Professional Baseball: A Quantile Analysis. Wen-Jhan Jane* Department of Economics, Shih Hsin University, Taiwan

Transcription

1 The Effects of Equities on Team Performance for Winners and Losers in Nippon Professional Baseball: A Quantile Analysis Wen-Jhan Jane* Department of Economics, Shih Hsin University, Taiwan Keywords: Employee Equity; Internal Equity; Nippon Professional Baseball; Quantile Regression; Tournament Theory. JEL Classification: J31, J33, J44. * Corresponding Author: Dept. of Economics, Shih Hsin University, No. 111, Sec.1, Mujha Rd., Wunshan District, Taipei, Taiwan 116, R.O.C. krisenwerk@gmail.com, Fax:

2 The Effects of Equities on Team Performance for Winners and Losers in Nippon Professional Baseball: A Quantile Analysis Abstract The paper introduces indices to measure the concepts of internal and employee equities in social psychology. The unbalanced panel data of Nippon Professional Baseball (NPB) for the period between 1996 and 2008 and the quantile regression are employed to examine the relationships between inequities induced by salary dispersions and team performance. The empirical findings are as follows. First, payroll has a significant and positive effect on team performance, and the positive effect of payroll on team performance is stronger for winners (high quantiles) and losers (low quantiles) than average teams. Second, internal inequity has an insignificant effect on performance. Third, salary inequality based on employee equity for the hitters has a significantly positive effect on team performance. Fourth, the positive effect of salary inequality based on the employee equity for pitchers on team performance is insignificant. The discrepancy between the last two findings reflects a difference in the similarity of abilities and the uncertainty in the production process between the two groups. The implication for team managers is that tournament-like compensation is suitable for hitters but not for pitchers. Managers in winning teams and losing teams should need to consider seriously about raising salary expenditure than owners of average-performing teams. Keywords: Employee Equity; Internal Equity; Professional Baseball; Team Performance; Tournament Theory. JEL Classification: J31, J33, J44. 2

3 1. Introduction Pay disparity is a topic receiving attention from both economists and social psychologists. Economics literature is concerned with the consequences of salary dispersion on organizational performance. Two opposite predictions have emerged. On the one hand, theories emphasizing incentive effects predict that salary dispersion improves organizational performance (Lazear and Rosen, 1981). On the other hand, theories emphasizing equity and fairness predict a negative link between salary dispersion and organizational performance (Akerlof and Yellen, 1990). Social-psychological literature is more concerned with the feelings of distress resulting from the inequity relative to a referent (Adams, 1963, 1965). Employees who perceive that they are either under or over compensated in terms of salary might experience inequity tension. Such tension motivates employees to alter their effort, or may cause them to leave the workplace (Mowday, 1983). The referent other might be a broad class of relevant people rather than a specific individual. Werner and Mero (1999) and Konopaske and Werner (2002) distinguish three distinct types of equity based on the common choices of referent others (comparison others): external equity, internal equity and employee equity. The referent others for these three types of equity are people with the same job but a different employer, people with different jobs but the same employer, and people with the same job and the same employer. It should be 3

4 noted that an individual may base his or her perceptions of equity on more than one equity comparison (Ronen, 1986). Although there are many studies measuring different kinds of disparity, the relationship between the disparity-induced inequity based on different referent others and organizational performance has received relatively little attention. In the literature of sports economics, the relationship between intra-team salary dispersion, which can be considered a generalized internal equity, and team performance has been extensively studied. The relationships between the other two concepts of inequity and team performance, however, have not been discussed. This paper tackles the relationship between salary disparity, based on the concept of internal equity and employee equity, and organizational performance. The analysis of the effects of each type of salary dispersion on organizational performance sheds light on the relationships between fairness and performance. Furthermore, these findings can be useful for the decision makers of salary policy. The paper proceeds as follows. The next section introduces theoretical arguments for internal and employee equities and the current literature of the connection between salary dispersion and team performance in sports economics. Section three outlines the labor market in Nippon Professional Baseball (NPB), explains some different measurements of salary dispersions with the social-psychological concept, and 4

