A century of player movement in Major League Baseball.

Schmidt, Martin B.

Introduction

Labor migration across firms is a common and significant component of most modern economies. Garino and Martin (2007), for example, argue that worker-initiated movement across firms is ten times as likely as separation due to adjustments in the number of jobs. The consequences of worker-initiated migration are also significant to both workers and firms. The worker, for example, may experience disruption to their and their family's lives or they may need to learn new job-specific skills, while the firm may experience a loss in firm-specific job skills and its associated productivity or they may incur significant costs in the search for a suitable replacement.

The reasons for labor migration are varied. Firth et al. (2004) cite job-related stress, lack of commitment by the organization and general job dissatisfaction as factors that may lead to the decision to change jobs. Abbassi and Hollman (2000) find that workers tend to migrate when their current firm has poor hiring practices, poor management style, a toxic work environment, and a lack of worker recognition. Moreover, they find that employees who feel that the firm does not provide competitive compensation are more likely to leave. Furthermore, Griffeth et al. (2000) find that organizations that provide adequate pecuniary incentives have lower turnover rates. Consequently, workers who are insufficiently, relative to performance, financially rewarded are more likely to migrate.

While job dissatisfaction may cause the desire for worker-initiated separation, the ability to do so is also an important determinant of actual labor migration. Trevor (2001) argues that strong labor market conditions increase the amount of labor migration. Specifically, Trevor finds that "job satisfaction appeared to have a negative effect of greater magnitude when jobs where more plentiful" (p. 633). (1)

Given the high visibility, depreciating skill set, and varying management motives, labor migration, both worker and firm-initiated, is likely more prevalent within the professional sports' labor markets than in more general labor markets. Morse et al. (2008), for example, find that nearly 40% of National Basketball Association team rosters are turned over each year (2). In addition, Kahane and Shmanske (1997) find a similar result for Major League Baseball where roster turnover amounts to nearly 30% each year. This is surprising on one level as the cost of a new hire can be quite high due to the asymmetric information on player productivity.

The relative importance of organizational factors in determining labor migration and its associated cost to both worker and firm is beyond the scope of the present paper. The factors that either increase or decrease player movement, however, are not. In particular the present paper is interested in tracing the institutional factors, many of which have affected the financial return to the player as well as labor market conditions, that have affected MLB players' movements across time.

Major League Baseball is a natural setting to investigate the importance of institutional factors due to the fact that it has been subject to numerous exogenous institutional shocks across its history. The MLB, for example, has been subject to increased competition from the Federal League during the mid-1910s as well as having changed its own labor market rules in terms of amateur player draft, racial integration, free agency, and revenue sharing.

We examine the impact that these, as well as others, exogenous shocks have had on player movement across time. Specifically, following Price (1977), we define labor movement, or turnover, as the ratio of organizational members who have left during a period divided by the total number of members employed during that same period (3). In order to capture the many dimensions of movement we incorporate three types of aggregate player movement: total players, total at-bats, and total innings.

The first measure, total players, simply calculates the percentage of all players that is turned over in a particular year. This data, however, makes no distinction between the type of player that is moving. Within the MLB a number of so-called fringe players rotate through teams frequently and may play little role in changes that occur across time. We therefore create two separate measures for player movement. The first is to examine the total number of player at-bats that move across time; the second is to track the total number of pitcher innings that move. A typical Major League Baseball positional starter can amass over 600 at bats in a season, while a seldom-used player may only have 50 or so at bats. One might expect that a seldom-used player may be easier and less costly to replace and, therefore, would be more likely to be turned over. The same may be said for Major League Baseball pitchers (4).

In several respects the present paper follows the approach of Hylan, Lage, and Treglia (1996) and Maxcy (2002). These authors are equally interested in the dynamics of player movements. In particular, both papers focus on the question of the impact of free agency on the probability of player movement and do so by following player movement across time. Maxcy (2002), for example, codes nearly 50,000 Major League Baseball players over the period 1951-1999 with a player coding (1) if the player moves to another Major League Baseball team the following year and a coding (0) if the player does not. Maxcy then uses this binary dependent variable to examine the impact of free agency and other factors on player movement.

