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Re: st: Economic Significance and Logged Independent Variables


From   Erasmo Giambona <e.giambona@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Economic Significance and Logged Independent Variables
Date   Wed, 8 Jul 2009 16:15:06 +0200

Thanks Austin for all the great ideas and suggestions. I think I have
addressed some of the issues that you raise. I hope you don't mind to
elaborate a bit more on the skewness concern. I thought that skewness
could be the cause of the problem. However, I am really working with
several sub-samples (extracted from the same sample) with similar
skewness. I find that the coefficient changes drammatically only for
one of the sub-samples. Could this also be due to some outliers?

Thanks,

Erasmo



On Wed, Jul 8, 2009 at 3:41 PM, Austin Nichols<austinnichols@gmail.com> wrote:
> 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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