The causality between salary structures and team performance: a panel analysis in a professional baseball league.

Jane, Wen-Jhan ; San, Gee ; Ou, Yi-Pey 等

Introduction

Economists usually pay more attention to the relationship, rather than the direction, of the linkage between salary structures and team performance. Studies of professional baseball teams (Depken, 2000; DeBrock et al., 2004; Wiseman & Chatterjee, 2003; Scully, 1974; Sommers & Quinton, 1982), soccer teams (Garcia-del-Barrio & Pujol, 2007; Lucifora & Simmons, 2003), and hockey teams (Idson & Kahane, 2000; Jones & Walsh, 1988) normally treat team performance as the dependent variable, and then search for relevant factors that shape it. Recently, Horowitz (2007) provided a detailed literature review looking into various measures of performance in sport. This paper is one of the few research studies focused on the direction of the linkage between salary structures and team performance. (1) The direction of the linkage (e.g., the causality between salary structures and team performance) is unclear and has rarely been rigorously investigated in the literature. Hall et al. (2002) stressed that such a link "plays a central role in the theory of team sports but is seldom investigated empirically" (p. 149). Therefore, we focus on two important concepts of salary structures, the total payroll and the dispersion of salary, to investigate the causality between them and team performance.

Total payroll and the dispersion of salary are important for understanding both the relationship and the causal link between salary structures and team performance in labor market theory. Since total payroll for a sports team is more likely to be affected by its talented players, a causality test between total payroll and team performance will enable us to understand whether expenditure on playing talent, as measured by the team's total payroll, will translate effectively into performance (or success). In other words, the question we want to answer is not whether a team with the highest total payroll, or an owner with very deep pockets, as in the case of the New York Yankees in baseball or Manchester United in soccer, is more likely to win a championship, but whether a causal link between them exists or not.

While the possible relationships between salary dispersion and organizational performance asserted by Tournament Theory (Lazear & Rosen, 1981) and the Fair Wage-Effort Hypothesis (Akerlof & Yellen, 1990) have been investigated for decades, almost none of the studies in the literature have focused on the issue of the direction of causality between salary dispersion and organizational performance. The causal link between salary dispersion and performance can help us to understand why a team with high performance also has a high degree of internal salary dispersion. One explanation would be that the team performs well because salary dispersion creates incentives. Another explanation is that the team performs well and shares rents with its workforce in such a way that it increases salary dispersion. Therefore, we want to answer the question by directly testing the direction of causality, rather than via investigating the relationship (coefficient) between them.

The arrangement of the remaining sections of this paper is as follows. First, we provide a short overview of the relevant literature, followed by the Data Description and Empirical Model section, which first describes the data of the Chinese Professional Baseball League (CPBL) and then presents the empirical model that we used to deal with the problem of heterogeneity when using panel data to perform a Granger Causality Test. The section that follows presents the empirical results and also provides a related discussion on professional baseball in Taiwan. Finally, we summarize our main findings and conclusions.

Literature Review

Salary disparities and organizational performance have long been an important topic of economic research. The two strands in this literature generate opposing predictions. One strand focuses on incentives and establishes a positive link between salary dispersion and firm performance. Employees will work harder if there is more money to be earned. Tournament Theory, as put forward by Lazear and Rosen (1981), is one example in this strand. The second strand focuses on equity and fairness (e.g., the Fair Wage-effort Hypothesis of Akerlof and Yellen [1990]). In this, an increase in salary dispersion within an organization may cause a breakdown of team cohesiveness and performance. As formulated by Levine (1991), the Pay Equality Hypothesis predicts that greater salary dispersion motivates jealousy and mistrust among players on teams and reduces team performance.

