The Coase Theorem, free agency, and Major League Baseball: a panel of pitcher mobility from 1961 to 1992.

I. Introduction

A great deal of conceptual and empirical work in the economic analysis of the law and property rights has been directed towards resolving a controversy surrounding the Coase Theorem. Many economists and legal scholars interpret the theorem as containing two propositions. The first is that, in the absence of transactions costs and wealth effects, parties will bargain to an efficient outcome. The second holds that the same outcome will be achieved regardless of the distribution of property rights. The latter is known as the invariance thesis and it has been a source of dispute among scholars and between economic theorists and owners of economic enterprises (e.g., owners of professional sports teams) [5; 11; 16; 23; 24; 25; 26; 28; 29].(1) This paper provides an econometric test of the invariance proposition. Major League Baseball presents a natural experiment consisting of an industry in which there has been an explicit change in the assignment of property rights. Beginning in 1879, the reserve clause gave monopsony power to team owners; a player could negotiate salary only with the team that owned his contract and the team could trade or sell the player as management saw fit. In 1976 this system was replaced by the institution of free agency whereby a player with at least six years of Major League experience acquired the right to sell his services to prospective buyers.(2) One implication of the invariance thesis is the testable hypothesis that the mobility decisions made by players after the introduction of free agency would be the same as those made by the owners in the pre-free agency era.

The abundance of data from professional baseball provides an excellent opportunity for testing many propositions from economics. Detailed measures of an individual player's productivity are collected annually as well as output measures of team performance. Also, one can clearly identify the team where each player is employed and can readily trace the mobility of players over time. Hence, there exist previous empirical examinations of the Coase Theorem, free agency, and the mobility decisions of Major League Baseball players. However, there does not appear to be agreement upon what constitutes an appropriate test of the invariance thesis in the case of baseball free agency. Previous examinations of this issue have used data that differed in terms of the period under analysis, the subset of the population of baseball players used for analysis, measures of labor mobility behavior, and measures of the outcomes of that behavior. The level of sophistication of the statistical tests has also varied widely.(3) A significant contribution of this paper is that it provides an econometric analysis of the mobility behavior of all pitchers who played in Major League Baseball during the 1961-92 period.

The results of this paper lead to a rejection of the invariance thesis of the Coase Theorem. The empirical analysis shows that after the introduction of free agency, the pitchers with greater longevity in the major leagues are less likely to move relative to their mobility in the pre-free agency period. The results also indicate that, in general, better pitchers are less likely to move and that pitchers playing on teams with higher winning percentages or in large market cities were less likely to move.

The rest of the paper is organized as follows: Section II provides brief reviews of the labor mobility decision and the Coase Theorem to motivate the expected effect of the introduction of free agency on labor mobility. It also critically examines previous empirical tests of the invariance thesis. Section III discusses the empirical model while section IV briefly describes the creation of the data set and relevant variables. The results of the empirical analysis are presented and discussed in section V. Section VI concludes and outlines an agenda for future research.

II. Labor Mobility, Baseball and the Coase Theorem

Conceptual Issues

Labor mobility can be broadly classified as involuntary or voluntary. Involuntary labor mobility is the result of workers being forced to leave their current employment. In general, this may be due to dismissal for poor performance, structural changes in the economy, or shifts in the demand for labor. Player mobility in Major League Baseball during the pre-free agency period would be classified as involuntary mobility. A player would cease to be a member of the team if management released the player from his contract or assigned that player to another team.(4) As the owner of the rights to the player's contract, the team has an incentive to realize the maximum value of that asset. Thus, it is expected that owners will trade players so as to achieve a distribution of player talent that equalizes marginal revenue product (MRP) across teams. If a player on Team A had a higher MRP with, say, Team B, the owners of the two teams would have an incentive to negotiate a deal sending the player to Team B for suitable compensation.

