agen ts it is optimal for the principal to set a h 2 > 0, in order to hedge the emplo y ees against the v olatilit y of w age misalignmen t. Moreo v er w e can measure the amoun t of exp ected comp ensation sa v ed b y the principal b y considering the follo wing piece rates ^ h N 1 = 1 (1+)(1+ 2 ) and ^ h N 2 = 0 whic h will induce the same eort b y the agen t as h N 1 and h N 2 . The dierence b et w een the principal prot p er emplo y ee under (32) and (33), and the prot p er emplo y ee under ^ h N 1 and ^ h N 2 is giv en b y: 53 N ^ N = 1 2 2 2 (1 +) 2 (1 + 2 ) (N 1) > 0 (36) Therefore also in this case, as w e observ ed in the t w o agen t case, the principal b y oering a con tract based on the o v erall organization p erformance will receiv e from the emplo y ees the pa ymen t of an insurance premium. Nonetheless, dieren tly from the t w o agen t case, as N increases this premium b ecomes smaller follo wing from the fact that the v olatilit y of the a v erage comp ensation diminishes, and b ecomes a degenerate random v ariable for N!1. In fact it can b e easily v eried that lim N!1 N ^ N = 0 and lim N!1 h N 1 = ^ h N 1 . Hence the necessit y for the principal to oer hedging against w age misalignmen t decreases with the size of the organization. 27 In sum, in the general m ulti-agen t case all the in tuitions dra wn in the t w o agen t setting still hold true. In addition w e can no w mak e some prediction based on the size of the organization: as N increases the v alue of the hedging against w ealth inequalit y for the emplo y ees b ecomes progressiv ely less v aluable, and in the limit it just b ecomes equiv alen t to a xed salary comp onen t. The ab o v e results apply to the case of N agen ts whose pro duction functions are indep enden t. F or the sak e of completeness I will no w extend the N agen t mo del to the case of correlated pro duction functions. Once again I in tro duce the correlation b et w een the p erformances of the agen ts assuming that the output for agen t i is giv en b y (16). Solving the same problem as in (31) but with a tec hnology giv en b y (16), w e obtain the follo wing piece rates: h N 0 1 = 2 (N 1) 2 + 2 (N + 1) [ 2 (N + 2 N 1) + 2 (1 + 2 )] (N (1 +) 1) (37) 27 Notice that for N !1, h N 2 do es not go to zero, but h N 2 P yj j6=i N1 b ecomes a comp onen t of the emplo y ee xed comp ensation. T o see this call ^ w N the xed salary under ^ h N 1 and ^ h N 2 , and callw N the xed salary giv en to the emplo y ee under h N 1 andh N 2 . It can b e v eried that lim N!1 w N +h N 2 P yj j6=i N1 = ^ w N . 54 h N 0 2 = (N 1) 2 ( 2 (1N) + 2 ) [ 2 (N + 2 N 1) + 2 (1 + 2 )] (N (1 +) 1) (38) All the implications deriv ed in the t w o agen t case still apply to the N agen t case. What needs further clarication is ho w the size of the organization ( N ) impacts on the magnitude of (37) and (38). The comparativ e statics results are cum b ersome and in b oth cases w e ha v e non-monotonic b eha vior of the piece rates follo wing a v ariation inN . F or the purp ose of this pap er the most in teresting comparativ e statics result is @h N 0 2 @N . There are dieren t forces acting on the sign of this partial deriv ativ e, dep ending on their relativ e imp ortance in the principal optimization problem: as w e sa w from (35), in the absence of an y correlation b et w een the pro duction functions, asN increases so do es h N 0 2 mo ving to w ards higher p ositiv e v alues. On the other side, follo wing from the informativ eness principle, as the n um b er of emplo y ees increases, the principal can obtain a more precise signal ab out the realization of the common random factor , and this will induce her to set the v alue of h N 0 2 to a smaller (more negativ e) v alue. Dep ending of whic h one of these t w o forces will impact more substan tially the principal exp ected prot, w e will observ e b oth dieren t signs of (38) and dieren t signs of @h N 0 2 @N . Ov erall the extension of the mo del to N agen ts is consisten t with all the results obtained in the t w o agen t case and con tributes to shed ligh t on what is the impact of the size of an organization on the linear incen tiv e con tracts a w arded to emplo y ees when they are status concerned. 2.4 Conclusions In this w ork I ha v e dev elop ed a principal-agen t mo del where agen ts ha v e status- concerned preferences and are risk a v erse when it comes to b oth their absolute w ealth 55 and their relativ e w ealth. The principal, on the other side, is assumed to b e risk neu- tral and self-concerned. The simple and in tuitiv e assumption that agen ts enjo y b eing ric her than their p eers (and dislik e b eing p o orer) allo ws us to obtain the in teresting conclusion that agen t’s comp ensation is optimally based on group p erformance rather than on the single emplo y ee p erformance, ev en if eac h agen t’s output is observ able, con tractible and indep enden t on the other agen ts actions. In addition I measured the amoun t of exp ected comp ensation that the principal is able to sa v e b y switc hing from a con tract that is based on individual p erformance to a con tract that is based on group (or rm-wide) p