A few studies find a loose association between team payroll and performance in North American sports (Fort, 2003; Quirk & Fort, 1999; Sanderson & Siegfried, 1997; Scully, 1995; Zimbalist, 1992). Quirk and Fort (1999) examined correlations between team payroll and winning percentages using season averages for the four major North American sports leagues over the period 1990-96. They found that the rank correlations between payrolls and the team's winning percentages were significant in the National Hockey League and the National Basketball Association, but not in the National Football League or Major League Baseball (MLB). Also, the correlation between team pay and performance are significant in English soccer leagues (Szymanski & Kuypers, 1999), and a strong team salary-performance relationship is found for the leagues in England and Italy (Forrest & Simmons, 2002). Moreover, Zimbalist (1992) found that variation in average team salary explained less than 10% of the variation winning percentage in MLB between 1984 and 1989. He argued that this rather weak correlation between average team salary and team performance may be due to the fact that the team's owners fail to sign top-performing free agents, and that the team also fails to pay players in accordance with their performance. Scully (1995) argued that increased expenditures on players and coaching and managerial talent is a necessary, but not a sufficient, condition for improving a team's success.

Team performance should be driven by team payrolls in a competitive labor market, in which salaries reflect marginal revenue product and any gaps are removed by trading players for cash. European football, where freedom of player movement is relatively unrestricted, is one example of this (Hall et al., 2002). (2) The institutional barriers that govern the limitation of a team's expenditure on salary, right to trade players, draft rules, revenue sharing and so on, have made it more likely that teams cannot use their financial advantage to buy success.

Policies aimed at improving balanced competition in a league can affect the causal link between payroll and team performance. The customary argument for competitive balance is couched in terms of league-welfare optimality, and the quality of the games is determined by the uncertainty of the outcomes of games between members of the league (Vrooman, 2000). Therefore, the objectives of the teams in the league are interdependent, because each game generates a zero-sum performance metric. Under such circumstances, the over accumulation of talent, as captured by team payroll, may actually lead to significantly negative externalities and dominance by large-market teams. This is the so-called Yankee Paradox. Ultimately, it can result in no games, no gate receipts, and no Yankees. Rosen and Sanderson (2001) argued that the issue of players' compensation reflected the distribution of talent, as well as competitive balance, across teams, so variation in payroll dictates different levels of competitive balance in a league. As in the case of the New York Yankees in baseball or Manchester United in soccer, these teams bring to the forefront the issue of whether teams with the highest payroll or owners with the deepest pockets win championships.

Recent developments in econometric methodology extended the application of Granger (1969) time-series causality tests to panel data. The panel Granger Causality Test has been used in several settings in recent reserch. For example, Hurlin and Venet (2008) analyzed the causal link between financial development and economic growth. Their results provide support for a robust causal link from economic growth to financial development. Erdil and Yetkiner (2008) provided evidence on income-health causality by employing a large micro panel data set with a VAR representation. They found that one-way causality generally runs from income to health in low- and middle-income countries, whereas the reverse holds for high-income countries. Hoffmann et al. (2005) and Bhaduri and Durai (2006) applied panel Granger Causality Tests to the analysis of the relationship between FDI and pollution and dividends and investment decisions. In this paper, panel Granger Causality Tests are employed for two reasons. First, using the panel data can more broadly illuminate possible causality across teams within a professional sport, strengthening the implications. Second, the robustness of the possible causality between salary payment and performance can be examined more rigorously, and the estimates of the direction of causality can serve as a valuable reference in the literature on the sports industry.

Based on this literature review, there exists some evidence of a causal link between total payroll and team performance in professional sports, but the existing evidence above is less than satisfactory for two reasons. First, it remains to be seen whether this causal relationship holds under different payroll specifications, like total payroll vs. the dispersion of salaries within a team. Second, it remains to be seen whether the causal relationship will be detected in panel data, which contains more information across teams and time horizons. We analyze panel data from professional baseball teams and players in Taiwan to address these issues.

