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12-1990
Do Tournaments Have Incentive Effects?
Ronald G. Ehrenberg
Cornell University, rge2@cornell.edu
Michael L. Bognanno
Temple University
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Do Tournaments Have Incentive Effects?
Abstract
Much attention has been devoted to studying models of tournaments or situations in which an individual's
payment depends only on his or her output or rank relative to that of other competitors. Academic interest
derives from the fact that under certain sets of assumptions, tournaments have desirable normative properties
because of the incentive structures they provide. Our paper uses nonexperimental data to test whether
tournaments actually elicit effort responses. We focus on professional golf tournaments because information
on the incentive structure (prize distribution) and measures of individual output (players' scores) are both
available. We find strong support for the proposition that the level and structure of prizes in PGA tournaments
influence players' performance.
Keywords
incentive effects, Professional Golf Association, PGA, tournaments, effort responses, performance
Disciplines
Labor Economics | Labor Relations | Organizational Behavior and Theory | Social and Behavioral Sciences |
Sports Sciences
Comments
Suggested Citation
Ehrenberg, R. G. & Bognanno, M. L. (1990). Do tournaments have incentive effects? [Electronic version].
Journal of Political Economy 98(6), 1307-1324.
Required Publisher Statement
© University of Chicago Press. Reprinted with permission. All rights reserved.
This article is available at DigitalCommons@ILR: http://digitalcommons.ilr.cornell.edu/articles/640
Do Tournaments Have Incentive Effects?
RonaldG. Ehrenberg
CornellUniversityand National Bureau of EconomicResearch
MichaelL. Bognanno
TempleUniversity
Much attention has been devoted to studying models of tournaments
or situations in which an individual's payment depends only on his
or her output or rank relative to that of other competitors. Academic
interest derives from the fact that under certain sets of assumptions,
tournaments have desirable normative properties because of the incentive
structures they provide. Our paper uses nonexperimental
data to test whether tournaments actually elicit effort responses. We
focus on professional golf tournaments because information on the
incentive structure (prize distribution) and measures of individual
output (players' scores) are both available. We find strong support
for the proposition that the level and structure of prizes in PGA
tournaments influence players' performance.
I. Introduction
In recent years economists have devoted considerable attention to the
normative properties of alternative compensation arrangements.
We have discussedour work in workshopsat Cornell, Columbia,North Carolina
(Greensboro),MassachusettsInstitute of Technology, Arizona, Minnesota,the National
Bureau of EconomicResearch,North CarolinaState, Oberlin,Chicago,Pittsburgh,
Brigham Young, Virginia, Northwestern, Amherst, Kentucky, Georgia State,
and Brandeis, and we are grateful to numerous colleagues at these institutions and to a
referee for their comments. This paper is based on work supported by the National
Science Foundation under grant SES-8719592. The data set used in this paper will be
archived at the Inter-University Consortium for Political and Social Research (P.O. Box
1248, Ann Arbor, Mich.) after January 1, 1991.
Journal of Political Economy,1990, vol. 98, no. 6]
? 1990 by The University of Chicago. All rights reserved. 0022-3808/90/9806-0001$01.50
1307
1308 JOURNAL OF POLITICAL ECONOMY
Among the arrangements discussed have been tournaments, or situations
in which an individual's payment depends only on his or her
output or rank relative to that of other competitors (see, e.g., Lazear
and Rosen 1981; Carmichael 1983; Green and Stokey 1983; Nalebuff
and Stiglitz 1983; Malcomson 1984; O'Keefe, Viscusi, and Zeckhauser
1986; Rosen 1986). Tournament models are of more than academic
interest since they may well describe the compensation structures applicable
to many corporate executives, to professors (who can be
thought of as being involved in promotion tournaments), to salespeople
(whose bonuses often depend on their relative outputs), and to the
more obvious example of professional sports tournaments. Academic
interest derives from the fact that, under certain sets of assumptions,
tournaments have desirable normative properties because of the incentive
structures they provide.