erformance, still inducing the second-b est eort lev el. The exp ected sa vings of the principal are an insurance premium paid b y the agen ts b y giving up part of their exp ected comp ensation for the reduction of the risk of w age misalignmen t. This last notion not only pro vides us with a reason for large scale incen tiv e plans but also helps us to justify the nding that nancially constrained rms seem to obtain nancing from the agen ts b y including in their comp ensation pac k ets call options (Core and Gua y (2001) or Bab enk o et al (2008)). In fact, agen ts rather than requesting a risk premium are willing to pa y an insurance premium to obtain this nancial con tract. Another eect of the status concerns is that agen ts prefer their comp ensation to p ositiv ely co-v ary with their p eers’, so that a RPE-t yp e comp ensation sc hedule, inducing a negativ e co v ariance, w ould induce the agen ts to ask for a higher exp ected comp ensation. F or this reason the informational b enets that the principal can obtain from an RPE con tract can b e out w eighed b y the ad- ditional rem uneration requested b y the emplo y ees. This last nding ma y pro vide us with an explanation of wh y w e do not observ e this con tracts along the lines of other w orks lik e F ersh tman et al (2003) or Bartling (2008). One last, but v ery imp ortan t, asp ect that needs to b e addressed is that status concerns do not justify b y themselv es the use of a v ariable pa y o comp ensation, they rather w ork as an amplier of the exten t to whic h these comp ensation sc hedules are 56 used. In this pap er I c hose to use the most common principal-agen t setting of action unobserv abilit y . Alternativ ely I could ha v e applied status concerns to an emplo y ee- sorting mo del suc h as the one in Ary a and Mittendorf (2005) or to an Oy er (2004)-t yp e mo del where the use of these con tracts stems from the necessit y to matc h the v arying reserv ation utilit y of the agen ts. In general, if w e add the status concern feature to an y other mo del in whic h at least a subset of the emplo y ees needs to receiv e a v ariable pa y o and agen ts are risk a v erse, this w ould trigger the in terest of the other emplo y ees in the same kind of rem uneration starting a con tagion pro cess that w ould lead to a larger than exp ected use of this sort of con tract if this class of preferences w ere not tak en in to consideration. 57 A Chapter 3 The Importance of Observ ation What follo ws describ es t w o simple exercises that sho w under what conditions it migh t b e optimal (or not) for a compan y to enforce a w age secrecy p olicy , or a v oid w ages visibilit y , in order to maximize its prot. Also, follo wing the same in tuition, this idea can b e useful to dev elop a theory in whic h the release of more information ab out agen t w ages, will induce an increase in their comp ensation. T ranslated in real-w orld terms, this idea can pro duce results that can b e applied to executiv e comp ensation. In the last y ears, the executiv e w ages raise has b een a great concern. This concern led to broader requiremen ts ab out executiv e comp ensation disclosure. In the framew ork I am ab out to exp ose, the increase in disclosure not only migh t not set bac k executiv e comp ensation lev el, but, parado xically , ev en mak e it gro w larger. This do cumen t pro ceeds as follo w: the rst section describ es the case of t w o agen ts, in whic h one has an uncertain reserv ation utilit y and the other has a kno wn reserv ation utilit y . The second section co v ers the case of t w o agen ts b oth ha ving an ex-an te uncertain reserv ation utilit y with the same v ariance. The third section briey discusses the utilit y sp ecication used in what follo ws. The last section outlines the future w ork. 58 3.1 Case 1: T wo Agents,Uncertain and Known Reserv ation Utility Consider t w o risk neutral agen ts that ha v e relativ e w ealth preferences represen ted b y the follo wing function: U i (t i ;t j ) =t i + 1 maxft i t j ; 0g + 2 minft i t j ; 0g Where U i : utilit y of agen t i t i : money transfer to agen t i 0 1 2 1 This utilit y function has man y traits in common with the utilit y function prop osed b y F ehr and Sc hmidt (1999) 28 . W e will indicate the t w o agen t with the indexes i and j . Agen t i has a xed reserv ation utilit y equal to u M . Agen t j has a reserv ation utilit y that a priori is not kno wn, but it migh t b e equal to u L or u H with probabilit y 1 2 : u L <u M <u H u L =u M u H =u M + > 0 Eac h agen t pro duces for the principal rev en ues equal to y . Consider no w t w o dieren t scenarios, the agen ts migh t b e w orking closely , and therefore kno w exactly their o wn reserv ation utilities, or, as a second scenario, they migh t b e apart. In this last case agen t j will kno w that agen t i’s reserv ation is u M , 28 The most notable dierence is that in F ehr and Sc hmidt 1999, 1 < 0, therefore agen ts w ould obtain a negativ e utilit y ev en when they are ric her than their p eers. Of course, ev en in this utilit y sp ecication, j 2 j>j 1 j. 59 but agen t i will ha v e a prior distribution regarding