Incentives and peer effects in the workplace: On the impact of envy and wage transparency on organizational design

K agl, Jenny; Ben al, Benjamin; Sa aynikoo, Peymaneh
A icle — Published Ve sion
Incen i es and pee e ec s in he wo kplace: On he
impac o en y and wage anspa ency on o ganiza ional
design
Economic Theo y
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: K agl, Jenny; Ben al, Benjamin; Sa aynikoo, Peymaneh (2025) : Incen i es and
pee e ec s in he wo kplace: On he impac o en y and wage anspa ency on o ganiza ional
design, Economic Theo y, ISSN 1432-0479, Sp inge , Be lin, Heidelbe g, Vol. 80, Iss. 1, pp. 87-124,
h ps://doi.o g/10.1007/s00199-024-01622-4
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Economic Theo y (2025) 80:87–124
h ps://doi.o g/10.1007/s00199-024-01622-4
RESEARCH ARTICLE
Incen i es and pee e ec s in he wo kplace: On he impac
o en y and wage anspa ency on o ganiza ional design
Jenny K agl1·Benjamin Ben al2·Peymaneh Sa aynikoo1
Recei ed: 25 Oc obe 2022 / Accep ed: 3 No embe 2024 / Published online: 20 Janua y 2025
© The Au ho (s) 2025
Abs ac
The a icle is conce ned wi h unde s anding he impac o social p e e ences and wage
anspa encyon heop imalo ganiza ionaldesigno i ms.Weconside amo al-haza d
en i onmen wi h en ious wo ke s. The in eg a ion o wo ke s in one o ganiza ional
uni yields p oduc i e complemen a i ies bu also igge s income compa isons and
en y. Sepa a ing wo ke s ules ou social compa ison bu also p ecludes p oduc i e
syne gies. Ins ead, he i m may impose a wage-sec ecy policy o keep he la e while
a oiding he o me . We show ha p oduc i e syne gies and en y a e subs i u es unde
unlimi ed liabili y when wages a e anspa en while hey become complemen s when
wo ke s ea n en s. As a esul , i ms a e much mo e likely o in eg a e wo ke s when
he la e a e p o ec ed by limi ed liabili y. Fu he mo e, e en when i ms can impose
wage sec ecy, hey p e e no o as long as wo ke s a e no oo en ious. In bo h cases,
i ms exploi he incen i e e ec o pay inequali y o aise p oduc i e e o s and
p o i s. Fo he same eason, i ms may delibe a ely es ablish pay inequali y by op ing
o indi idual pe o mance pay a he han g oup bonuses. In his sense, anspa ency
This pape ex ends he hi d chap e o Peymaneh Sa aynikoo’s disse a ion a he EBS Uni e si ä ü
Wi scha und Rech , Wiesbaden. We a e g a e ul o he co-edi o Da id J. Coope and wo anonymous
e e ees o e y help ul commen s on p e ious e sions o he pape . We also hank Simon Da o, M djan
M. Mladjan, Dana Sisak, and Ha ey Up on o aluable ema ks and discussions. We a e u he g a e ul
o eedback ecei ed a he Annual Mee ings o he Socie y o Ins i u ional & O ganiza ional Economics
(SIOE), he Copenhagen Ne wo k o Expe imen al Economis s (CNEE), he Colloquium on Pe sonnel
Economics (COPE), he Eu opean Associa ion o Resea ch in Indus ial Economics (EARIE), he
Ge man Economic Associa ion (Ve ein ü Socialpoli ik), and he Founda ions o U ili y and Risk
Con e ence (FUR).
BJenny K agl
jenny[email p o ec ed]
Benjamin Ben al
[email p o ec ed]
Peymaneh Sa aynikoo
peymaneh.sa [email p o ec ed]
1EBS Uni e si ä ü Wi scha und Rech , EBS Business School, Rheingaus . 1, 65375
Oes ich-Winkel, Ge many
2Depa men o Economics, Uni e si y o Hai a, Hai a, Is ael
123
88 J. K agl e al.
and “sunshine laws” may no be in he sel -in e es o employees, e en mo e so unde
a posi i e minimum wage.
Keywo ds O he - ega ding p e e ences ·Incen i es ·O ganiza ional design ·
In eg a ion ·Sepa a ion ·Inequali y ·T anspa ency ·Wage sec ecy ·En y ·Team ·
Syne gy
JEL Classi ica ions D63 ·D82 ·M52 ·M54
1 In oduc ion
“En y is he g ea le ele : i i canno le el hings up, i will le el hem down.”
Do o hy Saye s (1949: 771)
I is well-es ablished ha people compa e hemsel es o o he s. How such compa -
isons a ec economic ou comes has been examined heo e ically, expe imen ally and
empi ically, a bo h he mac o- and he mic oeconomic le els. In he cu en pape , we
u n o i ms’ op imal o ganiza ional s uc u es and hei a i ude owa ds wage ans-
pa ency and s udy how hese a e a ec ed by he p esence o social p e e ences. Using
an agency model and ocusing on en y as one o he mos ele an mani es a ions o
such p e e ences wi hin i ms, we speci ically conside whe he o ganiza ions p e e o
in eg a e wo ke s in o eams o sepa a e hem in o di e en uni s ins ead. In he o me
case, hey mo eo e ace he ques ion o whe he o en o ce a wage-sec ecy policy
o a he encou age wage anspa ency. Ou esul s demons a e ha he wo issues
a e in e ela ed and ha he op imal choices conce ning hese o ganiza ional aspec s
depend speci ically on whe he o no i ms can exploi en y o inc ease wo ke s’ e o
and gene a e highe p o i s. We show ha , when i ms can ex ac wo ke s’ su plus,
hey may p e e social dis ancing e en in he p esence o p oduc i e syne gies. In s a k
con as , when wo ke s ea n in o ma ional en s, i ms a e likely o in eg a e hem in o
eams and make wages delibe a ely anspa en , he eby gene a ing p o i able pee
e ec s a ising om en y.
Ou pape is mo i a ed by h ee common cha ac e is ics o many wo kplace en i-
onmen s: he p esence o socialcompa isons and en y, hep e alenceo wagesec ecy
ules, and he exis ence o pee e ec s.1Tha social and income compa isons a e ubiq-
ui ous in he o ganiza ional con ex is e idenced o example by Ca d e al. (2012),
Cohne al.(2014),CullenandPe ez-T uglia(2022),andDubee al. (2019). Wi hin his
con ex , i is en y ha has been ound o be o pa icula impo ance (see, e.g., Vecchio
2000,2005; Du y e al. 2008; S e ling and Labianca 2015; Du y e al. 2021).2In his
espec , he managemen li e a u e lis s bo h posi i e and nega i e consequences o
en y o employees and o ganiza ions and sugges s a ious o ganiza ional esponses,
1We p esen a comp ehensi e o e iew o he ela ed li e a u e in Sec .2.
2The me a-analysis by Nunna i and Pozzi (2022) co obo a es he empi ical ele ance o disad an ageous-
inequali y conce ns in game- heo e ic con ex s and expe imen s (see, e.g., Figu e 6).
123
Incen i es and pee e ec s... 89
a ec ing in pa icula he social and physical p oximi y o wo ke s.3Add essing he
nega i e consequences o en y, Obloj and Zenge (2017) no e he impo ance o pee -
p oximi y o he o ma ion o e e ence g oups. In oking he idea o “ou o sigh ,
ou o mind”, hey imply ha spa ial sepa a ion is likely o ule ou social compa -
isons (p. 16). These au ho s obse e ha some big pha ma i ms choose o ou sou ce
esea ch p ojec s a he han in eg a e hem in o de o a oid demo i a ional in e -
nal compa isons o high-powe ed incen i es ha a e common in small R&D s a ups
(p. 16). As ano he me hod o manage en y in he wo kplace, S e ling and Labianca
(2015) sugges , o “mix hings up” (p. 303) by occasionally changing o ice space and
eam assignmen s in an a emp o a oid social compa isons and hei mani es a ions.
Tha en y plays a ole also in he academic con ex is well known (Rome o 2022).
Some imes his becomes isible e en in e ms o o ganiza ional consequences. Fo
example, in 1998, S an o d Uni e si y decided o spli i s an h opology depa men
in o wo uni s as a consequence o long-las ing in e nal s i e. Clea ly, he eason o
he s i e was mul i ace ed, ye as indica ed by he S an o d Magazine, i had “much
o do wi h pe sonali y con lic s, [..] and es e ing disappoin men s,” which we ake he
libe y o in e p e as one mani es a ion o social p e e ences and pe haps en y.4
The second ele an wo kplace ea u e, wage sec ecy no ms, has ecen ly been he
subjec o ex ensi e esea ch and public deba e. The Glassdoo (2017) Global Sala y
T anspa ency Su ey, conduc ed in se e al ad anced OECD coun ies, documen s he
p e alence o sec ecy ules wi hin companies. Acco ding o ha su ey, only abou
one hi d o employees say ha hei company discloses sala ies in e nally. Fu he
e idence on he p ominence o wage sec ecy a ound he wo ld is p esen ed by Cullen
and Pe ez-T uglia (2022). In ac , employmen con ac s equen ly s ipula e clauses
on sala y- ela ed con iden iali y. In he Uni ed S a es, “be ween 2017–2018, nea ly
hal o ull- ime wo ke s epo ed hey we e ei he discou aged o p ohibi ed om
discussing wages and sala ies” (Sun e al. 2021)).5In he ecen pas , howe e , he e
is indica ion ha some companies ac i ely p omo e wage anspa ency ou o hei
own oli ion.6The Uni e si y o Cali o nia oo has made he compensa ion o all i s
employees public as o 2011.7Ano he example is he Whole Foods Ma ke , Inc.,
3The wo possible beha io al esponses o en y a e discussed, among o he s, by an de Ven e al. (2009)
and Tai e al. (2012).
