Is There a Wage Premium or Wage Discrimination For Foreign-Born Players in the NBA?

Hill, James Richard ; Groothuis, Peter A.

Introduction

As employers pursue talent, labor markets have increasingly become international. For instance, in the United States in the health care profession 27% of surgeons are foreign-born while in the education profession 40% of engineering professors are foreign-born. Aslanbeigui and Montecinos (1998) estimated that in the 1990s approximately 30% of US economics professors were foreign-born. The internationalization of labor markets has led researchers to question whether foreign workers are more productive because of self-selection on the part of immigrants (Borjas & Bratsberg, 1996), less productive due to language and cultural differences than native-born workers (Dustmann & Soest, 2002), or discriminated against (Aslund et al., 2014).

All sports leagues in pursuit of the most talented players have international labor markets. For instance, in 2014, 25% of Major League Baseball (MLB) players were foreign-born and 51% of National Hockey League (NHL) players were born in Canada, while 25% were born in the US and 25% were born in Europe. Sports leagues provide a fertile ground to further the research on immigration due to the increasing degree of internationalization. For instance, Kahane, Longley, and Simmons (2013) find that NHL teams who employ higher proportion of Europeans perform better if the Europeans are from the same country compared to teams with less Europeans or Europeans from many different countries. Alvarez et al. (2011) finds that increases in the number of international players in a domestic soccer league tends to generate improvements of a national team that is only comprised of domestic players.

Focusing of the National Basketball Association (NBA), Eschker, Perez, and Siegler (2004) find that there was a premium paid to international players for the 1996-97 and 1997-98 seasons due to a "winners curse" in the market from the inability of scouts and general managers to properly evaluate the worth of foreign-born players who did not play college basketball in the US. More recently, using an unbalanced panel dataset (1999-2008) and a two-stage double fixed-effect model, Yang and Lin (2012) find evidence of salary discrimination against international players. Hoffer and Freidel (2014), using data from the 2010-2011 season, however, find the opposite with foreign-born players paid a premium in the NBA.

The purpose of this paper is to extend the analysis on foreign wage discrimination and premium results by focusing on wage discrepancies devoid of the "winners curse" or market inefficiencies. Using a large unbalanced panel dataset (1990-2013) covering all the years of the previous studies and using two different econometric techniques, we attempt to verify either the existence of pay discrimination against foreign players or pay premiums toward foreign players. We use both yearly OLS regressions for all 24 years of our panel and also estimate a two-stage fixed-effect model developed by Bartel and Sicherman (1999) and utilized by Yang and Lin (2012) for three time periods. In addition, we interact race with foreign status to provide insights on how both might affect wages. However, our analysis utilizes only non-rookie-scale salaries as observations. This approach alleviates the possibility that foreign-born players are over-valued or under-valued in the draft due to an ability of NBA scouts to assess their talent properly.

Literature Review on Racial and Nationality Discrimination in the NBA

Market discrimination is the unequal treatment of a group of workers in the marketplace in terms of hiring, pay, retention, or promotional decisions. The motivation for such treatment can be based on statistics or personal animus.

Statistical discrimination is the belief that a group of workers is not as productive as the preferred group. In sports, apologists for the segregation of baseball in the heyday of the Negroe Leagues suggested that Black players just were not good enough to play in the Major Leagues. This created a "barrier to entry" for Black players until Jackie Robinson broke the color barrier. It may be that the NBA suffered from similar misgivings about the talent of foreign-born players. Until the US allowed professional NBA players to play in the Olympics in 1992 it was difficult to judge how foreign-born pro players would fare against the level of NBA talent.

Becker (1971) suggested that the origin of the personal animus could come from owners, coworkers, or customers. There is no doubt that personal prejudice was the underlying reason for the late arrival of Black players in MLB. Owners, White players, and fans were the source of this bias. If customers are the source of the prejudice, this leads to a lower marginal revenue product of the minority players resulting in lower pay. Unfortunately, it is often impossible to separate the motivation behind discrimination through empirical observation.

Empirical analysis of racial discrimination has a long history in the sport economics literature with most focusing on racial differentials and not country-of-origin differentials. Kahn and Sherer (1988), using salary data from the 1985-86 season, find pay premiums for White players. Brown, Spiro, and Keenan (1991) as well as Koch and Vander Hill (1988) estimate pay premiums for White players of 15% and 9%, respectively. All three studies cite customer discrimination as the driving force behind the pay discrimination (see Becker, 1971). McCormick and Tollison (2001) re-examine Kahn and Sherer s (1988) findings and suggest a theory of price discrimination, statistical discrimination, based on relative supplies and supply elasticities explains the results better than fan discrimination.