5 presents the econometric specifications and data descriptions. After that, the economic results are discussed in Section 4 (panel regression) and Section 5 (quantile regression), and Section 6 concludes the paper. 2. Pay Disparity and Organizational Performance Pay equity has an important effect on organizational performance. The reviewed studies describe two possible behavioral patterns that can follow team disparity. The first pattern portrays team disparity impacting negatively on performance. Group members engage in politics and coalitions in an attempt to counterbalance the inequality, making communication and collaboration difficult (Eisenhardt and Burgeois, 1988), the powerful group member is likely to be rejected, the consensus among group members is reached over a longer period of time (Curşeu et al., 2007). As a result, the group decreases its performance, making less creative, strategic or high-quality decisions (Smith, et al., 2006; Smith et al. 1994). Studies of baseball teams (Richards and Guell, 1998; Bloom, 1999; Depken, 2000; DeBrock et al, 2004; San and Jane, 2008; Jane, 2010), basketball teams (Berri and Jewell, 2004), and soccer teams (Franck and Nüesch, 2008) tend to agree that inequity has a negative impact on performance. The second pattern envisions disparity as having positive behavioral consequences at the group level. This idea focuses more on the group s ability to transform the 5

6 existing discrepancies into an advantage for the group. One manner is that the alpha group member elicits a constructive conflict to obtain high quality decisions, a climate for efficient decision-making (Roberto, 2005), whereas the less powerful members increase their efforts in order to compensate for the discrepancy (Frick et al., 2003). Another manner of turning disparity into a group advantage is by accepting and following the most knowledgeable member (Curşeu et al., 2007). Empirical findings on the relationship between pay disparity and team performance from Frick et al. (2003) and Jewell and Molina (2004) in professional sports are mixed. Frick et al. (2003) used data from four major league teams and the team s Gini coefficient to test the relationship between salary disparity and performance. It was found that a higher degree of salary disparity enhances the performance of basketball and hockey teams but decreases the winning percentage of football and baseball teams. Their findings suggest that neither the hypothesis of cohesion nor Tournament Theory is fully supported or rejected. Results may depend on specific factors such as the size of a team and the requirement for cooperation in that team. The complexity of the salary structure for an organization that links pay disparity to team performance is an open issue. 1 In an organization, the comparison between workers usually depends on the 1 There are some working papers, such as Franck and Nüesch (2008) and Vasilescu (2007), making great efforts to analyze the possible non-linear effects of wage dispersion in professional team sports. 6

7 perception of internal and employee equities. Internal equity refers to the relative fairness of the pay for different types of jobs within an organization. Internal equity is not acceptable for those who believe that jobs with different contents (e.g., skill, effort, responsibility and working conditions) should have different base wages associated with them. Employee equity refers to the fairness of pay based on the relative contributions of individuals working on the same type of job in the same organization. Much of the research investigating equity on individuals or teams, using this type of concept, has been experimental (Mowday, 1983). Moreover, it has been suggested that the impact of employee equity is greater than the impact of internal equity (Romanoff et al, 1986; Coff, 1997). 3. Data Description and an Empirical Model Since 1950, the NPB has consisted of two leagues, the Central League and the Pacific League. Each league contains 6 teams. At the end of the NPB season, the top teams in each league face off in the Japan Series. Compared with the MLB, the major differences are the NPB includes a much smaller farm system (only one minor league team per franchise), shorter seasons (usually ranging between 130 and 150 games), multiple all-star games per year and less player mobility. There are far fewer trades in the NPB than in the MLB. In addition, it takes more years before a player is eligible 7