Voluntary mobility occurs when workers choose to change jobs because they are dissatisfied with their current position or because they expect to find a better one elsewhere. The mobility decision in this scenario depends upon the acquisition of information about alternative opportunities, the costs of moving, and the increase in earnings expected from moving. The attainment of free agent status would allow a player the opportunity to voluntarily move to a team from which he could extract a better offer than he currently possessed.(5) The expected outcome is that a player will move to the team where his MRP is highest. However, this will result in the same distribution of talent that obtained when the owners moved the players. That is, the player distribution will be the one that maximizes league revenues, although in this case it would be the player receiving the rents associated with his provision of labor services.(6)

The existence of transactions costs and wealth effects may lead to observance of results that are inconsistent with the predictions of the Coase Theorem. The assumption of negligible transactions costs is central to the efficiency version. Should they be large, transactions costs may completely erode the gains from trade and inhibit the exchange of entitlements from lower-valued users to higher-valued users. Thus, the assignment of rights will have efficiency implications when transactions costs are relatively high. Whether transactions costs are significant in Major League Baseball is not clear. Agent fees and league conventions against sales of players are potentially important sources of transactions costs. Agent fees represent perhaps the biggest transactions costs players face in negotiating a salary with a team. Often the agent's fee is a fraction of the total compensation package and the size could be larger than the cooperative surplus. While player salaries generally increased in absolute terms following free agency, it is not clear whether agent fees or other kinds of transactions costs became larger in relative terms to the overall compensation package or even whether they are large enough to affect exchange. League agreements not to sell players for cash might also be a source of transactions costs. A well known example is that of Commissioner Kuhn blocking several player sales by Charley Finley of the Oakland A's during 1976. The action was justified as being in "the best interests of baseball."(7) Fan opposition to the selling of favored players might be a source of transactions costs that could lead owners to agreements not to make such sales. Ultimately, the role of transactions costs is an empirical issue.(8) However, while the absence of transactions costs is important for the efficiency version of the Coase Theorem, the invariance prediction does not necessarily depend upon this issue. Although transaction costs might impair some trades, if the level of transaction costs is roughly the same before and after free agency, then the degree of labor mobility need not have been altered.

The relevance of wealth effects is the second issue concerning the applicability of the Coase Theorem. In contrast to transactions costs, the absence of wealth effects is crucial for the in-variance proposition. Wealth effects are potentially important in the baseball setting because free agency shifts bargaining power previously held by the owners to the players. Assuming the team is a profit-maximizing firm, it will value a player the same regardless of whether the team or the player has the mobility entitlement. However, receiving the entitlement may affect the behavior of a utility-maximizing player [28]. For example, a preference to play for a championship team or a team near the player's home may manifest itself if the player is feeling wealthier after the change to free agency. As a specific example, when Kirby Puckett re-signed as a Minnesota Twin in December 1992, he reportedly turned down a higher paying offer from the Boston Red Sox, citing his ties to the community and to the Twins organization.(9) Thus, in general, a player's mobility decision could be affected by the change in assignment of property rights.

Assuming the absence of wealth effects and that the level of transactions costs did not change significantly after the introduction of free agency, the above considerations suggest that Major League Ballplayers will move to teams where their marginal revenue product is highest. During the period before free agency, team management has the incentive to find such a team for the player. Post-free agency, the player has the incentive to find the team where his skills are valued highest.(10) The invariance thesis predicts that the mobility decisions are not affected by the ownership of the property rights; i.e., controlling for player quality, the likelihood of a particular type of player moving from one team to another before the advent of free agency should not differ from the probability of that type of player changing teams in the post-free agency era.

Empirical Issues

A wide range of evidence has been brought to bear in examinations of the applicability of the invariance thesis to Major League Baseball. These include: casual observations of the baseball labor market; measures of aggregate labor mobility before and after the introduction of free agency; and, in an indirect attempt to get at the issue of invariance in behavior by focusing on the outcomes of that behavior, researchers have examined if competitiveness in baseball has been altered due to the institutional change. First have been the simple presentations of situations wherein a number of free agents failed to re-sign with their current team [19] or the assertion that the proportion of free agents re-signing with their current team is virtually insignificant [29]. This evidence is adduced to indicate the failure of the invariance thesis under the supposition that the free agents were already at the team that valued their services most highly. We return to this point below.