Data Description and Empirical Model

The difficulty obtaining data on salaries, payrolls, and performance complicates the analysis of economic relationships in labor research. Thanks to easy availability of data, professional sports represents unique laboratory for testing labor market theories and predictions. Professional baseball began in Taiwan in 1990, and the Chinese Professional Baseball League (CPBL) offers a rich source of data for the study of salary structures of baseball teams. We collected an unbalanced panel of salary data from seven CBPL teams, including 267 players, over the 10-year period from 1990 to 1999. (3)

An expanded Granger (1969) causality, based on the balanced panel data model with fixed coefficients proposed by Hurlin and Venet (2001), was employed to examine the causal link between payroll and performance. The advantage of using panel data is that we can fully utilize cross-sectional and time-series variation in the data, improving the efficiency of the Granger Causality Tests. Cross-sectional heterogeneity exists in any context; in order to correct for heterogeneity across teams in this setting, a panel data model with fixed coefficients is estimated as part of the model that is used to determine whether or not causality between a team's performance and its salary structure exists. (4)

Following the usual approach in panel Granger Causality Tests, we suppose that, for each team i [member of] [1, N] and time period t [member of] [1, T], the specification of the auto-regressive model is represented as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

with [nu.sub.i,t]=[[psi].sub.i]+[[epsilon].sub.i,t] and [[pi].sub.ji,t]=[[psi].sub.ji]+[[xi].sub.ji,t], where individual effects of [[psi].sub.i] and [[psi].sub.ji] (j=1, 2) are assumed to be fixed within each team. [[epsilon].sub.i,t] and [[xi].sub.ji,t] (j=1, 2) are error terms, and they are assumed to be distributed i.i.d. (0, [[sigma].sub.[epsilon].sup.2]) and i.i.d. (0, [[sigma].sub.[epsilon].sup.2]), respectively. y is team performance, as measured by the percentage of wins (WinP) and the total number of wins (WinN) in each year. [X.sub.1i,t] and [X.sub.2i,t] are different specifications of salary structure, namely, total payroll and the dispersion of salaries within a team, respectively. Total payroll (Totsal) is defined as the team's total monthly expenditures on players. The salary dispersion on a team is measured by a discrete Gini-coefficient formula (see Kendall & Stuart, 1969). (5) Judson and Owen (1999) provide Monte Carlo evidence to show that the biased fixed effects estimator developed by Kiviet (1995) generally outperforms other estimators for balanced panels, even when T is small. For this reason, the estimation of equations (1) and (2) above will rely on the fixed effects estimator (cf. Kiviet, 1995; Bruno, 2005).

In terms of the direction of causality from salary structure to team performance, there are four possible hypotheses in two major categories, as shown in Table 1.

In the first category, we test the salary dispersion effect (i.e., whether the slopes of the Gini coefficients ([[beta].sub.1]) are statistically significant when total payroll is included in the model). If the null hypothesis [H.sub.10] is rejected, there is evidence of Granger causality from salary dispersion to team performance. Such a causal relationship exists in at least one team in the panel. In the second category, we test the Granger-causality from total payroll to team performance controlling for variation in salary dispersion. If the null hypothesis [H.sub.20] is rejected, there is evidence of Granger causality from total payroll to team performance. The possibility of reverse causality from team performance to salary structure is examined in null hypotheses [H.sub.30] and [H.sub.40], where salary dispersion and total payroll are not included in equation (2). Here, Granger causality from team performance to salary dispersion (or total salary) exists if the respective null hypotheses are rejected. The test statistic for the panel Granger Causality Tests are computed by means of the following equation:

F = ([RSS.sub.2] - [RSS.sub.1]) / N/[RSS.sub.1] [TN - 2N - 1], (3)

where [RSS.sub.2] denotes the restricted sum of squared residuals obtained under the null hypothesis, [RSS.sub.1] is the unrestricted residual sum of squares of the model, and TN is the total number of observations. The statistic has a Fischer distribution with N and TN-2N-1 degrees of freedom, instead of the standard F distribution, under the null hypothesis.

We check the robustness of our results by constructing different specifications of the basic models described above. First of all, current period observations of all variables are incorporated in order to capture any instantaneous causality between team performance and salary structure. Second, we use the relative total salary ratio, denoted RTotsal and measured by the percent of total team payroll to league total salary, rather than the team total payroll, Totsal, to further investigate the causality between salary structure and team performance.

