Income Inequality and Performance in MLB
There’s been a lot of chatter on the economics blogs regarding the subject of income inequality (see Mark Thoma, Brad DeLong, Greg Mankiw, Tyler Cowen for a brief sample of recent commentary). I read through most of it, did some thinking about it, but didn’t dwell on it. Yesterday, I ran across this paper, Relative Income Position And Performance: An Empirical Panel Analysis by Benno Torgler, Sascha L. Schmidt and Bruno S. Frey, and it got me thinking a little more. Here’s the abstract.
Studies have established that people care a great deal about their relative economic position and not solely, as standard economic theory assumes, about their absolute economic position. However, behavioral evidence is rare. This paper provides an empirical analysis on how individuals’ relative income position affects their performance. Using a unique data set for 1114 soccer players over a period of eight seasons (2833 observations), our analysis suggests that the larger the income differences within a team, the worse the performance of the soccer players is. The more the players are integrated in a particular social environment (their team), the more evident this negative effect is.
So, I thought, why not try this with baseball? I wanted to look at how players performed in MLB based on their salary differences from their team and the league as a whole. Using a sample of players with more than 200 plate appearances in a season from 1985-2005, I used the above study of professional soccer as a guide. As a performance metric I used total linear weighted runs produced (LWTS) to capture the player performance in a season. To measure the envy effect, I used the percentage difference in seasonal salary from his team average and the league average (in separate regressions). The model controls for the salary of a player, age (quadratic), salary bargaining status (reserved, arbitration eligible, or free agent—estimated from service time), position played most that season (if tied then I assigned the player to the more difficult position on the defensive spectrum), the year, and team. I used dummy variables to control for the latter four factors. I also estimated the model by each salary bargaining class separately, to see if there were any different effects. I threw out players who switched teams during the year and corrected for serial correlation.
The general hypothesis is that those who make less than their peers may feel inferior and perform worse, and those who make more will perform better as they feel superior. Remember better players should make more than worse players, and the salary variable in the regression is a reasonable control for player quality. Here are the estimated impacts for the percentage difference of in salary from the team and league, along with the standard error of the impacts and the R2 of each regression model.
Impact SE R2 All Team 2.24 0.27 0.34 League 4.89 0.39 0.37 Reserved Team 14.63 2.62 0.27 League 31.81 5.19 0.27 Arbitration Team 3.73 0.68 0.35 League 6.73 0.98 0.36 Free Agent Team 1.83 0.34 0.39 League 5.08 0.50 0.42
All of the estimates are statistically significant at the 1% level. It’s interesting that the effect exists, and that it’s more pronounced among reserved and arbitration eligible players than free agents. Also, the effect is greater for league differences, rather than team differences. The coefficients are actually quite small; a ten-percentage-point increase in salary/team average index (disparity is shrinking) increases LWTS by only 0.224. That’s hardly worth noting. However, for purely reserved players the effects are large enough to be interesting. A ten-percentage-point increases in salary/league average index improves performances by 3.18 runs.
Hmm. It seems that there may be some gains to teams bumping up the pay of their reserved players. It might reduce some envy, or maybe it allows them to purchase some lifestyle comforts that help them produce. Maybe teams that buy out young players aren’t just trying to reduce costs in the future, but boost performance in the short-term as well. I need to think some more on this.
J.C. Bradbury is an economist and associate professor at Kennesaw State University in metropolitan Atlanta. He is the author of The Baseball Economist and has operated Sabernomics.com since March 2004.
September 6th, 2006 at 10:56 am
Or could it be that management can scout their own players and not offer as good salaries for likely underperforming players?
September 6th, 2006 at 10:58 am
Sorry I’m dense. How did you control the fact that better players will be paid more? You used both salary and salary/average_salary as separate independent variables?
September 6th, 2006 at 11:24 am
You might be able to use the NBA to explore the topic in more depth. I think the NBA’s CBA in the late 90s resulted in a substantial shift in relative pay by upping the minimum salary and capping the max salary. (I think there was a J of Sports Econ article examining the new CBA from a median voter perspective; that article should give you more precise info on the changes in min and max salaries.) If so, you could look at performance in the year before the new CBA and the year after the new CBA.