agen t j ’s reserv ation utilit y giv en b y a uniform distribution with parameter 1 2 . In the second scenario agen t i, although unable to p erfectly observ e agen t j ’s reserv ation utilit y , can observ e an informativ e signal s, suc h that: Pr (u H js =s H ) = Pr (u L js =s L ) =q> 1 2 Assume that in the second scenario w e ha v e t w o principals, and eac h principal has the same information set of the corresp onding agen t. The role of the principals in this case is to prop ose w ages in order to matc h the reserv ation utilit y of the agen ts. Scenario 1 In this case the problem for the principal is fairly simple, there are t w o alternativ e states of the w orld that will b e kno wn b y all the individuals: 1) u j =u H (that is, the reserv ation utilit y of agen t j is equal to u H ) In this case the problem the principal has to solv e is 29 : 8 > < > : t H iT + 2 t H iT t H jT =u M t H jT + 1 t H jT t H iT =u H The solution to this simple system giv es: 8 > < > : t H iT = u M (1 + 1 ) + 2 u H 1 + 1 + 2 t H jT = u H (1 + 2 ) + 1 u M 1 + 1 + 2 that is 8 > < > : t H iT =u M + 2 1 + 1 + 2 t H jT =u M + (1 + 2 ) 1 + 1 + 2 Where t H iT :is the w age when the state of the w orld is u j =u H for agen t i when the agen t are together (T ). 2) u j =u L 29 Note that at this stage w e are conjecturing that t i is smaller than t j when u j =u H . Once w e solv e the problem it will b e easy to v erify that this conjecture holds. 60 In this case the participation constrain ts the principal has to matc h are 8 > < > : t L iT + 1 t L iT t L jT =u M t L jT + 2 t L jT t L iT =u L That will ha v e the follo wing solution: 8 > < > : t L iT = u M (1 + 2 ) + 1 u L 1 + 1 + 2 t L jT = u L (1 + 1 ) + 2 u M 1 + 1 + 2 that is 8 > < > : t L iT =u M 1 1 + 1 + 2 t L jT =u M (1 + 1 ) 1 + 1 + 2 The o v erall ex-an te prot for the principal, in this case, will therefore b e: T = 2y 1 2 t H iT +t H jT 1 2 t L iT +t L jT Scenario 2 In this case I will consider separately eac h principal-agen t couple. Moreo v er, I assume that in the case of agen t i the reference w age (that is the w age to whic h he/she compares his/her o wn) will b e giv en b y the exp ected w age of the other agen t, according to the signal i receiv es. Therefore, for the principal-agen t couple i; there are t w o p ossible sub-scenarios, namely , s =s H or s =s L , in whic h the t w o participation constrain ts are giv en b y the follo wing: t H iS + 1 max n t H iS qt H jS + (1q)qt L jS ; 0 o + 2 min n t H iS qt H jS + (1q)qt L jS ; 0 o =u M if s =s H t L iS + 1 max n t L iS qt L jS + (1q)qt H jS ; 0 o + 2 min n t L iS qt L jS + (1q)qt H jS ; 0 o =u M if s =s L where t H iS : transfer to agen t i, when he/she receiv es the signal s H , when the t w o agen ts are separated (S ): Consider no w the principal-agen t couple j , in this case the t w o sub-scenarios are giv en b y agen t j observing his/her o wn reserv ation utilit y . By Ba y es rule assuming Pr (s =s H ) = Pr (s =s L ) = 1 2 : Pr (s H ju j =u H ) = Pr (s L ju j =u L ) =q 61 Therefore the participation constrain ts for agen t j are giv en b y: t H jS + 1 max n t H jS qt H iS + (1q)qt L iS ; 0 o + 2 min n t H jS qt H iS + (1q)qt L iS ; 0 o =u H if u j =u H t L jS + 1 max n t L jS qt L iS + (1q)qt H iS ; 0 o + 2 min n t L jS qt L iS + (1q)qt H iS ; 0 o =u L if u j =u L Therefore w e ha v e a system of four equation in four unkno wns: 8 > > > > > > > < > > > > > > > : t H iS + 1 max n t H iS qt H jS + (1q)qt L jS ; 0 o + 2 min n t H iS qt H jS + (1q)qt L jS ; 0 o =u M ifs =s H t L iS + 1 max n t L iS qt L jS + (1q)qt H jS ; 0 o + 2 min n t L iS qt L jS + (1q)qt H jS ; 0 o =u M ifs =s L t H jS + 1 max n t H jS qt H iS + (1q)qt L iS ; 0 o + 2 min n t H jS qt H iS + (1q)qt L iS ; 0 o =u H ifu j =u H t L jS + 1 max n t L jS qt L iS + (1q)qt H iS ; 0 o + 2 min n t L jS qt L iS + (1q)qt H iS ; 0 o =u L ifu j =u L (39) And the o v erall exp ected prot is giv en b y: S = 2y 1 2 t H iS +t H jS 1 2 t L iS +t L jS Consider no w (39), eac h equation, on the left hand side, is formed b y t w o terms. The rst one is the monetary transfer receiv ed b y the agen t and the second is the relativ e w ealth p osition of the agen t, m ultiplied b y a co ecien t (either 1 or 2 ). The co ecien t m ultiplying the second term is a function of the sign of this term, hence, it is imp ortan t to v erify under what conditions, the co ecien ts agree with the sign of the second term. Pr op osition 6. Ther e exists a q 2 1 2 ; 1 such that (i) if q<q then S T = ( 2 1 ) h (1q) 4 2 q 1 2 (1 2 ) 2 + (1 2 ) 2 + 1 (1 + 2 2 ) + 2 (1 + 2 ) i G ( 1 ; 2 ;q) (1 + 1 + 2 ) > 0 wher e G (:) is a p olynomial function always p ositive on the supp ort of the function (ii) if qq then 62 S T = 1 2 ( 2 1 ) (1q) (1 + 1 + 2 ) (1 +q 1 +q 2 ) > 0 Pr o of of Pr op osition 6. See App endix Prot Comparison W e can no w compare the exp ected prot in the t w o scenarios, and see whic h organizational form deliv ers the highest com bined exp ected w ealth to the principal(s). In b oth cases (q q or q < q ) under Scenario 2, the principal(s) alw a ys attain(s) a higher exp ected prot b y separating the t w o agen ts. There are t w o cases in whic h there is no dierence b et w een the o v erall exp ected prots in the t w o organizational forms. The rst case is when 1 = 2 , in fact, under this circumstance, the extra- comp ensation that the principal has to pa y to the agen t that receiv es the lo w est transfer, is p erfectly comp ensated b y the money he can sa v e for pa ying less the other agen t (the one who has the highest w age). The second circumstance, is when q = 1, that is when the signal is p erfectly informativ e, and therefore w e are in a situation equiv alen t to b oth agen t b eing able to observ e eac h other’s reserv ation utilit y (of course in this last instance w e will ha v e q>q ). 