Very few attempts have been made to test whether tournaments
actually elicit desired effort responses. One experimental study of
rank-order tournaments that used 225 paid undergraduate student
volunteers as subjects did find mixed support for the theory, although
disadvantaged (high-cost-of-effort) subjects provided more effort
than the theory predicted (see Bull, Schotter, and Weigelt 1987). The
lack of nonexperimental studies of tournaments is probably due to
the difficulty of measuring both individuals' effort levels and the incentive
structures competitors face in many circumstances.
To test in a nonexperimental setting whether tournaments do have
incentive effects, we focus on golf tournaments because information
on the incentive structure (prize distribution) and measures of individual
output (players' scores) are both available. Under suitable assumptions,
players' scores can be related to their effort and implications
for scores drawn. In addition, data are available to control for
factors other than the incentive structure that should affect output;
these factors include player quality, quality of the rest of the field,
difficulty of the course, and weather conditions. Implications can be
drawn for both how well a player will perform during an entire tournament
and how well he will perform on the last (fourth) round
contingent, other things equal, on the marginal return to effort he
faces in the tournament after the third round. Our empirical analyses
make use of data from the 1984 men's Professional Golf Association
(PGA) tour.1
1 A short nontechnical companion paper (Ehrenberg and Bognanno 1990) replicates
a portion of the empirical analyses presented here using data from the 1987 men's
European PGA tour.
INCENTIVE EFFECTS 1309
Percent of Total
Prize Money
18.0
10.8 ---
6.8
I l\ I
I l\I
6.8tour ameni thesmpe
I I I
I I I\
I I I
1.1 _ ___ _ _ _ _
1.0 a ----__
1 2 3 22 23
Player'sRank
InTournament
FIG. 1.-Share of total prize money going to players of different ranks: 1984 men's
PGA tournament in the sample.
II. The 1984 Men's PGA Tour: Institutional
Characteristics and Hypotheses to Be Tested
The typical golf tournament is composed of four rounds. Half the
field is "cut" at the end of the second round, two additional rounds
are played, and then prizes are awarded on the basis of the players'
ranks after the final round. Of the 45 tournaments on the 1984 men's
PGA tour, 40 were of this type, and data from them are used in our
analyses.
Across these tournaments the structureof prize money by rank was
virtually identical, although the level of prize money varied across
tournaments.2 Figure 1 summarizes this structure. A key element of
2 See Official1985 PGA TourMedia Guide(1984). Of the 39 tournaments actually used
in the study (the British Open was excluded for reasons that will be made clear shortly),
9 offered total prize levels between $200,000 and $350,000, 16 had a total prize level of
$400,000, 8 had a total prize level of $500,000, and 6 offered total prize money in the
$565,000-$800,000 range.
1310 JOURNAL OF POLITICAL ECONOMY
the prize structure is that the marginal return from improving one's
performance by one rank (or by not seeing one's performance decline
by one rank) was much higher for people who were close to the
leaders after three rounds than it was for people who were far from
the leaders. For example, the marginal prize received from finishing
second instead of third was 4.0 percent of the total tournament prize
money, while the marginal prize received from finishing twentysecond
instead of twenty-third was 0.1 percent of the total tournament
prize money.
This structure of prizes, coupled with variations in the level of
prizes across tournaments, suggests two types of tests of the hypothesis
that tournament-type prize structures have incentive effects.
First, since the structure of prizes is constant across tournaments, the
prize differential for "winning" depends only on the level of total
prize money. Thus one can focus on a tournament as a whole and ask,
other things equal, whether higher total prize money leads to lower
scores. Second, one can focus only on the last round of a tournament
and ask, other things equal, whether a player's performance on the
last round depends on the marginal return to effort he faces. The
marginal return to effort will depend in turn on the total prize money
in the tournament, the player's rank after the third round, and how
many players are tightly bunched around him after three rounds.
Both types of analyses are reported in the next section.