Summary statistics for the variables used in this study are shown in Table 2.

Empirical Results and Discussion

Prior to conducting the Granger Causality Tests, we tested for stationarity in the variables included in the dynamic panel data model. Fort and Lee (2006) provided a general process for investigation of nonstationary behavior of sports data. Based on the Fort and Lee (2006) process, the panel unit root test proposed by Im et al. (2003) was applied to the variables in our paned data set. Based on this approach, there is evidence of stationarity when the value of the test statistic exceeds a critical value at a specific level.

The results of the stationarity tests on the variables of interest are presented in Table 3. In terms of the team performance variables, WinP and WinN, the model specification includes a constant term and a time trend together with a number of lags of the dependent variable; 1, 1.5 and 21ags are tested separately. (6) Table 3 shows that the values of the test statistics for WinP and WinN are statistically significant; these variables appear to be stationary. Using the same method, the variables Gini and Totsal also appear to be stationary. (7) Therefore, all these variables can be included in the model estimated for the Granger Causality Tests.

The basic results of the panel Granger Causality Tests between salary structure and team performance are reported in Model 1 of Table 4. (8) In terms of the tests of causality from salary dispersion to team performance, both of the F statistic values suggest rejection of [H.sub.10] at the 1% significance level when controlling for variation in total team payroll. The rejection of the null hypothesis suggests that, for at least one team in the CPBL panel, past values of salary dispersion are relevant when it comes to forecasting current team performance. In terms of the tests of causality from total payroll to team performance, null hypothesis cannot be rejected--there is no evidence of a causal relationship when variation in salary dispersion is controlled for. In addition, when the reverse tests of causality, from team performance to salary structure, are conducted, as shown in Model 1, the corresponding F test values are low, indicating that the null cannot be rejected.

In terms of the robustness checks, Model 2 in the second column of Table 4 reports the results of regressions that include current period observations of variables to account for any instantaneous relationships in the data. Model 3 on Table 5 reports the results of regressions containing the alternative payroll variable, relative total payroll (RTotsal) instead of total payroll. (9) The presence of heteroscedasticity may also be important in this setting, as the variance of the equation error term may differ across teams. We control for heteroscedasticity in these data using White's (1980) correction. Table 6 reports the results of the causality tests correcting for the presence of heteroscedasticity, and the causality test statistics, which differ from those reported on Tables 4 and 5. The test statistics are adjusted using the corrected standard errors, if the null hypothesis of homoscedasticity can be rejected in that model specification. In general, the evidence about causality generated from the previous models still holds, and it tends to reinforce the conclusion that salary dispersion Granger causes team performance. In general, values of the test statistics on Table 6 are smaller than those reported on Tables 4 and 5.

Based on the results of the causality tests presented on Table 4 and Table 5, the direction of the causality from salary dispersion (Gini) to team performance (WinP and WinN) is confirmed. The results of these tests are in fine with Tournament Theory or Equity Theory, which stresses that salary dispersion improves team performance. In addition, our empirical results also confirm that total payroll (Totsal) and relative total payroll (RTotsal) do not Granger cause team performance (WinP and WinN). Even though the literature stresses the importance of the stock of human capital in an organization, the lack of a causal link from salary structure to team performance may be induced by league policies aimed at promoting competitive balance like the reverse clause.

In addition to the evidence that salary dispersion Granger causes performance, the estimated coefficients in the salary dispersion variable in the regressions are negative and statistically significant. (10) Increasing salary dispersion is associated with decreased team performance. Compared to the lack of support for wage fairness in the existing research using MLB data (DeBrock et al., 2004), our results indicate that teams with less salary dispersion perform better; evidence from the CPBL supports Equity Theory. The results indicate an interesting phenomenon: for a given the total payroll, a team with larger salary dispersion (e.g., a team with both star players and lower-talent players) has lower performance than a team with less dispersion (e.g., for one with a large number of average, but not star players) based on data from the CPBL.

