Log Transformation of Negative Pre-Tax Income Values

[Hoang Nguyen Student]

Dear all,

Currently, I'm working on a science research about Determinants of Transfer Pricing Aggressiveness in Vietnam. I'm stuck at handling some negative pre-tax income - one of the determinants (I'm using log transformations). There're some method (like add a constant value, or replace them by value 1), I don't know which method is the best. Please help.

Thanks,
Hoang

[Nick Cox]

I'd search the forum for mentions of neglog, which will take you to earlier discussions.

[Daniel Feenberg]

I take it that your negative incomes show up on the RHS of a regression, in which case you might consider just leaving them out. Sample selection on an exogenous variable won't bias your results (if the regression is otherwise kosher). Otherwise, I don't think there is an easy solution, largely because the conditions that make elasticity a sensible concept don't really work across the zero point. Perhaps you could put gross income on the LHS and expenses on the right which doesn't seem completely arbitrary, or use a cube root rather than a log, which does seem arbitrary.

[John Mullahy]

If the issue is with a RHS variable, then Dan's advice certainly makes sense. One alternative thereto would be to categorize the income measures and include them as a set of group dummies. Theu idea of adding a constant and then logging creates potential problems since which contant you add will affect the empirical results, sometimes a lot depending on the magnitudes of what you measure.

For what it's worth if the issue is with a LHS variable then a couple things you can do are:

http://mathworld.wolfram.com/InverseHyperbolicSine.html
https://www.statalist.org/forums/for...transformation (in the thread Nick suggested)

and a newer proposal:

https://econpapers.repec.org/article..._3a130-132.htm

[Nick Cox]

This is a difficult problem, as witness the fudges, kludges and nudges and the more systematic solutions, none of which have convinced all.

But denying yourself a transformation because it can't be interpreted easily in terms of elasticity and/or leaving out data that make sense but are awkward both seem backwards to me.

I can't speak for economics, but with environmental data both negative and positive and both tails heavy I've found cube root useful -- and expect to experiment with neglog next time the problem arises. Nothing against asinh except that most of my peers would not recognise it.

[Hoang Nguyen Student]

The issue is indeed with a RHS variable, and like Mr. Cox said, I cannot leave out these negative values because those are very important, especially when I'm researching about Transfer pricing. I will try cube root transformation.

Thank you, everyone.