Before turning to the empirical results, however, we must discuss
one institutional complication. Not every pro golfer who wanted to
enter any given PGA tournament in 1984 could. Rather, a system of
exemptions and priorities existed. At the risk of simplifying a very
complex system, the system worked as follows (see 1984 Player'sHandbook):(i)
Any golfer who had won a major tournament since 1975 or
any PGA tour tournament in 1983 could enter any tournament he
wanted in both 1984 and 1985. (ii) Any golfer who failed to qualify
under category i and had won a major tournament in 1975 or any
PGA tour tournament in 1982 could enter any tournament he wanted
in 1984 but had no promise of entry for tournaments in 1985. (iii) If
not all positions in a 1984 tournament were filled by individuals from
categories i and ii, any golfer who finished among the top 125 money
winners on the 1983 PGA tour could enter the tournament. (iv) Any
remaining vacancies in a tournament were filled using other criteria
(e.g., the sponsor-chosen players, lower-ranked players on the 1983
tour, or leaders from the PGA tour qualifying tournament).
As we shall show, this system of exemptions and priorities helps to
explain which players entered which 1984 PGA tour tournaments;
this is important because analyses that use data on the scores of entrants
to tournaments will be subject to potential selectivity biases. In
INCENTIVE EFFECTS 1311
addition, individuals in categories ii, iii, and iv had to be very concerned
about their total tour earnings in 1984. For unless they won a
PGA tour tournament during the year, they had to finish in the top
125 money winners during the year in order to be assured of virtual
automatic entry, if they desired, to PGA tour tournaments in 1985
(i.e., to be in category iii in 1985). In contrast, no matter what individuals
in category i accomplished during the 1984 tour, they were assured
the option of entry into any PGA tour tournament that they
wanted to enter in 1985.
Suppose that the latter group, whom we refer to henceforth as the
exemptplayers, exhibited effort levels that were sensitive to the level
and structure of prizes in a tournament. Because the former group,
whom we henceforth refer to as the nonexemptplayers, had to worry
about qualifying for the next year's tour, the level and structure of
prize money in a tournament may not be an accurate indicator of
their marginal financial return to effort. Rather, one would need to
know also how an increase in effort for one of them increased the
probability that he would be classified as an exempt player in 1985
and what the expected increase in the present value of his future
earnings would be if he was so classified. As such, even if the exempt
and nonexempt players' marginal responses to financial returns were
equal, one might intuitively "expect" nonexempt players' effort levels,
and hence scores, to be less sensitive to tournament-specific prize
variables. An appendix (available from the authors) presents a simple
omitted-variables model that indicates the precise (and restrictive)
conditions under which this expectation is theoretically correct, and
in the next section, we test to see whether responses differ between
the two groups.
III. Empirical Analyses
Our empirical analyses proceed in stages. First, we estimate finalscore
equations for players on the 1984 men's PGA tour. Next, we
estimate the score after the second-round equations. Finally, we estimate
final-round score equations.
A. Final-ScoreEquations
Our empirical work is based on two-contestant tournament models
with heterogeneous competitors. Assuming that an individual's score
is linearly related to his effort/concentration level, a tournamentspecific
effect (due to course difficulty and weather conditions), and
random factors and that effort/concentration has positive and increasing
marginal cost, one can show that a player's final score in a
1312 JOURNAL OF POLITICAL ECONOMY
tournament will depend on the prize differential for winning, measures
of his and his opponent's ability, and tournament-specific fac-
tors.3
Data are available in the 1985 Golf Digest Almanac (1984) and the
Official1985 PGA TourMedia Guide (1984) for each 1984 men's PGA
tournament on the score by round, final rank, and prize money won
for all players who entered and made the cut in each tournament.
Data on each player's scoring average on all rounds during the year, a
measure of his "ability," are available only for the top 160 money
winners during the year; consequently, the analyses reported below
are restricted to these individuals. Equations were estimated (with the
data pooled across individuals and tournaments) in the form
Sji = ao + ajTPRIZEj + a2X, + a3Yj + a4z, + Vii, (1)
where sj, is the final score of individuals in tournament i, TPRIZE is
the total prize money awarded in the tournament, xi is a vector of
variables to control for the difficulty of the tournament course and
weather conditions, yj is a vector of proxies for player j's ability, z-is a
vector of variables to control for the quality of other players in the
field, and vi0is a random error term. If the theory of tournaments is
correct, higher prizes should lead to lower scores; hence estimates of
a, should be negative.
