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?


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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