4See he S an o d Magazine: Di ided They S and a h ps://s an o dmag.o g/con en s/di ided- hey-s and
(Janua y/Feb ua y 2000). One o he coau ho s o he cu en pape can a es o a leas h ee simila
inciden s he has wi nessed whe e depa men al eo ganiza ion was clea ly d i en by in e pe sonal and
en y-d i en mo i es.
5In e es ingly, he Glassdoo su ey inds ha , compa ed o men, women a e mo e likely o wo k unde
a pay sec ecy policy and o iola e ha policy. In addi ion, F ench o English wo ke s end o cha mo e
easily abou hei sala y han Ge mans.
6See, e.g., h ps://hb .o g/2016/03/why-keeping-sala ies-a-sec e -may-hu -you -company. P omo ing
wage anspa ency may ei he ake he o m o es ablishing he “ igh o wo ke s o alk” o ac i ely
publishing sala y in o ma ion. In his espec , an in e es ing ecen s udy inds ha he o me app oach
may no be success ul since wo ke s a e s ill hesi an o discuss wages due o adi ional no ms s ipula ing
a “sala y aboo” ( Cullen and Pe ez-T uglia (2018)).
7Fo he UC websi e lis ing wo ke s’ pay, see h ps:// anspa en cali o nia.com/sala ies/uni e si y-o -
cali o nia. Ca d e al. (2012) ha e exploi ed he in oduc ion o wage anspa ency in he UC sys em in hei
analysis o wo ke sa is ac ion.
123
90 J. K agl e al.
which has implemen ed a comple e anspa ency policy.8A he public le el, public
sec o wo ke s in many Eu opean coun ies and ede al employees in he Uni ed S a es
a e paid acco ding o publicly a ailable sala y schemes. Mo eo e , many coun ies
ha e ecen ly unde aken e o s o implemen pay-equali y and an idisc imina ion
laws, he eby indi ec ly enhancing anspa ency. Typically, i ms a e equi ed o epo
da a agg ega ed along gende and e hnic dimensions. In he Uni ed S a es, so-called
“sunshine laws” explici ly p ohibi pay-sec ecy clauses, albei only in less han hal o
hes a es.A u he exampleisGe manywhichpassed heRemune a ionT anspa ency
Ac (2017), en i ling employees o inqui e abou hei pee s’ a e age pay. Sweden has
a long adi ion o maximum anspa ency, whe eby indi idual ax eco ds ha e been
publicly accessible since 1766. Much mo e ecen ly, No way has implemen ed simila
legisla ion in 2001.9
Finally, pee e ec s, cons i u ing he hi d ele an wo kplace ea u e, a ise when
he p esence o pee s has an impac on wo ke beha io and p oduc i i y. A mul i ude
o ield expe imen s in es iga es he mani es a ion o pee e ec s in a ious p oduc i e
en i onmen s such as supe ma ke s, ag icul u al i ms, online labo ma ke s, and he
like. They indica e ha pee e ec s end o inc ease wo ke e o s and p oduc i i y.
Rela ed o he o egoing anspa ency discussion, hese s udies also indica e ha he
eme gence o such pee e ec s depends on he in o ma ional en i onmen , speci ically
he obse abili y o pee s’ ac ions and wages. Acco dingly, pee e ec s may e en
p o ide a kind o a “ ee lunch” o i ms, enabling hem o exploi he associa ed
social incen i es as an al e na i e o mone a y ewa ds (see he li e a u e e iew in
Sec . 2.1).
No wi hs anding he impo ance and in e dependence o all h ee a o emen ioned
wo kplace ea u es, he e iew in Sec .2below es i ies ha he exis ing li e a u e
does no p o ide a comp ehensi e iew allowing o join ly analyze all o hem. To ill
his gap, we p o ide an in eg a ed analy ical amewo k ha embodies all h ee wo k-
place ea u es and hei in e ac ion wi h i ms’ o ganiza ional design. Di e en om
he li e a u e, in ou se ing, he i m can ac i ely choose i s o ganiza ional and in o -
ma ional s uc u e, he eby a ec ing whe he p oduc i e syne gies be ween wo ke s
eme ge and whe he social compa isons a ise. This in eg a ed amewo k allows us
o simul aneously conside he e ec s o i ms’ o ganiza ional a chi ec u e, i s in e -
nal wage- anspa ency policies, and p o ide some insigh s conce ning he no ma i e
e ec s o sunshine laws.
The unde lying o ce in ou en i onmen is en y. In pa icula , i is his social p e -
e ence ha d i es he eme gence o pee e ec s, he in eg a ion o sepa a ion decision,
and he wage- anspa ency o -sec ecy policy. Fo mally, we conside a s ylized mo al-
haza d en i onmen wi h wo en ious wo ke s. Ou pu is gene a ed by he wo ke s’
8The CEO o Whole Foods Ma ke , Inc. is ci ed as saying: “I’m challenged [on sala ies] all he ime. How
come you a e paying his egional p esiden his much, and I’m making his much?’ I ha e o say, ‘Because
ha pe son is mo e aluable. I you accomplish wha his pe son has accomplished, I’ll pay you ha oo.’”
See h ps://hb .o g/2016/03/why-keeping-sala ies-a-sec e -may-hu -you -company.
9Fo he Eu opean coun ies, see h ps://kompe enz-online.a /2018/05/15/lohn anspa enz-im-
in e na ionalen- e gleich/. To iden i y he U.S. s a es, see he map on h ps://www.dol.go /agencies/
wb/equal-pay-p o ec ions. Fu he de ails may be ound in Cullen and Pakzad-Hu son (2023), Foo no e
12. See Pe ez-T uglia (2020) o a sho discussion o anspa ency ules in he Scandina ian coun ies and
Iceland.
123

Incen i es and pee e ec s... 91
non-con ac ible e o . When wo ke s wo k join ly in an in eg a ed uni , ou pu is
u he enhanced h ough p oduc i e syne gies. The employe chooses whe he o in e-
g a e o sepa a e wo ke s, and in he o me case, whe he o impose a wage-sec ecy
ule o , on he con a y, make paymen s public. Wo ke s a e mo i a ed by op imally
designed indi idual bonus con ac s. In de e mining he op imal o ganiza ional a chi-
ec u e, wage- anspa ency policy, and con ac design, we sepa a ely conside wo
scena ios in which ex-pos wages a e ei he cons ained by a lowe bound o no . The
la e case cons i u es unlimi ed wo ke liabili y, whe eby he employe can ex ac
all in o ma ional en s om wo ke s by adjus ing he ixed wage acco dingly. In he
mo e ealis ic scena io whe e wo ke s a e p o ec ed by limi ed liabili y (pe haps a is-
ing om weal h cons ain s, s anda d wages, minimum wages, e c.), he employe is
o ced o lea e in o ma ional en s o he wo ke s.
We ind ha , unde unlimi ed liabili y whe e he employe can ex ac en s om
wo ke s, he p esence o en y inc eases employmen cos s, he eby making p oduc i e
syne gies and en y subs i u es.In ui i ely, exan ewo ke s o mexpec a ionsabou he
ex-pos occu ence o payo inequi y. To induce pa icipa ion, he employe needs o
compensa e hem by an inequi y (en y) p emium o he associa ed disu ili y s emming
om he o he - ega ding na u e o hei p e e ences. In his sense, he wo ke s’ social
p e e ences imply a nega i e pee e ec ha coun e ac s he p oduc i e syne gies.
As a esul , i wages a e anspa en , in eg a ed p oduc ion will be chosen only i
wo ke s a e no oo en ious and p oduc i e syne gies a e su icien ly p onounced.
Imposing wage sec ecy ins ead emo es he cos associa ed wi h social compa isons,
making wo ke in eg a ion he op imal choice. In s a k con as , unde limi ed liabili y,
p oduc i e syne gies and en y become complemen s as long as wo ke s ea n en s.
Speci ically, when wo king join ly unde wage anspa ency, wo ke s inc ease e o o
educe he likelihood o alling behind hei co-wo ke ’s wage ex pos , a consequence
known as he incen i e e ec o en y. This inc eased e o is mani es ed as posi i e
pee e ec s, p o iding he employe a “ ee lunch” in e ms o highe p oduc i e
ou pu and educed in o ma ional en s. Howe e , when en y is in ense, wo ke s’
en y p emia become so la ge ha en s anish.I hen becomes op imal o impose
wage sec ecy, i possible, o o sepa a e he wo ke s, i no , also unde limi ed liabili y.
This also explains why employe s may delibe a ely es ablish pay inequali y by op ing
o indi idual pe o mance pay a he han g oup bonuses.
On he no ma i e side, we conclude ha popula p essu es o anspa ency and
“sunshine laws” do no necessa ily aise wo ke s’ wel a e. In he absence o en s,
en o cing anspa ency may induce i ms o sepa a e wo ke s, he eby o going gains
om posi i e p oduc ion ex e nali ies and bea ing e iciency losses. Al e na i ely, in
he p esence o en s, sunshine laws bene i hose employe s who ailed o ecognize
he p o i able incen i e e ec o wage anspa ency a he expense o wo ke s.The
la e hen ind hemsel es placed in se ings which igge social compa isons and
en y.