The controls for other tournament-specific factors are PAR, the
par for the tournament course; DIST, the total course yardage; RATING,
the PGA's evaluation of the playing difficulty of the course as it
was set up for the tournament (expressed in strokes); and WAVE, the
average of three raters' perceptions of the number of days during the
tournament in which the weather significantly influenced player performance.
A player's ability is proxied by SCOREAVE, his scoring
average on all rounds played during the 1984 tour, and FCUT, the
fraction of tournaments he entered in which he made the cut during
the 1984 tour. Finally, quality of the other players in the field is
proxied by FRACT, the fraction of all players in the tournament who
made the cut that were ranked in the top 160 of total prize winners
during the 1984 tour, and MPERAVE, a measure of the mean "performance
average" on the 1984 tour of players in the tournament
who made the cut.4
3 See Ehrenberg and Bognanno (1989) for details.
4 A player's performance average is a measure of how well he placed in the tournaments
he entered during the year, with high performance averages indicating better
players. The factors PAR, DIST, SCOREAVE, FCUT, FRACT, and MPERAVE were
obtained from the 1985 Golf Digest Almanac. One-paragraph descriptions of the
weather conditions that players faced each day of each tournament were obtained from
the Official 1985 PGA Tour Media Guide; an average of three raters' perceptions of
whether the weather each day adversely affected player performance (WAVE) was
INCENTIVE EFFECTS 1313
Estimates are reported in table 1. Separate analyses are presented
for the entire sample, for the exempt players, and for the nonexempt
players.5 A dummy variable for whether a tournament is a "major"
tournament (i.e., the U.S. Open, the PGA, or the Masters) is also
included.6 Winning a major tournament typically provides substantial
opportunities for lucrative endorsements; hence the total prize
money variable understates the return to winning these tournaments.
As seen in the table, more difficult courses, as measured by PAR,
DIST, and RATING, are seen to lead to higher scores. Similarly, each
day of "bad" weather appears to raise players' scores by over two
strokes. As expected, poorer players, as measured by SCOREAVE,
play worse. Where significant, competing against a better field, as
measured by FRACT and MPERAVE, appears to lead to higher
scores.
Most striking, the coefficient of TPRIZE is negative as anticipated.
The variable TPRIZE is measured in thousands of dollars; hence
increasing the total prize money by $100,000 is associated with each
player's, on average, scoring 1.1 strokes lower during a tournament
(col. 1). The results of estimating an equation in which TPRIZE is
interacted with exempt status (col. 2) and of estimating separate equations
for exempt (col. 3) and nonexempt (col. 4) players suggest that
the coefficient of TPRIZE is slightly larger (in absolute value) for
exempt players. As noted in the previous section, this may reflect
either that exempt players' effort levels are more responsive to
financial variables or that the nonexempt players' TPRIZE coefficient
is biased toward zero because their marginal return to effort is also
based both on how doing well in a tournament increases their probability
of being classified as exempt in the next year and on what their
expected increase in the present value of future income would be if so
classified. Finally, other things equal, scores are lower in major tournaments
but significantly so only for exempt players (col. 3). Since
these players are the ones with the greatest chance of winning and
thus gaining the endorsement value, this result seems sensible.
Several extensions warrant brief mention here. First, the results in
table 1 may be subject to selection bias because the sample is restricted
to the subset of players who entered and made the cut in each tournathen
constructed. Finally, RATING was obtained for a majority of the courses from Jay
Matolla of the Metropolitan Golf Association and for the other courses through telephone
calls to state golf associations.
5 When a nonexempt player won a tournament, his status was changed to exempt for
subsequent tournaments in the year.
6 The British Open, the fourth major golf tournament, was excluded from the analyses
both because RATING was not available for it and because relatively few of the top
U.S. players enter it. As a result, our sample actually includes 39 tournaments.
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INCENTIVE EFFECTS 1315
ment. Because of this, the effect of the total prize variable on players'
final scores may be confounded with its effect on their entering and
making the cut in a tournament. To control for this possible problem,
one must have data on the players who entered each tournament and
failed to make the cut; fortunately the PGA was able to provide us this
information, as well as data on these players' scores during the first
two rounds of the tournament.