DeBrock et al. (2004) also found that high-wage strategies are associated with better won-loss percentage and higher attendance in MLB. Based on our results, the former relation between wage strategies and performance does not hold in the CPBL. The lack of Granger causality from total salary to performance suggests that the effects of total payroll are limited in the CPBL. Specifically, the reasons for the lack of a causal link may be mainly attributed to the immobility of players and a tacit agreement among team managers not to engage in trades. (11) In contrast to the EPL's "freedom of contract" for football players since 1978, the CPBL is less developed in the sense that there are no clear rules regarding the trading of players. In the CPBL, players are usually regarded as constituting part of the assets of a team. In addition, tacit collusion between team managers makes it impossible for the players to switch to other teams. Poaching good players from other teams by offering higher salaries is not feasible. If CPBL teams can spend money on good players outside the league, they may have a chance to "buy wins." But since the average salary in the data is $51,400 per year, this is not an attractive option for a good player on the international market. Therefore, turning higher salary expenditure into success is almost impossible in the CPBL under existing conditions.

The evidence of Granger causation from salary dispersion to team performance in the CPBL can be attributed to the flexibility of salary adjustment in the league, and the relative immobility of the players. Regular salary adjustment in the CPBL, unlike the relatively long-term contracts (3 to 5 years) in other professional sports leagues in the world, is quite common. The players in the CPBL are paid according to a short-term contract, which is more like an agreement. (12) Restrictions on player mobility in the CPBL are offset by very flexible salary adjustment. When players' mobility within a league is totally restricted and the internal salary dispersion is easily adjusted every year, the redistribution of internal salary causes team performance to improve. The flexibility of salary and the immobility of players may contribute to the one-way causality from salary dispersion to performance found here.

Conclusions

In this paper we provide a more comprehensive approach to investigating the relationship between salary structure and team performance by taking the dispersion of salaries as well as total payroll of professional baseball teams in Taiwan into consideration when examining the possibility that a causal link between salary structure and team performance exists. We conducted the panel Granger Causality Test to explore the possible causal links between salary structure and team performance using panel data from the CPBL. Our results indicate that Granger causality runs only from the dispersion of salaries to team performance, but not vice versa. These results are robust to a number of alternative model specifications, including heteroscedasticity correction. Surprisingly, the evidence that salary dispersion granger causes team performance is stronger when controlling for variation in total payroll.

Our results give rise to two conclusions. First, our empirical results confirm that both Tournament Theory, which stresses the incentives of salary dispersion, and Equity Theory, which posits that salary equity induces improved performance, affect the performance of professional baseball teams in Taiwan. In terms of the effects of salary dispersion, our results support Equity Theory, and imply that a team with many average players performs better than a team with a mix of super-star and less-talented players. Evidence of causality between total/relative payroll and team performance, which emphasizes the importance of the overall stock of human capital within an organization, was not found. Therefore, the over-accumulation of talent, reflected by large team payrolls, may actually lead to negative externalities. The existence of a "Yankee Paradox" is supported by the evidence.

Second, the one-way causality patterns in the data suggest that teams playing in a league with strict restrictions on the mobility of players must rely more on internal salary adjustments, especially on the dispersion of salaries, motivate players, and compensate for the fact that players are not able to move among teams.

Finally, since the wage structure of a professional sports team resembles that of a business enterprise, relevant theories of the effect of wages on performance can be explored in order to understand more about the wage structure and its influence on performance. In this paper we have shown that both Tournament Theory and Equity Theory are relevant for explaining the performance of professional sports teams. Therefore, these results can provide important context when examining the relationship between compensation structure and team performance.