The second approach examined the aggregate flows of player talent in an attempt to discern if players moved themselves in the post free-agency period in the same manner as the team owners had moved them previously. Comparing the rate of player transfers in the years before the introduction of free agency with that occurring in the following years, Spitzer and Hoffman [28] and Besanko and Simon [1] find the institutional change had no significant effect on the rate at which players switched teams. On the other hand, there have been mixed results about player mobility behavior vis-a-vis owner movement of players when team and market characteristics are included in the analysis. Rottenberg [24] was the first to point out that team winning percentage and market size were important factors determining the mobility of player talent. Assuming diminishing returns to player talent, Rottenberg's analysis implied that good players should move from better teams to worse teams because their marginal contribution would be greater on the weaker team. Also, since marginal revenue would be greater in large cities than small cities, ceteris paribus, players would be expected to move from small market teams to large market teams. Besanko and Simon [1] provide some evidence reporting no change in the correlation between player mobility and either team winning percentage or market size after the introduction of free agency. However, their result is sensitive to the correlation measure.(11) Drahozal [12] analyzed the subset of players signing long-term contracts between 1977-81 and reports that players entering the free agent draft and non-reentrants tend to come from same size cities. However, in his sample, players entering the free agent draft do not move from smaller to larger cities, a result contradicting a prediction made by Rottenberg.(12) Note that by basing the analysis upon data from 1977-81, Drahozal's study of the invariance thesis is a test of whether the owners move non-free agent eligible players the same way the free agent eligible players move themselves in the post-free agency era. Cymrot, Dunlevy and Even [9] also exploit the dual nature of the post-free agency Major League Baseball labor market. Using salary data on hitters from 1979-80, they find that free agent eligible players tend to move in response to estimated salary gains similarly to the mobility of non-free agent eligibles.

The third type of evidence marshaled in examinations of the invariance thesis was indirect evidence pertaining to team competitiveness. Since Rottenberg's analysis pertaining to the movement of good players from better to worse teams would hold under any institutional arrangement regarding property rights, this implied that competitive balance in baseball should be unaffected by changes in the ownership of property rights to players' services. Using measures of between-season competitiveness and within-season competitiveness, Besanko and Simon [1] fail to detect a change in the level of competitiveness in Major League Baseball after the introduction of free agency. Drahozal [12] calculates the standard deviations of winning percentages in the National and American Leagues before and after the introduction of free agency. Although a statistical test is not presented, he claims a failure to see a clear difference in the dispersion of winning percentages lends support to the invariance proposition. Scully [26], using a similar test but more data, finds that free agency led to increased competition in the National League.

The data and methodology employed in the above examinations of the invariance thesis, while suggestive, can be improved upon. First, the introduction of free agency into Major League Baseball was an important institutional change that might have disrupted the market and led to disequilibrium outcomes while agents were adjusting to the new environment. Ideally, a test of the invariance thesis as applied to the institutional change of free agency would focus on the mobility of individual players, encompass a period of time long enough to allow the market to adjust to the institutional change, and compare the movement of players before the change to player movement after the introduction of free agency. For the most part, the papers cited above were written when only a few years of data from the post-free agency period were available. By contrast, the analysis in this paper is based upon a period of time long enough so that a presumption exists that equilibrium behavior is being captured.(13) Also, while the analysis of data exclusively from the post-free agency era may not be revealing any current differences between the mobility behavior of free agent eligible and non-free agent eligible players, it is obvious that this strategy will fail to capture any inter-period differences. Since the test employed in this paper is based on panel data over an extended period, it does capture changes in mobility behavior across regimes.

Second, it is not clear that focusing on aggregate mobility patterns or the outcomes of those patterns constitutes an appropriate test of the invariance thesis as applied to the introduction of free agency. For example, even if the aggregate rate at which players moved in the pre-free agency period did not differ from the rate in the post-free agency era, if the types or quality of players transferring has been altered, then the invariance thesis would not hold. Similarly, the research examining team winning performance and competitiveness did not control for player quality and, hence, ignored this aspect of the invariance thesis. The analysis in this paper is based upon the complete player statistics of all pitchers from 1961-1992 as well as a number of team performance measures and institutional variables. Use of this rich data set and econometric techniques to control for player quality, team characteristics and other institutional factors provides a sharper analysis of the impact of free agency on pitcher mobility than has been obtained heretofore.

Note that by focusing on the mobility behavior of all pitchers, this paper's approach differs from those which examine the invariance thesis by considering only the mobility behavior of free agents [19; 29] or that of free agents that moved [10].(14) We believe that observing a number of free agents that fail to re-sign with their current team is beside the point in an evaluation of the invariance proposition. Our interpretation of the Coase Theorem's invariance thesis is that, ceteris paribus, the mobility behavior of players in the free agency period should be no different from that mobility in the pre-free agency era. The invariance proposition does not predict whether a particular player will move to another team, but only that he would be no more or less likely to move after free agency; the likelihood of moving would not be affected by the assignment of rights to the mobility decision.