To model separately the decision to enter a tournament and the
probability of making the cut and then to estimate a bivariate selection
model is a difficult task. Instead, we approximated this process and
estimated a univariate probit equation of the probability of entering
and making the cut. Following the approach initially suggested by
Heckman (1979), we then used estimates from this equation to compute
an estimate of the inverse Mills ratio for each individual, which
was entered as an additional explanatory variable in equation (1) to
control for selectivity bias. However, when this augmented final-score
equation was reestimated, the coefficient of the additional variable
never proved significant; nor did the TPRIZE coefficients differ from
those reported in table 1. Thus the estimates in table 1 do not appear
to be subject to selection bias.
Second, the precision of the estimates presented in table 1 may be
overstated because by implicitly assuming that the random error term
is independent and identically distributed, we have not allowed for
tournament-specific disturbances that are uncorrelated with the explanatory
variables. One way to take account of this problem is to pool
data within tournaments and to reestimate (1) using 39 observations
on within-tournament averages as the units of observation. When this
was done, the magnitude of the TPRIZE coefficient remained the
same; however, its t-statistic fell to approximately 1.9. Alternatively,
one can estimate a random effects model that allows for disturbances
that have a component that is drawn randomly for each tournament
from a distribution with zero mean but that is the same for each
player in each tournament. When this was done, the TPRIZE coefficient
was no longer statistically significant for nonexempt players;
however, the coefficient continued to have the correct sign and remained
statistically significant for exempt players.
B. Scoreafter Second-RoundEquations
Given the availability of data on the score after two rounds for all
individuals who enter each tournament, we can estimate how the level
of prize money influences players' performance in the early rounds of
a tournament. Table 2 presents estimates similar to those found in
table 1, except that the sample is now all entrants in each tournament
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INCENTIVE EFFECTS 1317
(among the top 160 money winners in the year) and the outcome
variable is now the player's score after the second round, prior to the
cut's being made. In addition, the weather variable now refers to the
weather on the first two days of the tournament and the field quality
variables to all entrants in each tournament rather than to those who
made the cut.
The most striking finding is that the total tournament prize money
does not appear to influence players' performance during the first
two rounds. Only for exempt players in the specification in which
exempt status is interacted with the prize variable (col. 2) is there any
evidence of an effect, and even for this group, an increase in prize
money of $100,000 would be associated with scores that were only 0.1
strokes lower per player after the first two rounds. This finding is
consistent with the hypothesis that a player's difficulty in maintaining
concentration occurs primarily in the later rounds of a tournament
when fatigue is more likely to have set in.7
Of course, the possibility still exists that the results in table 2 are
subject to selection bias because they are based on a sample of tournament
entrants; we may be confounding the effect of a tournament's
prize level on the probability that players enter the tournament with
its effect on their scores. To check for this, Heckman's (1979) two-step
procedure was once again employed. First, several probit equations of
the probability of entering a tournament were estimated in which
entry probabilities were specified to be a function of a player's exempt
status, his total career earnings prior to 1984, his age, the chronological
order of a tournament during the year, the status of the tournament
as a major tournament, the tournament's total prize money, and
the player's scoring average on all rounds in which he played during
the 1984 tour or on all first and second rounds in which he played
during the tour. Separate sets of coefficients were estimated for exempt
and nonexempt players.8
These estimates were used to obtain estimates of the inverse Mills
ratio for each individual entered in each tournament, and augmented
versions of the score after the second-round equations were then
7 Generalizations of tournament theory to the n-person case suggest that the marginal
response of effort to the prize spread declines as the number of competitors gets
larger (see McLaughlin 1988). Since roughly twice as many players compete in the first
two rounds of a tournament as in the last two, this provides another explanation for
why one might observe scores for the tournament as a whole that are more sensitive to
tournament prize levels than scores for the first two rounds.
8 These estimates are found in Ehrenberg and Bognanno (1989) and are consistent
with hypotheses from tournament theory that individuals will "sort" themselves into
tournaments. For example, exempt players were seen to be more likely, and nonexempt
players less likely, to enter major tournaments and tournaments with higher prize
money.