8 for free agency in the NPB. 2 In this study, the percentage of wins (WinP) and the number of wins (WinN) in each year are used as proxies for the team s on-field performance (TP). Following Depken (2000), the explanatory variables of the fixed and random effects models are the total salary (TSal), the index of a team s salary inequality (E), and other control variables (X). Variable E includes two salary dispersion indices: Internal Inequality, based on the concept of internal equity (IE), and Employee Inequality, based on the concept of employee equity (EmpE). Variable TSal is divided into the total salary of pitchers (TSalP) and the total salary of hitters (TSalH) in order to uncover correspondence between these different concepts of equity. Other control variables include the number of players on roster (Players) and dummies of league (League) and year. The fixed effects empirical model used in this study is specified as follows: TP kt LogTSal k E X. 1 kt 2 kt 3 kt kt (1) where the k are individual effects that vary across teams, the s are parameters which are constant across teams, and kt is a random term. Three methods are employed to measure salary dispersion: Herfindahl-Hirschman Index (HHI), Gini Coefficient (Gini), and coefficient of 2 Free agency (FA) started in 1993 in the NPB, but the qualification for free agency is a 9-year tenure. To discourage players from leaving for the MLB, or to compensate teams that lose excellent players, the NPB and MLB agreed on a posting system for players under contract. MLB teams who want to negotiate with a player need to submit bids for a posting fee. The MLB team pays the Japanese team when the player signs with the MLB team. However, free agents are not subject to the posting system. 8

9 variation (CV) for players salaries in a team. Internal Inequality indices, IE, are computed as follows. HHI is the summation of the square of player p s salary share (S p ) in team i in year t. CV is defined as the ratio of the standard deviation, σ, to the mean, μ, for players salaries in team i in year t. The formula are, HHI it = P i 2 S pit p 1, S pit = x pit P i p 1 x pit, (2) 2 Gini it = 2 P i P p 1 px pit Pi P i 1 i, (3) CV it =σ it /μ it, i=1, 2, 3,, n. t=1, 2, 3,,T., (4) where x p is defined as player p s salary, and P i is the number of players in team i. Employee Inequality indices are computed for the group of hitters within a team (EmpEH) and the group of pitchers within a team (EmpEP). For the jth group of team i in year t, EmpE jt is defined as the following: P i HHI jit = 2 S pjit p 1 2 Gini jit = 2 P i P p 1, (5) px pjit Pi P i 1 i, (6) CV jit =σ jit /μ jit, j=1, 2. i=1, 2, 3,, n. t=1, 2, 3,,T. (7) where j equals 1 (or 2) if players are hitters (or pitchers). Salary inequality in the MLB has increased considerably from 1985 to 2001 (Frick et. al., 2003). In contrast, there seems to be no trends in the salary inequality in the NPB. Figure 1 shows the teams average degree of inequality measured by HHI 9

10 between the two leagues from 1996 to Pay dispersion appears to be rather the same between the two leagues except The descriptive data provides a figure that team s pattern of salary strategies on pay distribution between two leagues in this period are quite the same, but there seems has a systematic difference between leagues over time. These differences may be related to differences in team performance. [Insert Figure 1 about here] The data used is taken from Professional Baseball Players 1997 to 2009, edited by the Japan Professional Baseball Committee. The sample of hitters and pitchers who played during the period 1996 to 2008 has been chosen according to the following criteria. The hitter s total number of slugging episodes and the number of times at bat must not be zero. The pitcher must have confronted more than one hitter. Professional minor league players are not included. The average number of players is 43 per team each year, and 23.8 hitters and 19.2 pitchers are included in the samples. Table 1 presents the variable definitions and the data description. [Insert Table 1 about here] 10

11 Lower salary levels reduce worker input, while higher salary levels attract better players and provide incentives for good performance (Adams, 1963). Therefore, the relationship between total salary expenditures and team performance (β 1 ) is thus expected to be positive. A lot of research on salary dispersion from the perspective of internal (intra-team) equity in the MLB supports equity theory, so the effect of IE in the NPB may also be negative. However, when plotting the winning percentage against the HHI and Gini in Figure 2, there is a positive-slope line in the estimation. The story in the NPB may not the same for the MLB. [Insert Figure 2 about here] 4. Empirical Results and Discussion The results of equation (1) are listed in Table 2 and 3. 3 In Table 2, the NPB s data are used in each regression. The regressions in Table 3 are almost the same as those in Table 2 except that salary data was adjusted for inflation. Each table is divided into two parts. The upper half shows the results of the models with Internal Inequality indices as explanatory variables, and the lower half shows the results of models with Employee Inequality indices as explanatory variables. As expected, the coefficients on 3 Two dependent variables (WP and Wins), three measures of inequality (HHI, GINI, and CV), and dummy of league in the model specifications construct twelve (2 3 2) Hausman tests of model selection. The null hypothesis is that the individual effects are uncorrelated with the other regressors in the model. If H 0 is rejected, a fixed effect model is preferred. 11

