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I'm a statistician and my colleagues work with income data every now and then, but they usually apply some arbitrary cut-off and go with logistic regression.

I know there's an infinite range of positive support distributions that could work, but I'd like to know if there's something in particular that is supported by economic theory (or perhaps empirical success).

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  • $\begingroup$ Three important questions: 1) What kind of income data, 2) what do you want to discuss, 3) is it censored - are you including the income of both employed and unemployed? $\endgroup$ – RegressForward Jun 10 '18 at 20:49
  • $\begingroup$ I wouldn't know in which terms to answer 1. In the most recent case, it was self-reported salary from a sample of doctors. Just wanted to throw some explanatory variables in there to see what affects it. No censoring or zero inflation for this one but I suppose those can be dealt with in the standard ways? $\endgroup$ – zipzapboing Jun 11 '18 at 19:38
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I find it awfully odd to use logistic regression since income is clearly not binary. Sometimes people use logistic to explore if people are in the "top X%" or other sorts of ad-hoc quantile regression. Using logistic seems sub-optimal to me, but perhaps passable. I would prefer quantile regression.

If everyone is employed and you have no unemployed doctors, then you have a wide range of incomes, it makes sense that the distribution would be approximately log normal. Income distributions have heavy(ish) tails. This is commonly held belief, tied to "Gibrats Law".

Here's an interesting paper on it- carefully note they chose to argue more log normal than. It implicitly confesses of the widely held belief that both consumption and income is log normally distributed. There are probably more basic papers, but JPE is pretty respected and this has 100+ cites and a good place to dig.

Battistin, Erich, Richard Blundell, and Arthur Lewbel. "Why is consumption more log normal than income? Gibrat’s law revisited." Journal of Political Economy 117.6 (2009): 1140-1154.

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