The paper differs, however, in several substantial ways. First, our data extends both analyses by examining player movement over most of the 20th century. This enabled us to examine a larger set of institutional characteristics over a longer period. Second, while these studies examined the individual player's probability of transfer as a function of both institutional and individual characteristics, the present paper examines the importance of these institutional characteristics, as well as others, on aggregate player movement. In this way, the present paper can be seen as a complement to these earlier studies in investigating whether individual results are in line with those found using more aggregate measures.

In addition, and perhaps more importantly, it partly addresses one concern with the specification of Hylan et al. and Maxcy. Specifically, much of their findings may hinge on incorporation of correct measures of individual productivity and their structurally similar measures of value across the estimation period. This likely is not the case. For example, consider the finding, as reported in Berri and Schmidt (2010) that the number of attempted stolen bases began to decline during the mid-1980s. If this is a structural change in the way the game of baseball is played and how individual players are valued and if slugging percentage and attempted stolen bases are negatively correlated than including slugging percentage and omitting stolen bases may lead to a change in player movement dynamics at this point, which has little to do with the institutions. Also, while outside the sample of these studies, the results of Hakes and Sauer (2006) suggest a change in valuation of slugging and on-base percentage during the mid-2000s that again may lead to spurious change that has little to do with institutional factors.

For aggregate data this is less of a concern, i.e., players with certain characteristics would be more likely to move, while others with different characteristics would be less likely to move but aggregate movements would be less variable. The specific data we use are the percentage of MLB players who move from one MLB team to another within a given period. Movement between teams may come about through several avenues: the player may be traded by a team, the player may be released by a team, or the player, after the institution of free agency, may choose to leave. The collection of the data came from examining individual MLB team rosters and tracking whether individual players remained with the team, moved to another team, or left MLB rosters over the period 1903-2004. (5) Those who left MLB were then removed and the percentage that moved was produced from the remaining total.

In the end, we found that the Federal League competition, racial integration, World War I, free agency, revenue sharing, and to less of an extent, the building of a new stadium increased player movement. In contrast, World War II and the limitations placed on free agency by the re-entry draft, the compensation draft, and the collusive behavior by the Major League Baseball owners reduced player movement. Finally, MLB expansion, the designated hitter rule, and the introduction of a reverse-order amateur draft had no impact.

[FIGURE 1 OMITTED]

Data and Estimation

The player movement data are reported in Table 1 and also in Figure 1 (6). Specifically, the top panel of Figure 1 reports the percentage of player who move to competing teams, the middle panel reports the percentage of total number of at-bats that move, and finally the bottom panel tracks the total number of innings pitched that move. All three panels show a similar variability across time and a similar upward trend in player movement.

Moreover, Table 1 suggests that of the player movement measures, the total player measure is substantially higher than the other measures. Specifically, while the typical MLB team turns over roughly 28% of its roster in a given year, it only turns over 17% of its total at-bats or innings. This suggests, not surprisingly, that a large component of team turnover revolves around changing so called fringe players. Also, the maximum and minimum figures for pitcher's innings movements are lower than those of the two other figures. This lower turnover may suggest that pitchers may be more valuable assets to a MLB team.

Overall our estimation approach may be highlighted by the following equation (1) and further in Table 2:

[RT.sub.jt] = [a.sub.j] + [b.sub.ij] * [C.sub.i] + [d.sub.kj] * [I.sub.k] + [e.sub.jt] (1)

where RT represents the percentage of the roster (turnover measure j) that was turned over in period t. RT is then influenced by a set of variables that are very loosely grouped into two categories: [C.sub.i] or those that may alter player movement through greater competition for players' services, i.e., exogenous shocks that increase the available outlets for MLB players, and [I.sub.k] those that may impact movement through the adoption of new market institutions (7).