12 total salary expenditures are significantly positive in all regressions. The coefficients of hitters' salary expenditures and pitchers' salary expenditures are significantly positive when dispersion is measured by HHI and CV (insignificant if it is measured by GINI). This evidence shows that raising players salaries increases a team s performance. [Insert Table 2 about here] [Insert Table 3 about here] Regarding the effects of salary dispersion, the coefficients of Internal Inequality indices (IE) are insignificant, but the coefficients of the Employee Inequality indices for hitters (EmpEH) are significant and positive in more than half of all the regressions. This finding suggests that increasing the salary dispersion for hitters in a team enlarges the incentive for effort and increases team performance. These empirical results are more in line with the tournament models than with the fairness, morale and cohesiveness models. In summary, the empirical evidence indicates that the hawkish type of management, i.e. a dispersed distribution of team expenditure for hitters salary, will stimulate better team performance. In particular, dispersed salary for hitters seems to dominate salary policy. The results are much 12

13 similar if the number of wins rather than the percentage of wins is chosen as the dependent variable, as reported in the Tables A and B of Appendix. Furthermore, the effects of employee inequalities (EmpEH) are much larger than the effects of salary expenditures on hitters (LTSalH) and pitchers (LTSalP). Take Tables 2 and 3 for example, the marginal effect of EmpEH on WinP ranges from 0.28 to 0.32, and it indicates that a 1% increase in salary inequality among the hitters in a team brings about a 0.3% increase in the winning percentage of that team. The economic implication is that increasing salary dispersion is more effective than spending money on hitters salaries. At first, it appears puzzling that the salary inequality among the hitters, not among the pitchers, has a positive effect on team performance. There are two explanations for this finding based on the tournament theory of Lazear and Rosen (1981). Their theory implies that the positive effect of salary inequality on team performance is stronger if the workers are more similar in terms of their abilities and if the output uncertainty is lower. This paper argues that the similarity of abilities is higher and the output uncertainty is lower for the group of hitters than for the group of pitchers. On the one hand, it seems obvious that the difference in abilities between any two hitters is smaller than that between any two pitchers in the same team. On the other hand, the performance of a pitcher depends on a lot of factors beyond his control. 13

14 That is, except for a strikeout, almost all pitcher s performance (outs) are affected by his teammates. In contrast, the uncertainty in a hitter s production process is relatively small. 5. Quantile Regression A standard approach to estimate the unknown parameters of Equation (1) is panel regression. This approach only measures the average behavior of a conditional distribution without providing enough information of the entire conditional distribution. To address this problem, Quantile regression (QR), as introduced by Koenker and Bassett (1978), is used to estimate various quantile regressions on their conditional distribution. The results of QR are listed in Tables 4, 5 and Tables C to F in the Appendix. Once again, the coefficients for total salary expenditures (LRTSal) are significantly positive in all regressions. What's interesting is that the coefficients for the 75th quantile and the 25th quantile are larger than that for the 50th quantile. In other words, the positive effect of salary on team performance is stronger for teams with relatively more wins (or winning percentages) and teams with relatively few wins (or winning percentages). A potential policy implication of this finding is that owners of frequently winning teams and frequently losing teams should consider more seriously about raising salaries than owners of average-performing teams. 14

15 [Insert Table 4 about here] [Insert Table 5 about here] There are only three cases in which the effects of Employee Inequality on team performance are significant. They are the coefficients of winning percentage and wins on Employee Inequality (HHI) for the 25th quantile (Tables 4 and 5), and the coefficient of wins on Employee Inequality (GINI) for the 50th quantile (Table D). All three cases are consistent with the findings in the standard panel regression in the sense that the effects apply to the hitters and the coefficients are positive. 6. Concluding Remarks and Further Discussion Salary distribution is an important incentive mechanism for an organization. Previous research on team performance has used internal equity to investigate the relationship of salary inequality and organizational performance. This paper constructs indices of salary dispersion to capture the concept of employee equity. The results indicate that dispersed salaries among hitters are positively related to team performance, and higher salary expenditure for players increases team performance. The conclusions are also supported in the quantile regression. Moreover, the positive effect of total salary on team performance is stronger for teams with relatively more wins and teams with relatively few wins. An important policy implication of this finding is that managers 15

