Tài liệu Interactions Between Workers and the Technology of Production: Evidence from Professional Baseball doc

IZA DP No. 3096
Interactions Between Workers and the Technology of
Production: Evidence from Professional Baseball
Eric D. Gould
Eyal Winter
DISCUSSION PAPER SERIES
Forschungsinstitut
zur Zukunft der Arbeit
Institute for the Study
of Labor
October 2007

Interactions Between Workers
and the Technology of Production:
Evidence from Professional Baseball


Eric D. Gould
Hebrew University
and IZA

Eyal Winter
Hebrew University



Discussion Paper No. 3096
October 2007

IZA

P.O. Box 7240
53072 Bonn
Germany

Phone: +49-228-3894-0
Fax: +49-228-3894-180
E-mail:






Any opinions expressed here are those of the author(s) and not those of the institute. Research
disseminated by IZA may include views on policy, but the institute itself takes no institutional policy
positions.

The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center
and a place of communication between science, politics and business. IZA is an independent nonprofit
company supported by Deutsche Post World Net. The center is associated with the University of Bonn
and offers a stimulating research environment through its research networks, research support, and
visitors and doctoral programs. IZA engages in (i) original and internationally competitive research in
all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research
results and concepts to the interested public.

IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion.
Citation of such a paper should account for its provisional character. A revised version may be

available directly from the author.
IZA Discussion Paper No. 3096
October 2007





ABSTRACT

Interactions Between Workers and the Technology of
Production: Evidence from Professional Baseball
*

This paper examines how the effort choices of workers within the same firm interact with
each other. In contrast to the existing literature, we show that workers can affect the
productivity of their co-workers based on income maximization considerations, rather than
relying on behavioral considerations such as peer pressure, social norms, and shame.
Theoretically, we show that a worker’s effort has a positive effect on the effort of co-workers if
they are complements in production, and a negative effect if they are substitutes. The theory
is tested using panel data on the performance of baseball players from 1970 to 2003. The
empirical analysis shows that a player’s batting average significantly increases with the
batting performance of his peers, but decreases with the quality of the team’s pitching.
Furthermore, a pitcher’s performance increases with the pitching quality of his teammates,
but is unaffected by the batting output of the team. These results are inconsistent with
behavioral explanations which predict that shirking by any kind of worker will increase
shirking by all fellow workers. The results are consistent with the idea that the effort choices
of workers interact in ways that are dependent on the technology of production. These
findings are robust to controlling for individual fixed-effects, and to using changes in the
composition of one’s co-workers in order to produce exogenous variation in the performance

of one’s peers.


JEL Classification: J2

Keywords: peer effects, team production, externalities


Corresponding author:

Eric D. Gould
Department of Economics
Hebrew University of Jerusalem
Mount Scopus
Jerusalem 91905
Israel
E-mail:





*
For helpful comments and discussions, we thank Todd Kaplan, Daniele Paserman, Victor Lavy,
Daron Acemoglu, two anonymous referees, and seminar participants at Hebrew University, the
European University Institute, the Norwegian School of Economics, Tel Aviv University, and the
University of Texas.
1 Introduction
This paper examines how t he effort ch oices of workers within the sam e firm in teract with
eac h oth er , and how this interaction depends on the techn ology of production. In contrast

to the existing liter ature, w e focus on show ing h ow t he effort choice of one w orker can
affect the effort choices of his co-workers based purely on income-m aximizing considera-
tions, rather than relyin g on behavio ral explanations such as peer pressure, sha me, etc.
In addition, w e break from the existing literature by s ho wing t hat the effortchoiceofone
worker could have a po sitive or negative e ffect o n his c o-wo r ker s. For e xam p le, a mec h a-
nism based on behavioral considera tions like peer pressure or shame predicts that a high
level of effort by one wo rker will induce oth er workers to increase their effort level, or that
alowereffort b y one wo rker cau ses other wo rkers to follow suit. We refer to both of these
cases a s a “positive interaction ” in the sense th at a change in e ffort by one wo rker causes
others to change their effort in the same direction. Howe ver, we show that a “ neg ative
in tera ctio n” between wo rke rs is also possible, in the sense that a ch an ge in effort by one
worker causes other wo rkers to c h ange their effort in the opposite direction.
Therefore, this paper con trib utes to the existin g literature by sho w ing that the in-
teraction of effort choices could work in both directions, ev en within the same firm at
the same time. In partic ular, we sho w that a “positive in teraction” should exist bet ween
comp lem entar y wor kers, while w o rkers who are substitutes may free ride off the effort of
eac h other, and th us genera te a “negative int eraction” in the effort choices of co-worke rs.
The theory is tested using panel data on the performance of baseball pla yers from
1970 to 2003. The game of baseball p rovides a clear case where pitchers and non-pitc hers
can safely be defined as substitutes fo r eac h other in team performan ce — since p reventing
runs and sco ring runs are perfect substitutes in th e team’s goal of scoring mor e runs th an
the o pposing t eam . In addition, p laye rs who are not pitc h ers are o ften comp lem ents with
eac h other since it u su ally takes more t han one player to get a h it in order to sco re a run
for the team . The empirical analysis show s that a pla ye r’s batting averag e significant ly
increases with the batting perform ance of other players on the team, but decreases with
the quality of the team’s pitch ing . Furth erm ore, a p itcher’s performance increases with the
1
pitching qualit y of the o ther pitchers, but is unaffected by the batting output of the team.
These results are in consistent with beh avioral explanations for how one w orke r affects the
per form ance of other w orkers, since a t y pical behavioral response should c ause w o rkers to

c hange their effort in the same direction regardless of the other player’s role or function.
Thu s, psychologic al conside ratio ns are unlike ly to exp lain o ur findings that players respond
differentially to th e actio ns of th eir co-workers according to their role a nd function on the
team. Ov erall, t he results a re more consistent with an interaction of effort c ho ices within
the team t hat a re based on a rational response to the tec hnology o f production.
Our empirical findings are robust to controlling for individual fixed-effects, expe-
rience, year effects, team, home ballpar k ch aracteristics, and managerial qualit y. The
inclusion of individual fixed-effects mea ns that the results canno t be e xp lain ed by assorta-
tiv e matching bet ween complementa ry o r su bstitutable p layers at the team lev el, since th e
analysis is exp loitin g variation o ve r time wit hin a give n player’s pe r formanc e. In ad dition ,
the results a re rob ust to using a first-differences specification, as well as restricting the
sample to only those workers who cha nge teams (chan ging all of their co-workers), or using
a s ample of only t hose wo rkers who re main with the sam e team, manager, and h ome ball-
park in consecutiv e years. Furtherm or e, in order to cont rol for unobserv ed yearly shocks
which ma y a ffect the performance of the whole team, we instrum ent the yearly performance
of one’s t eam mates with the lifetime performa nce of his teammates. Yearly variation in
this instrument stems only from ch anges in the composition of on e’s co-wo rkers, sin ce each
pla yer’s lifetim e performance is constant for ea ch ye ar. Results using this instrument are
v e ry similar t o the O L S estimates.
There is a grow in g literature that stresses the im portance of the environ m ent in deter-
mining the outcomes of individuals. Most of this literature is concerned w ith examining
ho w peers and environ m ental factors affect y outh behav ior regarding their educational
ac h ievem ents, h ea lth, criminal invo lvem ent, wo rk status, and other economic va riab les.
1
This paper differs by looking at the in teraction o f adult beha v ior in the wo rkp lace. Th e
1
See Angrist and Lang (2004), Guryan (2004), Hoxby (2000), Sacerdote (2001), Zimmermann (2003),
Katz, Kling and Liebman, (2001); Edin, Fredriksson and Aslund (2003); Oreopoulos (2003); Jacob (2004);
Weinberg, Reagan and Yankow (2004), Gould, Lavy and Pa serman (2004a and 2004b).
2