As to factors that have affected the level of competition, i.e., [C.sub.i], each of the series (j) shows a large upward spike, i.e., an increase in player movement, starting in 1914. This period likely corresponds to the introduction of a competing league, the Federal League. The Federal League was formed in 1913 and initially respected MLB contracts. A year later, however, the Federal League attempted to entice some contracted players away from MLB. The increased competition for player services caused some players to sell their services to the Federal League. While this would not directly alter the measures, the players who left did need to be replaced. This may have increased the incentive for MLB teams to trade and purchase players from other MLB teams. This, in turn, may have caused increased movement. When the Federal League folded in 1915, many of its players needed to be re-assimilated into MLB. As players were released to make room for these players, these measures remained abnormally high.

We also included dummy variables for the two world wars. While not directly in competition with Major League Baseball, both wars introduced a draft to provide military personal, with MLB players not having any special exemption from service (8). As with the competition from the Federal League, the player movement measures likely rose in response.

In addition, we included a measure for expansion in the total number of available outlets within MLB, i.e., the total number of expansion teams introduced in a given year (9). Given that most expansions included some form of an expansion draft that allowed incoming teams to select from a group of players on current team rosters, we might expected an increase in player movement during these periods.

Finally, we included dummy variables for the existence of new stadiums. Specifically we include a hybrid-dummy variable that captured the number of new stadiums that are placed online in a particular year. The argument for public provision of the funds for the construction of a new stadium typically revolves around the team requiring the new stadium to remain competitive, i.e., increase revenues. Increased team revenues would increase the team's ability to be active in the player labor market. In which case, a new stadium would affect player movement positively. In contrast, the increased revenue could allow a relatively low-revenue team to maintain their own free agents, which, in turn, would decrease turnover rates for these teams (10).

The second set of factors, [I.sub.k], revolves around institutional changes that have occurred in the MLB market. One obvious example is the breaking of the color line by Jackie Robinson. Jackie Robinson became the first Negro player in MLB when he joined the Brooklyn Dodgers in 1947. Prior to 1947, Negro baseball players were not allowed to compete for Major League positions and the typical Major League Baseball player was a white North American. After 1947, the racial composition of Major League Baseball teams changed forever. Schmidt and Berri (2006) show that the percentage of black MLB players rose from essentially 0 in late 1940s to roughly 32% by the late 1960s, where it has since leveled off. However, Schmidt and Berri also show that over the past 30 years Major League Baseball has increased its search for players, as measured by the percentage of foreign-born players, beyond the borders of North America into all regions of the world. One might expect that as each new labor-supply market is opened up increased turnover rates may result.

While the introduction of a reverse-order amateur draft in 1965 is an obvious institutional change, it is unclear what impact this might have on player movement. Specifically, the amateur draft is for first-year players and typically involves drafting young players between the ages of 18 and 22 years old. Most of these draftees end up playing several years of minor league baseball in order to hone their skills before making it onto major league roster.

We also included a dummy for the introduction of the rule change in the American League to allow for a designated hitter in 1972. The change, while only occurring in one league, may change the way in which resources are distributed--good hitters, poor fielders--and therefore marginally change the player movement measures.

Perhaps the most well known institutional change to occur in Major League Baseball was the removal of the reserve system and the introduction of free agency in 1977 (11). Prior to 1977, all major league baseball contracts contained a reserve clause that essentially granted MLB teams a perpetual option on the players' services. The 1977 collective bargaining agreement granted Major League Baseball players with six years of services the right to sell their services to other teams. Interestingly, each of the series shows a marked increase in its average value during the post-1976 period; the percentage of total at-bats and innings increased by nearly 40% and 70%, respectively. And while the data on total player movement have experienced a smaller rise, they still rose by nearly 20% (12).