16 in winning and losing teams need to be more conscious of their salary policies than average teams. The findings of this study in the NPB are different, but do not contradict other equity studies of professional baseball. The findings show that there is a Tournament incentive for hitters, but not for pitchers. This result may be caused by the difference in the similarity of abilities and the uncertainty in the production process between the two groups. 16

17 References Adams, J. S. (1963), Toward an understanding of inequity, Journal of Abnormal and Social Psychology, 67(5): Adams, J. S. (1965), Inequity in Social Exchange. In L. Berkowitz (Ed.), Advances in Experimental Social Psychology, 2: Akerlof, G. A. and J. L. Yellen (1990), The Fair-Wage Hypothesis and Unemployment, Quarterly Journal of Economics, 105: Berri, D. J. and R. T. Jewell (2004), Wage Inequality and Firm Performance: Professional Basketball s Natural Experiment, Atlantic Economic Journal, 32(2): Bloom, M. (1999), The Performance Effects of Pay Dispersion on Individuals and Organizations, Academy Management Journal, 42(1): Coff, R. W. (1997), Human Assets and Management Dilemmas: Coping with Hazards on the Road to Resource-Based Theory, Academy of Management Review, 22: Curşeu P. L., Schruijer, S., and S. Boros (2007), The Effects of Groups Variety and Disparity on Groups Cognitive Complexity, Group Dynamics: Theory, Research, and Practice, 11 (3): Debrock, L., Hendricks, W., and R. Koenker (2004), Pay and Performance: The 17

18 Impact of Salary Distribution on Firm-Level Outcomes in Baseball, Journal of Sports Economics, 5(3): Depken, C. A. (2000), Wage Disparity and Team Productivity: Evidence from Major League Baseball, Economics Letters, 67: Eisenhardt, K. M., and I. J. Bourgeois (1988), Politics of Strategic Decision-Making in High-Velocity Environments: Toward a Midrange Theory, Academy of Management Journal, 31: Franck, E. and S. Nüesch (2008), Wage Dispersion and Team Performance --- An Empirical Panel Analysis, University of Zurich, Institute for Strategy and Business Economics (ISU) in its series Working Papers, number Frick, B., Prinz, J., and K. Winkelmann, (2003), Pay Inequalities and Team Performance: Empirical Evidence from the North American Major Leagues, International Journal of Manpower, 24(4): Hausman, J. A. (1978), Specification Tests in Econometrics, Econometrica, 46: Jane, W. J. (2010), Raising salary or redistributing it: A panel analysis of Major League Baseball, Economics Letters, 107: Jewell, R. T. and D. J. Molina (2004), Productive Efficiency and Salary Distribution: The Case of US Major League Baseball, Scottish Journal of Political Economy, 18

19 51: Koenker, R. and G. S. Bassett (1978), Regression Quantile, Econometrica, 48: Konopaske, R. and S. Werner (2002), Equity in Non-North American Contexts: Adapting Equity Theory to the New Global Business Environment, Human Resource Management Review, 12: Lazear, E. and S. Rosen (1981), Rank-Order Tournaments as Optimum Labor Contracts, Journal of Political Economy, 89: Mowday, R. T. (1983), Equity Theory Predictions of Behavior in Organizations. In R. M. Steers and L. W. Porter (Eds.), Motivation and Work Behavior (3 rd Ed.). New York: McGraw-Hill: Richards, D. G. and R. C. Guell (1998), Baseball Success and the Structure of Salaries, Applied Economics Letters, 5: Roberto, M. A. (2005). Why Great Leaders Don t Take Yes for an Answer: Managing for Conflict and Consensus. Philadelphia: Wharton Publishing. Romanoff, K., Boehm, K. and E. Benson (1986), Pay Equity: Internal and External Considerations, Compensation and Benefits Review, 18(3): Ronen, S. (1986), Equity Perceptions in Multiple Comparisons: A Field Study, Human Relations, 39(4):