3.2 Case 2: T wo Agents, Both with Uncertain Reserv ation Utility I will consider no w the case of t w o agen ts that ha v e b oth ex an te uncertain reser- v ation utilit y . So, b oth of them can ha v e a reserv ation utilit y of u H or u L with probabilit y 1 2 eac h, assume further that the t w o reserv ation utilities are indep enden t. Once more, I will consider t w o dieren t scenarios, the rst one where the t w o agen ts 63 can p erfectly observ e their p eer’s reserv ation utilit y , and the second one where the t w o agen ts only receiv e a signal ab out their p eer’s reserv ation utilit y . Scenario 1 In this scenario the system of participation constrain ts for agen t i, is giv en b y: 8 > > > > > > > < > > > > > > > : t HH iT =u H t LL iT =u L t HL iT + 1 t HL iT t LH jT =u H t LH iT + 2 t LH iT t HL jT =u L And the equilibrium w ages are giv en b y: 8 > > > > > > > > < > > > > > > > > : t HH iT =u H t LL iT =u L t HL iT = 1 u L + (1 + 2 )u H 1 + 1 + 2 t LH iT = 2 u H + (1 + 1 )u L 1 + 1 + 2 The equilibrium comp ensation sc hedule for agen t j will b e the same. Scenario 2 In this case the t w o agen ts can not observ e their p eer’s reserv ation utilit y , but they receiv e a signal ab out it, just lik e in the case b efore. 8 > > > > > > > < > > > > > > > : t HH iS + 1 n t HH iS h q h qt HH jS + (1q)t HL jL i + (1q) h qt LH jS + (1q)t LL jS iio =u H if s =s H , u i =u H t HL iS + 1 n t HL iS h q h qt HH jS + (1q)t HL jL i + (1q) h qt LH jS + (1q)t LL jS iio =u H if s =s L , u i =u H t LH iS + 2 n t LH iS h q h qt HL jS + (1q)t HH jL i + (1q) h qt LL jS + (1q)t LH jS iio =u L if s =s H , u i =u L t LL iS + 2 n t LL iS h q h qt LL jS + (1q)t LH jL i + (1q) h qt HL jS + (1q)t HH jS iio =u L if s =s L , u i =u L (40) Since the t w o agen ts ha v e the same distribution of b oth reserv ation utilities and signals, agen t j participation constrain ts are giv en b y the same set of equations, and 64 his/her equilibrium comp ensation will b e just the same as the one receiv ed b y agen t i. It is also apparen t that I am conjecturing the follo wing: 8 > > > > > > > < > > > > > > > : t HH iS q qt HH jS + (1q)t HL jL + (1q) qt LH jS + (1q)t LL jS > 0 t HL iS q qt HH jS + (1q)t HL jL + (1q) qt LH jS + (1q)t LL jS > 0 t LH iS q qt HL jS + (1q)t HH jL + (1q) qt LL jS + (1q)t LH jS < 0 t LL iS q qt LL jS + (1q)t LH jL + (1q) qt HL jS + (1q)t HH jS < 0 It will b e easy to v erify that the ab o v e conditions will hold, once w e solv e system (40). The solution for the optimal w ages is once more cum b ersome and do es not add an y particular insigh t. Prot Comparison Subtracting the ex-an te exp ected prot in Scenario 2 from the ex-an te exp ected prot in Scenario 1, and dening =u H u L , w e obtain the follo wing: S T = q (1q) ( 2 1 ) (q 1)q [4 2 1 (1 + 1 ) + 8 1 2 ] 1 + 2 + 2 1 + 2 2 [(q 1)q4 1 2 (1 + 1 + 2 )] [2q (q 1) ( 1 + 2 ) 1] (1 + 1 + 2 ) < 0 Dieren tly from what w e found in the previous case, no w the optimal c hoice is not to separate the t w o agen ts, since this w ould lead to a reduction of the ex-an te exp ected o v erall prot for the principal(s). Similarly to what w e observ ed in Case 1 the dierence in the exp ected prots v anishes whenq = 1 (that is when the signal is p erfectly informativ e) or when 1 = 2 . 3.3 Case 1 vs. Case 2 Comparing the results obtained in Case 1 and Case 2, this mo del pro vides a prediction of aggregation or separation of agen ts, based on: - the distribution of their outside options 65 - the information they ha v e relativ e to their (and their p eers’) outside options. The reason wh y in the t w o cases w e obtain opp osite optimal organizational forms, is due to what can b e called the cost of asymmetry . One of the basic features of the relativ e w ealth preferences is that asymmetry in comp ensation is costly for a risk neutral and self concerned principal(s). This cost originates from the fact that 1 < 2 . In fact, should these t w o parameters b e equal (i.e. 1 = 2 ), in presence of asymmetry of rem uneration, the money the principal can sa v e on the highly-paid agen t p erfectly osets the money the principal has to a w ard to the lo w-paid agen t, therefore, the exp ected comp ensation cost will alw a ys b e giv en b y u i +u j . When 1 < 2 , an y dierence in rem uneration, mak es the o v erall comp ensation cost raise. In fact, simplifying the problem, calling d the dierence b et w een agen ts’ w ages, the principal will sa v e, in order to matc h the participation constrain