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Minority's salary discrimination in the Chinese Professional Baseball League.

Introduction

Empirical research in labor economics generally shows that, even after controlling for individual characteristics such as education and experience, Blacks have lower levels of employment and earnings than Whites. The residual earnings gap between races is commonly attributed to labor market discrimination. Beginning with the seminal work of Becker (1971), economists have been concerned with the persistence of labor market discrimination. Research devoted to the issue has investigated persistent salary differentials between equally productive workers of different races. Becker shows that salary differentials can arise from three types of labor market discrimination: employer-, employee-, and consumer-based discrimination. (1)

Estimating the extent and degree of discrimination, whether at the individual or the firm level, is a difficult matter. In the labor market, for example, a worker's productivity is rarely observed directly, so the analyst must instead use available data as a proxy to control for the relevant productivity characteristics. However, workers are highly visible to the public in the sports labor market. Therefore, many empirical models used to investigate racial discrimination in professional sports rely upon salary information and the very extensive and accurate statistics on productivity collected and maintained by various leagues.

The treatment of minorities in North America and Europe has been an issue in sports for decades. The bulk of the empirical evidence on salary discrimination in professional sports comes from baseball (Bodvarsson & Pettman, 2002; Christiano, 1986, 1988; Cymrot, 1983; Gwartney & Haworth, 1974; Hill & Spellman, 1984; Holmes, 2011; Raimondo, 1983; Scully, 1973), basketball (Brown et al.., 1991; Hamilton, 1997; Kahn & Sherer, 1988; Kanazawa & Funk, 2001), football (Preston & Szymanski, 2000; Szymanski, 2000; Wilson & Ying, 2003) and hockey (Jones & Walsh, 1988; Longley, 1995). The most common method is to regress salary (or its log) on a list of productivity indicators and a dummy variable for race. In the past, the research has focused heavily on Blacks. In some studies, race was broken down into additional categories, such as, White, Black, and Hispanic-Black. Another line of inquiry analyses coaching discrimination in baseball (Singell, 1991), basketball (Humphreys, 2000; Kahn, 2006), and hockey (Madden, 2004).

Taiwanese aborigines have long been a minority in Taiwan. (2) In 2010, the number of aborigines was approximately 512,000, accounting for 2.21% of the entire population (Ministry of Interior, 2011). Despite their minority status, they were important in the development of Taiwan baseball. (3) However, the ratio of aborigines in the Chinese Professional Baseball League (CPBL) is a disproportionate 23.6%.

Salary discrimination has been a primary issue in professional sports leagues. However, discrimination based on ethnic origin has never been examined before in the CPBL. Aborigines possess a culture that is quite different from the Taiwanese majority and hold an important position in the CPBL, but researchers have not examined whether such differences have adversely affected aborigines' pecuniary treatments. This study focuses on examining whether aborigines in Taiwan have suffered from discriminatory treatment with regards to salary. Compared with the MLB, it was suspected that the salary discrimination in the CPBL could be different and it could provide new evidence for the literature. As it turns out, I found that reverse- discrimination does exist for aboriginal players in Taiwan.

Literature Review of Salary Discrimination in Professional Sports

Almost all studies of salary discrimination in professional baseball focus on the MLB. Past research in the MLB suggests that discrimination by majority White fans led owners in sports to keep paying less-talented White players high salaries. In the 1950s, a non-White person had to overcome many challenges from the public when he played a so-called "White sport" There continues to be disagreement on the issue of discrimination. One of the first studies in baseball is Scully (1971) in which he found evidence of the existence of employment discrimination in the MLB. (4) One year later, Pascal and Rapping (1972) had similar findings.5 These two papers, primarily utilizing data from the 1960s, focused on earnings and productivity differences between players according to race. Scully (1973) argued that Black athletes were restricted to certain positions, and they were paid less for their performance. After that, Gwartney and Haworth (1974) focused on the transition period (1947-1959) to study the impact of differing responses by individual teams to a desegregation of the industry.6 They found low discriminators (i.e., teams willing to employ Black players) obtained a competitive advantage in the MLB relative to other teams. They were able to win more games, acquire quality players at a lower cost, and increase annual revenue from admissions. These gains offered an incentive for teams to desegregate. Later, Christiano (1986, 1988) indicated that there was a significant White shortfall in salary in the MLB, controlling for measured productivity.

Although Christiano (1986, 1988) found significant White salary shortfalls in regressions, Kahn (1993), using data similar to those Christiano used in his 1988 study but with a longer list of performance measures, found small, statistically insignificant racial differences. Other research like Raimondo (1983) and Hill and Spellman (1984) also found no significant evidence of racial discrimination in professional baseball salaries. More recently, work like Bodvarsson and Pettman (2002) used a logarithmic regression model with the dependent variable salary and independent variables such as race (White or non-White), productivity, population of the player's metropolitan area, and racial make-up of the player's metropolitan area. Their study attempted to determine whether or not the addition of more teams to MLB would mitigate any racial discrimination that existed. The theory was that more teams would increase the level of competition between teams for good players, thereby causing teams to offer fair salaries to get the best players. The results of this study showed that League expansion in 1993 indeed eliminated discrimination for pitchers.

Among this literature, several later studies suggested that racial salary discrimination in the major leagues was either nonexistent or slight (see Bodvarsson & Pettman, 2002; Hill & Spellman, 1984; Kahn, 1993; Raimondo, 1983). (7) The salary discrimination literature has tapered off since the early 1980s, perhaps because the issue seems to have been resolved in the MLB. Kahn (2000) reviewed the literature and made the conclusion that "... regression analyses of salaries in baseball and football have not found much evidence of racial salary discrimination against minorities" (p. 85). However, compared with the situation in the MLB, the league in Taiwan is relatively immature and still on the reserve clause era (see Jane et al., 2009, for details). The issue of salary discrimination in the CPBL needs to be examined.

In the empirical literature, it is not uncommon to find explanatory variables of interest in panel datasets that are time invariant (race, sex, or regional location). In a fixed-effects model, the coefficients of these variables are dropped in the regressions. Nevertheless, it is possible to identify and consistently estimate the effects of the time invariant regressors through two-stage procedures. (8) This study used a two-stage double fixed-effects model proposed by Bartel and Sicherman (1999) to provide insights into the CPBL as well as the labor market in general.