Appendix

Table A: Granger Causality Tests with Additional Control Variables

Direction of Granger Causality    Model (4)     Model (5)
                                   F value      F value

Gini    [right arrow] WinN          7.76 ***     8.22 ***
RTotsal [right arrow] WinN          2.08         1.93
WinN    [right arrow] Gini          0.80         0.66
WinN    [right arrow] RTotsal       0.05         0.22
Gini    [right arrow] WinP          9.06 ***     7.46***
RTotsal [right arrow] WinP          2.34         1.79
WinP    [right arrow] Gini          1.11         0.91
WinP    [right arrow] RTotsal       0.00         0.09

Notes: (a) *** denotes significance at the 1% level. The critical
value simulated by Huilin and Venet (2001) is 6.937 for the 1%
significance levels.

(b) The year dummies are included in the empirical model.

(c) The optimal lag-lengths for each equation is determined by
the Akaike Information Criterion (AIC). (c) The year
dummies are included in the empirical model.

Table B: Results of the Coefficients of Salary Dispersion from
the VAR Model

                      Gini [right arrow] WinN   Gin [right arrow] WinP

Model 1 (t-1)             -179.7891 ***             -1.9926 ***
                           (62.73)                  (0.63)

Model 2 (t and t-1)       -115.3049 ***             -1.3557 ***
                           (63.94)                  (0.67)

Model 3 (Rtosal)          -172.9032 ***             -1.9064 ***
                           (59.98)                  (0.61)

Model 4 (Control          -177.0839 ***             -1.9557 ***
variable: players'         (63.55)                  (0.65)
average tenure)

Model 5 (Control          -179.7891 ***             -1.7007 ***
variable: players'         (62.73)                  (0.62)
average age)

Notes: (a) *** denotes significance at the 1% level.

(b) Parentheses are the standard errors.

Table C: Determination of Optimal Lags by Akaike Information
Criterion (AIC)

Direction of Granger      Causality    Causality       lags

Gini      [right arrow]   WinN
                                        46.1629 *     47.2492
Totsal    [right arrow]   WinN
WinN      [right arrow]   Gini         -47.7814 *    -46.9648
WinN      [right arrow]   Totsal       215.2495 *    215.3734
Gini      [right arrow]   WinP
                                       -25.6110 *    -25.0827
Totsal    [right arrow]   WinP
WinP      [right arrow]   Gini         -47.6065 *    -46.6283
WinP      [right arrow]   Totsal       215.3824 *    215.6101

Note: * indicates the optimal lag.

Table D: Tests of Heteroscedasticity

Direction of Granger  Causality    Model (1)    Model (2)    Model (3)

Gini    [right arrow] WinN
                                    3.333        4.576       3.603
Totsal/ [right arrow] WinN
RTotsal
WinN    [right arrow] Gini          5.976 *      0.090       5.976 *
WinN    [right arrow] Totsal/       7.027 *      6.962 *     3.740
                      Rtotsal
Gini    [right arrow] WinP
                                    2.696        2.380       3.132
Totsal/ [right arrow] WinP
RTotsal
WinP    [right arrow] Gini          5.864 *      0.140       5.864 *
WinP    [right arrow] Totsal/       7.816 *      6.624 *     3.640
                      RTotsal

Notes: * denotes significance at the 10% level.

Authors' Note

The authors thank Professor Ngo Van Long for his valuable comments. We also thank two anonymous referees for valuable suggestions. All remaining errors are, of course, the responsibility of the authors.

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Wen-Jhan Jane [1], Gee San [2], and Yi-Pey Ou [2]

[1] Shih Hsin University, Taiwan

[2] National Central University, Taiwan

Wen-Jhan Jane, PhD, is an assistant professor in the Department of Economics. His current research focuses on the economics of sports, specifically the topics of wage theory, competitive balance, and worker discrimination.

Gee San, PhD, is a professor in the Graduate Institution of Industrial Economics. His research focuses on labor economics and industrial organization.

Yi-Pey Ou is a PhD candidate in the Graduate Institution of Industrial Economics. Her current research focuses on technological change and growth.

Endnotes

(1) Horowitz shows that bi-directional causality between annual attendance and team performance on the field exists for teams in Major League Baseball (MLB). Davis (2008) reports similar results.

