How do I know when to use log-transformation? [duplicate]

Question

I am quite new to econometrics and still struggle with recognizing when to use the log-transformed variable or just stick with the nominal form. From what I gathered, it has to do with getting closer to the normal distribution of each variable or when the relationship is multiplicative rather than additive (e.g. income).

I am currently researching whether there are any factors potentially driving up the level of Suspicious Activity Reports in the United States (got the idea from J. Braun - Drivers of Suspicious Transaction Reporting Levels, 2016). I am planning on using the fixed-effects model, but I am not sure in what form to include the variables (both dependent and independent).

Is there any step-by-step guide that I could follow (I am using R)? E.g. when I look at the graphic distribution of each variable, I can see that some of them are skewed and when I transform them, they seem to resemble normal distribution. Is it necessary to do this in other than OLS regression? What would happen if I violated the assumption of normal distribution?

Thank you!

Answer 1

It is not really anything to do with trying to get a normal distribution (and in most models, you don't really need to transform variables to make them normal anyway). We generally apply a logarithmic transformation to a positive variable when it either grows or decays on an exponential scale (i.e., it grows/shrinks by a percentage that has a roughly fixed distribution over time), and we want to convert it to a linear scale. This is common in econometrics because we often deal with variables (e.g., stock prices, GDP, population size, etc.) that tend to grow or shrink by a "percentage" each time period. By taking logarithms of these variables we get a variable that is roughly on a "linear scale" and this is more intuitive to model.