While the 1977 collective bargaining agreement granted players with 6 years of Major League Baseball service free agency, the free agency has not been completely free. For example, the 1977 agreement also called for a free agent reentry draft. The reentry draft required each MLB team to select the individual free agents they wished to pursue. It also limited the number of free agents a particular team could select. In addition, it placed a limit on the number of teams selecting a particular free agent player. Free agents were then limited to signing a contract with one of the teams that had selected them. One might suspect, and it was likely its intended consequence, that these stipulations would decrease player movement and player potential salaries.

The reentry draft was replaced in favor of a free agent compensation draft during the negotiations for the 1981 collective bargaining agreement. The free agent compensation draft compensated a team that lost a free agent (13). Specifically, a team that lost the free agent player was allowed to choose a player from a pool of players made available by the other Major League teams (14). Again, the intended consequence of the new policy was likely to decrease player movement and potential player salary (Stadohar, 1996).

A small but important feature was the short-lived movement downward over the 1985-1988 period. The downturn represents a period of collusion on the part of MLB players. An independent arbiter, Thomas Roberts, found the owners guilty of collusion for each of three off-seasons, 1985-86, 1986-87, and 1987-88. The ultimate cost to the owners was a fine of $280 million and immediate free agency to some 15 players. The collusive behavior on the part of the owners likely caused players to accept less advantageous terms with their respective teams and likely reduced player turnover rates.

The MLB market has also been subject institutional changes on the revenue side. For example, due to the increasing disparity in revenues between teams, MLB owners agreed to implement a degree of revenue-sharing beginning in 1994. The actual process was codified in the 1996 collective bargaining agreement. For the majority of this agreement, each MLB team placed 20% of their net local revenue into a pool. The pool was then divided with 75% of the total split evenly between all clubs and 25% unevenly split between those clubs with below average net revenues. The revenue-sharing formula was changed again in the 2002 collective bargaining agreement. For this period, each MLB team placed 34% of their net local revenue into a pool with the pool evenly divided among all teams.

The impact of revenue sharing on player movement is unclear. One might expect that the additional revenues received by low revenue teams would increase their competitiveness in the free agent market and therefore might increase player movement. However, on the other end, these funds were removed from the high revenue teams and, therefore, would decrease their ability to bid for these same players.

In addition, both the 1996 and the 2002 collective bargaining agreements included provisions for a so-called luxury tax. While not explicitly a salary cap, the tax was intended to give teams an incentive to keep player salaries below a certain threshold. Conceptually, a team was taxed at a certain rate (i.e., 35% in 1997) on the amount of payroll above a certain level (i.e., $51 million in 1997, Dosh, 2007). In the 1996 agreement, a portion of the tax proceeds was redistributed to the bottom-revenue teams. For the 2002 agreement no tax proceeds were returned to any teams. The likely impact on player movement of the tax was to constrain high spending teams and, therefore, reduce player movement and salaries.

Table 2 lists the particular factor and the years of its existence, i.e., the periods where the dummy variable has a non-zero value. In addition, the average level of movement for each of the three roster turnover measure over the years the factor was in effect.

Results

Table 3 reports the estimated coefficients and their associated estimated standard errors (15). The results are generally in line with expectation and are generally significant (16). For example, the competition for players introduced by the Federal League increased total at-bats movement by nearly 11%. However, it failed to significantly alter movement rates for the total amount of players or total innings. This suggests that Federal League attempted to entice very high quality positional players, at least as measured by playing time, to transfer.

Interestingly, the two world wars produced widely divergent results. World War I, for example, increased player movement and all three measures of player movement were similarly affected, increasing by nearly 6%, 7%, and 5%, respectively. This may suggest that draft boards provided little differential treatment to MLB baseball players in total but also across players. World War II, in contrast, failed to significantly affect any of our player movement measures.

