Comments on: Income Inequality and Performance in MLB

By: Skip

Skip — Thu, 21 Sep 2006 13:49:10 +0000

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.

By: Cyril Morong

Cyril Morong — Sun, 10 Sep 2006 14:13:33 +0000

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

By: J. Cross

J. Cross — Thu, 07 Sep 2006 22:52:03 +0000

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

By: Tom Timmerman

Tom Timmerman — Thu, 07 Sep 2006 15:46:40 +0000

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.

By: JC

JC — Thu, 07 Sep 2006 13:56:00 +0000

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.

By: studes

studes — Thu, 07 Sep 2006 13:44:24 +0000

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.

By: JC

JC — Thu, 07 Sep 2006 12:50:05 +0000

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.

By: studes

studes — Thu, 07 Sep 2006 11:56:03 +0000

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.

By: JC

JC — Thu, 07 Sep 2006 11:01:57 +0000

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).

By: studes

studes — Wed, 06 Sep 2006 22:29:11 +0000

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?