# Re: st: AW: Economic Significance and Logged Independent Variables

 From Erasmo Giambona To statalist@hsphsun2.harvard.edu Subject Re: st: AW: Economic Significance and Logged Independent Variables Date Wed, 8 Jul 2009 16:28:38 +0200

```Thanks Martin. I try to explain in detail what I do

I run a regression of Debt/Total Assets on logged Total Assets (TA)
and other variables. Then I multiply the coefficient estimate on
logged TA by the standard deviation of logged TA. This product is
equal to 0.15.

Then I repeat the same exercise except that I replace logged TA with
TA. I multiply the coefficient on TA by the standard deviation of TA.
This product is equal to 0.0002.

I am puzzled by the fact that the economic effect drops from 0.15 with
logged TA to 0.0002 when TA is not logged.

Thanks,

Erasmo

On Wed, Jul 8, 2009 at 4:10 PM, Martin Weiss<martin.weiss1@gmx.de> wrote:
>
> <>
>
>
>
> posted, I could not possibly suggest that it is not correct. What is it,
> though, that you read into the result of this calculation? With this
> information in hand, I _may_ be able to give you a hint whether the strategy
> is valid...
>
>
>
> 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 15:44
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: AW: Economic Significance and Logged Independent Variables
>
> Thanks Martin. Sorry, I think something is not completely clear to me.
> What I am doing to get the economic effect in the case of the logged
> covariate is to multiply the raw coefficient (on the logged covariate)
> by the standard deviation of the logged covariate. Are you suggesting
> that this is not correct?
>
> Thanks,
>
> Erasmo
>
> On Wed, Jul 8, 2009 at 3:19 PM, Martin Weiss<martin.weiss1@gmx.de> wrote:
>>
>> <>
>>
>> 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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