Expansion, in contrast, did not seem to have had an impact on player movement as none of the three series returns a significant response. The building of a new stadium, however, did seem to increase player movement. The impact, however, is localized in the total player movement measure with a rise of 1% in player movement when a new stadium was built. The remaining two measures were largely unaffected by the new revenue stream.

Racial integration had a significant positive impact on both the total players and total innings movement measures, but had little impact on the total at-bats measure. More specifically, racial integration increased total player and total innings moved 2-3%. Neither the draft nor the introduction of the designated hitter rule in the American League had any impact on any of the player movement measures.

Similar to the results reported in Maxcy (2002), the institution of limited free agency in 1977 increased player mobility. All three of the movement measures rose 5-7%. However, the initial restrictions placed on free agency by the reentry draft muted its initial impact. Specifically, the draft reduced the impact of free agency on player mobility by roughly 4% during the period from 1977 to 1980, leaving player movement rising only by a few percentage points during the period.

In a similar vein, but to a much greater extent, the restrictions placed on free agency by the compensation draft over the period from 1981 to 1984 essentially negated the impact of free agency. Specifically, the compensation draft reduced the player mobility measures 6-8%, suggesting that during this period mobility rates were at or below their pre-free agency levels. Finally, the period from 1985 to 1987--the period where the owners were found guilty of colluding to restrain player movement and salaries--also had a significant impact on two of our player mobility measures. Both the total player and total at-bats measures fell by 4% and 7%, respectively. Interestingly, the total innings measure was not affected, suggesting that the collusion was more closely focused on position players than pitchers.

On the revenue side, both revenue-sharing plans had a positive impact on player movement. The initial revenue-sharing plan that shared a smaller pool of money but redistributed the pool more unevenly increased player movement 4-5%, depending on the particular movement measure. Moreover, its impact was very similar across all the movement measures with total player movement increasing roughly equal to the total at-bats and total innings measures. The second revenue-sharing plan, however, had a much larger impact on the player quality movement measures. Specifically, it increased both the total at-bats and total innings movement by roughly 7% while it failed to have any impact on total player movement. This suggests that this revenue-sharing plan had the effect of encouraging marginal teams to increase their pursuit of higher quality players.

[FIGURE 2 OMITTED]

Expansion, in contrast, did not seem to have had an impact on player movement as none of the three series returns a significant response. The building of a new stadium, however, did seem to increase player movement. The impact, however, is localized in the total player movement measure with a rise of 1% in player movement when a new stadium was built. The remaining two measures were largely unaffected by the new revenue stream.

Conclusion

The present paper examined the impact of both competitive and institutional shocks on aggregate Major League Baseball player movement across much of the 20th century. It examined three dimensions of movement: total players, total at-bats, and total innings, the latter representing measures of player quality.

Overall, the results indicate that both increased competition for player services and labor market institutions have had a significant impact on player migration across time. Arguably, the most significant labor market change in MLB history was the transferring the rights to player services from the owners to the players in 1977. Interestingly, the transfer initially appeared to have little impact, as player movement remained relatively stable. But as Figure 3 highlights, this was largely due to the institutional restraints that were introduced in concert with free agency. Specifically, Figure 2 shows the impact of free agency and these limiting factors on the forecasted values of player mobility, i.e., the figure reports the forecasted values of the three player mobility measures from a period prior to free agency (1972) to the end of the sample (2004). The forecasted values suggest that the impact of free agency was not fully felt until the late 1980s. This is consistent with the results presented in Maxcy (2002) where the author finds its impact was muted until 1989.

These results do call into question the relevance of the Coase Theorem. Following the so-called Invariance Variance Principle, the Coase Theorem suggests that the distribution of resources is invariant to the assignment of rights (Schmidt and Berri, 2006). The results above suggest that the mobility of resources does change with the assignment of rights. In which case, the Invariance Principle would also need to suggest that the distribution of resources is invariant to the degree of mobility of resources.

Acknowledgments: I would like to thank, without implicating, two anonymous referees for helpful comments and suggestions.

