I have read in many different studies now that take the natural logarithm of one plus x. For example, in econometrics many studies use the natural logarithm of one plus the total assets.

I do not understand why, because assets are so big anyways that adding one would not make a difference, or?

For example:

Natural Logarithm of one plus Assets(1,000,000) would be NL(1,000,001).

  • 1
    $\begingroup$ This is just a guess. If one of the numbers in the data set is equal to $0$ then $\log(0)$ becomes undefined, or if you prefer, $-\infty$. To keep your quantities as real numbers you add $+1$ to them. In addition, $\log(1+x) \approx x$ if $x$ is a small quantity (the linear approximation). $\endgroup$ Dec 30, 2022 at 8:09
  • $\begingroup$ Thank you so much, so it is a rather "technical" cue and I can simply add one by log(1+x) without worrying that I skew the data? $\endgroup$
    – Limps
    Dec 30, 2022 at 8:28
  • $\begingroup$ You are definitely changing the distribution of your data, however, since you know what function was applied to your data, you can always go back to the original by reversing the process, so changing the data distribution is not a problem. In fact, it might actually be a good thing, since after taking logs your data will range from $-\infty$ to $\infty$, so in particular, there might be a chance that the transformed data will be normally distributed (which is probably what you want). $\endgroup$ Dec 30, 2022 at 8:49
  • $\begingroup$ Whenever this transformation makes sense -- because values are $\ge 0$ -- the usual effect will be to reduce skewness in the data. $\endgroup$
    – Nick Cox
    Dec 30, 2022 at 11:35
  • 2
    $\begingroup$ @NicolasBourbaki Negative results are impossible with this translation. The point is to map values 0 upwards to 0 upwards. $\endgroup$
    – Nick Cox
    Dec 30, 2022 at 11:56


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