(2) The Professional Footballers' Association succeeded in establishing freedom of contract in 1977, and players are now almost completely free to accept the best contract on offer. Players can sign contracts and move without impediment at the end of their contracts. Within the contract period, cash sales are permitted through the transfer system under which a club losing a player may demand compensation from the receiving club in the form of a cash payment (i.e., a transfer fee). Therefore, European football also has a much greater provision for the mobility of players.

(3) Due to data limitations imposed by the panel causality tests, the data were restricted to a balanced panel. The N and T dimensions of the panel are determined by the availability of salary and team performance data. Some teams exited and some entered the CPBL in this period. The most complete data were obtained from four teams from 1990 to 1999. The data was obtained from the "Professional Baseball Journal" and the official website of the CPBL (http://www.cpbl.com.tw/).

(4) Different from the traditional literature on Granger Casualty Tests in time series, the panel Granger Causality Test model proposed by Hurlin and Venet (2001) mentions two methods for dealing with heterogeneity among cross-sectional units: distinctive intercepts and variable slopes. The former one is simple and intuitive.

(5) The Herfindahl index is not used as the measure of salary dispersion because the potential range of the index is affected by the team's roster size. Several measures of inequality are compared by Allison (1978), who finds that both the Gini index and the coefficient of variation are superior in many respects. Harrison and Klein (2007) also recommend the same two measures to capture the effects of pay disparity.

(6) Because this test for panel unit roots allows a different number of lag lengths for each equation, a lag-order of 1.5 refers to the average of the lag lengths included in this test.

(7) We used the same model associated with team performance, but the statistics were insignificant at the 10% level. Regarding the different features in the time series between team performance and salary structure, we tried the model without a time trend. The results show that Gini and Totsal are stationary at the 5% level under appropriately controlled lag structures.

(8) We used the Akaike Information Criterion (AIC) to determine the optimal-lag length. In order to avoid the loss of degrees of freedom, we followed Justesen (2008) and included lag-lengths up to two for yit, xlit and x2it in the estimated equation. The results are shown in Table C in the Appendix.

(9) In addition, Table A in the Appendix reports the results of models that contain control variables for players' tenure and experience. Model 4 and Model 5 include control variables for players' average tenure and average team experience, respectively. The results show that our conclusions are still robust after controlling both tenure and experience.

(10) The results of the coefficients of salary dispersion from the VAR model are listed in Table B in the Appendix.

(11) Unless the player is released by the original team manager, he cannot become a free-agency player. Therefore, it seems that player's contract is permanent in the CPBL. The trading of players between teams is oriented by the employers. The rule of free agency was not legislated until 2007. The new rule states that a player who has a nine-year tenure is eligible to be a free-agency player, and the starting point for tenure was 2003. That is, the first free-agency players will emerge in 2012.

(12) Different from salary arbitration in other pro sports, the manager adjusts the players' salaries every year after the end of the season and the players have the right to bargain before the start of the next season. Moreover, some teams also have a mechanism for adjusting salaries in the middle of the season.

Table 1: Hypotheses for Granger Causality Tests

         Salary structure [right arrow]
         Team performance

Gini     [H.sub.11]:[[beta].sub.1] = 0
         [H.sub.11]:[[beta].sub.1] [not equal to] 0

Totsal   [H.sub.20]:[[beta].sub.1] = 0
         [H.sub.21]:[[beta].sub.1] [not equal to] 0

         Team performance [right arrow]
         Salary structure

Gini     [H.sub.30]:[[eta].sub.1] = 0
         [H.sub.31]:[[eta].sub.1] [not equal to] 0

Totsal   [H.sub.40]:[[eta].sub.2] = 0
         [H.sub.41]:[[eta].sub.2] [not equal to] 0

Table 2: Basic Statistics

Variable            Mean             S. D.       Observation

WinP               0.515            0.085           40
WinN              46.575            8.424           40
Gini               0.202            0.069           40
Totsal (NT$) *   2,460,919        919,547.3         40

* The average exchange rate during our data period (1990-1999)
was roughly 1US$=28.066NT$.

