Scaling of Salaries

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Scaling of Salaries

Postby blairfix » Sun Sep 21, 2014 7:50 pm

I've recently become interested in scaling laws. They seem to occur everywhere in nature, and also in the economy. I hope to post more in this in the days to come, but here is something that should be close to home for many users of the forum.

The chart below plots the salary of every York University employee (who makes over $100,000) against the size rank of this salary (from 1 to roughly 1500). The result is a strong scaling relation. Notice that the top 2 salaries are way off the spectrum ... these are the York U President and VP.

York Salaries.png
York Salaries.png (105.79 KiB) Viewed 1360 times
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Re: Scaling of Salaries

Postby shai » Sun Sep 21, 2014 8:57 pm

Hello Blair,

Nice result!

Few questions:
As far as I understand, the scaling laws that draw the most attention are power-laws. Such relations appear in a log-log plot as straight lines. Yours shows a straight line on a linear-log(rank) graph, which is an exponential distribution (if I’m not mistaken). Power-laws have some nice mathematical properties, like scale-invariance, and may suggest that interesting mechanisms lie behind them. Exponential distributions may also be interesting as they may arise from information-theoretic inference methods like maximum entropy.

The presence of a scaling relation immediately raises a couple of questions:
1. What mechanism may lie behind the apparent relation?
2. And\or what statistical generative model may underlie it?
3. What do the deviations from the fitted line and\or suggested null model may tell us?

References and analogies to other sciences may be very fruitful when such relations arise. Do you have any preliminary thoughts about this?
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Re: Scaling of Salaries

Postby blairfix » Mon Sep 22, 2014 1:43 pm

Yes, power scaling laws are what are most frequently found in nature. A straight line on a log-log plot produces a power law. The York U Salary plot turns out to be best fit with a negative logarithm.

As for the mechanisms that produce power laws, physicist have proposed many. See this article for a good summary:



For economic applications, I think the most straightforward mechanism is called preferential attachment.:

http://en.wikipedia.org/wiki/Preferential_attachment

The basic idea is that given the addition of a new piece of `wealth' to the economy, this wealth will `preferentially attach' itself to wealthier individuals. In other words, the probability of an individual gaining this extra piece of `wealth' is proportional to the person's existing income. So basically the rich get richer...

The interest in economic scaling laws dates back to Pareto, but neoclassical economists haven't pursued it much since then.
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Re: Scaling of Salaries

Postby DT Cochrane » Fri Oct 10, 2014 12:42 pm

This is great, Blair and that was a wonderful intervention, Shai.

Thank you both for sharing.
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