Articles by Dey (1997), Gius and Johnson (1998), and Bodvarsson and Brastow (1999) using data from the late 1980s and 1990s failed to find racial wage discrimination. Hamilton (1997) found evidence of racial pay differences only at the upper end of the 1994-1995 seasons salary distribution. Bodvarsson and Brastow (1999) suggested the disappearance of the pay discrimination in the NBA was the result of a decrease in owner monopsony power due to the negotiation of a new NBA collective bargaining agreement in 1988 combined with the addition of four new teams. They also provide empirical evidence that at least part of the racial salary gap was the result of owner and manager discrimination, not just fan discrimination (see Becker, 1971). Except for the article by Dey (1997), all the research in this area used single season salary data for model estimation. Dey (1997) used pooled data from five seasons in some of his empirical work.

Hill (2004) used an 11-year panel dataset beginning with 1990 salaries and ending with 2000 salaries. While the coefficients for the dummy variable for White players was positive and significant in 1990 and 1991 individual-year regression equations, the positive and significant finding in the overall pooled regression disappeared when height was added as an explanatory variable. Robst et al (2011) found only weak support for customer discrimination and no support for employer discrimination in the NBA when measuring racial discrimination based on skin tone. Lastly, Groothuis and Hill (2013) fail to find any evidence of either pay or exit discrimination in the NBA when controlling wage equations for survival bias; they do, however, find that there is a pay premium paid to White players over their career in the magnitude of 16-20% when analyzing career data.

To our knowledge only Eschker, Perez, and Siegler (2004), Yang and Lin (2012), and Hoffer and Freidel (2014) analyze pay differentials for foreign-born players. Some literature to date has found a wage premium paid to foreign players in the 1996-1997 and 1997-1998 seasons when international players were only a small percentage of the NBA that disappears after the 1998-1999 season (Eschker, Perez, & Siegler 2004). They found this true for the next three additional seasons as well. Eschker, Perez, and Siegler (2004) focus more on a market inefficiency or statistical discrimination explanation for their results. They argue that the NBA was not initially able to value foreign talent properly and this led to a wage premium. However, their analysis used all salaries, including rookie-scale contracts. Inability to properly value foreign talent and perhaps draft these players higher than warranted would only prejudice rookie-scale contracts. Yang and Lin (2012) focus on the 1999-2008 seasons and find that foreign players are paid less than domestic players, ceteris paribus. Yang and Lin (2012) suggest the same mechanisms that can cause a racial wage differential could also cause a wage differential for foreign-born players, particularly customer discrimination. They extend the analysis of customer discrimination by suggesting that foreign players from a larger market economy receive a wage premium. Hoffer and Freidel (2014) find a wage premium for foreign players using data from the 2010-2011 season.

Given these mixed results, we use various empirical tests to analyze if either wage discrimination or a wage premium exists for foreign-born players. In particular, we divide foreign-born NBA players into two categories: foreign born with US college experience and foreign born with no US college experience to provide a better comparison to the previous literature. To pinpoint the source of any wage discrepancies we limit our observations to non-rookie-scale contracts. This means that any differences between pay for native versus foreign-born players should not be the result of statistical discrimination or market inefficiency.

Dataset and Variables

The panel dataset for our analysis includes all players who had complete season contracts in the NBA from the 1989-90 season through the 2012-13 season. (1) Unlike Yang and Lin (2012) and Hoffer and Friedel (2014), who only use a dummy variable equal to 1 if the NBA player was born outside the US, we focus on two measures. The first is a dummy variable equal to 1 if the NBA player was foreign-born and also has no US college experience. This measure would include Yao Ming, who was drafted directly from China, but exclude Hakeem Olajuwon, who was born in Nigeria and played college basketball at the University of Houston. This measure is consistent with the measure used by Escher, Perez, and Siegler (2004) and more recently by Motomura (2016), who analyzes drafting international players into the NBA. Both articles use this measure because their primary focus was to test for inefficiency in the market due to information problems that arise from obtaining talent directly from other international leagues. The second measure we use is foreign-born with US college experience. This measure would include Hakeem Olajuwon and exclude Yao Ming. Groothuis and Hill (forthcoming) use both of these measures and find foreign-born players without US college experience have a higher likelihood of exit than do foreign-born players who had US college experience. In Table 1, we report the number of foreign-born players in each category (2) We find that in 1990 there were only 19 foreign-born players in the league and by 2013 the number of foreign-born players had grown to 74. Focusing on the two different groups, we find that all of the growth has come from foreign-born athletes without US college experience; this figure has grown from four players in 1990 to 58 players in 2013, while foreign-born players with college experience has held relatively steady in the middle teens to the low twenties. We will use the figures from this table to break up the fixed-effect regression analysis shown later into different time periods as a robust check on the results.

We exclude player salaries signed under a rookie-scale contract because their wages were set by the NBA collective bargaining agreement. Perhaps foreign-players were/are assigned higher than justified numbers in the draft due to an inability of the NBA scouts to assess talent from foreign leagues. Perhaps foreign-born players in leagues around the world were/are paid wage premiums through their initial rookie-scale contracts as an inducement to relocate to the US and leave their home country and extended family. By focusing on non-rookie-scale salaries our conclusions cannot be based on the possibility of statistical discrimination or market inefficiency. In addition, Krautmann et al. (2009) suggest that restricted players are underpaid, making the interpretation of wage differentials more difficult.