By he o egoing indings,ou pape ex endsandp o idesno elinsigh sin o he a -
ious s ands o he li e a u e conce ning he a o emen ioned wo kplace cha ac e is ics.
In pa icula , ou uni ied o mal heo y e eals ha en y is po en ially a key consid-
e a ion a ec ing i ms’ o ganiza ional and in o ma ional design, as has al eady been
indica ed by he managemen li e a u e. Howe e , ou model explici ly demons a es
123
92 J. K agl e al.
ha he impac o en y on he o egoing o ganiza ional dimensions is no s aigh -
o wa d. Speci ically, we a e he i s o show ha whe he wo ke s a e p o ec ed by
limi ed liabili y is decisi e o i ms’ op imal o ganiza ional a chi ec u e and hei a i-
ude owa ds wage anspa ency. In ac , we show ha , unde limi ed liabili y, i ms
may delibe a ely os e income compa isons by o ganiza ionally in eg a ing wo ke s
and ac i ely p omo ing wage anspa ency in o de o bene i om bo h p oduc i e
syne gies as well as in insic wo k incen i es a ising om en y. These mechanisms
p o ide a new explana ion o he eme gence o pee e ec s in he i s place and i ms’
(po en ial) ac i e and conscious ole in manipula ing hem.
The emainde o he pape is s uc u ed as ollows. In he ollowing sec ion, we
p esen li e a u e conce ning he a ious aspec s o he wo kplace en i onmen and
he model. Sec ion3p esen s he heo e ical en i onmen . In Sec .4, we conside , as a
benchma k, he mo al-haza d p oblem unde unlimi ed liabili y. Speci ically, we i s
analyze he wo ke s’ op imiza ion p oblem and hen de i e he op imal incen i e con-
ac s unde wo ke in eg a ion and sepa a ion. The ea e , we cha ac e ize he op imal
o ganiza ional a chi ec u e unde wage anspa ency and hen analyze whe he he la -
e policy is op imal. Sec ion5 u ns o he mo e ealis ic scena io whe e wo ke s a e
p o ec ed by limi ed liabili y. In pa icula , we econside he op imal o ganiza ional
design and discuss he s iking di e ences compa ed o he unlimi ed-liabili y case.
In Sec .6, we p esen se e al ex ensions o ou model conside ing he e ec s o a pos-
i i e minimum wage, impe ec wage sec ecy, and he inclusion o join pe o mance
pay. Mo eo e , we ex end ou model o he b oade speci ica ion o social p e e -
ences de eloped by Cha ness and Rabin (2002), accommoda ing inequali y a e sion
(Feh and Schmid 1999), social-wel a e p e e ences, and e iciency conce ns. Then,
in Sec .7, we discuss some o he simpli ying ea u es o ou model and conside pos-
sible mani es a ions o en y in u he social-p e e ence speci ica ions. Finally, he las
sec ion concludes and p esen s some gene al, socie al, and manage ial implica ions.
2 Li e a u e
2.1 Pee E ec s in he Wo kplace
While pee e ec s span a ious beha io al aspec s (see, e.g., Wel eke 2015), we ocus
he e on ield expe imen s ela ed o p oduc i i y, which is he measu e ele an o ou
s udy. In his con ex , a a ie y o di e en empi ical s udies a e consis en wi h ou
model’s heo e ical p edic ions. Fo example, Mas and Mo e i (2009) used p oduc-
i i y da a on supe ma ke cashie s a a supe ma ke chain. Thei indings indica e
he p esence o posi i e pee e ec s, he ex en o which depends on he equency
o in e ac ion in he wo kplace and, in line wi h ou app oach, on obse abili y,in
hei case o ac ions. Bandie a e al. (2010) iden i y wo ke s’ iends wi hin a U.K.
ag icul u al i m and combine his in o ma ion wi h each wo ke ’s p oduc i i y. In
line wi h ou esul s, hey conclude om he da a ha e en in he absence o p oduc-
i i y ex e nali ies “ i ms can exploi social incen i es as an al e na i e o mone a y
incen i es” (p. 417). In he same ein, using Ge man social-secu i y da a, Co nelis-
sen e al. (2017) iden i ied pee g oups by wo ke s’ occupa ion and hei employe .
123
Incen i es and pee e ec s... 93
Dis inguishing be ween jobs in which mu ual obse a ion and judgmen s a e easy
and hose whe e such compa isons a e mo e di icul , hey ound la ge pee e ec s on
e o , pa icula ly among wo ke s in he o me ype o occupa ions. Co nelissen e
al. (2017, p. 454) emphasize ha i is pee p essu e, a he han knowledge spillo e ,
ha p o ides an incen i e o wo ke s o inc ease hei e o s. Ho on and Zeckhause
(2018) conduc ield expe imen s on Amazon’s online labo ma ke , Mechanical Tu k
(MTu k). By con olling he in o ma ional en i onmen o wo ke s, hey could iden-
i y pee e ec s e en among wo ke s who did no physically in e ac . Mos ele an
o ou heo e ical en i onmen is hei inding ha exposing wo ke s o he ou pu
o hei pee s inc eases hei own e o s. This inding led Ho on and Zeckhause
(2018, pp. 25, 27) o conclude ha “(i)n se ings whe e e o and p oduc i i y a e
igh ly coupled and wo ke s can easily moni o each o he , pee p essu e would seem
o p o ide a kind o ee lunch o he i m.”
2.2 Wage anspa ency
Many s udies in es iga e he impac o he in o ma ional en i onmen , in pa icula
income anspa ency, on wo ke s’ wellbeing and beha io (see, e.g., Pe ez-T uglia
2020). While much o his li e a u e is mo i a ed by “ ai ness” conce ns and he ole
o wage anspa ency in alle ia ing hem (see, e.g., he discussion in Cha ness and
Kuhn 2007) many s udies epo ha wage anspa ency has signi ican beha io al
impac on a ec ed indi iduals. In ac , he e is inc easing e idence ha making wo k-
e s awa e o he wages o hei pee s has posi i e e ec s on e o . Bambe ge and
Belogolo sky (2010) ound his e ec in an expe imen al se ing, using a compu e
ma ching game wi h bonuses paid o success. In ha se ing, pay sec ecy was asso-
cia ed wi h dec eased pe o mance. Hue -Vaughn (2015) designed an expe imen on
MTu k o show ha exposing wo ke s o in o ma ion abou he ea nings o o he s,
who pe o m a simila ask a he same piece a e, inc eased ou pu o he in o med
g oup by abou 10 pe cen . Gao e al. (2021) exploi he na u al expe imen p o-
ided by changes in legisla ion o se e al U.S. s a es, passing explici laws p ohibi ing
wage sec ecy clauses (so-called pay-sec ecy laws). Using a di e ence-in-di e ence
app oach on a la ge sample o i m-yea obse a ions, hey we e able o show ha
(p. 2) “(o)n a e age, i ms headqua e ed in s a es ha ha e adop ed pay sec ecy laws
inc ease hei numbe o pa en s by 17.7% and inc ease hei numbe o pa en ci a ions
by 17.5%, ela i e o i ms headqua e ed in o he s a es.”10 Focusing on se ings wi h
incen i e pay, hese indings a e in line wi h he posi i e pee e ec s iden i ied in ou
model.
In a di e en se ing whe e wages a e ixed and independen o ou pu , Cohn e al.
(2014) ind ha pee s exposed o disad an ageous income inequali y end o eac by
educing e o . Cullen and Pe ez-T uglia (2022) also de ec e o educ ions esul -
ing om ho izon al disad an ageous pay di e ences. A simila e ec is ound in
a ield expe imen by B eza e al. (2017) and also implici ly by Bennedsen e al.
10 Gao e al. (2021) asc ibe he p oduc i i y e ec o inc eased anspa ency o he emo al o disc imina-
o y beha iou s owa ds women and e hnic mino i ies, helping aise he mo al and mo i a ion o scien is s
belonging o hese popula ion g oups.
123
94 J. K agl e al.
(2020) who exploi a na u al expe imen . Despi e his seeming con adic ion o ou
inding, whe eby wage compa isons ha e posi i e e o e ec s, his beha io is ne e -
heless consis en wi h ou p e e ence speci ica ion albei no wi h ou agency model.
Speci ically, he o egoings udies in es iga e hee o e ec so gi en ixed-wagedis-
c epancies. In con as o ou model, hey do no howe e conside incen i e con ac s,
whe e wo ke e o a ec s inal wage paymen s. The dis inc beha io al ou comes
a e due o his basic di e ence. Whe eas he only way o compensa e o disad an a-
geous ixed-wage inequali y is o educe e o , in ou scena io, wo ke s can and will
unde ake e o o educe he likelihood o en y o a ise.
In a e y di e en con ex , Cullen and Pakzad-Hu son (2023) analyze he e ec s
o wage anspa ency in a dynamic gene al-equilib ium ba gaining se ing. In hei
empi ical applica ion, hey ind ha disad an ageous income inequali y e en ually
leads o inc eased employmen cos (see also Cullen 2023). A he pa ial-equilib ium
le el, ou agency model also p edic s inc eased employmen cos , p o ided wo ke s
ecei e no en s.