20 San, G. and W. J. Jane (2008), Wage Dispersion and Team Performance: Evidence from the Small Size Professional Baseball League in Taiwan, Applied Economics Letters, 15 (11): Smith, K. G., Smith, K. A., Olian, J. D., Sims, H. P., O Bannon, D. P., and J. A. Scully (1994), Top Management Team Demography and Process: The Role of Social Integration and Communication. Administrative Science Quarterly, 39: Smith, A., Houghton, S. M., Hood, J. N., and J. A. Ryman (2006), Power Relationships Among Top Managers: Does Top Management Team Power Distribution Matter for Organizational Performance? Journal of Business Research, 59(5): Vasilescu, O. (2007), Team Performance, Efficiency and Wage Distribution in Professional Baseball, Social Science Research Network (SSRN) in its series Working Paper, number Werner, S. and N. P. Melo (1999), Fair or Foul? The Effects of External, Internal, and Employee Equity on Changes in Performance of Major League Baseball Players, Human Relations, 52:

21 HHI PL CL year Figure 1: Teams Average Salary Dispersion (HHI) in Each League 21

22 WP WP TGINI THHI Figure 2 Winning Percentage by Salary Dispersion 22

23 Table 1 Descriptive Statistics Variable Description Mean Std. Dev. Min. Max. WinP Winning percentage for each team each year WinN Wins for each team each year TSal a Total salary for each team each year TSalH a Hitters total salary for each team each year TSalP a Pitchers total salary for each team each year Players Number of Players for each team each year Equity measurement IE(HHI) Internal equity measured by HHI EmpEH Employee equity between (HHIH) hitters measured by HHI EmpEP Employee equity between (HHIP) pitchers measured by HHI IE(CV) Internal equity measured by CV EmpEP (CVH) EmpEH (CVP) IE(Gini) EmpEP (GiniH) EmpEH (GiniP) Employee equity between hitters measured by CV Employee equity between pitchers measured by CV Internal equity measured by Gini Employee equity between hitters measured by Gini Employee equity between pitchers measured by CV Note: a The unit is a thousand Yen, and the average exchange rate during 1996 to 2008 was 1US$= Yen$ 23

24 Table 2 Fixed or Random Effects Regression for Salary Dispersions in Different Concepts of Equity on Performances (Dependant Variable: Winning Percentage) Variable HHI GINI CV Internal Equity LTSal.068** (.027).062** (.025).0678** (.027).061** (.025).072*** (.027) IE (.246) (.245) (.083) (.082) (.030) Players (.001) (.001) (.001) (.001) (.001) League YES YES YES.066*** (.025).002 (.030).0004 (.001) Intercept (.290) (.272) (.294) (.275) (.288) (.272) Hausman test (χ 2 test) Employee Equity LTSalH.048** (.020).040** (.018) (.039) (.039).038* (.022) LTSalP.038**.038** * (.017) (.017) (.030) (.030) (.020) EmpEP (.167) (.167) (.115) (.115) (.026) EmpEH *.316*.316*.011 (.168) (.168) (.178) (.178) (.025) Players (.002) (.002) (.001) (.001) (.001) League YES YES YES.033 (.020).039** (.019) (.026).014 (.024).0002 (.001) Intercept -.431** (.217) -.356* (.207).771 (.495).771 (.495) (.263) (.245) Hausman test (χ 2 test) Note: 1. Standard errors are in the parentheses. 2. *Indicates that the level of significance is 10%. ** Indicates that the level of significance is 5%. *** Indicates that the level of significance is 1%. 24

25 Table 3 Fixed or Random Effects Regression for Salary Dispersions in Different Concepts of Equity via Real Pay on Performances (Dependant Variable: Winning Percentage) Variable HHI GINI CV Internal Equity LRTSal.068** (.027).062** (.025).068** (.027).061** (.025).072*** (.027) IE (.246) (.245) (.083) (.082) (.030) Players (.001) (.001) (.001) (.001) (.001) League YES YES YES.066*** (.025).002 (.030).0004 (.001) Intercept.017 (.168) (.272).021 (.169) (.275).002 (.167) (.272) Hausman test (χ 2 test) Employee Equity LRTSalH.048** (.020).040** (.018) (.039) (.039).038* (.022) LRTSalP.038**.038** * (.017) (.017) (.030) (.030) (.020) EmpEP (.167) (.167) (.115) (.115) (.026) EmpEH *.316*.316*.011 (.168) (.168) (.178) (.178) (.025) Players (.002) (.002) (.001) (.001) (.001) League YES YES YES.033 (.020).039** (.019) (.026).014 (.024).0002 (.001) Intercept (.123).007 (.119).556** (.249).556** (.249).037 (.144).057 (.135) Hausman test (χ 2 test) Note: 1. Standard errors are in the parentheses. 2. *Indicates that the level of significance is 10%. ** Indicates that the level of significance is 5%. *** Indicates that the level of significance is 1%. 25