Our findings from the CPBL study were contradictory to the results of the discrimination studies in the MLB: Reverse discrimination of aboriginal players exists in the CPBL.

Empirical Methodology and Data Description

Baseball is the most popular sport in Taiwan, and the country's national team is one of the best teams in the world. (9) However, there was no professional league in Taiwan until 1990. The CPBL had four teams in 1990, with each team being owned by a large Taiwanese corporation. The regular season starts from March and ends in October, and an all-star break is held in June or July and lasts 1 week. The CPBL offers a rich source of data for the study of salary discrimination in baseball teams. Taiwanese aboriginal players have been prominent throughout the history of the CPBL. On average, 23.6% of players are aboriginals in the League, and the percentage went up to 34.83% in 2002. Figure 1 summarizes the ratio of aboriginal players in the professional base ball league from 1990-2007. Although always comprising a relatively small minority of the total players in the League at any given time, Taiwanese aboriginals have been some of the all-time great players in the history of the CPBL. (10) Many of the most highly paid players are aborigines: The top three CPBL salaries for the 1990-2007 seasons went to Chin-Feng Chen with $10 million TWD and Chien-Fu Kuo Lee and Yuan-Zhi Kuo, both with $6 million TWD, who are all aboriginal players.

[FIGURE 1 OMITTED]

The key explanatory variable (i.e., the racial dummy), which does not vary over time, is dropped by the within estimator regression of the coefficients in a fixed-effects model. Therefore, two methods were employed to estimate the effect of discrimination. The first simply used a random-effects model, and the second utilized the twostage double fixed-effects model proposed by Bartel and Sicherman (1999).

Mincer-type earnings equations were adopted (Mincer, 1974) and the basic model for panel regression is listed in Equation 1. The individual effects of player i for the fixed-effects model and random-effects model are represented as [u.sub.i] and [v.sub.it] respectively, and [sub.it] denotes the error term. Explanatory variables include player's racial dummy (R), a vector of player's productivity variables (P), and player-specific and team-specific characteristics (C).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The vector of variable C includes the player's tenure (TEN) and age (AGE), player's square terms of tenure (SQTEN) and age (SQAGE), height (Height), weight (Weight), player's position dummies (POS), and team dummies (TEAM). (11)

The vector of variable P includes batters' and pitchers' parts. In baseball, a batter's value is measured by the Louisville Silver Slugger index (SSI), and a pitcher's value is measured by Cy Young Points (CYP). They are calculated by the following equations.

SSI = BA x 1000 + HR x 20 + RS x 5 + TB (2)

CYP = [(5 x IP / 9) - ER] + (SO / 12) + (SV x 2.5) + SHO + [(WX 6) - (L X 2)] + VB (3)

where BA is the batting average, HR is home runs, RS is runs scored, and TB is the total bases for batters. IP is the innings pitched, ER is earned runs, SO is strikeouts, SV is saves, SHO is shootouts, W is wins, L is losses, and VB is the victory bonus, which reflects a pitcher's contribution to helping their team to get into the playoff games. (12)

In addition, for a comprehensive performance investigation, other batters' performance indices were also included in the dataset. They are stolen bases (SB), bases on balls (BB), safety hits (SH), runs batted in (RBI), singles (FH), doubles (DB), triples (ThirdB), sacrifice bunts (SAC), sacrifice flies (SacF), intentional walks (IW), caught stealing (CS), and stolen base percentage (SBP). Pitchers' data also included games started (GS), games in relief (GR), blown saves (BlSv), holds (Hld), earned run average (ERA), total batters faced (TBF), pitches thrown (Pit), hits against (H), home runs allowed (HR), bases on balls (BB), intentional bases on balls (IBB), hit by pitch (HBP), strikeouts (SO), wild pitches (WP), balks (Bk), and runs (Runs).

The random-effects model was estimated following Equation 1, and the regressors were added to the previous categories step-by-step for the robust tests. After that, a two-stage double fixed-effects model was constructed as follows:

log[Sal.sub.it]= 1+[u.sub.i]+ [sub.1][P.sub.it]+ 2[C.sub.it]+ [sub.it] (4)

[u.sub.i] = 2+ 3[R.sub.i]+ [sub.i] (5)

In the first stage, I estimated a standard fixed-effects model in the previous setting that excluded the time-invariate variable (R). This was done in order to obtain the estimated parameter: individual premium on salary. The individual premium is a fixed component of the wage that is not explained by either observed characteristics or performance. Therefore, in the second stage, the individual premium was regressed by race, and the effect of race was obtained.

An unbalanced panel of salary data from nine CBPL teams, including 296 batters and 141 pitchers, was collected over the 18-year period from 1990 to 2007. Salary data were obtained from the Taiwan baseball website http://twbaseball.info/. Player's characteristics and performance were taken from the official website of the CPBL (http://www.cpbl.com.tw/). The descriptive statistics are listed in Table 1. Note that 23.6% of CPBL players were aboriginals. The mean salary for aborigines was $147,000 TWD and it was 25% greater than that of Taiwanese players. (13) The statistics of the null hypothesis for equal pay was significantly rejected at the 99% level.

Empirical Results and Discussion

The results of the random-effects estimates are listed in Tables 2 and 3. In Table 2, models A-B were the results of basic regression, which include the race dummy and characteristics for all players--the only difference between them is the position control. Models C-M are the batters' regressions, which control their different kinds of performance. Likewise, the results of the pitchers' regressions are listed in Table 3. All coefficients of race were significantly positive related to salary. It indicated that aborigines earn more than Taiwanese ceteris paribus. This evidence indicates that minority discrimination in the CPBL is reverse discrimination. As to the tenure effect, the coefficients of tenure were consistently positive, and its square term was consistently negative related to salary. This shows that batter's salary increased at a decreasing rate as tenure increased. However, the effect of age and its square term were precisely the opposite. The coefficients of age were consistently negative and its square term was consistently positive as related to salary. This means that salary decreased at an increasing rate as batters aged. The results for pitchers were similar (see Table 3).