literature on the in tera ctio n of worke rs within a firm is not extensive. Winte r (2004)
demo nstrate s the ore tically the o ptim a lity o f offerin g differen tial in centive c ontra cts in or-
der to elicit worker effort whic h genera tes externalities on other workers. Kandel and
Lazear (1992) examine the theory of team production within the firm and focus on how
teams produce social pressure to solve the free-riding problem. The most related papers
to ours are by Ichino and M aggi (2000) and Mas and Moretti (2006). Ic hino and M aggi
(2000) examine shirking behav ior within a large banking firm, and show that a worke r’s
shirking beha vior significant ly respo nd s to the beha v ior of his co-worke rs when they move
across branches within the sam e firm. Using data on workers from a large g rocery story
c hain, Mas and Moretti (2006) e xam ine ho w the productivity of a worker varies according
to the productivity of other w orkers on the same sh ift, and provid e additional evidence
that be havior consideratio ns such as peer pressure and social norm s are significan t. Som e
of our empirical specifications emplo y a similar identification stra tegy in the sense tha t we
exploit differences in the composition of one’s co-workers to explain var iation in an indi-
vidual’s performan ce level over time and across workp laces. However, o ur paper differs b y
examining the theoretical and empirical di fferences in the natur e of the interaction across
workers depending on whether they are substitutes or complements w ith eac h other. In
this m anner, o ur paper contributes to the literature by pro viding a theoretical foundation
and empirical evid en ce for both positiv e a nd negative interactions in the effort c h oices of
workers i n a real work environment.
2 The model
In this section, we show h ow the effort choices of workers within the same firm interact with
each other, and ho w this interaction depends on the tec hnology of the team production
function. To do t h is, we presen t a parsimonious p rincipal-a gent model where t h e o p tim al
contract is derived und er two d ifferen t scenarios. I n o ne scen ario, players are co mp le-
mentar y to one an other, and in th e second scenario, workers are consid ered substitutes.
In order to characterize the two different types of techn olog ies, we borro w t he co ncep t o f
strategic substitution and complemen tarit y (see Milgrom and Shannon (1994) a nd Topkis
3
(1998)). Our model is similar to Holmstrom (1982) and Holmstrom and Milgrom (1991)

in the s ense that the outcome of effo rt i s u n certain, b ut risk aversion p lays n o role in our
model. Th at is, our model is based on ly on th e issue of mor al hazard .
A t eam consists of two agen ts {1,2}. Eac h agen t is respo nsible for a task. A worker’s
task is successful with probab ility β if he exerts effort, but is successful with probabilit y
α<βif no effort is exerted. We assum e that the cost of effort is c for both agents.
2
On eac h team, the tasks of the two worker s jointly determine the success of a project
according to a techn ology p : {0, 1, 2} → [0, 1], where p(k) is the proba bility that the
project succeeds giv en that exactly k agents have successfully com p leted their tasks (the
assum ption of symmetry is used only for t he sake of simplicity). In order to allow wor kers
to ba se th eir e ffort choices on th e performance of other workers, we a ssum e th at player 1
performs his task first, and then play er 2 ch ooses his effort after ob ser ving the o utcome of
the t ask perform ed by agen t 1.
We derive th e o ptim al contra cts for two teams — each team representing a d ifferent
t ype of technology. The production function for team 1 is c haracterized by comple-
mentar ity or superm odularit y between the agents, which is represen ted by p(2) − p(1) >
p(1) − p(0). In con t rast, team 2 is char acterized by substitution bet ween workers, which
is represen ted by p(2) − p(1) <p(1) − p(0). This fram ework captures the b asic intuition
that, in the case where w orke rs are complements in prod uction, the success of one agen t
in com pleting his t ask c ontrib utes m ore to the prospects o f the entire p roject succeed ing if
the other ag ent s ucceed ed a s we ll. In contrast, in the case where workers a re sub stitutes,
the marginal con tribution of a successfully completed task by one w o rker is higher when
the other worker fails in his task.
The principal is facing moral h azard. He cannot monitor the effort of his workers,
nor is he informed about which tasks ha v e ended successfully. Instead, h e is informed only
about w h ether the project as a w h ole is successful. Therefore, the principal offers contracts
to a gents that are contin gent only on the wh ether the ove rall project su cceeded or no t.
2
In reality, the cost of effort would be a function of a person’s innate ability. Also, as we later discuss, the
probability of the task succeeding conditional on effort would also be a function of personal characteristics.

However, we maintain the assumption of a uniform cost for the sake of simplicity.
4
Specifically, t he p rinc ipal offers a contra ct to each member of the team, repr esented by a
v e ctor of reward s v =(v
1
,v
2
) w ith agen t i receiving v
i
if the project succeeds a nd zero
otherwise.
For a mechanism v, we have an extensive f orm game G(v) between the two play ers.
If the overall team project is successful, the project generates a benefit B for the principal.
Given a mechanism v, let q(v) be the probab ility of success in the uniqu e
3
(subgame
per fect) equilibrium of the game G(v). The principal designs the incentiv e mechanism v
optima lly, s o as t o maximize his net rev enu e, represen ted as v =argmaxq(v)[B −
P
j
v
j
].
We assu m e that th e ove rall p roject is valuable en ou gh so tha t the o ptim al m ech an ism
a wa rd s each player with a positive reward if the project is successful. That is, B is
sufficiently high (B>B
∗
) so that v
j
> 0 for both players in the optimal mech anism . N ote