To control for on-court performance that influences an individual's marginal revenue product, we include start age in the NBA, experience, experience squared, games played, and an aggregation of performance variables as measured by the NBA efficiency rating. Although Berri (2007, 2008) finds there are problems with the efficiency rating due to the fact it overvalues shooters and underpenalizes missed shots, we utilize the measure because it provides a simple summary statistic. (3) We also use time-invariant measures of height, draft number, and race as explanatory variables in addition to the foreign-born dummies. Race is defined as 1 if the player is White and 0 for all other races. (4)

Measures that our data does not include that two of the articles do include are dummy variables for position played. In the Eschker, Perez, and Siegler (2004) article these variables were seldom found to be significant in their wage equations. Yang and Lin (2012) also use positional dummy variables in their analysis and include them in the wage equations instead of the fixed-effects regression. We suggest that this is incorrect since player positions rarely, if ever, change from season to season and if they do change it may be due to an endogenous change. Thus the inclusion of these dummies is inappropriate in the fixed-effect model and we suggest that the time-invariant variable of height captures the same effect. We also suggest that performance variables and height can proxy for these variables, and excluding the variables should not lead to different results.

In Tables 2, we report the means and standard deviations of the variables for all the foreign-born player categories as well as native-born players. Some interesting insight can be gleaned from this data. First, on average, foreign-born players are taller by two inches or more. Second, the majority of foreign-born players who did not play basketball in college in the US are White. This is not true for foreign-born players who did play college basketball in the US; only around 40% of these players are White. Third, foreign-born players in all categories earned higher real salaries on average compared to their counterparts born in the US. This is true despite that fact that foreign-born players with no college are generally taken lower in the draft on average. In terms of performance statistics, foreign-born players who played college basketball in the US have the highest efficiency rating while foreign-born no college and US-born players have the same efficiency rating.

Econometric Techniques

We utilize both yearly ordinary least squares and the two-stage fixed-effects model. The yearly ordinary least squares technique was utilized by Eschker, Perez, and Siegler (2004) and Hoffer and Freidel (2014). Thus our equation can be written as:

ln[S.sub.i] = [X.sub.i][beta] + [e.sub.i]. (1)

where ln[S.sub.i] is the log of salary and [X.sub.i] is a vector of explanatory variables lagged by one year that includes age at start of NBA career, experience, experience squared, efficiency rating, games played, draft number, height, race, foreign-born no college, and foreign-born college. The efficiency rating for each player is calculated using the following: ((Points + Rebounds + Assists + Steals + Blocks) - ((Field Goals Att. - Field Goals Made) + (Free Throws Att. - Free Throws Made) + Turnovers))/Games Played. We estimate this equation for all 24 years of our panel.

We also estimate the two-stage fixed-effect model developed by Bartel and Sicherman (1999) and utilized by Yang and Tin (2012). In the first stage standard salary estimation equations utilize the natural logarithm of real salary as the dependent variable and a vector of productivity measures as the independent variables in a fixed-effect panel. In a panel setting this vector can be classified into two subsets, one which changes yearly with performance ([X.sub.it]) and one which does not change yearly but may affect productivity ([Y.sub.i]). Thus our equation can be written as:

In[S.sub.it] = [X.sub.it][alpha] + [Y.sub.i][beta] +[u.sub.i] + [e.sub.it]. (2)

In a panel setting it is assumed that the vector [Y.sub.i] consists of unchanging characteristics of each individual and therefore only variables found in vector [X.sub.it] are included in the initial fixed-effect regression. Since the panel is unbalanced the standard errors are clustered by player. The residuals resulting from this fixed-effect regression should reflect the unobserved fixed component of the error term attributable to time-invariant differences between individuals. Bartel and Sicherman (1999) identify this as an individual wage "premia." The premia for each player is the fixed component of the real salary that is not explained by time varying performance characteristics. This premia is individually fixed and can be either positive or negative.

Following Bartel and Sicherman (1999) and Yang and Lin (2012) these residuals or wage "premias" are then regressed on the unchanging individual characteristics of individuals, vector [Y.sub.i]. Given the unbalanced nature of the panel this regression is estimated using weighted least squares. The weights used by the STATA program are inversely proportional to the variance of an observation. This equation takes the format:

[u.sub.i] = [Y.sub.i][beta] + [[omega].sub.i]. (3)

The regression on the individual wage "premias" can then identify the influence of time-invariant characteristics such as height, race, draft number, or being foreign-born. One key component of the technique is that the wage "premia" is the residual from stage one regressions; therefore, the stage one specification is crucial for the stage two results.

For the estimation of equation 3 on each individual's wage "premia," we use the independent variables of time-invariant personal player characteristics that includes the player's height, a dummy variable for White players, draft number, a dummy variable for players born outside the US who did not play college basketball in the US, and lastly a dummy variable for players born outside the US who did play college basketball in the US. Once again, we follow Eschker, Perez, and Siegler (2004), who suggested the wage premium for foreign-born players in the NBA for the 1996-97 and 1997-98 seasons was only true for those players who did not play in college in the US. Therefore, our current research will designate each classification separately.