References

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Kahane, L. & Shmanske, S. (1997). Team roster turnover and attendance in Major League Baseball. Applied Economics, 29, 425-431.

Maxcy, J. G. (2002). Rethinking restrictions on player mobility in Major League Baseball. Contemporary Economic Policy, 20, 145-159.

Morse, A. L., Shapiro, S. L., McEvoy, C. D., & Rascher, D. A. (2008). The effects of roster turnover on demand in the National Basketball Association. International Journal of Sports Finance, 3, 8-18.

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Endnotes

(1) This result is consistent with Griffeth and Hom (1995), Price (1977), as well as many others.

(2) Actually, Morse et al. (2008) measure turnover as players who played 60% of a team's games and who are not on the team's roster the following year.

(3) This definition differs from the definitions of Morse et al. (2008) and Kahane and Shmanske (1997) who only incorporate a subset of players when measuring turnover.

(4) Pitchers innings are likely more problematic as specialization has increased the use of relief pitchers.

(5) The choice of sample period reflects the joining of the American and National leagues in 1903.

(6) The author would like to thank Tom Ruane for graciously providing a subset of the data.

(7) The lines of distinction are imprecisely defined and are used only for organizational purposes.

(8) We also included a dummy variable for the Korean War (1950-1953). The dummy was insignificant and did not qualitatively change the results. This was also true for a Great Depression (1930-1942) dummy.

(9) MLB has expanded its total number of teams several times. Specifically, MLB has expanded six times from the original 16 teams. In 1961, 1962, 1977, 1993, and 1998, the league expanded by two teams, while four teams were added in 1969.

(10) In an earlier iteration, we also included dummy variable for the MLB's first national television contract and for the modifications of these across time. Perhaps due to the fact that these revenues are distributed equally across teams, none of these were significant.

(11) While player free agency was negotiated into the 1977 collective bargaining agreement, an avenue by which players might obtain free agency opened up on December 23, 1975, when independent arbiter Peter Seitz ruled that both Andy Messersmith and Dave McNally had met the terms of their contracts and were free to negotiate with any team. See Staudohar (1996).

(12) A factor that may have muted mobility is the change in contract length, which has risen significantly since 1976. Under the reserve clause, nearly all MLB players played under one-year contracts. Under free agency, most free agents sign multiyear contracts. Even players without the mandatory service time are more likely to sign multiyear contracts due to owners' concern over salary arbitration. In addition, that most multiyear contracts are guaranteed may also mute turnover rates.

(13) The 1981 collective bargaining agreement called for free agents to be divided into three classes, i.e., types A, B, and C. These classes were based on playing time and performance measures over the previous two years. Only teams losing a Type A player could participate in the compensation draft. Type B players would continue to be compensated with draft choices, and Type Cs would not trigger any compensation.

(14) All teams could protect 26 players in their organization from the draft, except for teams who signed a Type A free agent that year, who would protect 24 players. Teams could opt out of the right to sign Type A free agents and therefore not have to place any names into the pool.

(15) The estimated coefficients were obtained by OLS. While the dependent variable is right and left censored around 1 and 0, respectively, none of the dependent variable values is close to the right and left constraints. OLS produces results equivalent to ML methods.

(16) For both the total player and total innings movement we report white heteroskedasticity-consistent standard errors, for both of these ARCH tests failed to reject the presence of heteroskedasticity.

Martin B. Schmidt ([double dagger])

([double dagger]) College of William and Mary

Martin B. Schmidt is a professor in the Department of Economics at the College of William and Mary. His academic interests include macroeconomics, monetary economics, and applied econometrics.