that th is assumption implies that player 1 exerts effort. If this were n ot the case, then
v
1
> 0 cannot be optimal since the principal would be better off paying zero t o playe r 1.
Depending o n the value of B as well as the values of the other parameters in the game, the
optima l mec han ism must yield one of the follow in g equilibria in the co rresponding game:
1. Player 1 exerts effort and player 2 exerts effort if and on ly if the first task succeeded.
2. Player 1 exerts effort a nd play er 2 exerts effort if and on ly if the fir st task failed.
3. Player 1 e xerts e ffort and player 2 e xerts effo rt regardless of the o u tcom e of the first
task.
If B is sufficiently high (B>B
∗
), then the project is so v aluable that the princi-
pal will induce equilibrium 3 so that pla yer 2 always finds it worthwhile to exert effort
regardless of wheth er playe r 1 succeeded an d regardless of wh ether th e tec h n ology is one
of substitution or complementarit y. If, ho wev er, B is high enough to induce the prin-
cipal to prov ide incen tives to exert effort but not so high that this is alw a ys the case
(B
∗
<B <B
∗
), the optimal str ategy will depend on the technology of production. The
follo w in g p roposition states wh at h ap pens whenever B is sufficien tly h igh (B>B
∗
) so
that the principal provid es at least some i nc entives to exert effort.
3
We assume that indifference is resolved in favor of exerting effort.
5
Proposition 1 (1) If th e team ’s technology satisfies c omplementarity, then the optimal

mecha n ism induces either equilibrium 1 or equ ilibrium 3. (2) If th e team’s tech nol ogy s at -
isfies su bs titutio n , t h en the op timal mech a nis m induces either equilib rium 2 o r equ ilibr ium
3.
Proposition 1 asserts that unless it is a dom in ant strategy f or agen t 2 to always exert
effort (B>B
∗
), the optim a l pattern o f behavior in equilibrium will be co nsist ent with
our em pirical resu lts. If workers are com p lem entary, a fa ilure on th e part of p layer 1 will
trigger player 2 to shirk. In contra st, if workers are substitutes in pr oduction, a failure on
the part of player 1 w ill trigger p laye r 2 to exert e ffort.
The intuition for Proposition 1 is straigh tforw ard. In general, the principal will
find it co st effectiv e to pro vide incen tives for the agent to exert effort when the ma rginal
return to the w orker’s effort is high. So, if w orkers are complementary to eac h other,
player 2’s effort will have a b igg er impact on the o verall success of the team if pla yer 1
succeeded rather tha n failed. Therefo re, i n order for player 2 to exert effort, he will need
to be com pensated fo r the lower probability of team success in the case w h ere player 1
failed versus the c ase where p layer 1 succeeded. If the project’s value is sufficien tly h igh
(B>B
∗
), the principal will find it profitable to pro vide incentives to player 2 even if
pla yer 1 failed. But, if the project’s va lue is lo wer than this threshold (B
∗
<B <B
∗
),
the princip al w ill findittoocostlytoprovideincentivestoplayer2toexerteffort if pla yer
1 failed. Althou gh it might seem in tuitive that the principal would create an incen tive
mechanism to counter the urge for pla y er 2 to shirk when pla y er 1 fails, the model shows
that this is only the case w h en the value of the project is sufficiently h igh. In intermediate
cases, it is o ptim al for the p rincipa l not to waste his money on provid ing in centive s to

player 2 when the chances are low that player 2’s effort will result in the overall success of
a p roject which is no t sufficien tly valuable.
In con tra st, if workers are substitutes in pr oduction, playe r 2’s effort is more effective
if player 1 fails in his t ask. If p layer 1 succeeds, then player 2 knows that his effort is not as
crucial for the team to be successful, and therefore, player 2 wou ld need a higher pa y m ent
to exert effort in the case where player 1 succeeds. If the project i s worth a lot (B>B
∗
),
6
then the prin cipa l will find it profitable to incur this cost in order to im prove the chances
of team success even w h en the success of player 1 has already rendered pla ye r 2’s effort to
be less crucial. But, in the interm ed iate case (B
∗
<B <B
∗
), the principal will find it
optimaltopayenoughtoplayer2toexerteffort only when pla ye r 1 fails, s ince this is the
case where playe r 2’s effort i s more critical to the success of th e team. Once again, we see
that the principal will not a lways design the optima l con tract to guard against shirking in
all cases — i f wo rke rs are s ub stitu tes, it is o ften th e ca se tha t it i s n ot p rofitable to g u ard
against shirking by p laye r 2 if p layer 1 h as alread y d one m ost of th e wo rk th at is cr itical
for team success.
Proof of Propositio n 1: We start b y deriving the optimal mechan ism for a team
where w o rkers are complementary with each other. Let u s examine the behavior of p layer
2, who is paid v
2
if the o ver all project is successful. Con sider playe r 2’s decision node
after t ask 1 succeeded. Player 2’s expected payoff will be [βp(2) + (1 − β)p(1)]v
2
− c if

he exerts effort and [αp(2) + (1 − α)p(1)]v
2
if he sh irks. T h e o ptimal rewa r d for playe r
2 should make him indifferent among these two options. Hence v
2
=
c
(β−α)[p(2)−p(1)]
,and
pla yer 2 w ill exert effort un der this contract if pla yer 1 succeed ed in his task. Furthermore,
bec au se the two worke rs are com p lem e ntar ity, player 2 will shirk if player 1 failed in his
task. This follo ws from th e fact that player 2’s effort has a lower m arginal effect when
play er 1 fails and from the fact that play er 2 is indifferent between sh irking a nd exerting
effort wh en p layer 1 succeeded. Hence v
2
is a mecha nism which indu ces equ ilibriu m 1.
Consid er now a mechanism v
0
2
under wh ich pla ye r 2 exerts effort when player 1 fails in h is
task. The incentive con straint for th is mech an ism must be [βp(1) + (1 − β)p(0)]v
0
2
− c ≥
[αp(1) + (1 − α)p(0)]v
0
2
and v
0
2

≥
c
(β−α)[p(1)−p(0)]
. D ue to the complementarity co nd ition
[p(2) − p(1)] > [p(1) − p(0)], it follows that v
0
2
>v
2
. Hence, if the contract is v
0
2
, it is a
dom inant strategy fo r player 2 to exert effort in t he comp lementarity case. Th is proves
that the optimal me chanism in the ca se where worke rs are com plem ents induces either
equilibriu m 1 or equilibrium 3. We now exam ine the case where workers are substitutes
in production. We have seen th at a mech an ism that in duces player 2 to exert effort when
player 1 fails in his task must pay v
0
2
=
c
(β−α)[p(1)−p(0)]
. C on sider an alternativ e mec hanism
which i nduces pla yer 2 to exert effort w hen player 1 succeeds. In this type o f mechan ism ,
7
pla yer 2 faces the fo llow ing con straint [βp(2) + (1 − β)p(1)]v
2
− c ≥ [αp(2) + (1 − α)p(1)]v
2