Empirical Results

In Tables 3a through 3e, we report the 24 single-season OLS results for equation 1. In the yearly OLS results, we find that there is a wage premium paid to foreign-born players with no college experience occurring in the 1991 and 1996 seasons that is consistent with Esckher, Perez, and Sieglers (2004) results. (5) We detect no pay premium from the 1997 through 2003 season for foreign-born players with no college experience. We then again find a pay premium for foreign-born players with no college experience for the 2004, 2007, 2008, 2009, and 2011 seasons. Hoffer and Freidel (2014) found a wage premium in the 2011 season. In the OLS yearly results, we find evidence of wage discrimination present in 1991, 1992, and 1993 against foreign-born players with college experience but a wage premium for this same class of players in 2001, 2011, and 2012. The premium that occurs in the 2011 season is also consistent with the Hoffer and Freidel's (2014) results since they used a dummy variable that includes all foreign-born players. Remember that our analysis is based on non-rookie-scale salaries.

In all 24 wage equations the coefficient on efficiency is always positive and significant, indicating performance influences salary; draft number is negative and significant in all but two seasons, 2008 and 2011. The coefficient on experience is always positive and significant in all but the first season while the coefficient on experience squared is always negative and almost always significant. Interestingly, we find that one time in the 24 years a wage premium is found for White players, 1991, and two times wage discrimination is found for White players, 1996 and 1997. Although OLS is informative, we suggest yearly wage equations are not robust given the small number of foreign players; giving the panel nature of the data a more appropriate econometric technique is the fixed-effect model.

We estimate three different two-stage fixed-effects models: one for the complete time period 1990-2013, one for the early time period 1990-1999 when foreign-born players with no college were a small number of total players in the NBA, and one for the 2000-2013 period when foreign-born players with no college were becoming a larger number of total players.

We report the results for the regression models for equation 2 and 3 in Table 4 for all three time periods. In the wage equation, we find that for all time periods the coefficient on experience is positive and significant and the coefficient on experience squared is negative and significant. The coefficient on the NBA efficiency per game is always positive and significant. Tastly, we find that games played is positive and significant for the entire period but insignificant or weakly significant for the two shorter periods.

To estimate equation 3, the individual wage "premias" from each of the wage equations are regressed on time-invariant personal characteristics using the same weighted least squares approach used by Yang and Lin (2015). In this individual wage premium equation, we find that for the complete time period a wage premium is found for foreign-born players with no college experience. This is a misleading result because when we break up the panel into the two smaller time periods we find that the wage premium for foreign-born with no college experience occurs only in the 1990-1999 period and is not detected for the later period from 2000-2013. The results of the model are consistent with Eschker, Perez, and Siegler's (2004) results. In all three periods we do not find a wage premium for college players with US college experience.

In the 1990-1999 time period, we find wage discrimination against White players as well as a wage premium for foreign-born players with no college experience. Given 80% of foreign-born players with no college experience are White, the White dummy may capture some of the foreign-born/no college differential. To further explore this relationship, we report three different specifications with various interactions of the foreign dummy variables with the White dummy variable in Table 4a. In the first specification we drop the White dummy but interact the White dummy with the two foreign-born categories and find that the foreign-born/no college White interaction coefficient is positive and significant while the other interaction is insignificant. In the second specification we include only the White dummy and drop all the foreign dummy variables and find that the coefficient on White is negative and significant. In the third specification we include all the dummy variables for foreign-born players and find that the dummy variable on White is negative and significant while the dummy variable on White interacted with foreign-born/no college is positive and significant. (6)

Given these differing results we draw no conclusions about discrimination against White players. When focusing on the total time period and the later time period we find that the White dummy becomes insignificant for the complete time period from 1990-2013 as well as for the later 2000-2013 period. Given the differing results, we suggest the results are not robust by time period. Our major result, however, is that a foreign wage premium for foreign-born players who did not play college basketball in the US exists early when these players were a small percentage of the league but has disappeared when this category of players became a bigger percentage of the league. Our results are consistent with Eschker, Perez, and Siegler's (2004) findings but not consistent with Yang and Lin's (2012) findings. This is of note given that our analysis excluded rookie-scale contracts. In terms of general interpretation, we find that for the overall time period wages increase with experience in a concave manner and peak at nine years of experience. In addition, we find as with past results that both performance and draft positon influence the NBA wage.

Conclusions and Implications

The influx of international players into the NBA has led researchers to investigate whether either pay discrimination or a pay premium exists for these foreign players. The results have been mixed depending upon the time period and the technique utilized. Using similar techniques with a longer unbalanced panel dataset (1990-2013) that covers all the years of the previous studies, we test for the robustness of the results and how the differential has changed over time. In particular, we use non-rookie-scale salaries to alleviate statistical discrimination or market inefficiencies arguments for our findings. Despite this limitation to our data, we find that a wage premium for foreign-born players who entered the league without US college experience exists for the early years but disappears by the later years.