September 6th, 2006 at 5:29 pm
Hi JC. Good work.
I don’t understand your table, but if the relationship between salary and performance in the “market” isn’t linear (and I don’t think it is), how does that impact the interpretation of your results?
September 7th, 2006 at 6:01 am
Thanks studes,
The non-linearity of salary and LWTS might have some slight biasing effect on the measured impact of the index, but I doubt it. The non-linearity would have to be correlated with the index. I’ll look into it.
Sorry for the confusing table. Each row contains the regression coefficient, the standard error of that coefficient, and the R2 of the regression model (which includes 50 or so variables).
September 7th, 2006 at 6:56 am
Thanks. Would you mind using a sentence with one of the coefficients in it? That would help me understand the table.
Reserved players are those not yet eligible for arbitration? If so, most of those players make the minimum, or just a bit above, and I don’t think the model really gives any insight into those situations. Salary is often a function of being in the second or third year, and that’s all.
September 7th, 2006 at 7:50 am
A coefficient measures the unit impact of an explanatory variable on the explained variable. Thus, a one unit increase in the explanatory factory is associated with a X-unit change in the explained variable. X = the coefficient value.
Yes, most players in the reserved class make close to the minimum, though some teams do have some wiggle room. And teams do sometimes buy out these years to create some variation. That’s why I think it’s curious that the result for these players is much larger. But, it could just be a function of outliers. However, I ran one model using a median regression technique that minimizes outlier impacts, and the results were about the same.
Also, I reran the models including non-linear controls for salary, and it didn’t impact the impact on the index much.
Overall, I haven’t put much thought into these models, though I may in the future. So, you’re right to be skeptical. I’m just surprised that my results mirror those in the soccer paper I linked to. This is why I love blogging. I stumble across a paper, and within hours I’ve posted a preliminary results and am getting feedback.
September 7th, 2006 at 8:44 am
Heh. Thanks for the sentence, JC. But I meant that I don’t know what the coefficients are doing in this case. I’m being thick, obviously, but what does the 14.63 for Reserveds signify, and why is it important?
Thanks.
September 7th, 2006 at 8:56 am
A one-unit increase in the index increases LWTS by 14.63. Since the units of the index are as a percent (i.e., 0.01 = 1%), a 1% increase in the index is associated with a 0.1463 increase in LWTS.
September 7th, 2006 at 10:46 am
Matt Bloom at Notre Dame published a study in a 1999 issue of the Academy of Management Journal using baseball data looking at this. He also found that more pay dispersion lowered performance.
Abstract
Pay distribution research is relatively scarce in the compensation literature, yet pay distributions are viewed as critically important by organizational decision makers. This study is a direct test of the relationship between one form of pay distribution–pay dispersion–and performance conducted in a field setting where individual and organizational performance could be reliably observed and measured. Findings suggest more compressed pay dispersions are positively related to multiple measures of individual and organizational performance.
September 7th, 2006 at 5:52 pm
JC, I think I’m being dense and not understanding this in the same was as Jobu in #2. You control for salary and then look at salary/lg. salary and salary/tm. salary?
If so, aren’t you just seeing the correlations of the inverses of league salary and team salary? I know I’m missing something here.
Also, what time period did you use for the study?
Thanks,
Jared
September 10th, 2006 at 9:13 am
Here is something that you might try. Use team winning percentage as the dependent variable in a regression. Total team salary would be one of the independent variables. The other independent variable might be a gini coefficient for each team. Then you could see if a team’s degree of equality in pay, holding total pay constant, has a significant effect on winning
September 21st, 2006 at 8:49 am
Craig Depken published what Cyril suggests in Economics Letters, 2000. Found the same result most have found without the team salary control: dispersion decreases winning percentage. This is pretty well traveled ground, a handful of papers have been published on it already.
I’ve been skeptical though, that the so-called “envy” effect is what is operating here. But JC’s is an independent look at the data, using a different outcome metric, and is the only one I know to break the model down by bargaining class.