Expert answer:Economics of Sports Research Paper

Expert answer:TOPIC: Determinants of an NFL QB SalaryThe general format of your investigation will follow the framework listed below:1. INTRODUCTION: A brief introduction, which introduces your sports-related topic, why you chose this topic and what you specifically plan to investigate. 2. RELEVANT LITERATURE REVIEW: This part of your study should focus on the findings of previous researchers as it related to your chosen topic. You will need to fully document and discuss all major economic articles dealing with your topic. 3. ECONOMIC THEORY. This part of the investigation will build upon the literature review and must contain your chosen theoretical model along with all a priori hypotheses regarding the impact of your economic factors.4. DATA COLLECTION: This section must contain actual data that will be used in your statistical investigation. In addition, each report is to contain a complete list of references to all data sources used in the course of your investigation.5. EMPIRICAL INVESTIGATION: This part of the investigation must include the statistical model and results (obtained by Excel/Megastat or an acceptable substitute). The results section should contain a complete discussion of the OVERALL statistical performance, as well as, the SPECIFIC statistical analysis of your model. 6. SPORTS ECONOMIC POLICY: Once the model has been estimated and it’s statistical validity has been investigated you will use the results to investigate the economics. It is in this section that the following should be completed (i) summary statistics with economic interpretation, (ii) statistical results based on your empirical model with an examination of your hypotheses and their economic meaning. In addition, you should investigate the impact of its modeling and statistical analysis as it relates to specific sports issues. 7. CONCLUSIONS: This final part of the investigation summarizes the major points of your investigation. It is at this point that you may want to point out what future investigations on your topic could do to improve upon what you did. 8. REFERENCES: The reference section must contain a full set of all documentation utilized in the report. You may also want to see the following: http://www.chicagomanualofstyle.org/tools_citation…the basic Chicago-style Guide to citations for more detail on proper referencing format for reference material. REPORT MUST FOLLOW SPECIFIC GUIDELINES LISTED ABOVE, AND BE IN THAT SAME ORDERFINAL WRITTEN REPORT DUE DATE: December 1, 2017
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Leeds, Kowalewski / WINNER
JOURNAL
TAKE ALL
OFIN
SPORTS
THE NFL
ECONOMICS / August 2001
Winner Take All in the NFL
The Effect of the Salary Cap and Free Agency
on the Compensation of Skill Position Players
MICHAEL A. LEEDS
SANDRA KOWALEWSKI
Temple University
In an earlier paper, Kowalewski and Leeds showed that free agency and the salary cap
brought profound changes to the level and nature of players’ salaries in the National Football League (NFL). Their study is limited, however, by the fact that—unlike most other professional athletes—football players are evaluated by position-specific statistics. The
authors improve on their earlier work by performing quantile regressions on data for specific positions to show how free agency and the salary cap affected compensation. They
show that the new bargaining regime greatly increased the reward to performance.
I
n 1993, the National Football League (NFL) management and National Football
League Players Association (NFLPA) entered into a new collective bargaining
agreement, since renewed with no substantive changes. Kowalewski and Leeds
(1999) showed that the agreement dramatically increased income inequality in the
league and altered the criteria by which teams rewarded players. Under the new
regime, the superstars and the veteran starters gained disproportionately at the
expense of the rookies and marginal players. In addition, the pay structure under the
new contract placed far less weight on a player’s position and far greater weight on
whether he was a starter than the previous contract had.
Kowalewski and Leeds’s (1999) findings, however, are limited by the nature of
the data they used. Because they used data for all players in the NFL, they could not
use position-specific performance measures. More than the other major sports, in
football one cannot compare the performance of two players at different positions.
In all other sports, overall performance measures exist that one can compare across
AUTHORS’ NOTE: An earlier version of this article was presented at the Western Economic Association meetings. We thank the participants and two anonymous referees for their comments and suggestions. We also thank Jennifer Gordon, Yelena Suris, and Elizabeth Wheaton for their excellent research
assistance.
JOURNAL OF SPORTS ECONOMICS, Vol. 2 No. 3, August 2001
© 2001 Sage Publications
244
244–256
Leeds, Kowalewski / WINNER TAKE ALL IN THE NFL
245
most positions. Batting and fielding statistics are reasonably comparable for all
nonpitchers in baseball. Whereas individual basketball players may focus on specific skills, the same set of performance measures (e.g., points, rebounds, and
steals) applies to all players. In hockey one can apply measures like the plus-minus
rating for all players except goalies. Only football lacks any overall performance
measure. As a result, one cannot directly compare the performance of a quarterback
with that of a defensive lineman. In this article, we employ separate regressions for
each of the so-called skill positions in football—quarterback, running back, wide
receiver, and tight end—to test whether the conclusions reached in Kowalewski and
Leeds (1999) hold when one uses more specific performance measures.