26 Table 4: Estimated Results of Quantile Regressions in HHI (Dependent Variable: Winning Percentage) WP Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal.083*** (.031).072*** (.027).086*** (.032) IE.049 (.372) (.393) Players (.002) (.002).0007 (.003) League (.019) (.017) (.021) Intercept (.345) (.291) (.332) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH.060* (.034).034 (.028).035 (.030) LRTSalP.031 (.026).033* (.019).052** (.021) EmpEP (.315) (.318) (.292) EmpEH.502** (.219).311 (.209).164 (.285) Players (.003) (.002) (.003) League (.019) (.016) (.017) Intercept (.314) (.256) (.287) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 26

27 Table 5: Estimated Results of Quantile Regressions in HHI (Dependent Variable: Wins) Wins Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal ** (4.722) *** (3.350) *** (4.212) IE (38.886) (47.519) (55.130) Players (.290) (.304).041 (.345) League (2.693) (2.221) (2.175) Intercept (55.252) (37.634) (45.931) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH (5.381) (3.732) 7.540** (3.321) LRTSalP (3.651) 4.963** (2.502) 6.878** (3.011) EmpEP (43.712) (34.654) (39.505) EmpEH ** (31.451) (27.084) (28.921) Players (.260) (.270) (.352) League (2.387) (2.19) (2.362) Intercept * (56.286) (37.418) (37.735) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 27

28 Appendix Table A: Fixed or Random Effects Regression for Salary Dispersions in Different Concepts of Equity on Performances (Dependant Variable: Wins) Variable HHI GINI CV Internal Equity LTSal 9.543*** (3.569) 9.643*** (3.244) 9.055** (3.668) 9.213*** (3.306) *** (3.551) IE (32.896) (32.714) (11.072) (10.852) (4.019) Players (.180) (.178) (.175) (.172) (.176) League YES YES YES *** (3.235).299 (3.989).035 (.173) Intercept (38.562) (35.442) (39.381) (36.027) (38.207) (35.161) Hausman test (χ 2 test) Employee Equity LTSalH 6.272** (2.657) 6.082** (2.450) (5.166) (5.167) 5.012* (2.949) LTSalP 5.694** 5.700*** ** (2.231) (2.223) (3.965) (3.965) (2.588) EmpEP (22.348) (22.158) (15.304) (15.304) (3.501) EmpEH * * * * (22.512) (22.392) (23.737) (23.737) (3.272) Players (.204) (.202) (.185) (.185) (.178) League YES YES YES 4.981* (2.637) 5.751** (2.503) (3.426) (3.197).006 (.175) Intercept ** (29.060) ** (27.522) (66.176) (66.176) (34.751) * (31.674) Hausman test (χ 2 test) Note: 1. Standard errors are in the parentheses. 2. *Indicates that the level of significance is 10%. ** Indicates that the level of significance is 5%. *** Indicates that the level of significance is 1%. 28