As to the effects of performance, the indices of batter's SSI (Models C and D in Table 2) and pitcher's CYP (Models A and C in Table 3) were significantly positive as related to salary. This showed that better performance increased a player's salary. Other significant factors for batters in Table 2 include games played, plate appearances, at bats, sacrifice bunts, bases on balls, intentional walks, stolen bases, caught stealing, runs scored, safety hits, and total bases. Pitcher significant factors in Table 3 also included games started, hits against, home runs allowed, wins, and losses.

The marginal effect of race was about $25,000 TWD per month for all players (see Model A of Table 2). Moreover, the marginal effect of race ranged from $12,000-$17,000 TWD per month for batters and ranged from $25,000-$29,000 TWD for pitchers. The results indicated that aborigine players tended to be paid more, especially for pitchers. As to the effects of tenure and age, the marginal effects for players were $16,000 and $23,000 TWD, respectively. The decreasing rate of positive tenure effect (-941) was bigger than the increasing rate of negative age effect (439).

Tables 4 and 5 show the results of two-stage double fixed-effects regressions, and the settings of explanatory variables for players, batters, and pitchers follow the previous models in Tables 2 and 3. The results of first stage regressions for fixed-effects are listed first, and the results of the second stage are listed on the bottom of these tables. For example, near the bottom of Table 5, all coefficients of race were significantly positively related to salary. This indicated that aboriginal pitchers earned more than Taiwanese ceteris paribus. (14) In general, the evidence, as listed in Tables 2-5, indicated that minority discrimination for players in the CPBL was a reverse discrimination. However, the results of batters in Table 4 did not reveal significant coefficients.

The coefficients of tenure were consistently positive and its square term was consistently negatively related to salary. Moreover, the effect of age and its square term were the opposite. All of these results corresponded with the human capital theory that a worker's salary increases at a decreasing rate as tenure increases and decreases at an increasing rate as the worker ages.

Player performance in professional baseball can easily be observed; however, salary determination is not made solely by merit. This study argues that aboriginal pitchers are paid much higher than Taiwanese. It could be argued that a salary premium (i.e., reverse discrimination) for minorities exists in the CPBL. If Taiwan's aboriginals are regarded as having the same social status as the Blacks in the U.S., our findings are contradictory to the previous research of salary discrimination in 1970s in the MLB (e.g., Pascal & Rapping, 1972; Scully, 1971, 1973).

An explanation of discrimination is based on employers' tastes for discrimination (Aigner & Cain, 1977). The tastes are usually presumed to provide a source of utility to the discriminator in a theoretical model. Therefore, once employers prefer specific groups, salary discrimination appears. In Taiwan, aboriginal players are often regarded as innate sportsmen because of their splendid history in baseball. These innate sportsmen are easily overevaluated by the team manager for two reasons. First, fans like these innate sportsmen, and they buy tickets in order to see them in the stadium. A team's revenue mainly counts on these players, so a manager is likely to overpay them. Second, managers may expect better performance of these innate sportsmen, and their productivity is rewarded much higher than other players.

As a labor market becomes more competitive, the incidence of discrimination should decrease (Bodvarsson & Pettman, 2002; Longley, 2003). However, the labor market in the CPBL is nearly a monopsony. Once a rookie is drafted, the player cannot leave the team unless he is released by the original team manager. In addition, there is no free agency or a powerful labor union in the League. The salary arbitration is actually commanded by the teams' manager committee. This results in a serious imbalance of bargaining power between employers and employees with employers easily adjusting a player's salary by their tastes. (15) The existence of salary discrimination in the league is comparable to the situation in the MLB before 1980. The difference between the two leagues is the employers' tastes for minorities. The CPBL will start a free agency in 2012, which will increase the competition in the labor market. As Becker (1971) has made clear, relatively nondiscriminating employers drive the discriminating employers out of business in the long-run competitive equilibrium. The practice of free agency in 2012 would be expected to reduce salary discrimination in the CPBL.

As to the different results between batters and pitchers, these reveal different degrees of reverse discrimination in different positions. According to Becker's theoretical implications of market competition on the issue of discrimination, it could be interpreted that more competition among batters reduces the degree of discrimination. (16) Therefore, the robust evidence of salary discrimination for batters cannot be found in the whole regressions of Table 4.

Conclusions

This study investigated the salary discrimination in the CPBL. An unbalanced panel data from nine CBPL teams, including 437 players over the period from 1990-2007, as well as the two stage double-fixed-effects model were employed. I have shown that, when all variables of players characteristics and performance were controlled, a reverse-discrimination for minority aborigines existed in both the investigation of random-effects and two-stage double fixed-effects models. The minority aborigines tended to be overpaid by $25,000-$27,000 TWD per month in the league. That is about 20%-22% higher than the average.

When the players were separated into batters and pitchers, the evidence from pitchers still supported the same conclusion in both models. However, the evidence from batters only supported salary discrimination in the random-effects model, not in the two-stage double fixed-effects model. More specifically, aboriginal pitchers tended to be overpaid by $25,000-$51,000 TWD per month in the League. Moreover, the effect of tenure increased at a decreasing rate and the effect of age decreased at an increasing rate. The results echo the literature of human capital. Overall, the analysis also found that good performance was positively related to salary.

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Endnotes

(1) With perfect competition and constant returns to scale (CRS) technology, the former two sources of wage disparity are only short-run phenomena. Kahn (1991) showed that customerbased discrimination could persist in general equilibrium even with CRS technology and nondiscriminating firms. Unlike employer or employee discrimination, customer discrimination can cause long-run wage differentials when the previous two conditions hold.

(2) Taiwanese aborigines mean the indigenous peoples of Taiwan. They are one of the Austronesian peoples. Fourteen tribes have been recognized by the government as of May 2008: Ami, Atayal, Bunun, Kavalan, Paiwan, Puyuma, Rukai, Saisiyat, Tao, Thao, Tsou, Truku, Sakizaya, and Sediq. The indigenous peoples of Taiwan face economic and social barriers, including a high unemployment rate and substandard education. However, they successfully incorporate elements of their culture into popular music and utilize their talents in sports.

(3) During the Japanese colonial period, the achievement of aboriginal players from the Gaosha, Nenggao, and Hongye eras was remarkable. See more detail in Yu and Bairner (2010).