Given the large influx of foreign-born players who have been drafted from foreign leagues over time we suggest that the premium paid these players in the early 1990s when there were just a few players has disappeared as drafting foreign players has become more common place. For instance, in 2016 a record 26 foreign players were selected in the NBA draft with 16 being drafted without US college experience. Given our focus on non-rookie-scale salaries it would appear the early wage premium was not the result of a market inefficiency. Perhaps the NBA was paying a premium to retain foreign-born players who migrated from non-NBA leagues in order to initially grow their international market. This does not appear to be the case today.

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Endnotes

(1) To be consistent with previous studies we use a panel study and yearly OLS regressions. One problem with a panel study and yearly OLS regressions is that many players sign long-term contracts, so the salary in noncontract years is not directly determined by the player's performance.

(2) This table lists all the foreign-born players in our dataset. For the regressions results shown later the analysis is restricted to only players not under a rookie scale contract.

(3) To provide a robustness check, we also control for on-court performance using each performance variable separately as well as including games played and minutes per game. The results are essentially the same. The reason we did not include total minutes is because the efficiency rating and total minute are 91.5% correlated. Including minutes per game in the regressions do not change our results. These results are available upon request.

(4) Race was determined by official pictures found in the NBA webpage by the two authors.

(5) When all of the observations are included in the regressions--not just players not covered by a rookie scale contract--the coefficient of foreign-born/no college is significant in all seasons from 1991 to 1997, except 1993. These results are available on request.

(6) The same interaction analysis was performed for the 2000-2013 time period. In this period none of the coefficients of the White dummy variable or interaction terms were significant at any level.

James Richard Hill (1) and Peter A. Groothuis (2)

(1) Central Michigan University

(2) Appalachian State University

James Richard Hill, PhD, is a professor of economics in the College of Business Administration. His teaching and research interest include sports, labor economics, and collective bargaining and labor law.