2.3 Social p e e ences in agency models
Ou heo e ical amewo k is embedded in he p incipal-agen li e a u e in es iga ing
o he - ega ding p e e ences in he i m. In his con ex , se e al s udies ha e ui ully
inco po a ed social-p e e ence ea u es in o classical con ac - heo e ic se ings (see
Köszegi 2014 o a e iew o he esea ch in beha io al con ac heo y). In he mo al-
haza d con ex , much o ha wo k has e isi ed he e ec i eness o di e en ypes
o pe o mance pay in he p esence o o he - ega ding p e e ences, in pa icula en y
o inequi y a e sion in he sense o Feh and Schmid (1999). In hese en i onmen s,
he ocus is ypically on agency ela ionships wi hin i ms, whe e wo ke s compa e
hei income wi h ha o co-wo ke s o hei boss. The exis ing s udies include wo k
on ho izon al and e ical social p e e ences as well as indi idual, join , and ela i e
pe o mance pay. Fo example, Du and Glaze (2008) and Englmaie and Wambach
(2010) examine op imal incen i e con ac s when agen s ca e abou inequali y ela i e
o he p incipal whe eas Demougin e al. (2006) and Neilson and S owe (2010) ocus
on mu ually inequi y a e se o en ious agen s. The impac o he la e p e e ences in
he con ex o ou namen s is analyzed by, e.g., Demougin and Flue (2003), G und
and Sliwka (2005), and Schö ne (2005). Fu he s udies compa e he e iciency o
di e en incen i e egimes o o he - ega ding wo ke s mo e gene ally (e.g., Goel and
Thako 2006;Ba ling 2011). Finally, I oh(2004) p esen s acomp ehensi emodel ha
encompasses a ich se o e ical and ho izon al dis ibu ional income conce ns as
well as a a ie y o con ac s uc u es. O e all, his li e a u e indica es ha bo h en y
and he joy o ou pe o ming make incen i e pay mo e e ec i e while he opposi e
is ue o compassion. Ne e heless, when wo ke s su e addi ional disu ili y due o
hei social p e e ences, i gene ally becomes mo e cos ly o induce pa icipa ion. In
pa icula , an inequi y p emium mus be paid o compensa e wo ke s o he expec ed
disu ili y om pay inequali y. To lowe a iabili y in payo s, p incipals hen ypically
espond by educing he op imal incen i e pay and, consequen ly, con ac s induce
lowe e o , he eby educing ou pu and p o i . Al oge he , his li e a u e ends o
123
Incen i es and pee e ec s... 101
Fig. 1 Op imal O ganiza ional A chi ec u e unde Unlimi ed Liabili y (a) wi hou and (b) wi h P oduc i e
Syne gies
In con as , p oduc i e complemen a i ies pe se mo i a e he employe o induce
highe e o . The combined e ec s o syne gy and inc eased e o shi p o i s unde
in eg a ionupwa dswhilep o i sunde wo ke sepa a ion emain una ec ed,as shown
in panel (b) o γ=1.2. S ill, en y o ces he employe o bea he en y-p emium
cos s. Acco dingly, as long as he in ensi y o en y is no oo high, in eg a ion becomes
supe io o wo ke sepa a ion. Beyond ha c i ical poin (αU(1.2)=0.87), sepa a-
ion domina es as he combined e o and syne gy e ec is no longe su icien o
o e come he agency cos e en hough he induced e o is s ill highe han i is unde
sepa a ion. I is in his sense ha he syne gy ac o γand he wo ke s’ p opensi y o
en y αa e subs i u es wi h ega d o he op imal o ganiza ional design.
4.3.2 Wage sec ecy
In his subsec ion we econside he op imal o ganiza ional a chi ec u e when he
employe can also choose he o ganiza ional policy. The esul is o mally summa ized
by he ollowing co olla y.
Co olla y 2 (Op imal O ganiza ional Policy unde Unlimi ed Liabili y) (i) Fo γ=0,
se ing δI=1and δS=1is equi alen o se ing δI=0. (ii) Fo γ>0and α>0,
se ing δI=1and δS=1s ic ly domina es se ing δI=1and δS=0as well as
se ing δI=0. (iii) Fo γ>0and α=0, se ing δI=1and δS=1is equi alen o
se ing δI=1and δS=0.
P oo Gi en he esul s o Co olla y 1, only γ>0 needs o be conside ed. F om
equa ion (7) i is ob ious ha U(1,1;·,γ)≥U(1,0;·,γ), wi h s ic inequali y
o α>0. 
The Co olla y implies ha choosing o in eg a e wo ke s (δI=1) and imposing
a sec ecy clause (δS=1) becomes (weakly) dominan o any le el o en y. Absen
social compa isons, in eg a ion domina es because i sus ains p oduc i e complemen-
a i ies. In he p esence o social compa isons wage sec ecy hen becomes he op imal
o ganiza ional policy as i ules ou any ad e se e ec o en y.
123

102 J. K agl e al.
Fig. 2 Op imal O ganiza ional Design unde Unlimi ed Liabili y
The esul is illus a ed o γ=1.2inFig.2. The ed cu e depic ing p o i s
unde in eg a ion and wage anspa ency, U(1,0;α, 1.2), and he dashed (da k blue)
one ep esen ing p o i s unde wo ke sepa a ion, U(0,·; ·,·), a e bo h iden ical o
hose shown in panel (b) o Fig.1.Wi h wage sec ecy he p o i unde in eg a ion
and p oduc i e syne gy (γ=1.2) is depic ed by he do -dashed (g ey-b ownish)
ho izon al line. As he sec ecy clause neu alizes he e ec o en y i o igina es a
U(1,0;0,1.2)which is, o cou se, la ge han U(0,·; ·,·).
Al oge he , heabo emay a ionalizeempi icalobse a ions ega ding he endency
o employe s o impose wage sec ecy despi e he ques ionable legali y he eo . In he
nex sec ion, we econside he i m’s op imal o ganiza ional design unde wo ke lim-
i ed liabili y and e i y ha he dominance o he wage policy is no longe uni e sally
ue.
5 The mo al-haza d p oblem unde limi ed liabili y
In his sec ion we analyze he employe ’s op imal o ganiza ional a chi ec u e unde
he cons ain ha wo ke s a e p o ec ed by limi ed liabili y, i.e., he e exis s a lowe
bound o ex-pos wage paymen s in any s a e o he wo ld. Fo simplici y and in line
wi h mos o he agency li e a u e we se his lowe bound o ze o. As i will u n ou ,
his es ic ion has a - eaching consequences o he op imal incen i e con ac s and
he esul ing o ganiza ional design. Speci ically, we highligh he essen ial e ec s on
he (non)op imali y o wo ke sepa a ion and wage sec ecy.
123
Incen i es and pee e ec s... 103
5.1 The employe ’s p oblem
The wo ke s’ choice o e o o a gi en con ac (w, b)is una ec ed by he in o-
duc ion o limi ed liabili y. Acco dingly, hei op imal e o eis cha ac e ized by he
same symme ic Nash-equilib ium desc ibed in Sec . 4.1.
Analogous o ou discussion abo e we s a he analysis o he employe ’s p oblem
by assuming ha he o ganiza ional a chi ec u e (δI,δS)is gi en:
max
w,b,e2e+δI·γ(e)2−2(w +p(e)b)(II)
s. .b=c(e)
(1+δI(1−δS)αp(e))p(e),(IC)
w+p(e)b−c(e)−δI(1−δS)α(1−p(e))p(e)b⩾0,(PC)
w⩾0,(NNC1)
w+b⩾0(NNC2)
whe e (NNC
1)and (NNC
2)ensu e ha a wo ke ea ns a non-nega i e wage o all
possible ealiza ions o his/he signal. Condi ion (IC)implies ha b≥0, and hence
(NNC
2)can be dis ega ded.
F om (IC),(PC)and (NNC
1)and simpli ying, he ixed wage sa is ies
w=max c(e)+δI(1−δS)α(1−p(e)) −1p(e)c(e)
(1+δI(1−δS)αp(e))p(e),0.
(8)
This implies ha ei he (PC)o (NNC
1)o bo h mus be binding. No e ha wo ke s
ea n a en when (PC)does no bind. Unde sepa a ion, (NNC
1)always binds and
en s a e posi i e a any e o e>0. Unde in eg a ion, his also holds o sel ish
wo ke s bu once wo ke s become su icien ly en ious, (PC)s a s binding. In u-
i i ely, as he wo ke s’ p opensi y o en y inc eases, a gi en e o , also he en y
p emium inc eases and e en ually exhaus s he en .
Subs i u ing w om Eq. (8)in o(II), he p oblem becomes:
L(δI,δS;α, γ )=max
e2e+δIγ(e)2
−2·max c(e)+δI(1−δS)·α(1−p(e)))
1+αp(e)
p(e)c(e)
p(e),
(9)
1
1+δI(1−δS)αp(e)·p(e)c(e)
p(e)
Rema k 1 Conside δI=1 and δS=0. Le αc
L(γ ) deno e he le el o en y a which
(NNC
1)and (PC)a e jus binding and αc
U(γ ) deno e he le el o en y whe e w=0
when (NNC
1)is no imposed. Then αc
L(γ ) < αc
U(γ ) o any γ≥0 and o α∈
[αc
L(γ ), αc
U(γ )] he op imal bonus, wage and e o a e join ly de e mined by (IC),
(NNC
1)and (PC)as binding cons ain s.