(4) In Scully's sample, non-whites also received higher pay for better performance and more experience. Non-whites may be suffering discrimination--even though they are paid more--if the differences in salary do not fully reflect the differences in performance and experience.

(5) Pascal and Rapping (1972) found that there was a significant negative effect for Hispanic nonpitchers and a significant negative effect for White pitchers.

(6) Transition period is defined by Gwartney and Haworth (1974). It means the period from discrimination to desegregation in the MLB.

(7) Other discrimination issues in professional sports include the following examples: Hamilton (1997) and Gius and Johnson (1998) tested for salary discrimination in the NBA; Jones, Nadeau, and Walsh (1999) performed similar analyses for the NHL; and Eshker et al. (2004) used NBA

data to study the winner's curse in hiring international basketball players. Other studies have analyzed the draft mechanism in choosing talent. Hendricks et al (2003) analyzed uncertainty, option value, and statistical discrimination in the NFL draft. Groothuis et. al. (2007) analyzed early entry in the NBA draft, while Lavoie (2003) focused on discrimination in the NHL draft.

(8) Hausman and Taylor (1981) analyzed models in which some of the variables--both time varying and time invariant--were endogenous. Polacheck and Kim (1994) examined a single equation model in which the slope parameters of time-invariant regressors varied across individuals. Baltagi (2005) provided a comprehensive treatment of panel data models in the context of both single equation and systems methods.

(9) Taiwan's national baseball team won numerous Little League World Series championships in the 1970s and 1980s, plus the bronze medal in the 1984 Summer Olympics. Between 1969 and 1991, Taiwan qualified for the Little League, Senior, and Big League World Championships for a total of 22, 20, and 18 times, respectively, and won the titles a total of 13, 17, and 13 times, respectively. Recently, Taiwan won the 15th Asian Games (Doha, 2006) championship and second place in the 16th Asian Games (Guangzhou, 2010).

(10) For example, Chin-Feng Chen, Chin-Lung Hu, Hong-Chih Kuo, Fu-Te Ni, and Chin-Hui Tsao.

(11) Nine POS were used to tell 10 positions, including pitcher, catcher, first baseman, second baseman, third baseman, short stop, left fielder, center fielder, right fielder, and designated hitter.

(12) A victory bonus is measured by the playoff dummy (VB = 1, team gets into the playoff games; otherwise, VB = 0). The two indices are important and they are still employed to measure the batter's and pitcher's contributions in the MLB now. The Silver Slugger Award is awarded annually to the best offensive player at each position, and the Cy Young Award is an annual baseball honor given to the best pitchers in both the American League and the National League. The winners of both awards are recorded by the official website of the MLB (http://mlb.mlb.com/mlb/awards/mlb_awards_content.jsp?content=silver_slugger_history).

(13) The average exchange rate during our data period (1990-2007) was roughly $1 USD = $30.34228 TWD.

(14) The robustness of race effect for pitchers is further checked, and the results support the previous conclusion. The results of the estimation are provided by the author if needed.

(15) Regular salary adjustment in the CPBL, unlike the relatively long-term contracts (3-5 years) in other professional sports leagues in the world, is quite common. Different from salary arbitration in other pro sports leagues, 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. Compared with the MLB and Nippon Professional Baseball, the league in Taiwan is still young and no player will be a free agent until 2012 (see Jane et al., 2010, for details).

(16) See empirical evidence in Longley (2003) and Bodvarsson and Pettman (2002).

Author's Note

The author thanks Professor Tsong-Min Wu for his valuable comments and suggestions and is grateful to the National Science Council for its financial support.

Wen-Jhan Jane is an associate professor in the Department of Economics at Shih Hsin University, Taiwan. His current research focuses on the economics of sports, specifically the topics of discrimination, peer effects, and competitive balance.

Wen-Jhan Jane

Shih Hsin University, Taiwan
Table 1. Descriptive Statistics of the Data (N = 1,875).

 Standard
Variable Description Mean deviation

Salb Player's salary 124,008.20 70,020.70

SalA Aborigine's salary 146,976.80 89,966.50
SalB Batter's salary 125,068.30 69,542.30

Player's Characteristics

TEN Player's tenure 4.00 2.84
Height Player's height 177.26 4.94

Player's Performance

 Batter's Performance

SSI Louisville Silver 464.51 258.64
 Slugger index
GP Games played 62.12 28.21
PA Plate appearance 205.39 133.91
AB At bats 181.98 118.18
SAC Sacrifice bunts 4.28 5.06
SacF Sacrifice flies 1.38 1.63
BB Bases on balls 15.18 12.81
IW Intentional walks 0.51 1.23
SOB Strikeouts 29.87 20.14
SB Stolen bases 4.53 6.82
CS Caught stealing 2.49 3.01
RBI Runs batted in 20.70 17.87
RS Runs scored 23.33 18.31
SH Safety hits 47.50 35.01
FH Singles 35.78 25.96
DB Doubles 7.94 6.70
ThirdB Triples 0.97 1.39
HR Home runs 2.81 4.21
TB Total bases 65.81 51.60
BA Batting average 0.24 0.08
SBP Stolen base percentage 0.48 0.35
OBP On base percentage 0.30 0.09
SLG Slugging percentage 0.32 0.12
TA Total average 0.57 0.22

 Standard
Variable Description Mean deviation

Race 1 = aboriginals; 0.24 0.43
 0 = Taiwanese
SalT Taiwanese salary 116,902.70 60,883.80
SalP Pitcher's salary 121,537.70 71,124.00

Player's Characteristics

AGE Player's age 28.37 4.02
Weight Player's weight 82.04 8.18

Player's Performance

 Pitcher's Performance

CYP Cy Young Points 31.28 42.38

GS Games started 7.14 8.04
GR Games in relief 14.85 12.77
BlSv Blown saves 0.20 0.68
Hld Holds 0.54 1.87
TBF Total batters faced 298.59 233.64
PT Pitches thrown 1,030.66 790.91
HA Hits Against 69.77 52.41
HRA Home runs allowed 5.27 4.65
BBP Bases on balls 21.00 16.37
IBB Intentional bases on balls 1.01 1.54
HBP Hit by pitch 3.03 3.46
WP Wild pitches 2.79 2.97
BK Balks 0.54 3.25
Runs Runs allowed 34.96 23.70
IP Innings pitched 67.39 53.22
ERA Earned run average 4.97 4.52
SOP Strikeouts 39.81 37.65
SV Saves 1.40 3.18
SHO Shout outs 0.20 0.67
W Wins 3.60 4.26
L Loses 3.48 3.39
VB Victory bonus 0.34 0.47

Note. The average exchange rate during the data period (1990-2007)
was roughly $1 USD = $30.34228 TWD. The salary refers to
monthly salary.

