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st: Economic Significance and Logged Independent Variables


From   Erasmo Giambona <e.giambona@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Economic Significance and Logged Independent Variables
Date   Wed, 8 Jul 2009 15:09:23 +0200

Dear Statalist,

I have a panel dataset for a sample of publicly listed firms.

I am fitting the following model using OLS: Debt/Total Assetsi = a +
b*ln_Total_Assets + control variables + firm dummies + year dummies +
ei. - where i is a subscript for firm i.

The dependent variable is total Debt divided by Total Assets (both
expressed in millions), which is a ratio ranging between 0 and 1;
ln_Total_Assets is the natural logarithm of total assets.

The output of the above regression shows that ln_Total_Asset is
statistically significant at the 1% level. This variable has also a
huge economic effect. In fact, a 1 standard deviation increase in
ln_Total Assets causes Debt/Total Assetsi to increase by 0.15 (while
its average is 0.202).

Then, I run Debt/Total Assetsi = a + b*Total_Assets + control
variables + firm dummies + year dummies + ei. This model differs from
the above one only because I am not logging Total_Assets. In this
case, I find that Total Assets is still highly statistically
significant at the 1% level. However, its economic effect is
negligible. In fact, a 1 standard deviation increase in Total Assets
causes Debt/Total Assetsi to increase by 0.0002 (while its average is
0.202).

I can see that logging a variable can make a difference on its
economic effect. However, changing the economic effect from 0.15 to
0.0002 seems really a big difference. Can somebody provide some hints
on why this might be happening? Is that an indicatio that there might
be something special about the structure of my data?

I would really appreciate any suggestions.

Thanks,

Erasmo
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