123
104 J. K agl e al.
The exis ence o his in e im egion ollows om he ac ha , as long as α<
αc
L(γ ), he cons ain (NNC
1)binds while (PC)does no bind. In his case he p o i -
maximizing e o is de e mined by he espec i e i s -o de condi ion associa ed wi h
(9), whe eby he employe is o ced o pay en s and o educe e o ela i e o he
case wi hou wo ke p o ec ion. Mo eo e , absen wo ke p o ec ion he ixed wage
would be s ic ly nega i e in ha egion. This is s ill ue a αc
L(γ ), whe e (NNC
1)
s ill binds and (PC)jus becomes binding. Acco dingly, when en y ises u he o
he poin αc
U(γ ),(NNC
1)jus s ops binding and wis op imally se o 0. Inside he
in e al [αc
L(γ ), αc
U(γ )], bonus, wage, and e o a e hence de e mined solely by he
cons ain s (IC),(PC), (NNC
1),and (NNC
2). Beyond αc
U(γ ), op imal e o is
again de i ed om he employe ’s i s -o de condi ion (9), and he associa ed ixed
wage and bonus a e de i ed om (IC)and (PC)o (II), espec i ely.
P oposi ion 2 Le δI=1and δS=0. (i) Fo any 0≤γ, hen, as long as α<α
c
L(γ ),
L(1,0;α, γ )is inc easing in α, and once α>α
c
U(γ ),L(1,0;α, γ )is dec easing
in α.
P oo (i) Conside he ollowing (pa ial) decomposi ion o (9):
L
L(1,0;α, γ )=max
e2e+γ(e)2−2p(e)c(e)
(1+δ·αp(e))p(e),α<α
c
L(γ )
L
U(1,0;α, γ )=max
e2e+γ(e)2
−2c(e)+α(1−p(e)))p(e)c(e)
(1+αp(e))p(e),α>α
c
U(γ )
Since (PC)is no binding in he egion α<α
c
L(γ ), he op imal e o is de e mined by
he i s -o de condi ion associa ed wi h he maximand and he en elope heo em can
be applied, yielding he esul . In he egion α>α
c
U(γ ) he unc ion L
U(1,0;α, γ )
coincides wi h U(1,0;α, γ )in (7) and is dec easing in α.
The abo e esul shows ha - in s ic con as o he case o unlimi ed liabili y -
unde wage anspa ency employing en ious wo ke s in a join -p oduc ion se ing may
be ad an ageous o he employe . Mo e speci ically, as long as (NNC
1)is binding
and wo ke s ea n en s, he employe exploi s he abo e-men ioned incen i e e ec o
en y o elici highe p oduc i e e o s. In ui i ely, inducing e o becomes cheape
because, gi en any bonus, bo h wo ke s inc ease e o in an a emp o a oid being
in e io o hei pee . As long as en s a e posi i e, his does no lead o an adjus men
o he ixed wage. Consequen ly, as αinc eases he employe inds i op imal o aise
he bonus and induce an e en highe e o . This implies ha - again in s ic con as
o he case wi h unlimi ed liabili y - he pa ame e s γand αbecome complemen s, as
long as wo ke s ea n en s. A some poin howe e , when wo ke s become su icien ly
en ious (α=αc
L(γ )), en s anish due o he la ge en y p emium. Wi h a u he
inc ease in en y (α>α
c
U(γ )) he limi ed-liabili y es ic ion becomes ine ec i e and
123
Incen i es and pee e ec s... 105
he employe ’s p o i coincides wi h ha unde unlimi ed liabili y, whe e no cons ain
on he ixed wage was p esen in he i s place.
5.2 The op imal o ganiza ional design
To de e mine he op imal o ganiza ional a chi ec u e we p oceed analogously o he
case o unlimi ed liabili y. Tha is, we i s analyze he op imal o ganiza ional a chi-
ec u e in he common-knowledge case and hen de e mine he op imal o ganiza ional
policy. As i u ns ou , unlike in he o egoing sec ion, wage sec ecy is no longe a
s ic ly dominan policy i wo ke s a e p o ec ed by limi ed liabili y. No ably, in ha
case he employe may choose o e ain om imposing a sec ecy policy o p o i ably
exploi he pee e ec .
5.2.1 Wage anspa ency
The nex Co olla y 3cha ac e izes he op imal o ganiza ional a chi ec u e o his
case, depending on he wo ke s’ p opensi y o en y and he syne gy ac o .
Co olla y 3 (Op imal O ganiza ional A chi ec u e unde Limi ed Liabili y)
Conside δS=0. Le αL(γ):L(0,·; ·,·)=L1,0;αU,γbe ini e. Then
(i) αc
U(γ)<α
L(γ). (ii) Fo α<α
L(γ ),δI=1while, o αL(γ ) < α,δI=0,
and a α=αL(γ ) he employe is indi e en be ween δI=0and δI=1. (iii)
αU(γ)<α
L(γ).(i )αL(·)is inc easing in γwi h αL(0)>0.( )I αL(γ) ails o
exis , hen δI=1is op imal o any α.
P oo (i) is an immedia e implica ion o pa (i) o P oposi ion 2. (ii) is analogous o
pa (i)o Co olla y1, since o α>α
c
U(γ ) he unc ionL
U(1,0;α, γ )coincideswi h
U(1,0;α, γ )in (7). (iii) ollows om he ac ha L(0,·; ·,·)<
U(0,·; ·,·).
The p oo s o (i )-( ) a e analogous o he espec i e ones in Co olla y 1.
By Co olla y 3, he p o i unc ions unde he wo o ganiza ional a chi ec u es in e -
sec a he c i ical le el αL(γ)o en y when wo ke s a e p o ec ed by limi ed liabili y.
Acco ding o pa (i) o he co olla y, in eg a ion always domina es wo ke sepa a-
ion when wo ke s ea n en s bu e en beyond ha poin . The main poin o Co olla y
3(iii) is ha , o any syne gy ac o , he employe chooses in eg a ion o a la ge ange
o αwhen wo ke s a e p o ec ed by limi ed liabili y as compa ed o scena ios wi h
unlimi ed liabili y. This implies ha he op imal o ganiza ional a chi ec u e c i ically
depends on whe he wo ke s a e p o ec ed by limi ed liabili y o no .
Fi s , conside he case when he e a e no p oduc i e syne gies. Recall ha , by
Co olla y 1(ii), in eg a ion is ne e op imal unde unlimi ed liabili y. In ac , by 3(i ),
when liabili y is limi ed he employe inds i op imal o implemen in eg a ion also
when wo ke s a e en ious. In ui i ely, whe eas unde unlimi ed liabili y social com-
pa ison is always ha m ul, in his case join alloca ion o wo ke s becomes bene icial.
E o and p o i abili y a e inc eased h ough he exploi a ion o wo k incen i es ig-
ge ed by he wo ke s’ en y. Mo eo e , in line wi h he unlimi ed-liabili y case, wi h
123
106 J. K agl e al.
Fig. 3 Op imal O ganiza ional A chi ec u e unde Limi ed Liabili y (a) wi hou and (b) wi h P oduc i e
Syne gies
p oduc i e syne gies, employe s ind i op imal o induce highe e o and he ange
o α- alues o which in eg a ion is chosen is aised e en u he . Al oge he , unde
limi ed liabili y, he employe is likely o delibe a ely implemen in eg a ion because
his no only allows o p oduc i e complemen a i ies bu also p o okes income com-
pa isons ac oss wo ke s, which in u n s eng hen wo k incen i es and aises p o i .
Figu e3illus a es he o egoing esul s. In bo h panels he p o i unde wo ke
sepa a ion shown by he dashed (blue) line has shi ed downwa ds by exac ly he
amoun o he wo ke s’ en s as compa ed o he case o unlimi ed liabili y shown in
Fig.1.18 In line wi h P oposi ion 2p o i s unde in eg a ion, shown in solid ( ed), ha e
kinks a αc
L(γ)and αc
U(γ)(no ma ked).19 The ea e , he cu es coincide exac ly
wi h hose o Fig.1. Again, panel (a) shows he case whe e he e a e no p oduc i e
syne gies. No ably, in con as o Fig.1, p o i s unde in eg a ion exceed hose unde
wo ke sepa a ion o su icien ly low in ensi ies o en y (α<α
L(0)=2.87). In
ac , o he ange αc
U(0),αL(0)in eg a ion emains op imal unde limi ed liabili y
e en hough p o i s al eady dec ease in en y. He e, e en wi hou he syne gy e ec ,
a αL(0)e o unde in eg a ion is highe han i is unde wo ke sepa a ion bu
p o i s a e e oded by he agency cos s. Acco dingly, when wo ke s become su icien ly
en ious α>α
L(0)wo ke sepa a ion domina es also unde limi ed liabili y. Wi h
p oduc i e syne gies, p o i unde in eg a ion shi s upwa ds due he p esence o
p oduc i e syne gy and he highe induced e o (panel (b)). As a esul , αc
L(γ),
αc
U(γ)and wi h hem he cu e’s kinks shi o he igh . Mo eo e , he in e sec ion o
he p o i cu es unde he al e na i e o ganiza ional a chi ec u es, αL(γ), shi s o he
igh as well, so ha in eg a ion is op imal o highe in ensi ies o en y. A compa ison
wi h he case o unlimi ed liabili y in Fig.1shows ha he p esence o limi ed liabili y
in ac inc eases he ange o α- alues o which he employe chooses in eg a ion. In
pa icula , as a consequence o he s ic ly lowe p o i s unde sepa a ion, he ange o
18 No ice ha , o he sake o cla i y, we adjus ed he scale o he y-axis in he igu e.
19 The in e im egions a e gi en by [αc
L(0),αc
U(0)]=[0.71,0.74]and [αc
L(1.2),αc
U(1.2)]=
[0.82,0.91], espec i ely. While e o is inc easing in αwi hin he in e im egions, p o i s ini ially con inue
o inc ease be o e hey s a o dec ease once he en y- ela ed cos s become dominan .
