Log of ROA, ROE and Tobin's Q

[Hanne Zwertvaegher]

Hello everyone,

The dependent variables of my research are growth in ROA, ROE and Tobin's Q over several years. When starting my first linear regression with ROA, the ramsey reset test pointed out that my model is not correctly specified. I changed the ROA variable to ln(ROA) and this turned out to be much better (normality etc). However, I only just realised taking the log indicates all ROA growths below 0 as missing values.

Do any of you have suggestions on how I can transform my data without losing the valuable information the negative growth in ROA holds?

Thank you in advance!

[Carlo Lazzaro]

Hanne:
normality is a (weak) requirement for residual distribution only.
You do not report anything about heteroskeadstcity and, more important, the meaning of "much better" when referred to quantitative issue (ie, does the -estat ovtest- outcome reject or not the null after you logged -ROA-?) is not that informative.
As far as transformations are concerned, you may want to take a look at -help ladder-.
As usual, following the FAQ recommendation to post what you typed and what Stata gave you back via CODE delimiters, you would increase your chances of getting (more) helpful replies.

[Phil Bromiley]

You might also look at Stata tip 96: Cube Roots by Nick Cox.

Taking the log of the dv when negative values are legitimate not only reduces sample size, it makes the sample selected based on values of the dv which renders most regression estimates inconsistent.

[Nick Cox]

The transformation

sign(y) ln(1 + |y|)

has, like cube roots properly applied, the nice properties that it preserves sign and treats positive and negative values symmetrically.

Unlike cube root, it behaves like ln y for y >> 0 and like -ln(-y) for y << 0.

It seems a lot less ad hoc than ln(y + c), where c is chosen to ensure that all logarithms are defined. That choice can be hard to justify and can bite you very hard if c is chosen poorly. In particular, it is a fallacy that if c is very small then the transformation behaves like ln y. That is true for large y but not for small y.