Log transformed independent variable affects other independent variables

[Ahmad MHN]

I transformed one of my independent variables into natural logarithm form in a fixed effect panel data. This is because the data of this independent variable (i.e., EXT) is heavily skewed.

This is the distribution before transformation.





And this is the distribution after log transformation





This transformation changed the coefficients and p values of other independent variables. Thus, some of them became significant. I also notes that the constant now became insignificant.

Can anyone please explain why this log transformation affects other variables in the model? Should I trust the result of this log transformation? Thanks in advance.


Cross-posted here: https://stats.stackexchange.com/questions/630374/log-transformed-independent-variable-affects-other-independent-variables

[Dimitriy V. Masterov]

You should mention the cross-posting here: https://stats.stackexchange.com/ques...dent-variables

[Ahmad MHN]

Hi, Dimitry. I apologize, I will edit my post. Thanks.

[Jeff Wooldridge]

We need to know more. Are you using fixed effects or something else? Does the variable BEH change over time? If so, it's unusual that you'd have it interacted with RI and EXT but not have it appear by itself. Also, did you include year dummy variables, as is standard with panel data?

It seems your N is not too large but I can't tell. You should almost always opt for fixed effects and cluster your standard errors by id if T is not too large relative to N.

My guess is EXT takes on a wide range of values, making the estimation more sensitive to extreme values. Using log(EXT) almost certainly shrinks the range of the variable, and this can lead to more precision of other estimators.

[Ahmad MHN]

Hi, Jeff Wooldridge . Thanks for you reply.

Yes, I'm using fixed effect model but without year dummies.
The BEH is categorical variable with the values of 1 and 0.
The purpose of this model is to determine the moderating role of BEH in both the RI-GDPG nexus and the EXT-GDPG nexus.

The N is 34 and T is 10. So, the total observations are 338 (unbalanced panel data).

So, do you think that I should proceed with the result from log transformation?
I am still figuring out whether this log transformation is appropriate in my case.
What do you think, Jeff?
I will happily provide more information as needed.
Thanks again in advance.

Edit: I also noticed that the residuals before log transformation were not normally distributed. However, after the log transformation, the residuals are now normally distributed.