Table 2. Random-Effects Model Estimation Results With the Dependent
Variables Player's Salary (Models A-B) and Batter's Salary
(Models C-M).

Salary Model A Model B Model C

Race 25111.99 *** 27223.61 *** 14677.24 **
 (6433.99) (6422.90) (6446.34)
TEN 19179.80 *** 19124 *** 17779.24 ***
 (1553.81) (1564.32) (1788.68)
SQTEN -1279.76 *** -1299.56 *** -1076.85 ***
 (108.98) (109.16) (131.03)
AGE -22298.59 *** -21638.08 *** -22735.09 ***
 (3745.09) (3748.50) (4414.91)
SQAGE 428.66 *** 420.56 *** 436.12 ***
 (61.10) (61.10) (73.65)
Height 892.41 989.14 457.07
 (583.61) (618.46) (619.69)
Weight 572.55 631.12 * 356.70
 (368.03) (383.93) (372.55)
SSI 57.08 ***
 (6.86)
GP

PA

AB

SAC

SacF

BB

IW

SOB

SB

CS

RBI

RS

SH

FH

DB

ThirdB

HR

TB

BA

_cons 143513.30 108536.30 223610 *
 (107842.60) (114292.30) (115185.70)
POS NO Yes NO
R2 0.260 0.262 0.276

Salary Model D Model E Model F

Race 16839.14 *** 14160.70 *** 12349.38 **
 (6447.13) (5379.14) (5387.80)
TEN 17952.38 *** 16058.74 *** 16434.37 ***
 (1803.88) (1745.67) (1737.38)
SQTEN -1100.91 *** -946.03 *** -953.70 ***
 (131.25) (133.55) (132.62)
AGE -21349.82 *** -22420.62 *** -24617.18 ***
 (4418.08) (4417.15) (4423.24)
SQAGE 412.13 *** 436.67 *** 469.68 ***
 (73.76) (74.27) (74.25)
Height 823.43 1128.20 ** 1228.57 **
 (651.47) (553.27) (552.49)
Weight 388.17 326.21 237.63
 (399.86) (345.07) (344.34)
SSI 54.59 ***
 (6.94)
GP 270.78 **
 (107.36)
PA 146.57 ***
 (31.27)
AB

SAC -486.77 -866.13 **
 (355.11) (363.27)
SacF 1055.42 151.73
 (959.52) (979.73)
BB 588.79 *** 267.21
 (198.31) (213.02)
IW 8156.74 *** 7587.24 ***
 (1307.81) (1305.93)
SOB 47.14 -163.48
 (134.36) (139.61)
SB 610.86 * 387.95
 (314.80) (317.41)
CS -1,048.98 -1286.79 *
 (675.57) (673.45)
RBI

RS

SH

FH

DB

ThirdB

HR

TB

BA

_cons 134941.50 141727.30 167258.40
 (130597.10) (106960.70) (106689)
POS Yes Yes Yes
R2 0.280 0.290 0.298

Salary Model G Model H Model I

Race 12421.67 ** 13682.51 ** 13221.89 **
 (5388.19) (5411.87) (5395.81)
TEN 16447.78 *** 15996.36 *** 15853.71 ***
 (1738.66) (1747.38) (1746.55)
SQTEN -954.37 *** -940.97 *** -928.67 ***
 (132.71) (133.62) (133.64)
AGE -24519.35 *** -22550.64 *** -23156.51 ***
 (4426.54) (4417.74) (4425.73)
SQAGE 468.09 *** 438.81 *** 450.08 ***
 (74.30) (74.28) (74.46)
Height 1228.21 * 1125.10 ** 1130.68 **
 (552.61) (554.22) (552.92)
Weight 241.60 294.00 349.34
 (344.37) (347.11) (345.02)
SSI

GP 235.60 ** 188.75 *
 (112.84) (114.45)
PA

AB 143.73 ***
 (31.77)
SAC -706.49 ** -438.54 -456.82
 (352.84) (358.33) (354.96)
SacF 333.04 670.59 772.25
 (972.42) (1029.51) (967.98)
BB 422.19 ** 541.66 *** 431.91 **
 (200.75) (203.30) (212.22)
IW 7735.23 *** 7841.06 *** 7747.25 ***
 (1304.09) (1339.56) (1320.73)
SOB -150.44 18.98 11.49
 (139.79) (137.13) (135.31)
SB 400.29 598.29 * 417.59
 (317.52) (314.88) (328.10)
CS -1273.28 * -1,036.14 -1,071.52
 (673.91) (675.34) (674.72)
RBI 174.24
 (170.99)
RS 379.70 **
 (185.07)
SH

FH

DB

ThirdB

HR

TB

BA

_cons 165609.40 104814.9 149436.1
 (106708.10) (117287.2) (106934.6)
POS Yes Yes Yes
R2 0.297 0.288 0.287

Salary Model J Model K

Race 12639.54 ** 13823.31 ***
 (5380.70) (5381.37)
TEN 16032.50 *** 16047.95 ***
 (1738.76) (1733.27)
SQTEN -937.09 *** -945.08 ***
 (133.02) (132.93)
AGE -23574.05 *** -23486.26 ***
 (4412.31) (4399.02)
SQAGE 454.70 *** 450.99 ***
 (74.16) (73.95)
Height 1164.21 ** 1275.47 **
 (551.53) (550.42)
Weight 242.38 170.02
 (344.81) (345.03)
SSI

