How to comment log numbers

[Chiara Tasselli]

Good Morning,
I need to compare simple averages of a logarithm variable (no regressions or models log-lin / log-log/... simple averages of the variables by groups). How can I comment results? for example if the average monthly earnings (in the log form) are 7,39. What I can state?

[Nick Cox]

If your logarithms are natural logarithms, and guessing at dp comma, then exp() is the inverse function.

. di exp(7.39)
1619.7061

If something like 7 is the result, then it seems unlikely that you're using logarithms to base 10, as back transforming would get you 10 million or so.

But, but, but: The average of a variable in logarithmic form is the logarithm of the geometric mean, and back-transforming gives you the geometric mean.

Statistics is taught in weird ways in many places. I suppose many economics students are expected to know lots about fixed and random effects, instrumental variables, difference-in-difference this, that and the other, but are never taught about geometric means. Or they were mentioned briefly in an introductory course some years ago..,,