t, 1 d for the comp ensation of the highly paid agen t, and will b ear a cost of 2 d for the comp ensation of the lo w- paid agen t. The o v erall cost originating b y the presence of comp ensation inequit y is, therefore, d ( 2 1 )> 0. Keeping this idea in mind, in Case 1 there are t w o p ossible states of the w orld, namely , one state when agen t j has a lo w er reserv ation utilit y than agen t i and one state where agen t j has a higher reserv ation utilit y . In this case, if the agen ts w ere able to observ e eac h other reserv ation utilit y , an asymmetry in pa ymen t w ould b e una v oidable. Making the information ab out eac h other outside option more opaque, w ould smo oth out this inequit y lo w ering the costs emerging from w age inequalit y . On the other hand, in the case of t w o agen t ha ving the same v ariance of the distribution of their reserv ation utilities, there are four p ossible states of the w orld for eac h individual, in t w o of whic h, the agen ts ha v e p erfectly aligned reserv ation utilities. In these last t w o cases, the cost induced b y the non observ abilit y (asymmetry cost) more than osets the gain obtained in the other cases. 66 3.4 A Short Discussion of the Utility F unction There is one relev an t p oin t that, ev en in this simple case, deserv es to b e discussed. It can b e argued that the w a y I pro ceeded ab o v e it is not correct, in fact, in analogy with the exp ected utilit y theory , the utilit y for an agen t when facing an uncertain w age of his p eer migh t b e describ ed b y: U i =t i +E [ 1 maxft i t j ; 0g + 2 minft i t j ; 0g] (41) Instead of U i =t i + 1 maxft i E [t j ] ; 0g + 2 minft i E [t j ] ; 0g (42) Under (41) the conclusions of the previous section, migh t b e completely rev ersed. The app eal of (41) is in the parallelism with the V on Neuman Morgenstern exp ected utilit y theory . In this theory , c hoices are ordered according to the (discoun ted) ex- p ected utilit y that the individual will obtain in unkno wn state of the w orld. But at some p oin t in the future the uncertain t y will b e resolv ed, and the agen t will observ e what is the actual state of the w orld o ccurring. In this exercise, the reserv ation utilit y of agen t j will nev er b e in agen t i’s information set. Moreo v er, the relativ e preference concept, requires a unique reference p oin t (the w age of the p eer or some exp ectation of it) as it is in (42). An argumen t fa v orable to (41) could b e made if agen t i w ould b e able to observ e j ’s w age at future p oin t in time, and therefore the uncertain t y w ould b e resolv ed. Ov erall, the sp ecication of (42) seems the most consisten t with the situation b eing mo deled. 67 3.5 Conclusions and F uture W ork The ab o v e discussion sho ws ho w this mo del could pro vide a b eha vioral explanation for the optimalit y of w age secrecy p olicies or the opp ortunit y of putting the agen ts in separate organizations (spin os). Also, w e could end up with a mo del sho wing that the disclosure and the information circulating ab out executiv e comp ensation migh t push up their w ages instead of lo w ering them. The steps I in tend to tak e in the immediate future are: 1) Consider the mo del where b oth agen ts ha v e imp erfect information ab out their p eer’s reserv ation utilit y and ha v e dieren t v ariance of their reserv ation utilities. 2) Consider the case in whic h b oth agen ts do not kno w exactly what their reser- v ation utilit y is, they receiv e a signal ab out it, and the signal receiv ed b y their p eer also con v eys information ab out their o wn reserv ation utilit y . 68 A References A dams, R. B., F erreira, D., (2008). W omen in the b oardro om and their impact on go v ernance and p erformance. Journal of Financial Ec onomics. F orthcoming. Aggarw al, R. K., Sam wic k, A. A., 1999. "Executiv e Comp ensation, Strategic Com- p etition, and Relativ e P erformance Ev aluation: Theory and Evidence". Journal of Financ e . V ol 54, 1999-2043. Aggarw al, R. K., Sam wic k, A. A., 1999. "The Other Side of the T rade-o: the Impact of Risk on Executiv e Comp ensation". Journal of Politic al Ec onomy . V ol 107, 65-105. Ak erlof, G., Y ellen, J., 1990. "The F air W age Hyp othesis and Unemplo ymen t". Quar- terly Journal of Ec onomics . V ol 105, 255-283. Alpizar, F., Carlsson, F., Johansson-Stenman, O., 2005. "Ho w Muc h Do W e Care Ab out Absolute V ersus Relativ e Income and Consumption?". Journal of Ec onomic Behavior and Or ganization . V ol 56, 405-421. Andreoni, J., V esterlund, L., 2001. Whic h is the F air Sex? Gender Dierences in Altruism. The Quarterly Journal of Ec onomics. V ol. 116, 293-312. Ary a, A., Mittendorf, B., (2005). Oering Sto c k Option to Gauge Managerial T al- en t. Journal of A ccoun ting and Economics. V ol. 40, 189-210. Bab enk o I., Lemmon, M., T serluk evic h, Y., 2008. Emplo y ee Sto c k Option, Financing Constrain t and Real In v estmen t. W orking pap er. Bandiera, O., Barank a y , I., Rasul, I., 2005. " So cial Preferences and the Resp onse to Incen tiv es: Evidence from P ersonnel Data". Quarterly Journal of Ec onomics . V ol 120, 917-962. Bartling, B., 2008. "Relativ e P erformance or T eam Ev aluation? Optimal Con tracts for Other-Regarding Agen ts". W orking p ap er . Bolton, G. E., Katok, E., 1995. An exp erimen tal test for gender dierences in b enecen t b eha vior. Ec onomic L etters. V ol 48, 287-292. Bushman, R. M., Indejejikian, R. J., Smith, A., 1995. "Aggregate P erformance Mea- sures in Business Unit Manager Comp ensation: The Role of In trarm In terdep en- dencies". Journal of A c c ounting R ese ar ch . V ol 33, 101-128. Camerer, C. F., F ehr, E., 2003. Measuring So cial Norms and Preferences using Ex- p erimen tal Games: A Guide for So cial Scien tists. in F oundation of Human So ciality: Exp erimental and Ethno gr aphic Evidenc e fr om 15 Smal l-sc ale So cieties . 