III. Econometric Specification

The empirical test of the invariance thesis employed in this paper focuses on the decision regarding a player's mobility. A player moves to another team if the expected net benefits from moving to another team are positive. The net benefits to moving are specified as:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is a variable reflecting the net benefits of individual i moving to another team in period t, [X.sub.i,t-1] is a vector of explanatory variables, [Beta] is a vector of parameters to be estimated, [Z.sub.i,t] is a variable controlling for whether the period is before or after free agency, [Gamma] is a parameter to be estimated, and [[Epsilon].sub.i,t] is an independent and identically distributed error term. The invariance thesis implies that [Gamma] equals zero and the slope coefficients, [Beta], are not significantly different in the pre- and post-free agency periods.

The net benefits to a player of moving are unobservable in practice. However, an indicator variable measuring whether the player moved to another team can be defined as follows:

[Mathematical Expression Omitted];

[Mathematical Expression Omitted].

Substitution of [Y.sub.i,t] as a proxy for [Mathematical Expression Omitted] allows maximum likelihood estimation of equation (1) using a probit analysis.

The empirical analysis exploits the panel nature of the dataset. In particular, repeated observations across individuals allow unobserved individual heterogeneity to be controlled for in the analysis. Important sources of heterogeneity in baseball pitchers may be the player's natural ability, his "heart," or team leadership characteristics. For example, Jack Morris (a three-time, twenty game winner) was recently signed by the Cincinnati Reds for the 1995 season. In response to a reporter's question, he said ". . . but the bottom line is that I've always been able to win. It's something I strive for. I hope my attitude can rub off."(15) Such traits are thought to be important in building winning teams and could affect mobility. To test for potentially important individual effects, a random effects probit model was estimated.(16) However, estimation of this model revealed that individual heterogeneity was not a significant determinant of pitcher mobility. Although not expected, given this result, it is more efficient to estimate the model treating the sample as a pooled cross section/time series data set.(17) These results are reported below.

IV. Data

The data in this study are the records of Major League Baseball pitchers who played between 1961 an 1992.(18) There were three main reasons for the choice of this data set. First, the data covers all pitchers over the period of analysis. By including the entire sample of pitchers, this paper differs from previous studies of baseball player mobility which were based upon more restricted subsets of the baseball player population. Second, the choice of pitchers allows for control over player heterogeneity across different positions. This dispenses with the need to control for positional differences through a large number of indicator variables. Third, by choosing a time frame of thirty-two periods, a balanced data set was obtained relative to the introduction of free agency. Free agency was instituted in November 1976; the data set extends both sixteen years before and sixteen years after that date. For these reasons, the panel data set used in this study is a much richer basis for an evaluation of the invariance hypothesis than has been utilized in previous analses of the effects from free agency.

The total number of pitchers in Major League Baseball between 1961 and 1992 is 2,403 which represents approximately thirty-eight per cent of all pitchers who ever played. Of the pitchers in this sample, 766 have at least six years of experience in the major leagues.(19) The final panel data set contains 11,699 pitcher-year observations.

The discrete choice analysis focuses on whether or not a player moved during a particular period. In the model, the start of a period is defined as the beginning of the off-season and the period runs through the end of the ensuing regular season. The dependent variable in the probit estimation is an indicator variable that is coded "1" if a player moved to another team during the period in question. For example, the period denoted 1990 would begin with the off-season following the 1989 regular season and extend to the end of the 1990 season. If a player remained with the same team throughout this period, the dependent variable would be coded as "0." Otherwise, the indicator would be coded "1."

Three classes of explanatory variables are included in the analysis to control for the effects of individual performance, team characteristics, and institutional effects. The measures of an individual's performance consist of the following: winning percentage (PCT); a dummy variable coded "1" if the pitcher was a twenty game winner, "0" otherwise (TWENT); opponents' batting average (OAV); adjusted earned run average (ERAPLUS); and an indicator variable coded "1" if the pitcher won the Cy Young award during the previous season and "0" otherwise (CYYOUNG). In addition, the number of games started divided by total number of appearances (GS) and the number of games saved divided by total number of appearances (SV) are also used as independent variables. These last two variables are intended to capture any differences between relief pitchers and starting pitchers, given the increasing importance of relief pitching over the duration of the sample period.

Since information about the productivities of the players becomes available over time and, in the post-free agency era, a player's tenure in the Major Leagues is a critical factor determining eligibility for contract rights, several controls are included to capture the effect of player longevity on mobility. Relatively inexperienced pitchers with zero to two years of service in the Major Leagues are treated as the base case. If a pitcher had three to five years of service in the league, then YRSLG0 is coded "1" and "0" otherwise; YRSLG1 is coded "1" if a pitcher has six years of service in the Majors, "0" otherwise; YRSLG2 is "1" for veteran players with seven to ten years of service; and YRSLG3 is coded "1" for pitchers with eleven or more years in Major League Baseball.