and hence v
2
≥
c
(β−α)[p(2)−p(1)]
. Since w o rker s are substitutes in production, the condition
must hold that [p(1) − p(0)] > [p(2) − p(1)]. Therefore, it must be the case that v
2
>v
0
2
,
which means that under v
2
it is a do m in ant strategy f or player 2 t o exert effort. Q .E.D.
Proposition 1 shows tha t the optim a l mecha n ism in o ur m ora l hazar d m odel yields
equilib ria which are consistent with the emp ir ical results presented in the rest of the p aper.
We h ave mana ged t o do so by s pecifying only t he rewards that p layer 2 receiv es. For the
sake of completeness, w e now presen t the entire optimal mec hanism in Proposit ion 2 b y
specifyin g the rewa rds of both players.
Proposition 2 Assume the tec hn o logy is one of co mplem e n ta rity (subs titu tio n ) and that
the optim a l mechan ism yields equ ilibriu m 1 (equilibr iu m 2). (The value of th e pro ject is B
where B
∗
<B <B
∗
.) Then th e optim a l contra ct is given b y:
v
1
=

c
(β−α)[βp(2)+(1−β)p(1)−(αp(1)+(1−α)p(0)]
and v
2
=
c
(β−α)[p(2)−p(1)]
(v
0
1
=
c
(β−α)[αp(2)+(1−α)p(1)−(βp( 1)+(1 −β)p(0)]
,v
0
2
=
c
(β−α)[p(1)−p(0)]
).
ProofofProposition2: C onsider t he strategy o f p layer 2 specified in equilibrium
1. If agen t 1 exerts effort, he will succeed with probability β, thus equilibrium 1 im -
plies that pla ye r 2 exerts effort with probabilit y β. T herefore, if player 1 exerts effort,
pla yer 2’s expected payoff is [β(βp(2) + (1 − β)p(1)) + (1 − β)(αp(1) + (1 − α)p(0))]v
1
− c.
If playe r 1 shirks, he succeeds in his task with proba bility α. Thu s, equilibriu m 1 im-
plies t hat pla y er 2 exerts effort with proba bility α, and t herefo re receives [α(βp(2) + (1 −
β)p(1)) + (1 − α)(αp(1) + (1 − α)p(0))]v
1

. By equating these two expression s, we get
v
1
=
c
(β−α)[βp(2)+(1−β)p(1)−(αp(1)+(1−α)p(0α)]
. Con sider now the strategy of player 2 specified in
equilibrium 2. In this case, if pla y er 1 exerts effort he w ill trigger pla yer 2 to exert effort
with p rob ab ility α. If playe r 1 shirks instead, he will trigger player 2 to ex er t e ffort with
probab ility β. The i ncentive constraint faced by pla yer 1 is now giv en by:
[β(αp(2) + (1 − α)p(1)) + (1 − β)(βp(1) + (1 − β)p(0))]v
0
1
− c =
[α(αp(2) + (1 − α)p(1)) + (1 − α)(βp(1) + (1 − β)p(0))]v
0
1
yielding v
0
1
as specified above.
8
Overa ll, the simple framewo rk in this section shows that a "po sitive" intera ction
should exist bet we en wo rkers who are c om plem ents in production, while a "negative" in-
teraction shou ld exist between workers who are substitutes. Psychologica l factors such as
peer pressure and s hame pla y no role in creating this interaction of effort c ho ices. Our
purpose is not to cla im that w orke rs can never affect each other due to beha vior al consid-
erations. Rath er, our p u rpose is to demo nstrate that t h ese intera ctio ns could r esu lt from
fully rational (income maxim izing) consideration s without relying on beha v ioral responses.
Indeed, the remain der of the pa per presen ts evidence from profession al baseball that these

t y pes of intera ction s betwe en workers a re significant, and appear to be based on a rational
response to the techno logy.
3 The Data and Background
The data was obtained from the “Base ball Arch ive” which is copyright ed by Sean Lahm an ,
and is a freely available on the intern et for research p ur poses. The data contains exten -
sive personal and yearly performance information on players, coach es, and tea ms from
1871 through th e 2003 season . The analysis focu ses on the modern period from 1970 to
2003 beca use Major League Baseball underwent a major expansion and restructuring into
divisions just prior to that period. However, a similar analysis using data from 1871 to
1969 reveals very sim ilar results.
The game of b aseb all presen ts an i deal case where the perfor ma nce of each pla yer is
easily measured in a uniform way, and in complete isolation from the performance of his
teamm a tes. T h is cont rasts with other s ports, suc h a s basketb all, w here total perfor m ance
is hard to quantify an d w here the ac tions of one player, which d o not alway s show up in
statistics, can comp lement o r co m e a t the expense of the performance o f h is team m a tes. In
addition, baseball players are easily d ivided in to two distinct types: p itchers and batters.
The function of pitchers is to prevent the other team from scoring runs, while the function
of a batter is primar ily to help score runs for the team. In this sense, the t wo types
of players are perfect substitutes for one another in team production — since the goal is
toscoremorerunsthantheotherteam. However,thereiscomplementarityamongthe
9
batters since it typically takes a series of hits within the same inning to score a run for
the team . That is, a typical “ hit” is meaningless for th e team by itself (u nless it is a
home run), and therefore, the marginal productivit y o f getting a hit increases w ith the
batting performance of the play ers who batted right before you. Therefore, batters can
be considered complements with each other while batters and pitchers can be considered
substitutes f or each other.
In addition, pitc h ers are typically divided into two ty pes: “starters” and “relief”
pitchers. Starting pitchers ty p ically start the gam e and con tinu e until they get tired or
into troub le, and then relief p itch ers are called in to finish the ga me. A relief pitc her

can ruin a good perfor m ance b y the starter with a bad per for m an ce, or he could “save”
the game with a good performance. Since mul tiple starting pitchers are nev er used in
the same game, starting pitchers can be considered substitutes and competitors with eac h
other, while being c omplem ent s with relief pitcher s.
Table 1 presents summary statistics for the samp le of p layer s from the 1 970 to 2003
seasons. The sample inclu des all batters who batted at least 50 time s in a season a nd
pitch ers w h o p itched in at least 10 games. Th e main performance measur e for batters is
the “batting average” (BA), w hic h is defined as the nu mber of hits divided b y the n umber
of opportunities to bat (“a t-bats” ) in a season. According t o Ta ble 1 , batters obta in a h it
in 26 percen t of their chances. Another conv entional measure of batting performance is the
“on-base-percen ta ge”, which takes into consideration o ther ways a b atter can get on base
(w alks, hit by pitc h, etc.).
4
The standard indicator of a pitcher’s performance is called
the E R A (Earned Run Avera ge). This measure take s t he nu mber of bases that a pitc her
allows the opposing team to obtain, and scales it b y the nu mber of innings played, so that
it represents the ave ra ge number of runs w h ich would have been scored o ff the pitch er in
afullgame.
5
As such, a higher ERA reflects poo rer performance. The avera ge ER A is
4.83 for starting pitch ers and 4.7 0 for relief p itch ers.
6
Another ind icator of a pitch er’s
4
The exact d efinitions of the batting m easures are as follows: batting average equals the number of
hits divided by the number of at-bats. On-base-percentage is defined a s (hits+walks+number of times hit
by pitch) divided by (at-bats+walks+sacrifice flies+number of times hit b y pitch). Slugging percen tage
is equal to (singles + 2*doubles + 3*triples + 4*home-runs)/(at-bats).
5
The ERA is calculated by: (number of earned runs/innings pitched)*9.