GP 58.02 40.22
 (124.16) (124.50)
PA

AB

SAC -439.78 -406.64
 (353.95) (360.44)
SacF 315.75 277.07
 (980.26) (977.95)
BB 449.48 ** 501.70 **
 (201.75) (202.94)
IW 7484.53 *** 7909.77 ***
 (1317.24) (1360.54)
SOB -25.69 -.93
 (135.55) (137.77)
SB 436.49 599.95*
 (317.71) (319.72)
CS -1288.22 * -1467.95 **
 (676.49) (678.93)
RBI

RS

SH 355.96 ***
 (105.53)
FH 443.81 ***
 (137.91)
DB 481.58
 (394.05)
ThirdB -3858.43 ***
 (1105.22)
HR -124.65
 (555.61)
TB

BA

_cons 162560.1 150972.8
 (106756.5) (106483.8)
POS Yes Yes
R2 0.292 0.304

Salary Model L Model M

Race 12668.24 ** 14169.11 ***
 (5409.16) (5391.66)
TEN 15964.25 *** 16064.26 ***
 (1742.66) (1746.49)
SQTEN -930.02 *** -946.51 ***
 (133.39) (133.59)
AGE -23173.80 *** -22427.14 ***
 (4417.28) (4418.75)
SQAGE 448.66 *** 436.76 ***
 (74.26) (74.30)
Height 1140.91 ** 1127.52 **
 (552.88) (554.25)
Weight 252.91 326.36
 (346.02) (345.52)
SSI

GP 139.01 270.75 **
 (119.27) (108.03)
PA

AB

SAC -390.61 -486.95
 (356.43) (355.77)
SacF 506.02 1053.38
 (981.55) (961.44)
BB 464.68 ** 588.13 ***
 (203.84) (198.55)
IW 7326.89 *** 8148.73 ***
 (1344.44) (1309.39)
SOB -29.96 47.10
 (137.52) (134.47)
SB 492.81 610.01 *
 (317.48) (314.90)
CS -1126.21 * -1,048.71
 (674.66) (676.30)
RBI

RS

SH

FH

DB

ThirdB

HR

TB 179.24 **
 (71.21)
BA 201.62
 (18271.44)
_cons 157583.2 141926.3
 (107011.6) (107053.1)
POS Yes Yes
R2 0.287 0.290

Note. *** denotes significance at the 1% level; ** denotes significance
at the 5% level; * denotes significance at the 10% level. Standard
errors are in parentheses.

Table 3. Random-Effects Model Estimation Results for Pitchers.

Pitcher's
salary Model A Model B

Race 28937.86 *** 26054.12 ***
 (9021.14) (8622.29)
TEN 20163.49 *** 20462.78 ***
 (2847.42) (2898.58)
SQTEN -1662.70 *** -1653.03 ***
 (218.42) (220.44)
AGE -38967.27 *** -35607.49 ***
 (6978.73) (7009.73)
SQAGE 739.71 *** 680.68 ***
 (113.35) (113.96)
Height 1654.64 ** 1352.04
 (837.21) (823.28)
Weight 616.50 357.13
 (523.17) (505.53)
CYP 281.99 ***
 (56.29)
GS 2212.72
 (1358.06)
GR 269.40
 (455.74)
BlSv -3,530.63
 (3761.66)
Hld 102.47
 (1428.17)
TBF 10.13
 (87.73)
PT -19.61
 (41.49)
HA 245.28 *
 (148.52)
HRA -2142.86 ***
 (804.80)
BBP -139.34
 (364.12)
IBB 2866.80
 (1774.36)
HBP 1192.45
 (1058.43)
WP -1,312.36
 (1050.95)
BK -1,363.50
 (1963.56)
Runs 363.96
 (509.21)
IP -585.01
 (595.93)
ERA -173.86
 (509.07)
SOP 166.07
 (215.56)
SV 824.65
 (973.07)
SHO 544.16
 (4104.78)
Win 5537.75 ***
 (1375.07)
Lose 2394.14 *
 (1338.28)
Vbo -5,760.88
 (4440.10)
_cons 217708.7 245363.9
 (175701.2) (171181.2)
Year No No
R2 0.146 0.202

Pitcher's
salary Model C Model D

Race 26890.64 *** 24516.44 ***
 (8377.11) (8061.22)
TEN 7235.41 ** 6635.83 **
 (3292.80) (3319.34)
SQTEN -735.89 *** -707.57 ***
 (236.44) (238.58)
AGE -6,321.18 -4,870.48
 (7419.91) (7326.89)
SQAGE 212.46 * 190.35
 (119.34) (118.02)
Height 2212.77 *** 1978.96 ***
 (774.31) (763.29)
Weight 599.70 288.08
 (475.44) (461.62)
CYP 328.74 ***
 (51.72)
GS 2860.27 **
 (1274.90)
GR 539.19
 (442.35)
BlSv -2,476.58
 (3727.05)
Hld 541.47
 (1388.07)
TBF 50.78
 (82.07)
PT 3.33
 (38.41)
HA 247.26*
 (138.58)
HRA -1613.25 **
 (770.82)
BBP -109.65
 (342.14)
IBB 1019.71
 (1647.10)
HBP -301.75
 (995.61)
WP -1,297.55
 (984.05)
BK -44.10
 (1826.11)
Runs 70.99
 (478.38)
IP -873.33
 (558.44)
ERA -98.39
 (475.83)
SOP -30.39
 (209.13)
SV 1369.83
 (913.39)
SHO 168.57
 (3787.08)
Win 4816.52 ***
 (1276.08)
Lose 2664.58**
 (1246.39)
Vbo -1,112.66
 (4270.42)
_cons -380169.3 ** -345474.4 **
 (171677.6) (167981.5)
Year Yes Yes
R2 0.365 0.400

Note. *** denotes significance at the 1% level; ** denotes significance
at the 5% level; * denotes significance at the 10% level. Standard
errors are in parentheses.

Table 4. Two-Stage Double Fixed-Effects Model Estimation Results With
Dependent Variables Player's Salary (Models A-B) and Batter's Salary
(Models C-M).