123

Incen i es and pee e ec s... 107
Fig. 4 Op imal O ganiza ional Design unde Limi ed Liabili y
γ- alues o which in eg a ion is p e e ed o any deg ee o en y is la ge han ha
unde unlimi ed liabili y (and may po en ially become e en nega i e).
5.2.2 Wage sec ecy
In his sec ion we again econside he op imal o ganiza ional a chi ec u e unde lim-
i ed liabili y, and mo eo e de e mine he op imal o ganiza ional policy. Speci ically,
we analyze unde wha ci cums ances imposing a wage-sec ecy clause is op imal. The
esul is summa ized by Co olla y 4as ollows:
Co olla y 4 (Op imal O ganiza ional Policy unde Limi ed Liabili y) Le αLS (γ)∈
α:L(1,0;α, γ )=L(1,1;·,γ)∩{α∈R+}. Then (i) αLS (γ)<α
L(γ). (ii)
Fo α<α
LS(γ ), se ing δI=1and δS=0is op imal, o α>α
LS(γ ), se ing
δI=1and δS=1becomes op imal, and, a α=αLS(γ ),δI=1is op imal while
he employe is indi e en be ween δS=0and δS=1. (iii) αLS (γ)is inc easing in
γ.
The p oo o Co olla y 4is analogous o ha o Co olla y 3and is hus omi ed.
Absen p oduc i e complemen a i ies, he esul coincides wi h panel (a) o Fig.3.
I is only once complemen a i ies a ise ha wage sec ecy becomes ele an as i neu-
alizes he impac o he wo ke s’ social p e e ences unde in eg a ion. The p o i
gene a ed by he imposi ion o sec ecy, L(1,1;·,γ), is ep esen ed o γ=1.2by
hedo -dashed(g ey-b ownish)ho izon al lineinFig.4.Acco dingly,in eg a iondom-
ina es wo ke sepa a ion, shown by he dashed (blue) line. Howe e , unlike he case
whe e wo ke s a e no p o ec ed by liabili y limi s, wage sec ecy is no always domi-
nan . In pa icula , as discussed abo e, wi h limi ed liabili y, en y induces high e o
as long as wo ke s ecei e a en and e en beyond. Clea ly, absen en y (α=0), he
employe ’s op imal p o i unde sec ecy, L(1,1;0,γ), is iden ical o ha unde in e-
g a ion wi hou sec ecy, L(1,0;0,γ). No ably, as αinc eases, wage anspa ency is
mo e p o i able han sec ecy. In ui i ely, in ha case he employe uses anspa ency o
123
108 J. K agl e al.
delibe a ely exploi social compa isons and aisep o i s. Howe e , once he p opensi y
o en y becomes su icien ly high (α>α
LS (γ)), he en y-p emium cos s associ-
a ed wi h social compa ison ou weigh he incen i e e ec s on wo ke mo i a ion,
he eby ende ing he imposi ion o wage sec ecy he op imal op ion (in he igu e,
αLS (1.2)=1.61). No ice ha bo h p o i s, L(1,0;α, γ )and L(1,1;·,γ),shi
upwa ds as γinc eases. As a esul , in his se ing, αLS (γ)is always ini e so ha ,
e en o e y high alues o γ, a some poin wage sec ecy becomes he p e e ed
policy.
6 Ex ensions
In he sequel, we discuss se e al ex ensions o ou model. We s a by in es iga ing he
impac o imposing a posi i e minimum wage. Then we analyze a scena io whe e wage
sec ecy is no ully en o ceable. Following ha , we conside he inclusion o a g oup-
bonus scheme, whe eby he employe join ly pays he wo ke s he same ewa ds. In
he las subsec ion, we ex end he scope o social p e e ences in line wi h Cha ness and
Rabin (2002). We show ha he gis o ou esul s con inues o hold when ex ending
he model in all o hese di ec ions.
6.1 Minimum wage
In ou main analysis, o simplici y we assumed ha - when exis ing - he lowe bound
o he wo ke s’ wage is se a 0. In his subsec ion, we p esen he e ec s o a s ic ly
posi i e lowe bound as o en p e alen unde minimum wages o collec i ely ag eed
s anda d wages. Figu e5(a) eplica es Fig.4, whe e a ze o lowe bound ˆw=0is
imposed. In he igu e below, we ha e adjus ed he ho izon al scale in o de o allow
o a compa ison o he case wi h a posi i e minimum wage ˆw>0, shown in Fig.5(b).
The e ec s a e mani old. Fi s ly, na u ally all p o i cu es shi down because
he i m is o ced o pay ou highe ixed wages unde all o ganiza ional designs.
Secondly, he ange o wo ke s’ en y o which in eg a ion is dominan unde wage
anspa ency has inc eased d ama ically. Thi dly, i sec ecy canno be implemen ed,
wo ke sepa a ion becomes op imal o la ge alues o α. And inally, i sec ecy is
implemen able, he ange o p opensi ies o en y o which he employe chooses o
impose his policy is smalle han i is in he absence o a posi i e minimum wage.
The esul s eme ge om he ac ha an inc eased lowe bound on he ixed wage
c ea es en s whe e none exis ed be o e. To mi iga e he nega i e impac o hese
cos s on p o i s, he employe con inues o u he exploi he o ces unleashed by he
exis ence o en y by inducing highe e o s. Technically speaking, he p opensi y o
en y o which he lowe -bound cons ain becomes slack, αc
L(γ ), is inc easing unde
a posi i e minimum wage. Fu he mo e, he alue o en y a which he wage unde
unlimi ed liabili y s a s o exceed he inc eased lowe bound, αc
U(γ ), also inc eases.20
20 Speci ying a 0.09 minimum wage, he in e im egions a e now gi en by [αc
L(0),αc
U(0)]=[1.44,2.40]
and [αc
L(1.2),αc
U(1.2)]=[1.31,1.32], espec i ely. Fo bo h alues o γ, hese a e s ic ly la ge han
hose wi h a ze o lowe bound (see Foo no e 19). In gene al, once he lowe bound on he ixed wage
123
Incen i es and pee e ec s... 109
Fig. 5 Op imal O ganiza ional Design wi h (a) Non-Nega i e Wages and (b) a Posi i e Minimum Wage
Al oge he , he in oduc ion o a posi i e minimum wage is a double-edged swo d.
On he one hand, i aises wo ke wel a e by ans e ing pa o he su plus om
he employe o he wo ke s ia he highe ixed wages. On he o he hand, he new
eme gence o en s causes he employe o eac by elici ing highe e o s unde
in eg a ion. As discussed abo e, he employe achie es his by exploi ing he incen i e
e ec o en y unde wage anspa ency. Qui e ob iously, his s ands in con lic wi h
he gene al policy goals ela ed o anspa ency. No ably, his con lic is e en mo e
p ominen unde a posi i e minimum wage since he employe can hen u ilize he
e o -enhancing e ec o income compa ison o an e en la ge ange o wo ke s’
en y.
6.2 Impe ec wage sec ecy
In he abo e analysis we ha e assumed ha wage sec ecy is ully en o ceable. How-
e e , in p ac ice, his may no be always ue. Speci ically, wo ke s canno be hinde ed
om e ealing (a leas some) in o ma ion abou hei wage o (a leas some o hei )
colleagues. Mo eo e , as s a ed in he in oduc ion, imposing a wage-sec ecy policy
may in ac be illegal. To ake his in o accoun we below discuss he in e im scena io
a isingunde in eg a ionwhenwages a eimpe ec ly anspa en o sec e , ocusingon
he limi ed-liabili y scena io. Su p isingly, he ollowing analysis e eals ha impe -
ec sec ecy en o cemen may be e en mo e p e alen as i is op imal o a b oade
ange o en y in ensi ies han pe ec sec ecy.
We allow o wage-sec ecy impe ec ion (unde in eg a ion) by adjus ing he ange
o he sec ecy indica o , o be δS∈[0,1], e lec ing he ex en o which sec ecy is
en o ceable. Speci ically, a alue o δSin he in e io o he in e al indica es ha
sec ecy can be main ained only wi h p obabili y δS. No ice ha his is obse a ionally
equi alen o assuming ha sec ecy can be en o ced wi h p obabili y 1, bu αhas
dec eased oα=(1−δS)·α. Figu e6depic s he si ua ion o γ=1.2 and δS=0.5.
The accen ua ed-dashed (pu ple) cu e L(1,0.5;α, 1.2)displays he p o i unc ion
becomes su icien ly la ge, he unlimi ed liabili y case is no longe ele an and he in e im egion is emp y.
As long as p o i s emain posi i e, o α>α
c
L(γ)e o is se a a le el ha join ly sa is ies he lowe
bound on he ixed wage, he incen i e cons ain , and he pa icipa ion con s ain .