The team performance measures include the team's prior year winning percentage (TPCT) as well as an indicator variable if the player was on a team that won their divisional pennant in the previous season. PW is coded "1" for a player on such a team and "0" otherwise. Also, a control was added to capture differences between National and American League teams. Baseball aficionados view the strike zone in the National League to be smaller than in the American League which is considered to favor hitters relative to pitchers in the National League (and vice-versa in the American). In addition, the American League adopted the Designated Hitter Rule in 1973 while this is not a part of the National League game. The variable NATL was coded "1" for players on teams in the National League and "0" otherwise.

One of the controls for changes in the institutional arrangements of the game captured the effect of league expansion on player mobility. The variable ROSTER is constructed by multiplying the number of roster spots per team by the total number of teams in MLB in a given year. This variable captures the effect of having an increasing number of players in Major League Baseball. For example, a player who was not good enough to play in the majors prior to expansion would not show up in the data set, while ceteris paribus, after an increase in the number of roster spots or the number of teams in the league, a player with equivalent skills may be able to make a team. If these players are marginal, they may be more likely to change teams as they try for an opening as a reserve player. Therefore, we might expect ROSTER to be positively related to mobility.

The introduction of free agency ushered in an era of rising player salaries. In an effort to control their costs, team owners apparently resorted to collusive practices after the 1980 players strike. A professional arbitrator found baseball team owners guilty of collusion in the free agent market during the 1985 and 1986 seasons. Since collusive behavior on the owners part meant restricted offers for player services and this could affect player mobility, the variable COLLUS is coded "1" for the years 1985-86 and is "0" otherwise.(20)

A third institutional change which occurred in Major League Baseball during the period of analysis is the increasing importance of television as a source of revenues. For example, between 1965 and 1987 the fees from the sale of broadcast rights for the average team rose over one thousand percent [26]. Furthermore, Scully [26, 110] has argued that ". . . the value of the local rights more or less is determined by the size of the broadcast market." Therefore, we have included the variable POP, which is equal to the population of the metropolitan area (measured in millions) divided by the square root of the number of teams in the city.(21) This variable also captures any differences between "big city" and "small city" teams.(22)

The final variables used to control for institutional changes are those which measure the effect of free agency on player mobility. Since free agency did not begin formally until November 1976, the indicator variable FREE is coded "1" for the 1977 through 1992 seasons and "0" otherwise. Also, FREE is interacted with each of the longevity variables to test if player mobility in the free agency period differs from the pre-free agency period depending upon the type of player. In particular, since free agency is a right limited to players with six or more years of experience, the interaction of YRSLG1 with FREE (YRSLG1F) will identify the effect of attaining the minimum service requirement for free agent eligibility on pitcher mobility. The interactions of YRSLG2 with FREE and that of YRSLG3 with FREE is designed to capture any changes in the mobility behavior of veteran players after free agency.(23) Finally, although players with zero to five years of experience are generally not eligible for free agency, those with three to five years are eligible for salary arbitration. This is a right not held by the players with only zero to two years of service. Furthermore, if the team does not agree to salary arbitration, the players in the former category may become free agents. The interaction of YRSLG0 with FREE captures any differences in the mobility between pitchers with zero to two years in the major leagues and those with three to five years of service in the post-free agency era.(24)

The variable AGENT was included to control for those pitchers who declared themselves free agents.(25) AGENT is coded "1" if the player was declared a free agent during the previous year and "0" otherwise. This proxies for "true" eligibility to move since some pitchers may have signed long term contracts. Thus, although some individuals may have the requisite number of years of service to be eligible for free agent status, a long term contract binding them to a certain team would preclude those individuals from exercising this right.