We consider the skill positions for two reasons. First, these positions are the
most popular among fans and generally subject to more public scrutiny than other
positions. More important, because the players at these positions handle the ball
more frequently than players at other positions, they have more direct performance
measures than other players, allowing us to establish better tests of the impact of
personal performance. For some positions, such as offensive linemen, performance
measures are hard to find. For other positions, such as defensive backs, the measures are hard to interpret. The very best defensive back, for example, may have
very few interceptions because teams refuse to throw the ball in his direction.
Although players at skill positions may occasionally be used as decoys, such difficulties in interpreting data generally do not exist for them.
The results provide a deeper insight into the impact of the new collective bargaining agreement. These findings will be of clear value to NFL executives seeking
to plan their teams’ financial futures. In addition, players and owners in other sports
contemplating free agency (hockey) or a salary cap (baseball) would have yet
another illustration of how they affect pay structures.
We find that the new bargaining agreement’s impact varied by year, position,
and quantile. A comparison of the results for 1992 and 1994 strongly reinforces the
initial findings by Kowalewski and Leeds (1999). The advent of free agency and the
salary cap reduced the returns to playing a specific position and increased the return
to performance at that position. In general, the impact of performance was stronger
at the .25 quantile than at the .75 quantile, suggesting that players who were underpaid for the level of their performance had greater returns to performance than
highly paid players. Finally, we find that the impact of the performance in 1994 was
less discernible for wide receivers than for quarterbacks or running backs and was
still less discernible for tight ends, the least glamorous of the skill positions.
The remainder of this article is organized as follows. The next section outlines a
simple model of salary determination and the changes that occur in the model due to
the salary cap and free agency. We then describe our estimation method, data, and
the variables used in the estimation, and present and interpret our results. The final
section contains conclusions.1
246
JOURNAL OF SPORTS ECONOMICS / August 2001
THE MODEL
Unlike unions outside the sports industry, the NFLPA and other unions in professional sports bargain over a basic agreement that applies to all teams and players
while players (and their agents) negotiate individual contracts with specific teams.
Prior to the advent of free agency, a monopsony setting prevailed. Lacking mobility
among teams, players had little countervailing market power. In the limit, the
monopsonistic team would be constrained only by the fact that it must offer the
player a salary greater than or equal to the player’s salary in his next-best occupation. In fact, players—especially star players—can force owners to pay more than
this because they possess unique skills and thus exert a degree of monopoly power.
McLaughlin (1994) points out that in thin labor markets like those present in
professional sports, heterogeneous workers and firms create rents if they are
matched appropriately. For example, if player i plays position k for team j, he generates the value Vijk. For our purposes, we think of Vijk as player i’s marginal revenue
product.2 In reality, income may be only one argument of a broader utility function
that includes factors like the pleasure the player and owner take in having a winning
team. Because no two players are exactly alike and no two teams’ needs and opportunities are alike, Vijk is a unique value for each player-team-position combination.
For example, the value a team places on abilities at one position depends on the abilities present at other positions (e.g., a team with an outstanding quarterback may
want offensive linemen who pass-block well, whereas a team with an outstanding
runner may want offensive linemen who run-block well). An optimal match results
in a return that is greater than either the player or the team could get elsewhere, so
Vijk is greater than other player-team-position combinations. Once matched, the
team and player must divide this surplus return between the playerV i jk and the team
V jik .
A simple bargaining model based on the classic Nash (1950) framework captures the forces at work in this bargaining setting. Nash showed that the solution to
such a bargaining problem depends crucially on the two sides’ respective threat
points, the value each attaches to failing to make a deal. For example, if team j does
not sign player i to play position k, it must make do with some other player who provides some lesser value,V jk0 . The net value of the match with player i to team j is thus
(V jik − V jk0 ), whereV jk0 is the team’s threat point. Similarly, if player i cannot reach an
agreement with team j, he must go to some other team. Because there is no reason to
believe that alternative opportunities outside of football differ systematically, we
assume that the best opportunity outside of football is a constant, V 0. The net return
of the match to the player is thus (V i jk − V 0 ), where V 0 is the player’s threat point.