6
Apitcherwasdefined as a starting pitcher if he started at least one game in the season.
10
perform ance is the “opponent’s batting averag e” which is d efined a s the number of hits
allo wed divid ed by the number of batters fac ed. Although th ere are only sm all differences
in the ave rage performance measures betwe en startin g and relief pitc h ers, the differences
in their roles is high lighte d b y the average nu mber of games pitche d (44 f or relief p itche rs
v ersus 30 for starters) and the average n umber of games started (19 for starters v ersus 0
for relief pitchers).
There is very little mobilit y bet ween the two types o f pitchers, and b atters c an also be
categorized into three m ain categor ies: (1) “ skilled positions” (second base, th ird base, and
short-stop) which emphasize fielding skills a t the expense of hitting pro wess, (2) “power
po sition s” (first base, outfielders, a nd desig na ted hitters) which prim arily emp ha size power
hitting, and (3) “cat chers” which h ave d istinct field ing skills an d ar e typic ally power hitters.
The specialization of b atters into these three categories m eans that players in two differen t
categories can be considered as complements in the production of team runs, and not as
competitors or substitutes with each other. The next section examines whether a player’s
per form ance int eracts with the actions of his teamm ates as indicated b y the theory in
Section 2.
4 T he Basic R eg re ssion Analy sis
This section examines how the perform an ce of ind ividual players varies with the perfor -
man ce of his fellow wor kers. The basic r egression equation is the following:
performance
it
= β
0
+ β
1
(teammates
0

pitching ERA)
t
+ β
2
(teammates
0
batting ave)
t
+µ
i
+ β
3
(other controls)
t
+ ε
it
where the performance of pla ye r i in year t depends on his teammates’ pitching
performance in year t, his team m ates’ batting performance in yea r t (not in clu d in g the
batting performance of pitchers), the ability of pla yer i represen ted b y µ
i
, other observa ble
con trol vari ables, and th e u nobserved random componen t, ε
it
. The other control variables
include: the batting a verage in p layer i’s division (excluding his own team) in y ear t whic h
controls for the quality of the pitching and batting in the team’s division in the sam e year ,
the team manager ’s lifetime winning percentage which is an indicator for th e qualit y of
11
the team’s coach ing, the ballpark hitting and pitc h ing factors whic h con trol for whether
theteam’sballparkiseasyordifficult for batters in yea r t, the pla yer’s ye ars o f experience

(n u mber seasons played in the league), year effec ts, and du mmy variables for each division.
The unobserv ed ability of pla yer i, µ
i
, is co nt rolled for by using a fixed-effects specification
or by using a first-differences specification bet ween consecutive years.
Teams n aturally choose their rosters i n an endogenous way. G iv en a team’s budget
constraint, team ow ner s will maxim ize the team’s success by pick ing pla yers who will
in tera ct in an optimal way. This process will produce some teams whic h concentrate
on acquiring a group of strong batters (since a group is necessary to produ ce runs) at
the expense of acquiring g ood pitcher s. In fa ct, there is a nega tive correlation between
team batting and team pitch ing performa nce in a cro ss-section of teams within a given
y ear. Ho wever, this negativ e relationship will not produce spurious effects in the regression
specification abo v e due to the inclusion of player fixed-effects and the use of other controls
at the individual, team, ye ar, and division level. In particular, after con tro llin g for t he
fixed-effect of playe r i and for a typical player’s experien ce profile, id ent ification com es
from seeing whether variation within a given player from the typical player’s exper ience
profile can be explain ed by va riation i n his team m a tes’ perfor m ance levels.
It is importan t to note that th e pitchin g and batting variab les for the teammates of
player i do not include t he performance of pla yer i. Therefore, identification of the model
does not suffer from the r eflection prob lem poin ted out b y Manski (1993) wh ic h occurs
when a variable is regressed on a transformation of itself. As stated above, iden tification
of β
1
and β
2
comes from seeing whether variation within player i’s perform a nce levels
across yea rs is correlated with the perform ance levels of his teamm ates. Within a given
pla yer’s career, variation in his perform ance o ver time ca nno t be aggregated to p roduce
the m ea n of his team m ates’ perform ance levels. So, th e ba sic regression specification does
not suffer f rom this aspect of the reflection problem poin ted out by Manski (1993), but as

we discuss in th e nex t section, prob lems cou ld ar ise if there is a com mon shock to a ll team
membersinagivenyear.
The basic fixed-effect regressions for pitchers and batters are presented in Table
2. Colum n (1) sho w s that after con tr olling for all the other va r iab les, a giv en batter
12
has better than average years when the other batters on the team are doing well. In
contrast, column (2 ) show s that a batter ’s performance decreases when th e pitchers on his
team are pitc h ing well. (A lowe r ERA indicates stronger pitc hin g per fo rm a nc e.) The
specification in column (3) inclu d es the pe rform a n ce measures of bo th the batters and
pitc hers as explana tory va riab les, and the r esu lts are essentially unc hang ed. Thus, th e
results are robust to estimating t h e effect of pitchers and batters separately (columns (1)
and (2 )) or when they are estimated together in column (3). Therefore, the results are
not a product of a high correlation between the t wo variables.
Colum n s (5)-(7 ) present t he basic results for pitchers, and sh ow that a p itcher per-
forms better when his fellow pitc hers are doing better, but there is no significant effect
of th e team’s batting performan ce on a pitc her’s perform ance — a finding w hich repeats
itself throughout the paper. Again, the effect of the playe r’s fellow pitchers on his o w n
performance is robust to the inclusion or exclusion of the team ’s batting performance.
Regarding the other con trol variables, they all have the expected signs and are generally
significant for the batting and pitc hing regressions, although it is w orth noting that the
results are robust to excluding them.
One possible explanation f or the pitc hing re sults is that a coach is more likely t o let
a pitcher stay in the gam e lon ger, or use him in more games, if the other p itchers on th e
team are w eaker. That is, t h e coach will l et the pitc her struggle longer in the gam e when
there are weaker repl acements on the bench, t hus i nducing a positiv e correla tion bet ween
a p itch er’s ERA and tho se of his fello w pitc h ers. We can con tro l for this by including
the number o f innings a nd games played by the pitch er into the reg ression . After adding
these va riab les in to the specification, the coefficien t on his teamm ate’s ERA goes from
0.523 (t-statistic o f 6.51) to 0.62 5 (t-statistic 8.01). Therefor e, th e in tera ction be tween
pitchers appears eve n stronger after con tr o lling for how long the pitch er is left in the game.

