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What is the reason for taking the natural logarithm of annual income, my outcome variable, instead of just leaving the variable as it is?

What relationship would I be linearizing if I took the ln of the annual income? The relationship with the annual income and the number of people who reported a certain income or the relationship that of my independent variables with the outcome variable ln annual income?

Why take the ln of annual income?


marked as duplicate by whuber Jun 5 '13 at 20:49

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Even if you are not using it as a dependent variable, log of income often makes more intuitive sense.

If a guy making \$ 30,000 per year is given a \$ 5,000 raise, he's happy. If a guy making \$ 300,000 per year is given a \$ 5,000 raise, he's insulted.

In some extreme cases, even log might not be enough to account for the utility of money: Would Warren Buffett's life change in any way if his income doubled? Was halved? And, in many places, the first few dollars means life vs. death.

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    $\begingroup$ More directly, income changes are often multiplicative, at least to a good approximation, as when people in a firm might get a 5% raise. That's multiplying by 1.05, which is adding a constant on any logarithmic scale. $\endgroup$ – Nick Cox Jun 5 '13 at 22:35

The logarithm of income is usually more normally distributed (have a look at the histograms of income and of log income). Using log income as dependent variable also has the nice feature that your regression coefficients are semi-elasticities, i.e. they show you the approximate percentage change in income for a one-unit increase in your explanatory variable.

You can find a more detailled explanation together with examples here


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