Table I. Descriptive Statistics

Variable                  Mean               Standard Deviation

PCT                        0.174                     0.167
TWENT                      0.018                     0.135
GS                         0.407                     0.414
SV                         0.048                     0.098
SO                         2.014                     1.440
OAV                        0.267                     0.068
ERAPLUS                   98.318                    48.911
CYYOUNG                    0.005                     0.074
YRSLG0                     0.250                     0.433
YRSLG1                     0.060                     0.238
YRSLG2                     0.156                     0.363
YRSLG3                     0.090                     0.287
YRSLG0F                    0.141                     0.348
YRSLG1F                    0.033                     0.179
YRSLG2F                    0.086                     0.280
YRSLG3F                    0.056                     0.230
NATL                       0.477                     0.499
PW                         0.079                     0.271
POP                        3.171                     1.689
TPCT                       0.492                     0.089
ROSTER                   600.15                     56.834
COLLUS                     0.071                     0.257
FREE                       0.562                     0.496
AGENT                      0.046                     0.210

The invariance proposition of the Coase Theorem holds that the institutional change (FREE) should have no effect on player mobility taken by itself, that players of different service levels should not move differently due to this change (the interaction between YRSLG(*) and FREE should be insignificant for all variables YRSLG0, YRSLG1, YRSLG2, YRSLG3) and, additionally, the slope coefficients should not statistically differ before and after free agency.

V. Results

Table I presents the descriptive statistics of all variables used in the regression. Of all the pitchers covered in the sample, 56.2% played in the post-free agency era while only 4.6% declared themselves free agents.

The main results are presented in Table II. The first results show that "better" pitchers were less likely to move. Pitcher winning percentage, games started, saves, strikeouts, and winning the Cy Young award all had negative coefficients that were statistically significant. The results also show that pitchers become more likely to move as their longevity increases. Taking pitchers with zero to two years of experience as the base case, the coefficients on YRSLG0, YRSLG1, YRSLG2 and YRSLG3 are positive, increasing and highly significant. The last column of Table II shows the contribution to the probability of moving of each of the variables, i.e., the marginal effects.(26) These show that the longevity variables, as well as CYYOUNG and SV, had much higher contribution to the likelihood of moving than did the other variables which captured individual performance; the former variables were generally two to three times the magnitude of the latter.

Table II. Maximum Likelihood Regression Results

Variable      Coefficient      t-statistic(a)      Marginal Effects

INTERCEPT       -0.3500          -1.486                 -0.0840
PCT              0.3878          -2.460(***)            -0.0931
TWENT           -0.1362          -1.106                 -0.0327
GS              -0.3660          -5.420(***)            -0.0879
SV              -1.2811          -7.636(***)            -0.3075
SO              -0.0719          -3.744(***)            -0.0173
OAV              0.2053           0.916                  0.0493
ERAPLUS         -0.0002          -0.649                 -0.0001
CYYOUNG         -0.6884          -2.601(***)            -0.1652
YRSLG0           0.8324          15.940(***)             0.1998
YRSLG1           0.8966          10.727(***)             0.2151
YRSLG2           0.9780          16.310(***)             0.2348
YRSLG3           1.2795          17.015(***)             0.3071
ROSTER           0.0007           1.783(*)               0.0002
COLLUS           0.0340           0.618                  0.0082
NATL            -0.0120          -0.726                 -0.0048
PW               0.0424           0.755                  0.0102
TPCT            -1.8640         -11.676(***)            -0.4474
POP             -0.0151          -1.848(*)              -0.0036
FREE            -0.0030          -0.052                  0.0007
YRSLG0F         -0.1244          -1.800(*)              -0.0495
YRSLG1F         -0.0196          -0.174                 -0.0471
YRSLG2F         -0.2109          -2.630(***)            -0.0506
YRSLG3F         -0.6608          -6.674(***)            -0.1586
AGENT            1.2477          18.852(***)             0.2995

a. *, **, and *** represent significance at the 10, 5 and 1% level,
respectively.

League expansion and/or increases in the team's roster size (ROSTER) had the expected positive effect on pitcher mobility. However, the results indicate that the collusion era was not a significant determinant of mobility. In addition, playing on National League teams or a team that won its divisional pennant did not appear to be a significant determinant of mobility. On the other hand, the variables capturing team winning percentage and city population size show significant negative effects on player mobility. The negative sign on POP shows that pitchers are less likely to leave large city teams. This result complements both Rottenberg's [24] prediction that players would move to large city teams and Cymrot's [7] empirical results that free agents move to large market teams. However, the negative sign on TPCT (indicating that better teams are less likely to lose players) contrasts with another of Cymrot's results. He found that good teams did lose free agents.