Howe ver, inc lud ing these va r iables is problema tic s ince a player’s performan ce and playing
time are clea rly de term ine d simultaneou sly. For this reason, we choose not to include
these variables in t h e core specification, but it i s wo rth noting that the results a re robust
to including the amount of playing time into the regressions for both pitc hers and batters.
An additional complication could arise if the terms of the contract are endogenous
13
(see Kendall (2003)). For example, if a team own er guards against “psychological” shirking
beh avior b y creating more incentive s to exert effort when a batter is playing with less
talented batters (or batters that lik e to shirk), we should see batters play better when they
are p layin g with less t alent ed batters, which is the opposite of what we see in Tab le 2.
Therefor e, if contracts are structured to prev ent “group shirking”, the response of a batter
to his f ellow batters w o uld be b iased towards zero in Table 2, but the response of a batter
to his fello w pitc h ers w ou ld be biased away from zero. In addition , if this scenario w er e
true, the response of a pitcher to his fellow pitchers would a lso be biased towa rd s zero i n
Table 2. T herefore, the overall significance of t h e r esu lts sug gests t ha t co ntra cts a re written
in a w ay that is consisten t with the theory in Section 2, so that a “positive inter act ion”
exists bet ween worker s who a re complem e nts while a “negative intera ction ” exists between
workers who are s ubst itute s. Howeve r, to see whether the results a re robust to co ntrolling
for the va rious incentiv es built into the con tract, Table 2 includes the individual’s salary
as a con trol va riab le in column (4) for batters and column (8) for pitchers. S alary data
is available only for th e y ears 1985-2003, so the s am ple is sm aller than th e other colu m ns,
but the results are similar to w hat is found without in clu ding salary in the r egression s.
Therefor e, the results appear to be robust to the various confounding fa ctors built into
eac h player’s con tract.
Although many of the coefficien ts in Table 2 a re significa nt statistically, the implied
magnitudes are not very large. If we take a two standard deviation change in the batting
a v erage of a player’s teamm ates (0.024 from Table 1), the predicted change in a player’s
batting average based on the results in the third c olumn o f Table 2 is 0.005, w hic h is only
13 percent of the standard deviation in a player’s batting average (0.039 in Table 1). The
predicted change in a bat ter’s batting average due to a two s tandard deviation change in

the team’s pitc h ing ER A wo u ld be 0.0032 (the coefficie nt 0.282 in Table 2 m u ltiplied by
100, multiplied by two times 0.579, the stan d ard deviation of Team ER A in Table 1).
The predicted change in a pitcher’s ERA due toatwostandarddeviation c hange in his
teammates’ ERA is 0.588 . This p red icted increase represen ts a little more than 23 percen t
of the sta nda rd deviation of a starting pitc her’s ERA . Although these p redicted ch an ges
are not ve ry large, adding five points (the p r edicted change of 0.005 f or a batter from the
14
other b atters on the team) or increasing a pitcher’s ERA by 0.562 wo u ld probably n ot be
considered en tirely trivial to a fan or a player.
Table 3 perfor m s a sim ilar analysis to Table 2 b u t controls for unobserve d hetero-
geneitybyusingafirst-difference specification bet ween consecutive y ears rather than using
fixed-effects. The results are very similar in the sense that a batter is show n to be affected
by the batting and p itching performan ce of his teammates, while a pitc h er is affected only
b y his fellow pitc h ers. The magnitudes of the coefficients are a little differen t from the
estimates in Table 2, w ith s o m e s m a ller a n d some bigger in size, but inferen ces regarding
significance are very similar.
Overa ll, the resu lts are con sistent with the th eo ry th at players should be positively
affected by th e performance of their fello w workers w hen th ey are complements in pro-
duction (like batters between themselves), but negatively affected b y the performance of
their fellow wo rkers when they are su bstitutes in p roduction (like batters and pitchers).
Although the finding that a pitc her is positiv ely affected by other p itchers is consistent
with the t heor y, th e theory can not explain why a pitcher d oes not seem to react in e ither
direction to the team’s batting performance. However, the fact that there is a d ifferential
reaction to both types of pla yers from both t ypes of players is strong evidence against a
behavior al explanation for the results. A typical behavioral response wou ld be for any
worker to wor k hard er w hen his co-wo r kers are wo rking ha rder, regardless of wh ether th ey
are complem ents or sub stitu tes in team production. Th is prediction is clearly rejected in
the analysis. So , the differentia l responses according to the role of ea ch type of pla yer can
be viewed as evidence for the idea that the tec hnology of production significa ntly in fluences
the i nt eractio n of effort ch oices across workers.

5 Alternative Explanations and Robustness Checks
5.1 Di fferent P erformance Measures
We now examine whether t he res ults in Tab les 2 a nd 3 are r obust to using different mea sures
of a player’s performance. A s a b asis for comparison, the first column in the upper panels
of Tables 4 and 5 replicate the batting regression results already seen in Tables 2 and
15
3forthefixed-effects a nd first-differences specifications respectively. T h e first column
in the bottom pan els of Tables 4 and 5 use the “on-base-percentag e” of a player instead
of a play er’s b atting a verage as t he dependent varia ble. T his measure differs from the
batting av erage b y considering the abilit y of a play er to get on base by a “walk” or getting
hit by a pitc h rather than only by hitting. Tables 4 and 5 sho w that the results using
“on-base-percentage” as the dependen t v ariable are virtually identical to those using a
pla yer’s batting average as the perform an ce measure. Although not shown , the results
are also similar if we use a player’s home-run output as the dependen t variable. Tables 6
and 7 presen t results for pitchers using a different measure of a p itcher ’s perform ance: the
opposing team’s batting a verage while he was pitching. As a basis fo r com parison, the first
colum ns in Tables 6 and 7 replicate th e results for pitchers seen in Tables 2 and 3 using
a pitch er ’s ERA as his performa nce measu re. The firstcolumninthebottompaneluses
the opposing team’s batting average as t he dependen t va riable, and the results are very
similar to those obtained using t he ERA. Therefore, the resu lts for pitch ers and batters
appear to be robust to using alternative, convent ional measures of a player’s performance.
5.2 Switc hing Teams
One can think of players switchin g teams as pote ntially an ideal “natural exper im ent”
which produces variation in one’s co-w orkers. Ichino and Maggi (2000) use this type
of variation to test w hether chan ging locations affects t he sh irking behavior of workers.
The second column i n Table 5 replicates t he first-differences a n alysis, bu t uses only the
samp le of years where the player changed team s across consecutive years. The results are
virtually identic al to those using the full sample in column (1). Th e resu lts are also very
similar using the restricted sample of pitchers who c hanged teams in column (2) of Table
7. Therefore, the results show th at p layers bat better when they move to teams with