Peter A. Groothuis, PhD, is a professor of economics in the Walker College of Business. His research interests are in labor market applications in sport economics and stated preference methods. Table 1. Yearly Count of Foreign-Born Players/All Observations Year Foreign-Born Foreign-Born Foreign-Born No college College 1990 19 4 15 1991 20 5 15 1992 20 5 15 1993 21 5 16 1994 24 8 16 1995 26 11 15 1996 29 12 17 1997 26 9 17 1998 32 14 18 1999 33 14 19 2000 40 19 21 2001 43 25 18 2002 51 36 15 2003 56 43 13 2004 68 49 19 2005 75 52 23 2006 77 52 25 2007 73 53 20 2008 73 51 22 2009 73 53 20 2010 80 57 23 2011 69 51 18 2012 71 57 14 2013 74 58 16 Note: This table lists all the foreign-born players in our dataset, not just those without a rookie-scale contract. Table 2. Means/Std. Dev. of Variables by Foreign-Born Status for Overall Time Period: 1990-2013 (No Rookie-Scale Contracts) Variables Overall Foreign-Born, Foreign-Born, College in US No College Height 79.11 81.39 81.47 (0.0559) (0.267) (0.208) White 0.192 0.385 0.767 (0.00572) (0.0330) (0.0245) Draft Number 25.49 20.32 32.36 (0.353) (1.541) (1.367) Real Salary 2.880e+06 3.227e+06 3.625e+06 (40,972) (200,779) (165,497) Experience 6.764 7.064 5.290 (0.0553) (0.284) (0.207) Start Age in NBA 22.33 22.74 21.56 (0.0225) (0.105) (0.138) NBA Efficiency per game 10.52 11.89 10.48 (0.0961) (0.529) (0.396) Games Played 57.80 57.11 56.05 (0.328) (1.577) (1.339) Number of Clusters 952 48 79 Observations 4,746 218 300 Variables US-Born Players Height 78.83 (0.0580) White 0.141 (0.00536) Draft Number 25.27 (0.374) Real Salary 2.809e+06 (43,118) Experience 6.853 (0.0581) Start Age in NBA 22.37 (0.0223) NBA Efficiency per game 10.45 (0.100) Games Played 57.96 (0.346) Number of Clusters 825 Observations 4228 Standard deviation in parentheses Table 3a. OLS Yearly Regressions for 1990-1994 (No Rookie-Scale Contracts) Variables 1990 1991 1992 lnsal lnsal lnsal Start Age in NBA -0.0392 -0.0545 -0.0756 (*) (0.0424) (0.0724) (0.0453) Experience 0.0865 0.199 (***) 0.150 (**) (0.0934) (0.0622) (0.0667) Experience -0.00534 -0.0119 (***) -0.00675 Squared (0.00579) (0.00437) (0.00429) NBA Efficiency 0.0426 (***) 0.0542 (***) 0.0528 (***) per game (0.00709) (0.00809) (0.00874) Games Played 0.00137 0.00309 0.00187 (0.00323) (0.00263) (0.00230) Draft Number -0.0203 (***) -0.0133 (***) -0.0144 (***) (0.00552) (0.00416) (0.00419) White 0.0314 0.239 (**) 0.0492 (0.0933) (0.106) (0.102) Height 0.0408 (**) 0.0404 (***) 0.0451 (***) (0.0164) (0.0137) (0.0127) Foreign-Born/ 0.275 1.132 (***) 0.276 No College (2.671) (0.241) (0.605) Foreign-Born/ -0.0882 -0.386 (**) -0.619 (**) College (0.132) (0.187) (0.312) Constant 10.68 (***) 10.49 (***) 10.97 (***) (1.516) (1.919) (1.457) Observations 136 140 151 R-squared 0.768 0.794 0.807 Variables 1993 1994 lnsal lnsal Start Age in NBA 0.0415 -0.0134 (0.0555) (0.0554) Experience 0.204 (***) 0.176 (***) (0.0687) (0.0536) Experience -0.00976 (**) -0.00960 (***) Squared (0.00443) (0.00294) NBA Efficiency 0.0657 (***) 0.0515 (***) per game (0.0104) (0.00895) Games Played -0.000647 0.00183 (0.00294) (0.00250) Draft Number -0.0133 (***) -0.0171 (***) (0.00372) (0.00416) White -0.0325 -0.0915 (0.136) (0.155) Height 0.0261 (*) 0.0172 (0.0139) (0.0140) Foreign-Born/ 0.222 0.0612 No College (0.792) (0.336) Foreign-Born/ -0.700 (*) -0.0564 College (0.365) (0.174) Constant 9.695 (***) 12.02 (***) (1.886) (1.820) Observations 1163 166 R-squared 0.688 0.682 Table 3b. OLS Yearly Regressions for 1995-1999 (No Rookie-Scale Contracts) Variables 1995 1996 1997 lnsal lnsal lnsal Start Age in NBA 0.000102 -0.0373 -0.0178 (0.0464) (0.0436) (0.0547) Experience 0.207 (**) 0.173 (**) 0.209 (***) (0.100) (0.0680) (0.0567) Experience -0.0109 -0.0109 (**) -0.0124 (***) Squared (0.00749) (0.00479) (0.00326) NBA Efficiency 0.0596 (***) 0.0839 (***) 0.0810 (***) per game (0.00992) (0.0112) (0.0113) Games Played -0.000614 -0.00176 -0.000897 (0.00287) (0.00237) (0.00311) Draft number -0.0144 (***) -0.0159 (***) -0.0157 (***) (0.00372) (0.00360) (0.00389) White -0.248 -0.332 (**) -0.333 (*) (0.153) (0.148) (0.175) Height 0.00687 0.0188 0.00988 (0.0133) (0.0137) (0.0151) Foreign-Born/ 0.597 1.054 (**) 1.343 No College (0.381) (0.523) (1.251) Foreign-Born/ 