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In an econometric point of view when I have a variable such as unemployment rate which is a percentage, should I transform it with logarithm?

This question came to my mind cause when we have variable in levels we use log so when I differenciate it I get a variation.

In the case of unemployment if I take the logarithm and then the difference which I get it's not the variation on unemployment level, but variation on unemployment rate, which is kind of acceleration of unemployment, isn't it?

Have you ever faced this kind of problem?

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  • $\begingroup$ The kind folks at Economics might be able to provide an answer tailored to economic analysis. $\endgroup$
    – Sycorax
    Feb 2 '18 at 3:23
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This is very much dependent on your context and the purpose for which you might want to apply the logarithmic transformation. You did not provide enough detail to go really in depth with my answer. There are in general two main reasons to do something like this:

(1) In your model you believe that the transformation helps you to achieve better fit. For example you have a linear regression but think that the log transformed unemployment rate might be more linearly related to your dependent variable. This answer provides good treatment on this

(2) Also mentioned in the answer linked above. You want to control the way you interpret your model. Assuming a linear regression again, lets say that you have a model like this:

$$ P_{beer} = \beta_0 + \beta_1 unemployment\text{ }rate(\%) + u $$

Where $P_{beer}$ is the price of beer across countries in USD. The interpretation would be, for 1% rise in unemployment rate (e.g. from 5 to 6%) there is $\beta_1$ USD change in $P_{beer}$. Alternatively, for: $$ P_{beer} = \beta_0 + \beta_1 log(unemployment\text{ }rate(\%)) + u $$

You would say that for 50% relative increase in unemployment rate (e.g. from 10% to 15%), $P_{beer}$ changes by $ 50* \frac{\beta_1}{100} $

There's plenty of resources on how to interpret linear regression, like here.

Back to your initial question: there is nothing in econometrics which could dictate you to use a logarithmic transformation on a variable of unemployment rate. Use it if it seems reasonable in your setting.

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