1318 JOURNAL OF POLITICAL ECONOMY
estimated. However, again the coefficients of the estimated inverse
Mills ratio never proved significant, and the estimated coefficients of
the total prize variable were identical to those found in table 2. Thus
the conclusion that the level of prize money at best only marginally
affects the level of effort during the first two rounds for exempt
players and does not affect the level of effort during that time for
nonexempt players appears to be valid.
C. Final-Round ScoreEquations
Consider a golfer playing in two tournaments with the same total
prize money. Suppose that he scores a 72 on each of the first 3 days of
both tournaments, but because of random factors that influence his
opponents' performance, he finds himself in third place in the first
tournament but in twentieth place in the second tournament. Given
the structure of PGA tournament prizes (fig. 1), he faces a greater
marginal return to effort/concentration in the first tournament,
should exert more effort/concentration there, and, on average,
should have a lower final-round score in that tournament.
Of course, a player's rank after three rounds and the total tournament
prize money are only two of the elements that influence the
marginal return to effort/concentration that he faces. One must also
take into account how closely his competitors are "bunched" around
him. As such, we defined six different variables to serve as proxies for
the marginal return to effort an individual faces. These are all illustrated
in figure 2.
In the figure, suppose that the curve PP shows the relationship
between a player's final rank in a tournament and the prize money he
will be awarded. Consider an individual who after the third round is
at rank R. If he remains at that rank, he will be awarded the amount
OA at the end of the tournament.
The first three marginal return variables we compute ignore how
tightly bunched competitors are around the player and are based on
the return to improving performance, or of having it get worse, by
one rank. The variable DPRIZE3 is the actual marginal reduction in
prize money if the individual's rank at the end of the tournament was
one higher (worse) than his current rank; this is given by AD in the
figure. The variable UPRIZE3 is the actual increase in prize money
the individual would gain if he improved his rank by one; this is given
by AC. The variable MIDPRIZ3 assumes that the individual takes into
account the cost of losing one rank, as well as the benefit from improving
one rank. It is defined as the actual average absolute change
in prize money if the rank at the end of the tournament is either one
INCENTIVE EFFECTS 1319
Prize for Finishing
at Rank
P
G
F 4
E Lt--.-
A
D -i--i--i,
U T S R-1 R R+1
Player's Rank
in Tournament
FIG. 2.-Alternative measures of marginal return to effort/concentration in a tour-
nament.
lower or one higher than R, and it is given in the figure by the average
of the lengths of AC and AD.
Presumably, increased effort/concentration directly affects a player's
score, not his rank. The effect of increased concentration on rank
then depends on the number of competitors closely bunched around
the player. The next three measures take this into account. They are
the actual increase in prize money the individual would receive if he
improved his scores relative to those of his competitors by one stroke
(LESIPRIZ), two strokes (LES2PRIZ), or three strokes (LES3PRIZ).
If improvements of one, two, and three strokes would cause the individual's
rank to improve, respectively, to S, T, and U in the figure,
these variables' magnitudes in turn would be given by AE, AF, and
AG.
Each of these six variables was computed for each individual in
each tournament. Equations were then estimated, using data pooled
across individuals and tournaments, in which a player's score in the
1320 JOURNAL OF POLITICAL ECONOMY
final round of a tournament was specified to be a function of his
scores on the first 3 days of the tournament, the adverse effect of
weather, if any, on players' performance on the first 3 days and on the
final day of the tournament, and a marginal return to effort variable.
Given the weather, a player's scores on the first 3 days, which are
probably the best predictors of how well he is currently playing,
should be positively associated with his score on the final day. Given
his scores on the first 3 days, the poorer the weather was on those
days, the lower his score on the final day should be. However, the
poorer the weather on the final day, other things equal, the higher his
score on the final day should be.
A player's scores on the first 3 days of a tournament are not exogenous,
but rather depend on the prize differential for winning, measures
of his and his opponents' ability, and tournament-specific factors
such as course difficulty and the weather on those days. Similarly,
the estimated marginal return to effort a player faces is also not
exogenous since it depends on his scores and his opponents' scores on
the first 3 days, both of which depend in turn on the factors described
above. As such, a player's scores on the first 3 days and the marginal
return to effort he faces on the last day are treated as endogenous and
the equations are estimated using an instrumental variable method.