29 Table B: Fixed or Random Effects Regression for Salary Dispersions in Different Concepts of Equity with Real Pay on Performances (Dependant Variable: Wins) Variable HHI GINI CV Internal Equity LRTSal 9.543*** (3.569) 9.643*** (3.244) 9.055** (3.668) 9.213*** (3.306) *** (3.551) IE (32.896) (32.714) (11.072) (10.852) (4.019) Players (.180) (.178) (.175) (.172) (.176) League YES YES YES *** (3.235).299 (3.989).035 (.173) Intercept (22.420) (35.442) (22.738) (36.027) (22.157) (35.161) Hausman test (χ 2 test) Employee Equity LRTSalH 6.272** (2.657) 6.082** (2.450) (5.166) (5.166) 5.012* (2.949) LRTSalP 5.694** 5.700*** ** (2.231) (2.222) (3.965) (3.965) (2.588) EmpEP (22.347) (22.158) (15.304) (15.304) (3.501) EmpEH * * * * (22.512) (22.392) (23.737) (23.737) (3.272) Players (.204) (.202) (.185) (.185) (.178) League YES YES YES Intercept (16.467) (15.783) * * (33.242) ** (33.242) (19.028) 4.981* (2.637) 5.751** (2.503) (3.426) (3.197).006 (.175) (17.497) Hausman test (χ 2 test) Note: 1. Standard errors are in the parentheses. 2. *Indicates that the level of significance is 10%. ** Indicates that the level of significance is 5%. *** Indicates that the level of significance is 1%. 29

30 Table C: Estimated Results of Quantile Regressions in Gini Coefficient (Dependent Variable: Winning Percentage) WP Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal.078** (.039).071** (.034).061* (.034) IE.133 (.150).037 (.112).109 (.113) Players (.002) (.002) 3.14e-06 (.002) League (.020) (.016) (.019) Intercept (.413) (.371) (.382) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH.030 (.041).014 (.033).006 (.032) LRTSalP.017 (.032).031 (.025).066** (.032) EmpEP.145 (.157).026 (.135) (.184) EmpEH.145 (.201).235 (.186).173 (.209) Players (.002) (.002) (.002) League (.021) (.016) (.017) Intercept (.429) (.346) (.299) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 30

31 Table D: Estimated Results of Quantile Regressions in Gini Coefficient (Dependent Variable: Wins) Wins Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal ** (4.655) 8.471** (4.281) ** (4.629) IE (15.258) (13.772) (17.240) Players (.331) (.321) (.364) League (2.432) (2.472) (2.604) Intercept (52.212) (45.726) (46.753) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH (5.574) (4.866) (5.253) LRTSalP (4.077) 7.489** (3.425) 8.972** (3.827) EmpEP (24.242) (22.079) (25.522) EmpEH (23.690) ** (21.950) (26.837) Players (.223) (.252) (.3169) League (2.341) (2.040) (2.487) Intercept (60.120) (49.627) (51.655) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 31

32 Table E: Estimated Results of Quantile Regressions in Correlation of Variation (Dependent Variable: Winning Percentage) WP Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal.092*** (.031).076*** (.026).086** (.039) IE.032.(036).018 (.036) (.042) Players (.002) (.002).0008 (.003) League (.022) (.016) (.022) Intercept (.357) (.286) (.393) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH.072* (.037).015 (.032).019 (.030) LRTSalP.034 (.028).035* (.021).060** (.026) EmpEP (.044) (.036) (.041) EmpEH.028 (.034).038 (.026).018 (.038) Players (.003) (.002) (.003) League (.019) (.017) (.022) Intercept (.397) (.299) (.330) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 32

33 Table F: Estimated Results of Quantile Regressions in Correlation of Variation (Dependent Variable: Wins) Wins Quantile 25-th 50-th 75-th Coef. (S.D.) Coef. (S.D.) Coef. (S.D.) Internal Equity LRTSal *** (4.655) *** (3.267) *** (4.374) IE (5.148) (5.055) (6.721) Players (.302) (.279).128 (.346) League (2.482) (2.196) (2.391) Intercept (52.928) (36.240) (44.786) Year Yes Yes Yes (Pseudo)-R Employee Equity LRTSalH (5.306) (4.143) (4.234) LRTSalP (3.905) 6.136** (2.780) 9.309*** (3.176) EmpEP (6.636) (4.826) (5.928) EmpEH (3.979) (3.845).464 (5.088) Players (.310) (.256) (.333) League (2.291) (2.146) (2.715) Intercept (55.968) (35.711) (42.280) Year Yes Yes Yes (Pseudo)-R Notes: (a)*** denotes significance at the 1% level, ** denotes significance at the 5% level, and * denotes significance at the 10% level. (b) Values in parentheses are the stand errors. 33