The Nash (1950) solution to this bargaining problem maximizes the product
(V i jk − V 0 ) (V jik − V jk0 ) subject to the constraint thatV i jk + V jik ≤ V ijk . This framework
allows us to see the impact of free agency on the division of the surplus between the
player and the team. Because free agency allows players to sell their services to any
team in the league, the alternatives available to players now include the pay avail-
Leeds, Kowalewski / WINNER TAKE ALL IN THE NFL
Figure 1:
247
Mix of Running Backs and Quarterbacks With a Convex Expansion Path
able at another team, not just another occupation. This has two important effects on
the model. First, it increases the threat point of the players in general, as their value
to another NFL franchise is likely to be significantly greater than their value in an
outside occupation. As a result, one would expect free agency to increase the pay of
the typical player.
Free agency also introduces a new source of heterogeneity to wages. Free
agency allows a player’s threat point to become the value of his employment with
another NFL franchise, rather than just his value outside the sport. Because specific
positions and specific players may have radically different alternatives throughout
the league, individual threat points become individual and position-specific, V ik0 ,
and may vary dramatically across positions and across individuals at specific
positions.
In addition to free agency, the new agreement introduced a salary cap designed
to keep each team’s salary bill within a relatively narrow range. Although in fact
teams seek out ways to circumvent this limit, we shall assume for illustrative purposes that all teams’ salaries equal a specific amount. The salary cap thus forms an
additional constraint so that the bargaining solution for team j and player i maximizes (V i jk − V ik0 )(V jik − V jk0 ) subject to V i jk + V jik ≤ V ijk for each individual contract
and ∑i , k V ijk < C for each team, where C is the salary cap. The salary cap does not have a predictable impact on the distribution of salaries for a given team. If the salary bill that the team would choose in the absence of outside constraints lies within the band permitted by the salary cap, then the cap has no impact. The cap could also have no impact if restricting expenditure (again, we 248 Figure 2: JOURNAL OF SPORTS ECONOMICS / August 2001 Mix of Running Backs and Quarterbacks With a Concave Expansion Path ignore the possibility that a team would have to increase its expenditures) affects the demand for all position-skill combinations in the same proportion. The cap affects a team’s distribution of salaries when restricting expenditure changes its optimal position-skill combinations. A simple example appears in Figures 1 and 2, where we assume for simplicity that the team is choosing between passing and running inputs (provided by a talented quarterback and running back) in the production of wins. The optimal combination of passing and rushing is given by the tangency of an isoquant (representing the production of wins) and a team’s expenditure constraint. Figure 1 shows that a salary cap causes a team to cut back more severely on its demand rushing yardage when its expenditure expansion path is convex. In this case, the salary cap causes the team to forego star running backs in favor of a star quarterback. If the expansion path is concave, as in Figure 2, then the team responds to a salary cap by cutting back more severely on its demand for quarterbacks to assure itself of a star runner. When the production function is homothetic (not shown here), the expansion path is linear and the salary cap does not alter the optimal mix of inputs. If all teams face similar expansion paths, then restricting expenditure affects the overall demand for—and value of—specific positions and skills. The empirical results thus reflect in part the shape of the n-dimensional expenditure expansion path. We have no a priori beliefs as to the shape of this expansion path. In some sports, such as baseball and basketball, the above model would apply only to players who are free agents, as players and teams under contract generally cannot renegotiate their contracts. However, the nature of the labor market in the Leeds, Kowalewski / WINNER TAKE ALL IN THE NFL 249 NFL allows us to apply the model to all players, not just free agents. Star players sometimes force their teams to renegotiate contracts in response to a good season. More important, the NFL does not allow players and teams to sign guaranteed contracts. This leaves teams free to revise contracts downward for players who are no longer worth the salary in the original contract. Players in the NFL thus face an asymmetric situation in which star players can revise their contracts upward, whereas lesser players may see their contracts revised downward. EMPIRICAL MODEL AND DATA Several testable hypotheses follow from the model presented above. First, the model suggests that the new collective bargaining agreement will cause greater income inequality among players due to the greater heterogeneity in the players’ threat points. In their study of all players in the NFL, Kowalewski and Leeds (1999) found some evidence that free agency caused teams to link salaries more closely to performance. We test this hypothesis on a position-by-position basis.