0.0361 -0.0924 0.188 College (0.273) (0.217) (0.223) Constant 12.61 (***) 12.64 (***) 12.96 (***) (1.684) (1.655) (1.830) Observations 176 189 202 R-squared 0.693 0.691 0.647 Variables 1998 1999 lnsal lnsal Start Age in NBA 0.00365 -0.00405 (0.0397) (0.0464) Experience 0.279 (***) 0.208 (***) (0.0441) (0.0384) Experience -0.0155 (***) -0.00940 (***) Squared (0.00274) (0.00224) NBA Efficiency 0.101 (***) 0.0949 (***) per game (0.0111) (0.00836) Games Played -0.00390 0.00153 (0.00415) (0.00220) Draft number -0.00665 (**) -0.00743 (***) (0.00258) (0.00265) White -0.0502 0.0566 (0.114) (0.128) Height 0.0304 (***) 0.0179 (0.0109) (0.0120) Foreign-Born/ 0.335 0.0747 No College (0.761) (0.350) Foreign-Born/ 0.0280 0.0798 College (0.250) (0.250) Constant 10.40 (***) 11.60 (***) (1.300) (1.486) Observations 202 215 R-squared 0.679 0.689 Standard errors in parentheses (***) p<0.01, (**) p<0.05, (*) p<0.1 Table 3c. OLS Yearly Regressions for 2000-2004 (No Rookie-Scale Contracts) Variables 2000 2001 2002 lnsal lnsal lnsal Start Age in NBA 0.000102 -0.0373 -0.0178 (0.0464) (0.0436) (0.0547) Experience 0.207 (**) 0.173 (**) 0.209 (***) (0.100) (0.0680) (0.0567) Experience -0.0109 -0.0109 (**) -0.0124 (***) Squared (0.00749) (0.00479) (0.00326) NBA Efficiency 0.0596 (***) 0.0839 (***) 0.0810 (***) per game (0.00992) (0.0112) (0.0113) Games Played -0.000614 -0.00176 -0.000897 (0.00287) (0.00237) (0.00311) Draft number -0.0144 (***) -0.0159 (***) -0.0157 (***) (0.00372) (0.00360) (0.00389) White -0.248 -0.332 (**) -0.333 (*) (0.153) (0.148) (0.175) Height 0.00687 0.0188 0.00988 (0.0133) (0.0137) (0.0151) Foreign-Born/ 0.597 1.054 (**) 1.343 No College (0.381) (0.523) (1.251) Foreign-Born/ 0.0361 -0.0924 0.188 College (0.273) (0.217) (0.223) Constant 12.61 (***) 12.64 (***) 12.96 (***) (1.684) (1.655) (1.830) Observations 176 189 202 R-squared 0.693 0.691 0.647 Variables 2003 2004 lnsal lnsal Start Age in NBA 0.00365 -0.00405 (0.0397) (0.0464) Experience 0.279 (***) 0.208 (***) (0.0441) (0.0384) Experience -0.0155 (***) -0.00940 (***) Squared (0.00274) (0.00224) NBA Efficiency 0.101 (***) 0.0949 (***) per game (0.0111) (0.00836) Games Played -0.00390 0.00153 (0.00415) (0.00220) Draft number -0.00665 (**) -0.00743 (***) (0.00258) (0.00265) White -0.0502 0.0566 (0.114) (0.128) Height 0.0304 (***) 0.0179 (0.0109) (0.0120) Foreign-Born/ 0.335 0.0747 No College (0.761) (0.350) Foreign-Born/ 0.0280 0.0798 College (0.250) (0.250) Constant 10.40 (***) 11.60 (***) (1.300) (1.486) Observations 202 215 R-squared 0.679 0.689 Standard errors in parentheses (***) p<0.01, (**) p<0.05, (*) p<0.1 Table 3d. Yearly Regressions for 2005-2009 (No Rookie-Scale Contracts) Variables 2005 2006 2007 lnsal lnsal lnsal Start Age in NBA -0.0253 0.0126 -0.0265 (0.0308) (0.0311) (0.0297) Experience 0.278 (***) 0.290 (***) 0.319 (***) (0.0498) (0.0480) (0.0580) Experience -0.0167 (***) -0.0167 (***) -0.0175 (***) Squared (0.00363) (0.00338) (0.00391) NBA Efficiency 0.0755 (***) 0.0816 (***) 0.0867 (***) per game (0.00813) (0.00820) (0.00828) Games Played 0.000312 8.22e-05 -0.00149 (0.00268) (0.00236) (0.00255) Draft number -0.00921 (***) -0.00914 (***) -0.00472 (*) (0.00243) (0.00261) (0.00260) White 0.0793 0.163 0.0191 (0.111) (0.121) (0.118) Height -0.00274 0.0128 0.0160 (0.0117) (0.0104) (0.0136) Foreign-Born/ 0.0967 0.00931 0.268 (*) No College (0.180) (0.161) (0.153) Foreign-Born/ 0.189 -0.0150 -0.194 College (0.253) (0.246) (0.193) Constant 14.42 (***) 12.26 (***) 12.63 (***) (1.281) (1.199) (1.421) Observations 225 222 217 R-squared 0.731 0.732 0.692 Variables 2008 2009 lnsal lnsal Start Age in NBA -0.0613 (*) -0.0301 (0.0318) (0.0391) Experience 0.376 (***) 0.272 (***) (0.0580) (0.0760) Experience -0.0197 (***) -0.0143 (***) Squared (0.00383) (0.00501) NBA Efficiency 0.0869 (***) 0.0607 (***) per game (0.00798) (0.0159) Games Played -0.00334 0.00237 (0.00254) (0.00383) Draft number -0.00292 -0.0118 (***) (0.00302) (0.00363) White 0.0382 0.0473 (0.135) (0.144) Height -0.00837 0.0202 (0.0129) (0.0138) Foreign-Born/ 0.340 (**) 0.320 (**) No College (0.132) (0.162) Foreign-Born/ -0.0500 0.135 College (0.224) (0.208) Constant 15.16 (***) 12.76 (***) (1.368) (1.471) Observations 212 211 R-squared 0.673 0.602 Standard errors in