Table 1: Major League Baseball Player Movement Descriptive
Statistics: 1904-2004

                          Standard
[RT.sub.j]        Mean    deviation   Maximum    Minimum

Total players    0.283      0.058      0.508      0.144
Total at-bats    0.176      0.061      0.427      0.073
Total innings    0.174      0.069      0.376      0.052

Table 2: Shocks to Competition and Institutions in Major
League Baseball

Institution             Years            Average movement

                                   Players   At-bats   Innings

All                   1904-2004     0.283     0.176     0.174

Competition
Federal League        1914-1915     0.341     0.260     0.253
World War I           1917-1918     0.309     0.219     0.174
World War II          1942-1946     0.229     0.141     0.130

Institutions
Racial integration    1946-2004     0.299     0.189     0.203
Amateur draft         1965-2004     0.308     0.207     0.228
DH (only AL)          1972-2004     0.314     0.216     0.238
Free agency           1977-2004     0.320     0.222     0.245
Re-entry draft        1977-1980     0.291     0.193     0.202
Compensation          1981-1984     0.254     0.163     0.184
Collusion             1985-1987     0.280     0.161     0.218
Revenue sharing I     1996-2001     0.377     0.273     0.297
Revenue sharing II    2002-2004     0.342     0.293     0.316

Table 3: Player Movement and Institutions: Estimated Coefficients (OLS)

Variable                              [RT.sub.j]

                     Total players   Total at-bats   Total innings

Constant               0.304 ***       0.183 ***       0.115 **
                        (0.062)         (0.059)         (0.043)
Federal League           0.079         0.109 ***         0.124
                        (0.065)         (0.025)         (0.094)
World War I            0.056 ***       0.070 ***       0.045 ***
                        (0.010)         (0.025)         (0.012)
World War II            -0.029          -0.009          -0.017
                        (0.022)         (0.016)         (0.018)
Teams                   -0.003          -0.002           0.001
                        (0.004)         (0.004)         (0.003)
New stadiums             0.009           0.001           0.002
                        (0.006)         (0.005)         (0.004)
Racial integration     0.026 **          0.003         0.020 **
                        (0.012)         (0.010)         (0.009)
Amateur draft            0.007           0.024           0.023
                        (0.029)         (0.024)         (0.015)
DH (only AL)             0.012           0.011           0.013
                        (0.017)         (0.024)         (0.025)
Free agency            0.065 ***       0.067 ***        0.054 *
                        (0.019)         (0.023)         (0.028)
Re-entry draft         -0.043 *        -0.038 *        -0.044 *
                        (0.026)         (0.020)         (0.024)
Compensation          -0.078 ***      -0.067 ***      -0.063 ***
                        (0.017)         (0.021)         (0.015)
Collusion             -0.042 ***      -0.069 ***        -0.029
                        (0.015)         (0.024)         (0.020)

Table 3: Player Movement and Institutions: Estimated
Coefficients (OLS), continued

Variable                       [RT.sub.j]

              Total players   Total at-bats   Total innings

Revenue          0.041 *        0.050 **        0.042 ***
sharing I        (0.020)         (0.021)         (0.015)

Revenue           0.016         0.071 ***       0.065 ***
sharing II       (0.025)         (0.026)         (0.016)

R                 0.520           0.608           0.712

n                  100             100             100

Diagnostic
statistics

B-G (2)       0.550 (0.579)   0.334 (0.718)   2.212 (0.116)

ARCH (4)      0.001 (0.001)   0.811 (0.134)   12.286 (0.000)

RESET (1)     0.124 (0.726)   0.003 (0.950)   0.001 (0.995)

Notes: The estimated coefficients are reported with their
associated standard errors. For both the total player and total
innings movement, we report white heteroskedasticity-consistent
standard errors as for both of these ARCH tests failed to reject
the presence of heteroskedasticity. In addition, *, **, ***
represent significance at the 10, 5, & 1% critical level,
respectively. B-G(q) reports the Breusch-Godfrey statistic for
serial correlation with lag order q; ARCH(q) reports the Engle ARCH
statistic for heteroskedasiticy with lag order q; RESET reports the
Ramsey RESET test for specification with q fitted values. P-values
are in parenthesis.