Table 3: Panel Unit Root (IPS) Tests with Heterogeneous Individuals

Variable        lags           t-bar          p-value

Gini            1              -2.221         0.095 *
                1.5            -2.422         0.039 **
                2              -1.407         0.442

Totsal          1              -2.040         0.162
                1.5            -7.581         0.000 ***
                2              -0.887         0.766

WinN            1              -1.852         0.703
                1.5            -2.972         0.067 *
                2              -2.751         0.095 *

WinP            1              -1.575         0.839
                1.5            -4.399         0.000 ***
                2              -4.189         0.000 ***

Notes: (a) Im et al.'s (2003) t-abr statistics for the panel unit
root. *** denotes significance at the 1% level, ** denotes
significance at the 5% level and * denotes significance at the
10% level.

(b) Under the original model with a constant and a trend term, the
test statistic for Gini and Totsal was insignificant at the 10% level,
so we tried the other specification to test the model without the
trend term.

(c) Based on the mean of the individual Dickey-Fuller t-statistics of
each unit in the panel, the IPS test assumes that all series are
non-stationary under the null hypothesis.

Table 4: Granger Causality Tests

Direction of Granger Causality       Model 1       Model 2
                                     F value       F value

Gini     [right arrow]    WinN        19.96 ***     7.33 ***
Totsal   [right arrow]    WinN         3.04         1.36
WinN     [right arrow]    Gini         0.00         1.73
WinN     [right arrow]    Totsal       0.75         0.18
Gini     [right arrow]    WinP        17.99 ***     7.50 ***
Totsal   [right arrow]    WinP         4.30         1.40
WinP     [right arrow]    Gini         0.81         2.27
WinP     [right arrow]    Totsal       0.12         0.56

Notes: (a) *** denotes significance at the 1% level, ** denotes
significance at the 5% level, and * denotes significance at the
10% level. The critical values simulated by Huilin and Venet (2001)
are 4.315 and 6.937 for the 5% and 1% significance levels,
respectively.

(b) The year dummies are included in the empirical model.

(c) The optimal lag-length for each equation is determined by the
Akaike Information Criterion (AIC), and the results are listed in
Table C in the Appendix.

Table 5: Granger Causality Tests

Direction of Granger Causality          Model 3
                                        F value

Gini      [right arrow]    WinN           8.31 ***
RTotsal   [right arrow]    WinN           2.68
WinN      [right arrow]    Gini           0.00
WinN      [right arrow]    RTotsal        0.30

Gini      [right arrow]    WinP           9.64 ***
RTotsal   [right arrow]    WinP           2.92
WinP      [right arrow]    Gini           0.81
WinP      [right arrow]    RTotsal        0.41

Notes: (a) *** denotes significance at the 1% level. The critical
value is 6.937 for the 1% significance level.

(b) The year dummies are included in the empirical model.

Table 6: Granger Causality Tests Correcting for Heteroscedasticity

Direction of Granger Causality    Model (1)    Model (2)   Model (3)

Gini     [right arrow]  WinN       19.96 ***     7.33 ***    8.31 ***
Totsal/  [right arrow]  WinN        3.04         1.36        2.68
RTotsal
WinN     [right arrow]  Gini        0.29         1.73        0.29
WinN     [right arrow]  Totsal/     0.59         0.28        0.30
                        RTotsal
Gini     [right arrow]  WinP       17.99 ***     7.50 ***    9.64 ***
Totsal/  [right arrow]  WinP        4.30         1.40        2.92
RTotsal
WinP     [right arrow]  Gini        0.05         2.27        0.05
WinP     [right arrow]  Totsal/     0.53         2.51        0.41
                        RTotsal

Notes: (a) The bold numbers are the value corrected for
heteroscedasticity.

(b) *** denotes significance at the 1% level.

(c) The year dummies are included in the empirical model.