Log normal

A comment to my previous post correctly points out that the income distribution is approximately log-normal. What this means is that while income itself is not normally distributed, the logarithm of income is.  The log-normal distribution has a pretty fat tail for high incomes. A variable will be log-normal if it is the product of a lot of random variables, since the log of a product is a sum. It has been argued for many years that achievement should be log-normal because it involves the product of many independent events. This is why a good programmer can be hundreds of times better than a mediocre one.  I even gave a version of this argument here. Hence, small differences in innate ability can lead to potentially large differences in outcome. However, despite the fact that income may deviate from log-normality in some cases and in particular between sectors of the economy (e.g. finance vs. philosophy), there is still a question of whether the compensation scheme needs to follow log-normal even if productivity does. After all, if small differences in innate ability are magnified to such a large extent, one could argue that income should be pegged to the log of productivity.

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One thought on “Log normal

  1. Thanks for the response.

    > whether the compensation scheme needs to follow log-normal even if productivity does. After all, if small differences in innate ability are magnified to such a large extent, one could argue that income should be pegged to the log of productivity.

    There are at least two ways to look at this:

    1) If companies have too much income inequality within their workforce, then the people who are paid relatively less will come to resent it, which will lower the morale of the rest of the firm. (I think there is some empirical evidence, though from my quick google search I only found things like this: http://books.google.com/books?hl=en&lr=&id=V6UL2vICzHwC&oi=fnd&pg=PA315&dq=inequality+workplace+income+&ots=FC_gOpXCmW&sig=NZpVpgwmBiyYcfKVBkQVKWGO32M#v=onepage&q=inequality%20workplace%20income&f=false, which seem like they might be biased.) Anyway, firms will have incentives to minimize this themselves, to increase their own productivity.

    2) As our economy becomes increasingly globalized, the gains increasingly go to being the best in your given field. E.g., there’s less point in listening to the second best flute musician on youtube when you could listen to the very best. From the perspective of maximizing the future talent pool of flute musicians, we should discourage huge gaps based on small innate differences, because otherwise prospective flute musicians will see that they could get very unlucky, and, given some understandable amount of risk aversion, not enter the field. So, in order to increase the future pool of productive flute musicians, I agree that in this case it might be useful to peg income to log productivity. Though, it’s not always clear how to do that.

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