Transformations of dependent variable or independent variable and growth rates

[Joan Stein]

Good morning everyone

I have two general questions that are confusing me for quite a while. Hopefully you can help me, i would really appreciate it. Thank you in advance!


1. I am wondering whether it is ok to use untransformed variables as dependent or independent variables in a panel data model (FE or RE)?
When looking at empirical papers, without any exception the variables are either logarithmized or ratios e.g. (Variable/Total assets, Variable/Net Income etc.) instead of the raw Variable.
I don´t have the feeling, that this even depends on the topic or the subject area. Thus, I feel like I have to transform variables before implementing them in a model.

Since my results are most often the best when using the raw variable, I am wondering whether this is a good sign, or whether the transformations are indeed necessary and the results for the raw variable are distorted. I can imagine, that such transformations reduce the threat of outliers, but in my case I have no outlier problems and in some rare cases I use winsorizing (cutting; I know its discussable if this is a good empirical practise).


2. My second question is also very broad. I wonder whether it is known, that growth rates in the dependent variable are leading to excessive insignificances for the independent variables?
All over my examinations, my results are clearly better when using variables in levels rather than in growth rates. And the difference is sometimes remarkably. Switching to a Growth rate DV sometimes take all significances of my IVs.

I am using a data Panel with N=33; T=7 (respectively T=6 in the regression since I use lagged IVs)

Greetings
Joan

[John Mullahy]

It's hard to respond to #1 without knowing what particular parameter(s) you are trying to estimate. A related consideration is whether transformation would subsequently require doing a re-transformation to recover the parameter(s) of interest (sometimes it will; sometimes it will not).

(That said, my general philosophy is that one's default should be to not transform and should transform only if compelling reasons can be articulated … not vice-versa. Others may reasonably disagree.)

As a smart person once said: "The government spends dollars, not log-dollars."

[Carlo Lazzaro]

Joan:
as an aside to John's excellent advice, oftentimes log-linear regression models are appealing in that it is more informative to disseminate that. say, one unit increase in the independent variable X1 causes, when adjusted for the remaining predictors, say, a 10% increase in the conditional mean of the regressand than to explain that the same variation, in a linear-linear regression odels, causes, say, $1000 increase in the conditional mean of the regressand, other things being equal,

[Nick Cox]

"The government spends dollars, not log-dollars."

[There are lots of governments, and they spend lots of different currencies..... The world is more than the United States!]

The riposte to that is that a good economist thinks logarithmically whenever that is what helps makes sense of the economy. And so too in epidemiology, environmental science, and so on, and so on. A very minor but pertinent side-effect of the pandemic has been that more people have seen that log scales are often a good idea.

I had a happy experience working on a couple of projects with foresters, who are very impressive and individual people. It turns out that they like trees. I even went to a forestry fair where they had some amazing kit for climbing trees, cutting them down, and yet more. I had to restrain myself from buying lots of kit I didn't really need. Any way, at the meeting between our team of academics and the foresters I had to explain very carefully when I suggested that log transformation was probably the best thing to do with their tree data, or if not then root transformation might work.

[John Mullahy]

🤣

[Joan Stein]

@all Thank you very much for your explanations!

[Nick Cox]

Oliver Keene wrote a splendid paper on why the log transformation is special.

https://onlinelibrary.wiley.com/doi/...sim.4780140810

It's behind a pay wall but copies are somehow easy to find.

The answers at https://stats.stackexchange.com/ques...d-distribution are standard stuff but draw things together nicelyl

[Mike Lacy]

I also have worked with foresters, and would support Nick's incisive (i.e., "cutting") point about foresters and the use of log or root transformations. I wonder if he had considered suggesting that stem and leaf plots might be useful to them as well.

[Nick Cox]

I was at the wedding of the economist John Hardman Moore, sometimes tipped for the Nobel Prize in Economics (*), which was the only wedding I have been to where the best man's speech featured flip charts and equations.

The only one I can remember was the very hoary joke that the integral of 1 ./ cabin is log cabin + c (c being conventional notation at least in Britain for the constant that appears, and which is naturally pronounced "sea"). At that 20% of the audience spontaneously shouted out "houseboat". The other 80% presumably thought that their loved ones were even crazier than they had realised.

(*) That always reliable site EJMR once featured a comment that Nick Cox will never win the Nobel Prize in Economics, which wasn't exactly a surprise to me. That did turn into a compliment, which for EJMR really was a surprise.