better batters an d worse p itch ers, wh ile p itch ers play better if they move to a place with
better pitchers.
16
5.3 No t Sw it ching Teams
One explanation for th e previous set of results is that there m ight be an un observed reason
wh y certain team s ha ve good batting but bad pitching, and when a player moves to that
team his performance changes accordingly. For exam p le, it could be that the p layer is
affected by the coaching change, or that certain ballp arks favor batters over pitc hers, or the
team could pla y in a new division w here teams are v ery strong in pitching or batting, or the
team’s city may be i n a part of the country wher e t he w eather f avor s pitching or b attin g.
The basic regressions in Tables 2 and 3, as w ell as the previous regressions using only
the sample of team-c han gers, con trol for man y of these scenarios by in clud ing measur es of
managerial qualit y, indices for whether the ballpark fa vors batting or pitching, t he batting
a verage of the division in the sam e y ear, and division dummy variables. Ho wever, these
measu res ma y be im perfect. So, to c om pletely contro l for this scenario, we restrict th e
fixed-effect analysis only to the seasons in whic h the player pla yed for the same team,
man ager, and ballpark (the combination of which t he player stayed with the longest). For
batters, the fixed-effect analysis is presen ted in colum n (2) of Table 4, while the first-
difference an alysis usin g a sample of players w ho do not c ha ng e team s in consecutive yea rs
is show n i n column (3) of Table 5. For pitc h ers, th e respective regressions a re in column
(2) of Table 6 and column (3) in Table 7. Over all, the results are very similar to those
using the whole sample and the sample of pla yers who changed teams. Ho wever, the
magnitu des of the coefficients tend to be weaker for the pla yers w ho stay on the same
team over consecutiv e y ears v ersus th ose that c hange teams. T his tendency is most likely
due to the fact that most of the var iation in one’s co-w orkers com es from players changing
teams. The f act t ha t there is enough variation in o n e’s co -wo rke rs even within the same
team in consecutive seasons to explain variation in an individual’s performance supports
the in terpretation that the main results a re no t due to endogenous m o ving.
5.4 Complem ents or Competition bet we en Pla y ers?
The positive effect of fellow batters on the ind ividu al perform an ce of a b atter, or fellow

pitchers on the pitching performance of an individual pitcher, could theoretically be due
17
to the complementarity bet ween playe rs or the com petition between players f or increased
playing tim e. We now attempt to isolate these two stories b y dividing batters and pitchers
into ty pes o f positions whic h are cle arly not su bstitut ab le (i.e. no com petition bet ween
pla yers of ea ch type).
As discu ssed a bo ve, pitchers can be divid ed into “starters” o r “non-starters,” while
batters can be categorized as eith er a “ skilled position”, a “power position ”, or a “catcher .”
There is very little m ob ility between these ty pes of positions, so it is reasonable to assu m e
that there is very little competitio n between p layer s across th ese types of positions. There-
fore, the a na lysis is no w perform e d using the ave rag e performan ce of player i’s teamm a tes,
but usin g only those team mates w hich play a different position than player i. For batters,
the fixed-effectresultsarepresentedincolumn(3)ofTable4whilethefirst-difference
results a r e in column (4) of Table 5. The r esults are virtu ally iden tica l to those u sing
the avera ge performance of all the player’s fellow teammates, including tho se th at play
the same po sition. For pitc h ers, the r egr essions are ru n separately for starting pitch ers
and non-starting pitchers, where the explanatory variable is the performance measure of
the oth er group. T he fixed-effect resu lts for pitchers are in columns (3) and (4) of Table
6whilethefirst-differen ce results a re in colum n s (4) and (5) of Table 7. Interestingly,
the pitch ing perfo rmance of non-starters has a bigger e ffect on starting pitchers than vice
v ersa. However, fo r starters and non-starters, the coefficients are s ign ificant and g enerally
larger in magnitude than the coefficients in previous specifications which lum ped all pitc h -
ers t ogeth er. This general pattern points to larger “cross” e ffects across t ypes of pitc hers
than within types of pitchers. This pattern bolsters the techn ology-b ased interpreta tion
of the result s since eac h pitcher is clearly more complementary with a pitc h er of the other
t ype than pitc hers w ithin the sam e type.
5.5 IV Results
The resu lts so far are rob ust to looking at the whole sample, a restricted samp le of players
c ha nging team s, a restricted sample of players sta ying w ith the same team, and to using
the performance of teamm a tes playin g in non-competing positio ns. In addition, our use

of fixed-effe cts co ntrols fo r t he overall, unobserved a bility o f each player. Howeve r, as
18
Manski ( 1993) poin ts out , t here c ould be an unobserved factor r esponsible fo r t he high or
lo w performance of all players on the team in a given y ear, and t herefore, this p roduces
a correlation bet ween the performance s of playe rs without there actually being a ca usal
effect. If this explanation w ere true, it seems incon sistent with our results which sho w
that the s ign o f t he e ffect depends on the degree of substitutability and complemen tarit y
bet ween play ers — since it is unlikely that an unobserv ed factor is inducing all batters to
do better in the same year that t h e team’s pitcher s are having bad ye ars.
Howe ve r, to fu rth er examine this possibility, we r epeat the analysis using the lifetime
performance of player i’s teammates instead of th eir curren t perform ance in year t. Using
lifetime performance allo w s us to wash out all the idiosyncratic shocks to a specificteamin
a giv en year, since the lifetime perform ance of any given pla yer d oes not c h ange from yea r
to year. As a result, variation in the lifetime performa nce o f p laye r i’s team mates stems
only from c han ges in the composition of h is co-workers. This identification str ategy is
similar to the one employed by Ichin o and M agg i (2000) and used above wh en we restricted
thesampletoplayerswhomoveteams. However,theuseofthelifetimeperformanceof
one’s teammates allows us to exp loit c ha nges in the c om position of on e’s teamm ates within
the s a m e team as well as across teams when players mo ve.
The results for ba tters are p resented in column (4) of Table 4 an d colu m n (5) o f
Table 5 , and are virtually identical to column (1) which u ses the b atting average of one’s
teamm ates i n t h e current ye ar. The first-differ en ce results in Table 5 a r e little w eaker in
significance, but the magnitude is not much lower than the coefficien t estimates in other
specifications. For pitch ers, the fixed-effect res ults are in c olumn (5) of Table 6 w h ile
the first-differen ce results appear in colum n (6) of Ta ble 7. The pitchin g results using
the l ifetim e achievements of one’s t eam mates are very similar t o those u sing their current
ac h ievements. Furtherm ore, t he last column of Tables 5, 6, 7, and 8 repeats th e an alysis
for batters and pitc hers, but uses the lifetime perform an ce as an instrumental var iable for
the current performance of one’s co-workers in a 2SLS regression. Again, the results are
v e ry sim ila r to using the lifetim e ach ieve m ent s directly as a regre ssor an d to using th e