At first glance, the test for changes in the salary structure seems straightforward:
One simply compares separate OLS regressions for years prior to and following the
change in regime. Koenker and Bassett (1978) and Buchinsky (1994) have pointed
out, however, that OLS may not be the appropriate tool for the job. OLS may be a
good predictor of the mean of the dependent variable conditional on the values of
the independent variables, but it does not accurately predict the dependent variable
for large segments of the income distribution. Because one of our premises is that
free agency has distended the distribution of wages and altered the returns to performance, a quantile regression procedure is more appropriate. In addition, the residuals in our regression may be correlated with omitted variables (e.g., charisma, leadership, or marketability) that enhance the bargaining power of an individual player.3
This implies that the return to a given characteristic may vary with a player’s position in the conditional distribution of salaries. Because OLS estimates provide a
single value for the return to a given characteristic, they may yield an inaccurate
picture of what confronts individual players.
In light of the above drawbacks to the standard OLS approach, we estimate the
impact of performance on a player’s compensation by employing quantile regressions for the 25th and 75th percentile of the conditional wage distribution for 1992
and 1994. This enables us to contrast players who are relatively high-paid with
those who are comparatively low-paid. We can thus compare players within each
year as well as between years, rather than having to make just one grand comparison. Quantile regressions also allow us to see what characteristics, if any, are
affected by our unobserved measures of bargaining power in any given year.
We estimate the model using salary data from articles in USA Today (see the
tables accompanying Wire Service Reports [1993] and McLean [1995a, 1995b]).
We used data for all quarterbacks, running backs, wide receivers, and tight ends
who were on a team’s roster at the start of the season. Because of the difficulty in
250
JOURNAL OF SPORTS ECONOMICS / August 2001
organizing data on players who were traded during the regular season or the preseason, we excluded them from the sample. Because our performance measures are
based on performance in NFL games, we excluded all 1992 and 1994 rookies and
players who were on rosters in 1991 or 1993 but who did not have any receptions,
rushing attempts, or passes that year. Some of the data reflect the roster moves; for
example, our sample of quarterbacks is smaller in 1994 than it was in 1992.
The dependent variable in our regressions is the natural logarithm of the player’s
salary plus bonus payments. Unfortunately, the reporting method for bonuses
changed slightly between 1992 and 1994, largely because of the salary cap rules.
The data for 1992 consisted of yearly pay per player, computed as base salary plus
most bonuses including signing, reporting, and roster bonuses for the 1992 season.
The 1994 salary data were calculated using the same method the NFL uses to determine team salary caps. They consisted of yearly pay per player, computed as base
salary plus most bonuses, with the exception of signing bonuses. The exception was
based on the fact that signing bonuses are prorated during the life of multiyear contracts and thus should not be included as a lump sum. For example, if a player
signed a 4-year contract with an $8 million signing bonus, the salary cap would
regard his total yearly salary to be his base salary plus $2 million (one quarter of the
signing bonus). Although we do not expect the change in the treatment of signing
bonuses to have a severe impact on our results, they do force us to regard the results
with some humility.
All other data, including experience, games played, games started, and performance statistics came from The Sporting News Pro Football Guide (Carter, 1992,
1994) for the 1991 and 1993 seasons. Because our years bracket the new Collective
Bargaining Agreement, they may not fully reflect the impact of the changed market
conditions. However, as noted earlier, the lack of guaranteed contracts in the NFL
and the tendency of star players to renegotiate their contracts suggest that the
impact of the change in the bargaining setting would have a more immediate impact
than in baseball or basketball, in which a substantial number of players have
long-term, guaranteed contracts.
In addition to position-specific performance variables, we included several general measures. “NFL experience,” measured as the number of years a player had
been in the NFL, reflects the effect of experience on salary. “NFL experience
squared” captures nonlinearities in the returns to experience. We expect the quadratic term to be negative, reflecting the fact that the returns to experience decrease
with years of experience.
We expect the number of games played and started by a player to have a positive
impact on his salary. To account for these effects, we include the number of regular
season games in which a player appeared in 1991 and 1993, as well as those in
which he was in the starting lineup. For all players except the quarterback, we also
included a dummy variable that shows whether a player appeared in the 1991 or
1993 Pro Bowl. Because participating in the Pro Bowl certifies a player as being
among the best at his position, this dummy variable captures superstar effects. We
Leeds, Kowalewski / WINNER TAKE ALL IN THE NFL
251
TABLE 1: Relevant Means for Quarterbacks
Variable
Games played
Games started
Experience
Passing yards
Salarya
Median salary
1992
7.97
5.96
5.78
1,297.33
$1.065 million
$800,000
1994
9.78
7.33
7.33
1,490.33
$1.393 million …
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