Estimates of the coefficients of the marginal return to effort variables
from these equations are reported in table 3. The pattern of
results is remarkably consistent across specifications. The marginal
return to effort variables do affect players' scores in the final round,
with larger marginal returns associated with lower scores.9 This result
is observed, however, only for exempt players. The magnitudes of the
relationship for each of the marginal return to effort variables (except
for LES3PRIZ) are such that, other things equal, a player whose marginal
return to effort was one standard deviation above the mean
marginal return in the sample would score 1.0-1.7 strokes lower in
the final round of the tournament.10
One may argue that, in theory, a player's effort in the last round of
a tournament also depends on his ability relative to that of the players
who are closely bunched around him. To see how inclusion of such
measures would influence the importance of financial variables, we
9 Formal specification tests (see Hausman 1978) permit one to reject the hypothesis
that the set of variables treated as endogenous should be treated as exogenous. This
finding is important because if one erroneously treats them as exogenous, many of the
coefficients of the marginal prize variables switch signs and become positive.
10 See Ehrenberg and Bognanno (1989) for details. The estimated LES3PRIZ effect
is less than one stroke. Improving one's performance by three strokes relative to that of
one's competitors in a round is a difficult task, so this measure is probably less relevant
than the others.
INCENTIVE EFFECTS 1321
TABLE 3
COEFFICIENTS OF MARGINAL RETURN TO EFFORT VARIABLES IN FINAL-ROUND-SCORE
EQUATIONS FOR THE 1984 MEN'S PGA TOUR: VARIOUS SPECIFICATIONS
Specification All Exempt Nonexempt
DPRIZE3 -.042 -.042 -.032
(2.7) (1.8) (.9)
UPRIZE3 - .236 -.310 -.070
(3.5) (2.6) (.6)
MIDPRIZ3 -.212 -.278 -.088
(3.3) (2.5) (.8)
LES3PRIZ -.049 -.052 .009
(2.0) (1.3) (.3)
LES2PRIZ -.088 -.135 .025
(2.6) (2.4) (.5)
LES1PRIZ -.181 -.306 .105
(2.7) (2.5) (1.0)
NOTE.-Absolute values of t-statistics are in parentheses. DPRIZE3 is the actual marginal reduction in prize
money (in thousands) if rank at the end of the tournament is one higher (worse) than the individual's third-round
rank; UPRIZE3 is the actual marginal increase in prize money (in thousands) if rank at the end of the tournament is
one lower than the individual's third-round rank; MIDPRIZ3 is the actual average marginal absolute changes in
prize money (in thousands) if rank at the end of the tournament is one lower or one higher than the individual's
third-round rank; and LES3PRIZ is the actual marginal increase in prize money (in thousands) if the individual
improved his rank after the third round by reducing his score by three strokes relative to the rest of the field
(LES2PRIZ = two strokes, LESIPRIZ = one stroke). All specifications also include SCOREI, SCORE2, SCORE3,
WAVE123, and WAVE4 and use instruments used for SCOREI, SCORE2, SCORE3, and the marginal return to
effort variables. The instruments were obtained using TPRIZE, MAJ, PAR, DIST, RATING, FRACT, MPERAVE,
FCUT, SCOREAVE (which are all defined in table 1), and SCORE12, the player's scoring average on all first and
second rounds he played on the 1984 tour; SCORE3A, the player's scoring average on all third rounds he played in
the 1984 tour; WAVE1-WAVE3, average of three raters' perceptions of whether the weather significantly influenced
player performance during the first, second, and third rounds, respectively, of the tournament; and
PERAVE, the player's performance average on the 1984 PGA tour (see table 1).
computed for each player in each tournament the differences between
his average score per round during the year and the average of
the average scores per round during the year of all players within two
and three strokes of him, in either direction, at the end of the third
round of play in the tournament. These variables (one at a time) were
added to the specifications that underlie table 3, and these extended
equations were reestimated for the exempt sample. Since the average
ability of the players around a player after the third round is endogenous,
instruments for these relative ability variables were also used.
