#  How to Take Log of Zero Income 

 





March 07, 2009

 

 

I encounter a problem when using a Log normal distribution to model income distribution. Namely, there are a bunch of people in my dataset who report zero income, maybe due to unemployment, and I am wondering how to logarize the zero incomes. I notice some researchers just drop the observations with zero income while others assign a small amount of income to them so that logarithm can be taken legitimately. Obviously, we can try both ways to see how the results stand. But I am wondering if there are some experts on this topic who can clarify the pros and cons of these and other approaches treating zero incomes.

A related question is what model you think fits the income distribution best, a Lognormal, a power distribution, or a mixture model of a Normal and a point mass at zero, and so on.   
Look forward to your thoughts on these questions.

Lastly, [here ](http://www.youtube.com/watch?v=QsgeU_HUNV4&eurl=http://www.visualizingeconomics.com/2008/11/04/income-distribution-animation/)is an interesting animation of the income distribution in the USA.

Posted by [Weihua An](http://www.iq.harvard.edu/blog/sss/archives/author/weihua-an/) at March 7, 2009 6:07 PM



 

 

 



 

 

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