parentheses (***) p<0.01, (**) p<0.05, (*) p<0.1 Table 3e. OLS Yearly Regressions for 2010-2014 (No Rookie-Scale Contracts) Variables 2010 2011 2012 lnsal lnsal lnsal Start Age in NBA -0.0186 0.0111 -0.0178 (0.0361) (0.0295) (0.0397) Experience 0.257 (***) 0.250 (***) 0.169 (***) (0.0423) (0.0410) (0.0410) Experience -0.0137 (***) -0.0115 (***) -0.00931 (***) Squared (0.00241) (0.00231) (0.00218) NBA Efficiency 0.0899 (***) 0.103 (***) 0.0943 (***) per game (0.00841) (0.00851) (0.00911) Games Played 0.00157 0.00591 (*) -0.00295 (0.00278) (0.00347) (0.00256) Draft number -0.00734 (***) -0.00362 -0.0112 (***) (0.00238) (0.00268) (0.00310) White 0.190 -0.0270 0.102 (0.127) (0.131) (0.123) Height -0.00719 0.0174 0.0153 (0.0116) (0.0129) (0.0124) Foreign-Born/ 0.221 0.263 (*) 0.222 No College (0.137) (0.151) (0.152) Foreign-Born/ 0.00863 0.312 (*) 0.631 (***) College (0.246) (0.184) (0.174) Constant 14.36 (***) 11.24 (***) 13.19 (***) (1.301) (1.309) (1.498) Observations 213 203 216 R-squared 0.680 0.693 0.624 Variables 2013 2014 lnsal lnsal Start Age in NBA -0.0670 (*) -0.0301 (0.0382) (0.0391) Experience 0.169 (***) 0.272 (***) (0.0471) (0.0760) Experience -0.00800 (***) -0.0143 (***) Squared (0.00279) (0.00501) NBA Efficiency 0.0890 (***) 0.0607 (***) per game (0.00915) (0.0159) Games Played -0.00170 0.00237 (0.00289) (0.00383) Draft number -0.00670** -0.0118 (***) (0.00325) (0.00363) White -0.0451 0.0473 (0.140) (0.144) Height 0.00752 0.0202 (0.0145) (0.0138) Foreign-Born/ 0.170 0.320 (**) No College (0.175) (0.162) Foreign-Born/ 0.167 0.135 College (0.279) (0.208) Constant 14.67 (***) 12.76 (***) (1.559) (1.471) Observations 220 211 R-squared 0.595 0.602 Standard errors in parentheses (***) p>0.01, (**) p<0.05, (*) p<0.1 Table 4. Fixed Effect and WLS Regressions Using Panel Data (No Rookie-Scale Contracts) Variables lnrealsal residual lnrealsal Start Age -0.000358 (***) in NBA (4.95e-05) White -0.0773 (0.0800) Height 0.0116 (0.00793) Draft Number -0.00945 (***) (0.00108) Foreign-Born/ 0.490 (***) No College (0.103) Foreign-Born/ 0.0294 College (0.153) Experience 0.313 (***) 0.354 (***) (0.0202) (0.0288) Experience -0.0168 (***) -0.0155 (***) Squared (0.00136) (0.00178) Efficiency 0.0255 (***) 0.0162 (***) (0.00454) (0.00618) Games Played 0.00155 (**) 0.00126 (0.000626) (0.000848) Constant 12.88 (***) 2.211 (***) 12.20 (***) (0.0886) (0.786) (0.132) Observations 4,746 4,746 1,740 R-squared 0.216 0.282 0.251 Number 952 461 of Clusters Variables residual lnrealsal residual Start Age -8.41e-05 -0.000176 (***) in NBA (9.03e-05) (5.26e-05) White -0.308 (***) 0.0408 (0.107) (0.0851) Height 0.0223 (*) 0.0172 (*) (0.0118) (0.00944) Draft Number -0.00745 (***) -0.0161 (***) (0.00155) (0.00138) Foreign-Born/ 1.187 (***) 0.133 No College (0.254) (0.113) Foreign-Born/ 0.0745 0.101 College (0.201) (0.147) Experience 0.284 (***) (0.0244) Experience -0.0187 (***) Squared (0.00167) Efficiency 0.0237 (***) (0.00533) Games Played 0.00144 (*) (0.000778) Constant -0.843 13.48 (***) 0.449 (1.276) (0.0948) (0.881) Observations 1,740 3,006 3,006 R-squared 0.139 0.264 0.376 Number 690 of Clusters Clustered Robust standard errors in parentheses: (***) p<0.01, (**) p<0.05, (*) p<0.1 Table 4a. WLS Regressions using Residuals from Fixed Effect Regression (No Rookie-Scale Contracts) 1990-1999 Variables residl residl Start Age in NBA -0.000113 -1.97e-05 (9.19e-05) (0.000102) Height 0.0184 0.0279 (**) (0.0117) (0.0119) Draft Number -0.00743 (***) -0.00716 (***) (0.00160) (0.00156) Foreign-Born/ -0.143 No College (0.150) Foreign-Born/ 0.123 College (0.267) Foreign-Born/ 1.236 (***) No College*White (0.217) Foreign-Born/ -0.275 College* White (0.370) White -0.252 (**) (0.109) Constant -0.343 -1.825 (1.280) (1.418) Observations 1,740 1,740 R-squared 0.117 0.110 1990-1999 Variables residl Start Age in NBA -8.01e-05 (8.85e-05) Height 0.0222 (*) (0.0118) Draft Number -0.00746 (***) (0.00154) Foreign-Born/ -0.245 No College (0.149) Foreign-Born/ 0.0519 College (0.265) Foreign-Born/ 1.561 (***) No College*White (0.234) Foreign-Born/ 0.0494 College* White (0.381) White -0.324 (***) (0.111) Constant -0.869 (1.271) Observations 1,740 R-squared 0.143 Robust standard errors in parentheses (***) p<0.01, (**) p<0.05, (*) p<0.1