Turning to the invariance proposition, the coefficient on the FREE variable is positive but insignificant. Taken by itself, this might be interpreted as lending support to the invariance thesis. However, our broad interpretation of the Coase Theorem is that the mobility behavior of all players must not change due to an institutional change. This does not occur in the data. Seasoned pitchers (those with seven or more years of service) have significantly lower likelihood of moving during the post-free agency era as is shown in the interaction of the YRSLG(*) variables with the FREE variable; i.e., YRSLG2F and YRSLG3F were negative and significant.(27) The invariance thesis is rejected on this basis. In particular, YRSLG3F shows that the probability of moving for the pitchers with the most years of service is reduced by approximately 50% in the post-free agency era. Interestingly, YRSLG1F was not significantly different from zero. This means that the pitchers with six years of service in the majors, the minimum requirement to attain free agent status, were not any less likely to move after the introduction of free agency than before.

To emphasize the above, recall that free agency applies to all those with six years of experience and who are not under long-term contracts. Recognizably, free agency could increase the value of long-term contracts and potentially reduce the mobility of players who sign such a contract. The issuance of long-term contracts may be more likely under free agency as teams attempt to buy back the property rights to the player.(28) The invariance thesis would view the long-term contract as just another mechanism for moving the right to its highest valued use.

The data shows that pitchers who declare themselves to be free agents have a strong likelihood of moving; the coefficient on the AGENT variable is positive and significant. Kelman [19] and Thaler [29] would reject the invariance proposition on this basis. However, since the AGENT variable is controlling for players who have signaled a desire to change teams, this may be capturing self-selection. Since there is no way of knowing if these players would have moved in the absence of free agency, we believe that the FREE variable and the interaction of FREE with the longevity variables (YRSLG0, YRSLG1, YRSLG2, YRSLG3) provides the correct basis for evaluating the invariance thesis. A fair test of the invariance thesis would consider the mobility behavior of all players and not just that of declared free agents.(29)

VI. Conclusion

The invariance thesis of the Coase Theorem holds that a change in the distribution of property rights will not affect the allocation of resources. In this paper, the mobility behavior of all pitchers playing in Major League Baseball from 1961-1992 is examined to shed light on the invariance proposition. The evidence shows that, while controlling for player ability, team characteristics, and self-selection by the players, the mobility behavior of veteran pitchers changed after the introduction of free agency in 1976. Specifically, those pitchers with seven or more years of service in the Major Leagues were less likely to move than had been the case when team owners had the rights to the rents from the player's services. These results lead to a rejection of the invariance proposition of the Coase Theorem.

One obvious extension of this methodology would be to extend the analysis to hitters. Cymrot and Dunlevy [8] postulate that mobility behavior should not differ between offensive and defensive players. This remains to be seen. In addition, obtaining measures of wealth effects and transactions costs would be useful variables. It may be argued that this paper's rejection of the invariance thesis for the veteran pitchers could reflect the presence of wealth effects. The fact that previous studies failed to reject the invariance proposition implies that wealth effects, if present, were not significant in the past. This may no longer be true given the escalating salaries in Major League Baseball.

Thanks to Don Cymrot, James Dunlevy, Rodney Fort, John Heywood, Richard Thaler and an anonymous referee for comments and suggestions on earlier drafts of this paper. In addition, we thank workshop participants at the CNA Corporation, Miami University, the University of Illinois College of Law, the Pennsylvania State University, and West Virginia University for their helpful comments as well.

1. It should be noted that Rottenberg [24] first discussed the invariance proposition, which is a particular application of the Coase Theorem.

2. Dworkin [13] and Scully [26] provide description and analysis of the institutional details.

3. These issues are critically discussed in the following section.

4. Note that a player being traded might desire such a change in employers. Nevertheless, the terminology reflects that team management has the power in the mobility decision during the pre-free agency period.

5. In the first year of free agency, 1977, the average salary rose from $51,501 to $76,066. At the start of the 1994 season, the average player's salary was $1.2 million. A partial list of studies on the effect of free agency on player salaries includes Sommers and Quinton [27], Hill and Spelman [17], Noll [20], Scully [26], Quirk and Fort [21], and Fort and Quirk [14].

6. Scully [26] and Fort and Quirk [14] contain graphical analyses of the distribution of player talent.

7. This episode is discussed in Scully [26].

8. It should be noted that a strand in the literature views the Coase Theorem as a tautology rather than an empirical proposition. To the tautologists, if an inefficient outcome is observed, it must be due to the presence of transactions costs [3; 25].

9. Baseball Tonight, ESPN, 30 July 1995.

10. Fort and Quirk [14] indicate that although the player goes to the team where his MRP is highest, he is paid only the MRP at the next highest team. Cassing and Douglas [4] suggest that the auction mechanism leads to bias and that free agents may be paid "too much."

