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st: AW: Economic Significance and Logged Independent Variables


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: Economic Significance and Logged Independent Variables
Date   Wed, 8 Jul 2009 15:19:15 +0200

<> 

You put a covariate into logs, right? So the interpretation should be that a
one percent increase (not standard deviation) in this covariate causes an
absolute increase in the dependent to the tune of the respective
coefficient. The huge difference can be traced back to this different
interpretation of the output, as the example shows:


***
sysuse auto, clear
reg we pr len he
loc level=_b[pr]
gen lnpr=log(pr)
reg we lnpr len he

di in red "Coeff in levels: " /* 
 */ `level' ", in logs: `=_b[lnpr]'"
***



HTH
Martin


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Erasmo Giambona
Gesendet: Mittwoch, 8. Juli 2009 15:09
An: statalist
Betreff: st: Economic Significance and Logged Independent Variables

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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