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.