Salary Model A Model B Model C

TEN 30645.09 *** 32310.46 *** 38353.19 ***
 (3305.99) (3835.80) (5799.60)
SQTEN -1288.26 *** -1289.44 *** -1295.28 ***
 (111.88) (112.90) (129.55)
AGE -33772.89 *** -35857.20 *** -44762.84 ***
 (5233.25) (5609.73) (8111.98)
SQAGE 430.13 *** 436.75 *** 496.54 ***
 (66.05) (66.44) (78.61)
Height -2,027.36 -1,788.97 2408.62
 (1646.36) (1808.50) (6049.47)
Weight 1022.27 960.05 2605.08 *
 (1185.79) (1251.03) (1480.03)
SSI 11.55
 (7.76)
GP

PA

AB

SAC

SacF

BB

IW

SOB

SB

CS

RBI

RS

SH

FH

DB

ThirdB

HR

TB

BA

cons 912958 *** 907261.40 *** 221666.20
 (275480.2) (306715.7) (907187.1)
POS No Yes No
[R.sup.2] 0.273 0.279 0.312
Race 21300.59 *** 17147.54 *** 6282.23
 (3360.12) (3646.27) (4704.29)
cons -5032.62 *** -4051.39 ** -1,582.51
 (1633.26) (1772.35) (2361.80)
[R.sup.2] 0.021 0.012 0.001
Adjusted [R.sup.2]

Salary Model D Model E Model F

TEN 42029.15 *** 41392.47 *** 41679.02 ***
 (5861.63) (5846.75) (5828.22)
SQTEN -1298.47 *** -1253.95 *** -1261.54 ***
 (130.96) (130.45) (130.04)
AGE -50104.74 *** -53073.18 *** -55233.20 ***
 (8252.85) (8222.15) (8233.35)
SQAGE 524.15 *** 578.88 *** 613.70 ***
 (79.31) (79.25) (80.01)
Height 7135.47 9227.41 9243.64
 (7635.34) (7593.39) (7563.27)
Weight 2430.15 2103.69 1921.50
 (1641.79) (1633.68) (1629.82)
SSI 13.14 *
 (7.77)
GP 305.58 ***
 (114.11)
PA 125.95 ***
 (33.85)
AB

SAC -528.31 -733.00 *
 (367.56) (374.56)
SacF 520.36 -18.43
 (918.73) (917.75)
BB 161.96 -52.06
 (205.78) (220.60)
IW 2341.07 * 2057.82
 (1289.17) (1289.42)
SOB -71.83 -218.08
 (142.19) (151.97)
SB 107.31 -52.87
 (319.08) (323.19)
CS -373.77 -471.33
 (648.34) (647.28)
RBI

RS

SH

FH

DB

ThirdB

HR

TB

BA

cons -434,101.80 -751,059.60 -708,253.90
 (1185329) (1179249) (1174194)
POS Yes Yes Yes
[R.sup.2] 0.323 0.341 0.346
Race 8991.04 6414.99 4527.01
 (6453.45) (6533.67) (6356.76)
cons -2,264.87 -1,615.95 -1,140.37
 (3238.98) (3279.24) (3190.45)
[R.sup.2] 0.002 0.0007 0.0004
Adjusted [R.sup.2]

Salary Model G Model H Model I

TEN 41756.44 *** 41410.42 *** 41548.80 ***
 (5832.46) (5844.25) (5848.85)
SQTEN -1262.34 *** 1263.95 *** -1264.08 ***
 (130.13) (130.60) (130.84)
AGE -55170.01 *** -52593.53 *** -52577.85 ***
 (8241.78) (8226.15) (8237.10)
SQAGE 611.58 *** 572.57 *** 569.27 ***
 (80.08) (79.35) (79.84)
Height 9273.02 9271.91 9238.13
 (7569.02) (7590.20) (7593.41)
Weight 1933.25 2117.31 2115.76
 (1630.94) (1633.01) (1633.73)
SSI

GP 358.83 *** 349.12 ***
 (120.56) (122.15)
PA

AB 122.12 ***
 (34.46)
SAC -592.92 -582.75 -543.55
 (364.54) (369.56) (367.87)
SacF 137.86 987.59 640.88
 (935.79) (928.87) (979.29)
BB 83.61 210.15 232.44
 (207.52) (208.71) (217.54)
IW 2179.17 * 2605.91 ** 2445.37 *
 (1287.63) (1303.18) (1293.40)
SOB -203.19 -36.89 -54.93
 (152.46) (144.42) (143.19)
SB -38.57 117.33 190.16
 (323.23) (319.03) (329.68)
CS -461.03 -388.24 -376.96
 (647.70) (648.15) (648.35)
RBI -232.50
 (170.55)
RS -187.43
 (187.63)
SH

FH

DB

ThirdB

HR

TB

BA

cons -714,323.10 -769,593.10 -760,185.90
 (1175040) (1178820) (1179286)
POS Yes Yes Yes
[R.sup.2] 0.345 0.342 0.342
Race 4611.51 7463.377 6902.54
 (6378.52) (6527.77) (6574.92)
cons -1,161.65 -1,880.04 -1,738.77
 (3201.37) (3276.28) (3299.94)
[R.sup.2] 0.0004
Adjusted [R.sup.2] 0.001 0.0008

Salary Model J Model K

TEN 41211.66 *** 41343.93 ***
 (5848.24) (5781.25)
SQTEN -1249.16 *** -1295.98 ***
 (130.50) (129.30)
AGE -53484.99 *** -52683.02 ***
 (8229.35) (8149.58)
SQAGE 588.03 *** 574.82 ***
 (79.66) (78.87)
Height 9148.05 9765.33
 (7592.76) (7492.86)
Weight 2026.64 1813.96
 (1634.93) (1613.78)
SSI

GP 229.51 * 182.60
 (132.81) (131.40)
PA

AB

SAC -502.11 -672.62 *
 (368.26) (367.05)
SacF 302.72 301.59
 (925.64) (938.01)
BB 123.66 261.33
 (208.58) (207.31)
IW 2200.48* 3574.10 ***
 (1295.12) (1304.08)
SOB -100.96 -18.69
 (144.53) (143.90)
SB 50.64 77.40
 (323.04) (320.44)
CS -441.77 -888.46
 (651.10) (647.31)
RBI

RS

SH 124.65
 (111.38)
FH 415.08 ***
 (141.77)
DB 22.24
 (379.75)
ThirdB -3519.17 ***
 (1080.23)
HR -2503.35 ***
 (575.19)
TB