69 Charnes, G., 2004. "A ttribution and Recipro cit y in an Exp erimen tal Lab or Mark et". Journal of L ab or Ec onomics . V ol 22, 665-688. Charnes, G., Kuhn, P ., 2007. "Do es P a y Inequalit y Aect W ork er Eort? Exp eri- men tal Evidence". Journal of L ab or Ec onomics . V ol 25, 693-723. Clark, A. E. ,Osw ald, A. J., 1998. "Comparison Conca v e Utilit y and F ollo wing Be- ha viour in So cial and Economic Settings". Journal of Public Ec onomics . V ol 70, 133-155. Core, J. E. ,Gua y , W. R., 2001. "Sto c k Option Plans for non-executiv e emplo y ees". Journal of Financial Ec onomics . V ol 61, 253-287. Englmaier,F. , W am bac h, A., 2006. "Optimal Incen tiv e Con tracts under Inequit y A v ersion". W orking Pap er . Easterlin, R., A., 1995. "Will raising the incomes of all increase the happiness of all?". Journal of Ec onomic Behavior and Or ganization . V ol 27, 35-47. Ec k el C. C., Grossman, P . J., 1998. "Are W omen Less Selsh Than Men?: Evidence from Dictator Exp erimen ts". The Ec onomic Journal. V ol 108, 726-735. F ehr, E., F alk, A., 1998. W age rigidities in a comp etitiv e incomplete con tracts mark et. Journal of Politic al Ec onomy. V ol. 107, 106-134. F ehr, E., Kirc hsteiger, G., Riedl, A., 1996. In v olun tary Unemplo ymen t and Non- Comp ensating W age Dieren tials in an Exp erimen tal Lab our Mark et. The Ec onomic Journal. V ol. 106, 106-121. F ehr, E.,Sc hmidt, K. M., 1999. "A Theory of F airness, Comp etition and Co op era- tion". Quarterly Journal of Ec onomics . V ol 114, 817-868. F ersh tman C., Hvide, H. K., W eiss Y., 2003. "A Beha vioral explanation of the Rel- ativ e P erformance Ev aluation Puzzle". Annales d’e c onomie et de statistique . 71-72, 349-361. F ersh tman C., Hvide, H. K., W eiss Y., 2005. "Cultural Div ersit y , Status Concerns and the Organization of W ork". R ese ar ch in L ab or Ec onomics . F rank, R. H., 1984. Are W ork ers P aid their Marginal Pro ducts?. Americ an Ec o- nomic R eview . V ol. 74, 549-571. F rank, R. H., 1984. In terdep enden t Preferences and the Comp etitiv e W age Struc- ture. R and Journal of Ec onomics . V ol. 15, 510-520. Hall, B. J., Murph y , K. J., 2003. "The T rouble with Sto c k Options". Journal of Ec onomic Persp e ctives . V ol 17, 49-70. 70 Holmstrom, B., 1979. Moral Hazard and Observ abilit y. Bel l Journal of Ec onomics . V ol. 10, 74-91. Holmstrom, B., 1982 "Moral Hazard in T eams". Bel l Journal of Ec onomics . V ol 13, 324-340. Holt, C. A., Laury , S. K., 2002. Risk A v ersion and Incen tiv e Eects. The Americ an Ec onomic R eview . V ol 92, 1644-1655. Kedia, S., Ra jgopal, S., 2008. "Neigh b orho o d Matters: The Impact of Lo cation on Broad Based Sto c k Option Plans". Journal of Financial Ec onomics . F orthcoming. K oszegi, B., Rabin, M., 2006. Amo del of Reference-Dep enden t Preferences. Quar- terly Journal of Ec onomics . V ol 121, 1133-1165. Miglietta, S., 2009. "Incen tiv e Con tracts and Status-Concerned Agen ts". W orking Pap er. Murph y , K. J., 1999. "Executiv e Comp ensation". Handb o ok of L ab or Ec onomics . V ol 3. North Holland. Oy er, P ., 2004. "Wh y Do Firms Use Incen tiv es that Ha v e No Incen tiv e Eects?". Journal of Financ e . 59, 1619-1640. Oy er, P ., Sc haefer, S., 2005. "Wh y do Some Firms Giv e Sto c k Options to All Em- plo y ees? An Empirical Examination of Alternativ e Theories". Journal of Financial Ec onomics . V ol 76, 99-133. Sha v ell, S., 1979. Risk Sharing and Incen tiv es in the Principal and Agen t Relation- ship. Bel l Journal of Ec onomics . V ol. 10, 55-73. Sc h ub ert, R., Bro wn, M., Gysler, M., Brac hinger, H. W., 1999. Financial Decision- Making: Are W omen Really More Risk-A v erse?. The Americ an Ec onomic R eview. V ol. 89, 381 -385. 