11. Besanko and Simon [1] reject the Coase Theorem using the Pearson correlation coefficient but fail to reject using the Spearman coefficient.

12. Cymrot [7] showed that good teams tend to lose "non-marginal" free agents. While this supports Rottenberg's prediction, it does not shed light on the invariance proposition.

13. It should be noted that by using the period of 1961-1992 in this paper, any possible disequilibrium period is included in the analysis. As a test of robustness, our results were re-estimated, omitting the sample period 1976-1980 (i.e., immediately after the implementation of free agency). The results remain unchanged. Note that this does not rule out the possibility that using data only from such a period might lead to different results.

14. In this regard, the paper is following the literature on migration which recognizes that some people move while others stay put. See Cymrot and Dunlevy [8] for an application of this literature to the baseball players labor market.

15. Washington Post, 9 April 1995.

16. The individual effect may be modeled as a fixed effect or a random effect. However, fixed effects probit estimation is not possible with panel data. Since the maximum likelihood estimation jointly determines the parameter estimates and the individual effects, the individual specific effects cannot be removed. The random effects specification was estimated using the Butler-Moffitt quadrature procedure [2].

17. Greene [15] contains a review of the literature and an accessible introduction to random effects probit procedures. Diagnostic checking revealed that adding team performance measures rendered the individual effects insignificant.

18. Unless otherwise indicated, all statistics are taken from Thorn and Palmer [30].

19. Pitchers with at least six years of experience represent approximately thirty-two per cent of the sample. The average tenure in the major leagues of the pitchers in the sample is 4.87 years.

20. See Scully [26] for discussion of the collusion amongst the owners. Some evidence suggests that the collusion era lasted much longer than 1985-1986. For example, Marvin Miller testified before Congress in 1982 about the possibility of clubs colluding. Scully has argued that, "There is no prospect of solution to the (collusion) dispute . . . until the current labor-management agreement expires on 31 December 1989" [26, 42]. In order to allow for the possibility of a lengthier collusion era, we also set COLLUS equal to one during the entire period of the 1981-89 labor-management agreement. Results reported are not sensitive to alternative specifications of COLLUS.

21. Source for this variable is The Statistical Abstract of the United States, various editions. Division of the population by the square root of the number of teams is consistent with Coffin [6], who argues that this is the best way to account for the cities which have more than one major league team. This variable was also calculated as simply the population of the metropolitan area and as the population divided by the number of teams in the city. Results reported are not sensitive to alternative specifications.

22. We thank the referee for suggesting the use of population data.

23. The choice of ten years of service as the break between YRSLG2 and YRSLG3 was somewhat arbitrary. Experimenting with other choices for this break point did not affect the results.

24. The 1976 Basic Agreement and subsequent agreements provide for a number of circumstances in which a player with fewer than six years of service may become a free agent. See Wong [31] for details. Also, arbitration eligibility has been determined by two years of service for most of the period in the dataset. The 1986 Basic Agreement raised the arbitration eligibility requirement to three years of service but the 1990 lockout led to compromise on this issue and 17% of players with two years of service again became eligible for arbitration. Diagnostic checks using zero to three years of service as the omitted category did not affect the magnitude nor the significance of the results.

25. The source for the AGENT variable is various issues of the Official Baseball Guide [22].

26. For continuous variables, the marginal effects were calculated by computing [Phi](X, B) for each observation, summing up over all observations, and dividing the sum by the number of observations in the data set. Each variable was separately increased by one standard deviation from the mean and [Phi](X, B)/N was computed. The difference is the marginal effect. For dichotomous variables, the marginal effect was calculated in a similar fashion with the variable set to 0 for all observations and then set to 1.

27. Note that all pitchers with more than two years of experience have negative coefficients on the interaction term.

28. Kahn [18] found that free agency raised contract duration.

29. One caveat in interpreting the results is the advent of final-offer arbitration in 1973. Given the timing of this policy, it is difficult to completely disentangle any possible effects that arbitration as opposed to free agency may have on player mobility. Examination of YRSLG0F shows that pitchers with years of service which make them eligible for arbitration but not free agency are significantly less likely to move during the free agency era. As a diagnostic check, we estimate Table II for the years 1971-76, setting ARB equal to "1" during the era of final-offer arbitration (after the 1973 season) and "0" otherwise. Results indicate that arbitration had a minimal effect on player mobility. It should be noted however, that such results may be biased due to any possible disequilibrium effect which might have occurred immediately after the implementation of final-offer arbitration.

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