- The logarithm of 0 is undefined, the double logarithm of that would be undefined too. When z=1 the natural logarithm is 0, and the second transformation is also undefined. Here we can detect another problem when some authors, in order to normalize the data, apply logarithms indiscriminately. The result would be potential missing data problem due to the monotonic transformation when values of the data are zero.
- If we got a range of data between 0 and 1, the logarithm transformation will induce the calculus to a negative value. Therefore, the second logarithm transformation it’s pointless since all the data in this range is now undefined.
- When we use logarithms in growth rates, one thing surely can happen: If we got potential negative values in the original growth rate, and then apply logarithms on those, the value becomes undefined, thus missing data that will occur. And the interpretation becomes harder.
- Now if we apply some double transformation of log values, the zero and the negative values in the data will become undefined, thus missing data problem will appear again.
- Econometricians should take this in considerations since it’s often a question that arises during researches, and in order to do right inferences, analyzing the original data before applying logarithms should be a step before doing any econometric procedure.
Sumber:
https://blog.ms-researchhub.com/2019/09/16/taking-logarithms-of-growth-rates-and-log-based-data/#comments
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