123
110 J. K agl e al.
Fig. 6 Op imal O ganiza ional Design wi h Limi ed Liabili y and Impe ec Wage Sec ecy
unde a pa ially implemen able sec ecy policy. Fo he sake o cla i y, we ha e also
included he c i ical alues, now deno ed by α(γ,δS), sepa a ing he ange whe e i
is op imal no o impose (e en impe ec ) sec ecy and he ange o which (im)pe ec
sec ecy becomes he op imal op ion. As is ob ious om he abo e-men ioned obse a-
ional equi alence, o any δS<1, αLS(γ, δS)<α
LS(γ, 1)( o he abo e pa ame e s,
αLS(1.2,0.5)=1.10 whe eas αLS (1.2,1)=1.61). Tha is, somewha su p isingly,
as i becomes ha de o en o ce sec ecy, he employe is inclined o impose i o
e e lowe p opensi ies o en y. Consequen ly, as sec ecy becomes mo e en o ceable,
i.e. δS ises, he uppe dashed (pu ple) p o i cu e is s e ched o he igh , he eby
becoming la e . In he limi when δS→1, i con e ges o he pe ec -sec ecy case,
shown o e e ence, by he dash-do ed (g ey-b ownish) ho izon al line.
No ice ha he abo e sounds pa adoxical a i s as i implies ha i ms may ha e
an in e es o impe ec ly en o ce sec ecy e en when hey could pe ec ly en o ce i .
In ui i ely, analogous o he case whe e δS=1, he pa ial success o he sec ecy
policy allows he employe o bene i om he incen i e e ec o en y ( o a weake
ex en ) as long as wo ke s a e paid en s. Acco dingly, o δS<1, p o i s a e ising
wi h αe en beyond he poin αLS(γ, δS). As a ma e o ac , he ange o α- alues o
which he employe p o i s om social compa ison is consequen ly e en la ge unde
impe ec wage sec ecy as compa ed o pe ec sec ecy. Mo e p ecisely, imposing
wage sec ecy - i impe ec - becomes op imal al eady o smalle p opensi ies o en y
han i does unde pe ec sec ecy. E en ually, en s a e exhaus ed by he inequali y
p emia also unde impe ec sec ecy, howe e a a highe le el o en y, and p o i s
s a dec easing. This has wo ob ious consequences. Fi s , when en y becomes e y
in ense p o i s ob ained unde pa ial sec ecy all below hose ha would ha e eme ged
unde pe ec sec ecy. Second and mo e impo an , in con as o he la e case whe e
wo ke sepa a ion was always domina ed, sepa a ing wo ke s (dashed (blue) line)
becomes again he op imal o ganiza ional a chi ec u e i αis su icien ly high (no
shown in he igu e).
6.3 G oup-bonus scheme
The abo e analysis igno es he possibili y o join pe o mance pay unde in eg a ion.
As an ex eme case he eo , conside a g oup-bonus scheme whe eby he employe
123
Incen i es and pee e ec s... 117
obse e he ou come o jus an icipa e i . Howe e , he e is abundan e idence ega d-
ing he s iking u ili y e ec s o ac ually obse ing pee - ela ed pay in o ma ion
( o example, Ca d e al. 2012, Pe ez-T uglia 2020). Ou simpli ying assump ion
ha only ex-pos obse ed wage di e ences ma e e lec s p ecisely his e idence,
he eby allowing us o cap u e he ele ance o he in o ma ional en i onmen ega d-
ing wage- anspa ency policies.
Ano he possibili y is ha wo ke s do o m an icipa ions abou hei pee s’ possible
pay bu ha e consis en biases conce ning ei he he p obabili y o a disad an ageous
wage di e en ial o i s size. The e ec o a downwa d bias in ei he is simila o
ha o impe ec sec ecy and he eby obse a ionally equi alen o educed en y.
Acco dingly, ou esul s in Sec . 6.2, as illus a ed in Fig.6, would ca y o e o such
en i onmen s, he ebyb oadening hescopeo heposi i ee ec so socialp e e ences
on i m p o i s.
Due o ou ocus on he i m’s a chi ec u al and con ac ual design, we dis ega d
po en ial social compa isons ac oss i ms. Howe e , in some cases wage anspa ency
anscends no only i m bounda ies bu also na ional bo de s. No ice ha such pub-
lished in o ma ion does no lead o o he - ega ding e o incen i es in he sense o
ou model. In pa icula , his in o ma ional di usion is exogenous o o ganiza ions
and wo ke s o he han hose belonging o i s o igina o (e.g., he UC sys em) and
bea s no esemblance o ou se ing (see Ben al and K agl (2021) o an analysis
o he ole o social compa ison wi hin a socie al amewo k).31 Finally, ou pape
conce ns ho izon al income compa isons a ising be ween wo ke s a he han e ical
compa isons be ween wo ke s and hei boss. Mo eo e , we ocus solely on ex-an e
iden ical wo ke s who may expe ience ex-pos income di e ences. Beyond p o iding
analy ical cla i y, his se ing is likely o apply o la e al compa ison si ua ions. This
is no o say ha ex-pos income di e ences esul ing om ex-an e dis inc ions do no
a ec en ious wo ke s. Howe e , he ex en o which such ex-an e di e ences, e.g., in
abili y, p oduc i i y le els, o li e ci cums ances, a ec u ili y whe e o he - ega ding
p e e ences a e conce ned, goes beyond he scope o his pape (see ou companion
pape , Ben al and K agl (2024), o an analysis o he ole o en y in he ace o wo ke
he e ogenei y).
7.2 En y in o he ypes o social p e e ences
No wi hs anding he undoub ed impo ance o en y in employmen ela ionships,
many expe imen al se ings and he me a-analysis by Nunna i and Pozzi (2022),
hough, show ha people may in gene al beha e bene olen ly owa ds one ano he .
P ominen examples a e ul ima um and dic a o games in alloca ional si ua ions whe e
indi iduals o en end o display compassion o co-playe s and p e e ences owa ds
equali y. Signi ican e o has been de o ed o a ionalize such beha io pa e ns by
a ious o mal p e e ence speci ica ions. In line wi h he li e a u e e iew o Coope
and Kagel (2016), in his subsec ion, we b ie ly and in o mally discuss he ele ance
31 The eisapa allelli e a u econce ning he oleo socialp e e encesin hecon ex o gene al-equilib ium
heo y (see, e.g., Caucu 2001; Sobel 2005; Bosmans 2007; Kilen hong and Madei 2017; Fleu baey e al.
2024; Thomson 2024).
123

118 J. K agl e al.
and possible implica ions o some u he leading speci ica ions beyond he models
by Cha ness and Rabin (2002) and Feh and Schmid (1999) analyzed in Sec . 6.4.
The eby we ocus on hose al e na i e o mula ions ha may be ele an o ou eco-
nomicen i onmen and esea ch ques ion.In pa icula , we discusswhe he heyadmi
en y among wo ke s and whe he his is a dominan ac o . We dis ega d ecip oci y
and in en ions, which a e also conside ed by many p e e ence speci ica ions, since
he e is no di ec gi e-and- ake ela ionship be ween he wo ke s in ou se ing.
Ano he impo an o mula iono equali yconce nsisp esen edbyBol onandOck-
en els (2000) whose model encompasses equi y, ecip oci y and compe i ion (ERC)
in he con ex o social p e e ences. In hei speci ica ion (p. 171), people a e sensi i e
o hei sha e ela i e o he equal sha e o he o al pecunia y payou , whe eby any
de ia ion om ha sha e induces disu ili y. In hei speci ic example (p. 173), ha pa
o he p e e ence speci ica ion is quad a ic, implying symme y be ween upwa d and
downwa d de ia ions o he same absolu e magni ude om he equal sha e. Applying
his speci ica ion o he CR-en i onmen would imply ha en y and compassion a e
equally weigh ed, (in he CR no a ion ρ=−σ) enhancing he inequali y p emium
bu mi iga ing he incen i e e ec . As Figs.7and 8show, his combina ion has no
pa icula e ec on ou conclusions.
Rabin (1993) exempli ies an ea ly a emp o o mula e social p e e ences accoun -
ing o ai ness, al uis ic beha io , and ecip oci y. In Rabin’s o mula ion (p. 1287)
indi iduals conside he“kindness”o co-playe s owa ds hemin he con ex o alloca-
ional choices. In pa icula , an indi idual’s u ili y depends on he pe cei ed de ia ion
o he o he pe son’s no ional alloca ion om an equal spli . U ili y is educed i
ha pe son is deemed o be “unkind” (alloca ing o himsel mo e han he equi able
amoun ). A a o able de ia ion, on he o he hand, is u ili y-enhancing. The u ili y’s
nega i e eac ion o he pe cep ion o “unkind” beha io is akin o he p esence o
en y. The posi i e impac o “kind” beha io would be simila o he “compe i i e”
a i udes discussed in Sec . 6.4.32
Le ine (1998) a ionalizes expe imen al ou comes o ul ima um and he inal ound
o cen ipede games. The p e e ence speci ica ion (p. 597) allows pe sons o be “al u-
is ic” o “spi e ul” owa ds co-playe s, whe eby he u ili y also depends on whe he
he o he playe s in u n a e al uis ic o spi e ul owa ds hem. A spi e ul (al uis ic)
pe son’s u ili y is nega i ely (posi i ely) a ec ed by he u ili y o he o he pa ies.