It is quite striking that, although the magnitudes of the coefficients
of the marginal prize variables declined slightly when the controls for
competitor quality were included, one still observes larger marginal
prizes being associated with lower final-round scores. " Furthermore,
all the marginal prize variables' coefficients, except one, remained
statistically significantly different from zero.
" See Ehrenberg and Bognanno (1989) for results.
1322 JOURNAL OF POLITICAL ECONOMY
IV. Concluding Remarks
This paper has provided nonexperimental evidence that tournaments
have incentive effects. Our analyses of data from the 1984 men's PGA
tour suggest that the level and structure of prize money do influence
players' performance. Higher prize levels do lead, other things equal,
to lower scores, but this effect occurs primarily in the later rounds of a
tournament when fatigue has set in and it is more difficult for players
to maintain concentration. Given a player's performance in the first
three rounds of a tournament, his performance in the last round also
appears, other things equal, to depend on the marginal returns to
effort he faces, with players who face larger marginal returns scoring
lower. The level of prize money in tournaments also influences who
enters the tournaments, with higher prize money attracting better
(exempt) players.
The influence of tournament prizes on performance was observed
primarily for exempt players. As described above, this may reflect
either that exempt players are more responsive to the reward structure
or that a tournament's prize level does not adequately reflect the
reward structure that nonexempt players face, since these players
must be concerned with how their finish in a tournament will influence
their probability of qualifying for exempt status on next year's
tour. Evidence we have obtained from analyses of data from the 1984
men's senior tour for golfers aged 50 and older, which are reported
elsewhere, provides some support for the former hypotheses: that
better players are, in fact, more responsive to financial incentives.12
Our work is only an initial empirical study of the incentive effects of
tournaments, and there are a number of directions in which future
research might proceed. First, replications and extensions using data
from other sports in which absolute measures of output are available,
the level and structure of prize money differ, and the form of tournaments
differs would obviously be desirable. Professional bowling is
particularly attractive in this regard because bowling tournaments
have a match play element to them in their concluding stages.'3 Analyses
using data from more than one year would also be desirable; our
within-year analyses focus on how players allocate effort/concentration
within a year but show no evidence on how increasing prize
levels over time influence who enters the profession and the resources
they devote to conditioning and practice during the "off-
season."
12
These analyses are not reported here for brevity (see Ehrenberg and Bognanno
1989).
13 Research using data from professional bowling is undertaken in Bognanno (1990).
INCENTIVE EFFECTS 1323
Second, all our analyses are derived from simple two-person models
that yield implications for the output/scores of an individual
player. Generalization to n-person tournaments would yield implications
about the entire distribution of scores one might expect to observe,
and empirical analyses of the distribution of final scores could
then be undertaken.
Third, our analyses assumed that the tournament prize structure
influences output/scores through its effect on effort/concentration
levels. Players can also choose conservative (e.g., hit down the center
of a fairway) or risky (e.g., try to cut across a dogleg) strategies, and
depending on a player's ability relative to the rest of the field or his
rank after each round, different strategies may be pursued. Models
that also included the choice of strategies that differ in risk undoubtedly
would yield additional empirical implications.'4
Fourth, there are normative issues relating to the level and structure
of prizes that we actually observe in tournaments. Can we infer
from this structure what the objective functions of the PGA tour and
tournament sponsors actually are? Can we estimate whether the marginal
cost to sponsors of higher-prize tournaments is less than, equal
to, or greater than the marginal benefits they receive? Can we infer
whether golf tournaments' prizes are structured efficiently? To answer
such questions will require one to go far beyond the scores of
players in tournaments and to analyze more generally the operations
of the PGA tour and its sponsors.
Finally, while analyses of sports tournaments are of interest in
themselves, there is the broader question of the extent to which tournament
theory can help to provide an explanation for the structure of
compensation we observe among corporate executives. As is well
known, situations in which opportunities exist for one executive to
sabotage a rival's performance are not conducive to tournament-type
pay structures (see Lazear 1989). Nevertheless, devising ways to empirically
address this question should rank high on the research
agenda of economists interested in compensation issues.
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