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Saturday, May 14, 2005

Salaries and Ticket Prices

This is a follow up to my post over at Division of Labour about the causation/correlation between ticket price increases and salary increases in professional baseball. It is commonly claimed that salary increases cause ticket prices to increase, whereas economists claim that it is quality improvements which "cause" ticket prices to increase, and increased salaries might just cause the quality of the team to increase.

Over at DoL I posted some conditional means on ticket price increases and salary increases. Here, I post some regression (probit) results and a couple of pictures. I estimated a probit model where the dependent variable was real ticket prices increasing (1 or 0) and the explanatory variables were real salaries increasing (1 or 0), lagged winning percentage, city population and city real per-capita income. Here are the estimation results (these are not marginal effects):

Number of obs = 290
LR chi2(4) = 32.86
Prob > chi2 = 0.0000
Log likelihood = -184.33224
Pseudo R2 = 0.0818

rtixup | Coef. Std. Err. z P>|z| [95% Conf. Interval]
salup | -.1000612 .1690499 -0.59 0.554 -.4313929 .2312705
lagwin | .0049105 .001164 4.22 0.000 .0026292 .0071919
pop | -.0123291 .0148283 -0.83 0.406 -.041392 .0167338
rincome | .0602735 .0217401 2.77 0.006 .0176636 .1028833
_cons | -4.10322 .8462817 -4.85 0.000 -5.761901 -2.444538
The results suggest that real salaries increasing doesn't have a statistically significant impact on ticket prices increasing, which is what the conditional means suggested. We see that population (size) of the market alone doesn't cause ticket prices to increase, which is reassuring. We do see that the previous year's quality (as measured by lagged winning percentage) does contribute to the odds that ticket prices increase. Also, real per-capita income contributes to the odds that ticket prices will increase. All of this is consistent with economic theory, although it shoots a hole in the "salaries went up and thus tickets went up" rant on the local sports radio.

Plotting the predicted odds that real ticket prices will increase in the same year that real salaries increase yields:
Whew, there doesn't seem to be any significant difference between salaries increasing and salaries decreasing.

However, plotting the predicted odds that real prices will increase against the previous year's winning percentage we get a much clearer relationship, and one that makes sense:

Upshot: Salary increases do not cause ticket prices to increase.

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