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Re: st: Economic Significance and Logged Independent Variables


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Economic Significance and Logged Independent Variables
Date   Wed, 8 Jul 2009 09:41:31 -0400

Erasmo Giambona <e.giambona@gmail.com> :

The change in coefficients is common in highly skewed variables, but
you have much larger problems. For starters, you are explaining y/x as
a function of x, which leads to division bias (see e.g. Borjas, 1980).
 Also, I doubt Debt/Total Assets is really constrained to lie in
[0,1], since outstanding debt can exceed assets (also, how do you
count loans from the firm, which could count as negative debt). Also,
if your dependent variable is constrained to the unit interval, linear
regression is almost certainly inappropriate; see e.g.
http://www.stata.com/support/faqs/stat/logit.html or -ssc inst locpr-
for a graphing tool to see the likely functional form in a
cross-section; for the panel case, see
http://www.stata.com/meeting/snasug08/abstracts.html#wooldridge

More importantly, what is the direction of a causal effect here?  If a
firm issues bonds worth $100, they have $100 more debt and $100 cash
on hand, increasing y/x (as long as y/x<1 as you claim) and increasing
x, leading to a positive correlation.  But why are they issuing debt?
It's not because they have higher assets (that is an outcome as well),
it's because the marginal value of investment exceeds the interest
rate.  The positive correlation is not causal, not even close.  Or
should we read that as Total Net Assets, i.e. are you subtracting Debt
from Total Assets?  In that case, I am sure Debt/NetAssets is not
constrained to lie in [0,1], since debt can certainly exceed assets
less debt.

Borjas, George J. “The Relationship Between Wages and Weekly Hours of
Work: The Role of Division Bias,” Journal of Human Resources, Summer
1980, pp. 409-423.

On Wed, Jul 8, 2009 at 9:09 AM, Erasmo Giambona<e.giambona@gmail.com> wrote:
> 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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