Again e e ing o he CR-model, such p e e ences would en ail inc eased ( educed)
inequali y-p emium cos s and an in ensi ied (mi iga ed) incen i e e ec .
Finally, he ocus o And eoni and Mille (2002)isonal uis ic beha io . The pape
shows ha axioms o e ealed p e e ences can be applied o a ionalize such beha io .
In ac , he au ho s es ima e a CES u ili y unc ion which depends on own payo
and ha o he o he pe son. Depending on he elas ici y o subs i u ion be ween
he wo a gumen s and he cos associa ed wi h ans e ing esou ces o he o he
pe son, he model is consis en wi h al uis ic sha ing bu also wi h pe ec ly sel ish
beha io . No ably, And eoni and Mille (2002) ound ha a signi ican mino i y o
32 Rabin’s model has been ex ended by Du wenbe g and Ki chs eige (2004) o a dynamic epea ed game
se ing whe e i becomes c ucial how belie s on o he s’ u u e in en ion-based ecip oci y a e upda ed.
123
Incen i es and pee e ec s... 119
subjec s beha e “jealously”, whe eby hese subjec s in en ionally e ode he alue o
he ans e ed esou ces o educe disad an ageous inequali y.
8 Conclusion
Wi h his s udy, we con ibu e o li e a u e conce ning he p esence o en y, he ole o
wage anspa ency, and he impo ance o pee e ec s in he wo kplace. We p o ide a
o mal heo y ha in eg a es hese aspec s in o a uni ied analy ical amewo k. Taking
en y o be he d i ing o ce, we in es iga e i s impac on i ms’ op imal o ganiza ional
design and hei a i ude owa ds wage anspa ency wi hin a mo al-haza d amewo k.
Ou analysis shows ha anspa ency may p o e o be a double-edged swo d. In
ac ,i maye en ually u nagains he employeesandbene i he employe ins ead, and
e en mo e so unde a posi i e minimum wage. Speci ically, ou esul s o Sec .4.3 may
a ionalize obse a ions ega ding he endency o employe s o impose wage sec ecy,
despi ei sques ionablelegali y. This occu s because payinequali y aisesagencycos s
when wo ke s a e no p o ec ed by limi ed liabili y. By con as , in Sec . 5.2,weshow
ha he popula p essu e o anspa ency (“sunshine laws”) may no be necessa ily in
he sel -in e es o employees. In ac , he main conce n o sunshine laws is o educe
pay inequali y and disc imina ion as well as en o ce go e nmen accoun abili y. Ye
hey also gene a e social compa isons and hus a ec o ganiza ional design. In ou
se ing, when wo ke s ea n en s, anspa ency igge s pay compa isons and gene a es
en y, he eby aising wo ke s’ in insic wo k incen i es and e o s. I is he la e ha
a e mani es ed as posi i e pee e ec s and p o ide a “ ee lunch” o i ms. On he
o he hand, when wo ke s do no ea n en s, o ced anspa ency and he associa ed
en y- ela ed agency cos s gene a e nega i e pee e ec s and may induce employe s
o sepa a e wo ke s e en a he expense o p oduc i e syne gies.
Rega ding he o ganiza ional consequences, we ind ha , unde unlimi ed wo ke
liabili y, agency cos s gene a ed by wage compa isons u n ou o be o p ima y con-
ce n. To a oid hese cos s, i ms may choose o o go p oduc i e syne gies and sepa a e
wo ke s in o independen p oduc i e uni s. In con as , wo ke in eg a ion becomes
o en op imal when wo ke s a e p o ec ed by limi ed liabili y and may hus ea n
en s. By delibe a ely placing wo ke s join ly in one p oduc i e uni , i ms igge
pay compa isons and p o oke en y o aise p o i s. No ably, wi h wage anspa ency,
in eg a ion emains op imal e en when en s a e dissipa ed unless en y becomes su i-
cien ly in ense, he eby making he cos s esul ing om social compa isons dominan .
In ex ensions, we show ha , ollowing he same a ionale, i ms may op o indi id-
ual pe o mance pay a he han g oup bonuses when wo ke s ea n en s. Howe e , as
jus no ed, when wo ke s a e highly sensi i e o inequali y, i ms abandon wage ans-
pa ency and impose sec ecy in in eg a ed se ings. In e es ingly, when wage sec ecy
is no ully en o ceable, i ms u n ou o be mo e ole an ega ding wo ke en y and,
acco dingly, p e e wo ke in eg a ion o e sepa a ion o highe in ensi ies o social
p e e ences. We also discuss he impac o a minimum wage, showing ha in eg a-
ion becomes hen mo e likely because he limi ed-liabili y scena io is mo e likely
o apply. Ou esul s a e hus in line wi h he p ominen e idence on he p esence o
posi i e pee e ec s amongs wo ke s a he lowe end o he wage scale. We u he
123
120 J. K agl e al.
in es iga e a b oad class o social p e e ences using he speci ica ion o Cha ness and
Rabin (2002), including inequali y a e sion, compe i i eness, and social-wel a e p e -
e ences. We demons a e ha ou esul s ex end o a la ge ange o empi ically ele an
pa ame e combina ions, whe eby compe i i e p e e ences s eng hen he impac o
en y u he while he less likely speci ica ions ep esen ing compassion and al uism
mi iga e i s e ec .
Finally, ou model may be used o e alua e popula “new-wo k” en i onmen s and
he ecen lywidesp ead use o emo ewo k.The eise idence ha wo king omhome
educes in e pe sonal con ac s among cowo ke s. In he sense o ou discussion, his
may o may no lowe p oduc i e syne gies, ye i is likely o educe he ex en o social
compa isons. Howe e , i seems ha a e a d as ic inc ease o i ms’ use o emo e
wo k du ing he Co id-19 pandemic, employe s now s i e o ge wo ke s physically
back o he wo kplace. This “na u al expe imen ” may p o ide some insigh s in o he
in e ela ionships o syne gies, social compa isons, pee e ec s, e o , and ou pu .
Appendix
G oup-bonus scheme
Conside a bonus scheme whe eby bo h wo ke s ob ain a bonus B1i one o hem
emi s he signal s=1 and a bonus B2i bo h do. Taking he e o choice o wo ke
j,ej, as gi en, wo ke i’s pa icipa ion cons ain becomes:
w+p(ei)1−p(ej)+p(ej)(1−p(ei))B1+p(ei)pejB2−c(ei)≥0
(A.PC)
The associa ed incen i e cons ain is:
p(ei)1−2p(ej)B1+p(ei)pejB2−c(ei)=0(A.IC)
Absen any cons ain s on he paymen scheme, he employe se s e1=e2and
sol es:
UGB =max
e,b,B2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2
s. .
(A.PC)
(A.IC)
(A.I)
Wi h condi ion (A.PC)binding, he employe chooses o induce he i s -bes e o
le el, e∗∗, and any pai o (B1,B2) ha sa is ies (A.IC)a e∗∗ is consis en wi h his
choice.
123
Incen i es and pee e ec s... 121
Suppose now ha wo ke s a e p o ec ed by limi ed liabili y. Focusing again on he
symme ic case, he employe aces he ollowing p oblem:
LGB =max
e,b,B2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2
s. .
(A.PC)
(A.IC)
w, B1,B2≥0
(A.II)
Taking in o accoun ha a he op imum unde limi ed liabili y he employe is
o ced o se w∗=0 and ha condi ion (A.PC)is no binding, he p oblem (A.II)
u ns in o:
GB =max
e,b,B
⎧
⎨
⎩
2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2
+λp(e)(1−2p(e))b+p(e)p(e)B2−c(e)
+μB1B1+μB2B2
⎫
⎬
⎭,(A.III)
whe e λ,μB1and μB2a e non-nega i e mul iplie s associa ed wi h (A.IC)and he
non-nega i i y cons ain s on B1and B2. Focusing on he la e , we ob ain:
−2p(e)(1−p(e)) +λp(e)(1−2p(e))+μB1=0
−2p2(e)+λp(e)p(e)+μB2=0
(A.mul )
We will nex ule ou he case whe e bo h B1and B2a e s ic ly posi i e as well as
he case ha B1>0 and B2=0.
Suppose ha bo hbonuspaymen sa es ic lyposi i e.In ha case,μb1=μB2=0,
by he second ow o (A.mul )implying λ=p(e)
p(e). Subs i u ing his in he i s ow
leads o −p(e)=0,a con adic ion o e>0.
Suppose nex ha B1>0bu B2=0. In his case, μB1=0,implying λ=
2p(e)(1−p(e))
p(e)(1−2p(e)). F om he second ow o (A.mul )we hen ob ain 2 p3(e)
1−2p(e)+
μB2=0. Since, o B1>0,cons ain (A.IC)implies ha 1 −2p(e)>0, his
con adic s he equi emen ha μB2>0.
As a esul , he only emaining case is B1=0 and B2>0. F om (A.IC)we ob ain:
B2=c(e)
p(e)p(e)(A.B)
Finally, he p oblem (A.I)becomes:
GB =max
e,B2e+γe2−2p(e)c(e)
p(e)(A.IV)
123
122 J. K agl e al.
Compa ing his p oblem o p oblem (II) shows ha he employe induces exac ly he
same e o as unde pe ec wage sec ecy and ob ains he same p o i . No ice ha
he e he indi idual bonus is adjus ed o accommoda e he ac ha i is paid less o en.
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