curren t performance o f one’s teamm ates.
Finally, in order to net out the effect of p layer i’s e ffect on the lifetime performance
19
of his teamm a tes, colum n (5) in Ta ble 4 r epeats the analysis for b atters but restricts t he
samp le to only those years wh en player i isplayingonanewteam,andthenexplains
his curren t perform a nce with the lifetime a ch ievem e nts of h is new teamm at es up to the
y e ar prior to him joining the team . C olumn (6) of Table 6 runs a similar regressio n for
pitc hers. U sing this specification, the results for batters in Table 4 are unchanged from
previous regressions, but th e resu lts for p itchers in Ta ble 6 a re n ot sig nificant. T h is last
result is p r obab ly due to t h e fact that prior lifetime results are more lik ely to be noisy for
pitchers than batters (the coefficien t of variation fo r a pitcher’s ERA is 12 times larger
than the coefficient of variation of a batter’s batting aver age: 1 .94 for pitchers v ersu s
0.152 for b atters in Table 1). T h e overall r esu lts in t his section point once ag ain t o i dea
that batters are positively affected by other batters but negative ly affected by their fello w
pitchers, while pitchers seem to be positively affected by other pitchers, but not b y their
fellow batters.
6Conclusion
This paper a na lyzes how a player’s performance is dependent on the performance of h is
co-worke rs. Using da ta on p rofessional ba seba ll pla ye rs, the results show th at a batter’s
per form ance increases with those o f his fello w batters, b ut decreases with the qualit y of h is
team’s pitc hing. T he results also indicate that a pitcher’s performance increases with the
pitching perform ance of the other pitchers on the team, but is unaffected by the batting
performa nce o f the team.
The differential reaction to both types of players from both types of players suggests
that the results are not lik ely to be explained by behavioral explanations such as peer
pressure, guilt, and social norms. These t y pes of explanations wo uld predict that an y
t ype of workers will w ork harder when his co-workers are working harder, r egardless of the
function of his j ob in relation to the function o f his co-workers. Therefore, the differential
responses according to the role of eac h type of pla yer can be viewed as evidence in favor
oftheideathatworkersadjusttheireffort in a rational w a y whic h is dependen t on the

tec h nolog y of team production. T his int erp retation i s strengthened by the many robustness
20
c hec ks with di fferen t samples and specifications, as well as instrumenting the performance
of on e’s co-w orker s with th eir lifetim e perform an ce. All of the va riation in this in strum ent
comes fr om changes in the composition of on e’s co-w orkers, and therefore, is un affected
by transitory shocks which may affect t h e perfor m an ce of a ll players on a team in a given
year.
Although the empirical analysis is performed using dat a on baseball pla yers, the re-
sults are likely to apply to m a ny w o rk en v ironments where the r e is an elemen t of team
production. Whenev er w orkers have to w ork in teams, there is bound to be complementar-
ities and substitutability between different kinds of workers, and t h erefore, the framew o rk
analyzed in this p aper is likely to be relevan t. It is important to note t h a t a key assumption
driving the theoretical results is that an individual’s w age is a functio n of the aggregate
team performance. If this assumption did not hold, there would be no “technological” ba-
sis for a work er to alter his performance according to the output of his fellow work ers, since
his wa ge w ould be purely a function of his own individual perfor mance. However, there
are two main reasons to expect that an individual’s w age is affected b y the performance
of the whole team, e ve n in cases where there a re effective w a ys to evaluate individual per-
forma nces (see also A lch ian a n d Dem setz (1 97 2)). First, a h igher team perform a nce m ay
generate higher profits, a nd th us, increase the value of the marginal product of labor. Sec-
ondly, a hig her team performance can serve as a signal fo r aspects of a pla yer’s ability that
are hard to observe or quantify, and th us, not reflected in typica l performance mea sures.
For example, individuals on a winning team project m a y be consid ered industrious workers
who are able to w ork well together with fellow wo rkers. Therefore, the “tec hn ologica l”
interaction o f effort choic es high lighte d in th is pa per is likely to be relevant for many wo rk
en vironments where cooperation among workers i s importan t.
21
References
[1] Alchian , Armen and Harold Demsetz, ”Prod uction, Information Costs and E c onom ic
Organization,” American Econom ic Review (1972) 5, 777-795.

[2] Angrist, Joshua D . a nd Lang, Kevin. “Does Sc hool In teg ration Generate Peer effects?
Eviden ce from Boston’s Metco Program ,” A m erican Econom ic Re view, 9 4(5), D ecem-
ber 2004, 1613-1634.
[3] Edin, P er-A nder s, Peter Fredriksson, and Olof Åslund, “Ethnic Enclaves and th e
Econom ic Su ccess of Immigrants — Evidence from a Natur al E xperimen t,” Quarterly
Journal of Economics, CXV III (2003), 329-357.
[4] Falk, Armin, and Andrea Ic h ino, “Clean Evid ence on P eer E ffects,” Working Paper,
Euro pean University Institute, 2 00 3.
[5] Glaeser, E. L., B . Sacerdote, a n d J. S che inkman, “C rime and Social Inte rac tio ns,”
Quarterly Journal of Economics, CX I (1996), 507-548.
[6] Gould, Eric D.; La vy Victor and Paserman, M. Daniele. “Imm igra ting to Opportunit y:
Estim ating the Effects of School Quality Using a N atur al Experiment on E th iopians
in Isra el.” Quarterly Journal of Economics, May 2004.
[7] Gould, Eric D .; La vy Victor and Paserman, M . Daniele. “D oes Imm igration Affect
the Long-Term Educational Outcomes of N atives? Q uasi-Ex perimen tal Evidence,”
Working Paper, 2 004.
[8] Guryan, Jonathan, “Desegreg ation and Black Dropout Rates,” A meric an Ec onomic
Review, 94(4), S eptember 2004, 919-943.
[9] Hanushek, Eric, John F. Kain, and Stev en G. Rivkin, “N ew Evidence About Bro wn V .
Board of Education: The C omplex E ffects of School R a cial Composition on Ac hieve-
ment,” NBE R Working Paper No. 8 741, 2002.
[10] Holmstrom, Bengt. (1982) “M oral H azard in Te ams,” Bell Journal of Econom ics 13( 2)
324-340.
[11] Holmstrom , Bengt, and P a ul M ilgrom . “M ultitask P rincipal-A gent A nalyses: Incen-
tiv e Con t racts, Asset Ow nersh ip, and Jo b Design,”
Journal of L aw, Economics, & Or ganization,7,1991,24-52.
[12] Ho x by, Caroline M. “P eer Effects in the Classroom : Learning from Gender and R ace
Variation.” N B ER Working Paper N o. 7867, August 2 000.
[13] Ichino, Andrea and Giovanni M aggi, “Work En viro nm ent and Indiv idual Backg round :
Explaining Regional Shirking Different entials in a Large Italian Firm,” Quarterly

Journal of Economics, CXV (3), A u gust 2 000, 1057-1090.
[14] Itoh, H. (1991) “In ce ntives t o Help M u lti-Agent S itua tions,” Econ ometrica, 59, 611-
636.
[15] Jacob, B r ian A., (2004 ).“P ub lic Housing, Housing Vouchers and Student Achievement:
Evid en ce from Pub lic Housin g Dem o lition s in Chica go ”American Econom ic Review
94(1), March 2004, 233-258.
22