71 A Appendix A: Proof of Proposition 1 I will rst sho w that if agen t C preferences are represen ted b y (2) and if she is matc hed with an agen t D who can receiv e a pa y o as in (3), then C will prefer to receiv e a pa y o that is p ositiv ely correlated with agen t D’s pa y o rather than receiv e a riskless pa ymen t with same exp ected v alue. Without loss of generalit y , assume that the participation for the agen t has no cost. If agen t C receiv es a risk free pa y o equal to t, then her exp ected utilit y will b e: U C ( t;t D ) =u C ( t) +p C g tt H D + (1p) C g tt L D Consider no w an alternativ e pa ymen t t C suc h that t C = 8 > > < > > : t + p if D receives t H D t 1p if D receives t L D where > 0 and 1>p> 0. The exp ected utilit y for agen t C is no w U C (t C ;t D ) =pu C t + p + (1p)u C t 1p +p C g t + p t H D + (1p) C g t 1p t L D Consider no w the dierence b et w een the exp ected utilit y under t and t C : U =U C (t C ;t D )U C ( t;t D ) = p h u C t + p + C g t + p t H D C g tt H D i + + (1p) h u C t 1p + C g t 1p t L D C g tt L D i u C ( t) appro ximating the ab o v e expression, for small v alues of U C g 0 tt H D g 0 tt L D > 0 whic h follo ws from the conca vit y of g(). The pro of for p oin t 2 can b e obtained b y follo wing the same steps as in the pro of of p oin t 1, and b y c ho osing < 0. In this case the rst-order appro ximation of dierence in the exp ected utilit y , mo ving from a risk free pa y o to a mo derately random pa y o that is negativ ely correlated with the pa y o of agen t D is giv en b y 72 U C g 0 tt H D g 0 tt L D < 0. While the rst order eect for a self-concerned agen t w ould b e just 0. The uniqueness of the agen t pa y o that minimizes the exp ense for a h yp othetical risk neutral and self concerned principal, follo ws from the solution of the follo wing problem 8 > > > > > > < > > > > > > : min pt H C + (1p)t L C s:t: p u t H C + C g t H C t H D + (1p) u t L C + C g t L C t L D U where U is the reserv ation utilit y of the agen t. First of all, notice that the par- ticipation constrain t has to b e binding otherwise for the principal is alw a ys p ossible to reduce t H C or t L C and mak e the participation constrain bind. Giv en the binding condition, w e can compute the follo wing implicit deriv ativ e: dt H C dt L C = 1p p u 0 t L C + C g 0 t L C t L D u 0 (t H C ) + C g 0 (t H C t H D ) (43) Applying the c hain rule w e also ha v e d 2 t H C dt L 2 C = 1p p @ @t L C u 0 t L C + C g 0 t L C t L D 1 u 0 (t H C )+g 0 (t H C t H D ) = 1p p u 00 (t L C )+ C g 00 (t L C t L D ) u 0 (t H C )+ C g 0 (t H C t H D ) + u 0 t L C + C g 0 t L C t L D @ @t L C 1 u 0 (t H C )+ C g 0 (t H C t H D ) Substituting (43) in to the ab o v e, w e nally obtain d 2 t H C dt L 2 C = 1p p u 00 (t L C )+ C g 00 (t L C t L D ) u 0 (t H C )+ C g 0 (t H C t H D ) + (u 0 (t L C )+ C g 0 (t L C t L D )) 2 u 0 (t H C )+ C g 0 (t H C t H D ) u 00 (t H C )+ C g 00 (t H C t H D ) (u 0 (t H C )+ C g 0 (t H C t H D )) 2 1p p > 0 so dt H C dt L C is monotone. Notice that as long as dt H C dt L C > 1p p it is con v enien t for the principal to decrease t L C and increase t H C . While if dt H C dt L C < 1p p , it is con v enien t for the principal to decrease t H C and increase t L C . The optimal pa y o t C for the principal, giv en the pa y o for agen t D, will b e reac hed when dt H C dt L C = 1p p . The uniqueness of t C follo ws from d 2 t H C dt L 2 C > 0. F rom the condition dt H C dt L C = 1p p , follo ws that 1p p u 0 (t L C )+ C g 0 (t L C t L D ) u 0 (t H C )+ C g 0 (t H C t H D ) = 1p p 73 that is u 0 (t L C )+ C g 0 (t L C t L D ) u 0 (t H C )+ C g 0 (t H C t H D ) = 1 rearranging: u 0 (t H C )u 0 (t L C ) [g 0 (t L C t L D )g 0 (t H C t H D )] = C 74 Appendix B: Proof of Proposition 2 P oin t 1. can b e pro v ed b y considering the stand-alone IC condition. Agen t D will c ho ose to exert eort e i if 8 > > < > > : u t H D u t L D c i c j p i p j 8j6=i if p i >p j u t H D u t L D c i c j p i p j 8j6=i if p i <p j (44) When agen t D is matc hed with an agen t C, the incen tiv e compatibilit y condition b ecomes: 8 > > < > > : u t H D u t L D + D g t H D t H C g t L D t L C c i c j p i p j 8j6=i if p i >p j u t H D u t L D + D g t H D t H C g t L D t L C c i c j p i p j 8j6=i if p i <p j (45) Since t H D t H C > t L D t L C , g t H D t g t L D t > 0. Therefore, while the IC conditions in the rst inequalit y of (44) will b e still holding in the rst inequalit y of (45), some of the IC condition represen ted in the second inequalit y of (44), migh t b e violated. This last circumstance w ould induce the c hoice of a higher eort. P oin t 2. can b e pro v ed in a similar fashion, assume that agen t C receiv es a risk- free pa y o t, then an agen t D will c ho ose an eort lev el e i if the IC conditions in (45) are resp ected once w e set t H C =t L C = t, that is 8 > > < > > : u t H D u t L D + D g t H D t g t L D t c i c j p i p j 8j6=i if p i >p j u t H D u t L D + D g t H D t g t L D t c i c j p i p j 8j6=i if p i <p j (46) Assume no w that agen t C c ho oses a pa y o t C = t H C ;t L C p ositiv ely correlated with agen t D’s pa y o, suc h that t H C > t>t L C , then 75 g t H D t g t L D t >g t H D t H C g t L D t L C (47) Giv en (47), the set of conditions represen ted b y the last inequalit y in (46) will still hold. On the other hand if the left-hand side of (47) is larger enough than the righ t-hand side, than some of the conditions in the set of conditions represen ted b y the rst inequalit y in (46) can b e violated. This circumstance w ould imply the c hoice of a lo w er lev el of eort 76 Appendix C: Proof of Proposition 6 The strategy to pro v e this prop osition is to conjecture a solution and v erify it later. Let us conjecture that in equilibrium the participation constrain ts are giv en b y: 8 > > > > > > > < > > > > > > > : t