BA

cons -726,872.90 -837,619.90
 (1179298) (1163633)
POS Yes Yes
[R.sup.2] 0.342 0.362
Race 5762.90 8957.52
 (6431.95) (6278.12)
cons -1,451.69 -2,256.42
 (3228.19) (3150.98)
[R.sup.2]
Adjusted 0.0006 0.0015
[R.sup.2]

Salary Model L Model M

TEN 41588.69 *** 41437.76 ***
 (5850.58) (5846.51)
SQTEN -1261.93 ** -1250.87 **
 (130.72) (130.47)
AGE -52754.59 *** -53041.87 ***
 (8229.22) (8221.65)
SQAGE 571.28 ** 577.54 **
 (79.65) (79.26)
Height 9363.87 9265.66
 (7595.04) (7592.96)
Weight 2147.93 2113.39
 (1634.40) (1633.60)
SSI

GP 361.78 ** 314.98 ***
 (128.31) (114.44)
PA

AB

SAC -565.26 -547.19
 (369.59) (367.96)
SacF 699.65 567.16
 (926.98) (936.68)
BB 200.36 168.22
 (209.66) (205.85)
IW 2552.92 2368.15
 (1308.06) (1289.34)
SOB -42.06 -73.94
 (145.55) (142.19)
SB 148.70 110.60
 (322.01) (319.07)
CS -351.13 -347.37
 (648.80) (648.77)
RBI

RS

SH

FH

DB

ThirdB

HR

TB -71.62
 (74.769)
BA -20061.47
 (18823.01)
cons -781,884.80 -753,867
 (1179737) (1179172)
POS Yes Yes
[R.sup.2] 0.342 0.342
Race 7189.86 6852.52
 (6613.93) (6566.17)
cons -1,811.14 -1,726.17
 (3319.53) (3295.56)
[R.sup.2]
Adjusted 0.0009 0.0008
[R.sup.2]

Note. *** denotes significance at the 1% level; ** denotes significance
at the 5% level; * denotes significance at the 10% level. Standard
errors are in parentheses.

Table 5. Two-Stage Double Fixed-Effects Model Estimation Results
for Pitcher's Salary.

Salary Model A Model B

 First stage: Fixed-effects model

TEN 30766.37 33115.22 ***
 (8010.33) (7875.18)
SQTEN -1302.22 ** -1256.96 **
 (226.06) (224.87)
AGE -33038.67 *** -29794.56 ***
 (10676.78) (10608.05)
SQAGE 391.15 294.99
 (138.16) (141.10)
Height -585.52 -9.69
 (2063.75) (2081.13)
Weight -6,058.32 -6216.92 *
 (2751.36) (2706.64)
CYP -53.60
 (62.18)
GS 1019.15
 (1356.97)
GR 264.64
 (461.78)
BlSv -458.74
 (3994.14)
Hld -1,871.06
 (1418.68)
TBF -114.88
 (88.52)
PT -69.45
 (45.53)
HA 1282.77 **
 (344.41)
HRA -699.31
 (806.25)
BBP 826.72 **
 (419.40)
IBB 3798.91 *
 (1707.08)
HBP 1815.48 *
 (1094.60)
WP 218.70
 (1095.48)
BK 1453.13
 (1931.01)
Runs -718.74
 (534.30)
IP -225.11
 (585.16)
ERA -141.84
 (503.63)
SOP 127.57
 (234.22)
SV -912.09
 (953.90)
SHO 4155.81
 (3991.52)
Win 3528.35 **
 (1328.78)
Lose 2205.61
 (1270.50)
Vbo -9651.58 **
 (4377.05)
_cons 1252179 ** 1141157 **
 (489034.10) (486715.60)
Year No No
[R.sup.2] 0.207 0.291

 Second stage: Model of
 salary premium (ui)

Race 36571.90 ** 32668.71 ***
 (9466.07) (9957.68)
_cons -7327.35 * -6,545.33
 (4237.11) (4457.16)
Adjusted 0.026 0.019
[R.sup.2]

Salary Model C Model D

 First stage: Fixed-effects model

TEN 32544.94 *** 33013.77 ***
 (9496.963) (9411.93)
SQTEN 49.11902 17.94
 (237.606) (239.56)
AGE 14806.77 13438.50
 (10252.5) (10118.21)
SQAGE -455.762 *** -444.52 **
 (139.393) (138.55)
Height 6108.966 ** 5589.28 **
 (2617.43) (2608.13)
Weight -6410.353 *** -6,529.03
 (2343.232) (2313.07)
CYP -40.315
 (52.665)
GS 1383.27
 (1164.61)
GR 614.31
 (413.29)
BlSv -2,045.18
 (3620.55)
Hld -1,474.45
 (1312.27)
TBF -28.11
 (76.27)
PT -21.62
 (39.72)
HA 845.78 **
 (302.95)
HRA -380.63
 (715.49)
BBP 661.67*
 (365.37)
IBB 1023.78
 (1475.32)
HBP -491.54
 (958.72)
WP -204.85
 (964.52)
BK 2197.71
 (1654.87)
Runs -511.58
 (457.85)
IP -642.18
 (504.68)
ERA 1.41
 (434.74)
SOP -220.52
 (214.26)
SV -164.20
 (826.07)
SHO 2537.05
 (3403.90)
Win 2760.64 *
 (1139.82)
Lose 2235.68 **
 (1096.10)
Vbo -4,305.16
 (3908.12)
_cons -512,822 -396261.6
 (504042.40) (502007.30)
Year Yes Yes
[R.sup.2] 0.474 0.525

 Second stage: Model of
 salary premium (ui)

Race 54732.82 *** 50885.33 ***
 (12513.18) (12417.93)
_cons -10965.97 * -10195.11 *
 (5601.02) (5558.39)
Adjusted 0.033 0.029
[R.sup.2]

Note. *** denotes significance at the 1% level; ** denotes
significance at the 5% level; * denotes significance at the 10%
level. Standard errors are in parentheses.
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Author:Jane, Wen-Jhan
Publication:International Journal of Sport Finance
Date:Feb 1, 2012
Words:8709
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