S iH + 2 t S iH qt S jH + (1q)qt S jL =u M ifs =s H (a) t S iL + 1 t S iL qt S jL + (1q)qt S jH =u M if s =s L (b) t S jH + 1 t S jH qt S iH + (1q)qt S iL =u H if u j =u H (c) t S jL + 2 t S jL qt S iL + (1q)qt S iH =u L if u j =u L (d) Equations (a), (c) and (d), can b e sho wn to alw a ys hold true. Equation (b) do es not. Plugging in (b) the solutions w ages obtained b y solving the ab o v e system, and substituting 1 = 2 h, where h2 (0; 2 ], the term t S iL qt S jL + (1q)qt S jH in equation (b) is giv en b y: (4q 2 qh 2 2 + 2q 2q 2 h + 2 2 q 2 h 1) (2q 2 + 4 2 2 q 4q 2 h 4 2 4 2 2 + 4 2 h 1qh + 2h) (2q 2 + 1qh) (e) in order for (e) to b e p ositiv e it m ust b e the case that: q> 1 4 (h 2) (1 + 2 2 ) + q (1 + 2 2 ) (2 2 (4 +h 2 ) + (2h) 2 ) 2 h =q q is clearly a function of 2 and h, and it is increasing in b oth these parameters. The only thing w e ha v e left to pro v e is that q 2 1 2 ; 1 . Kno wing that q is a con tin uous monotone function of and h, to ha v e the t w o extremes of the v alue range q can tak e, w e rst compute the limit of q for h! 0, and the v alue tak en b y q for h = 2 = 1. lim h!0 1 4 (h 2) (1 + 2 2 ) + q (1 + 2 2 ) (2 2 (4 +h 2 ) + (2h) 2 ) 2 h = lim h!0 1 4 @ @h (h 2) (1 + 2 2 ) + q (1 + 2 2 ) (2 2 (4 +h 2 ) + (2h) 2 ) @ @h 2 h = 1 2 77 and q ( 2 = 1;h = 1)' 0:68. Hence, if q q equation (b) will hold true in equilibrium. If q < q the system of participation constrain ts will b e, in equilibrium: 8 > > > > > > > < > > > > > > > : t S iH + 2 t S iH qt S jH + (1q)qt S jL =u M ifs =s H t S iL + 2 t S iL qt S jL + (1q)qt S jH =u M if s =s L t S jH + 1 t S jH qt S iH + (1q)qt S iL =u H if u j =u H t S jL + 2 t S jL qt S iL + (1q)qt S iH =u L if u j =u L The t w o v alues of the prot dieren tial ( S T ) will follo w from the t w o dieren t systems of participation constrain ts 78
Abstract (if available)
Abstract
In this work I show that if risk-averse agents prefer both to be richer in absolute terms and to be richer than their peers (relative-wealth concerns), then 1) they will prefer positive correlation between their payoffs and the payoffs of other agents, and 2) they will be averse to negative correlation between payoffs. I test these theoretical predictions in a laboratory experiment. I find that subjects prefer positively correlated payoffs over risk-free and negatively correlated payoffs. Furthermore, subjects who by observing other participants' payoffs signal stronger relative-wealth concerns, also show stronger aversion to negatively correlated payoffs. Women appear to be concerned about other agents' payoffs more than men. This novel evidence has implications that help explain why firms apparently use profit-sharing and broad-based incentives contracts too extensively, and why Relative Performance Evaluation (RPE) contracts are scarcely used in common compensation practice. Further, I show that in the presence of relative-wealth concerns 1) it is optimal for a principal to offer a compensation schedule linked to the overall firm or team performance, even when each agent's performance is observable, contractible and independent on the actions taken by his/her colleagues, 2) Relative Performance Evaluation is less desirable for the principal. Finally I investigate under what conditions it is optimal for a self-concerned principal to enforce a wage secrecy policy within an organization.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Incorporating social preferences into incentive system design
PDF
Essays in behavioral and entrepreneurial finance
PDF
Essays in tail risks
PDF
Empirical analysis of factors driving stock options grants and firms volatility
PDF
Essays on delegated portfolio management under market imperfections
PDF
Does mandatory adoption of international financial reporting standards decrease the voting premium for dual-class shares: theory and evidence
Asset Metadata
Creator
Miglietta, Salvatore
(author)
Core Title
Incentives and relative-wealth concerns: theory and evidence
School
Marshall School of Business
Degree
Doctor of Philosophy
Degree Program
Business Administration
Publication Date
05/05/2010
Defense Date
03/09/2010
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
employee compensation,executive compensation,experimental economics,incentive contracts,OAI-PMH Harvest,relative-wealth concerns
Place Name
California
(states)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Murphy, Kevin J. (
committee chair
), Carrillo, Juan D. (
committee member
), Ozbas, Oguzhan (
committee member
), Rantakari, Heikki (
committee member
), Zapatero, Fernando (
committee member
)
Creator Email
migliett@usc.edu,salvo.miglietta@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m2986
Unique identifier
UC1329950
Identifier
etd-Miglietta-3673 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-310954 (legacy record id),usctheses-m2986 (legacy record id)
Legacy Identifier
etd-Miglietta-3673.pdf
Dmrecord
310954
Document Type
Dissertation
Rights
Miglietta, Salvatore
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
employee compensation
executive compensation
experimental economics
incentive contracts
relative-wealth concerns