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

 From "Martin Weiss" To Subject AW: st: AW: Economic Significance and Logged Independent Variables Date Wed, 8 Jul 2009 17:40:32 +0200

```<>

Also note that to arrive at beta coefficients (which would square with your
stated aim to arrive at the effects of one standard deviation changes), you
have to scale your product by the sd of the dependent:

*************
sysuse auto, clear

su we
loc sdwe=r(sd)

su pr
loc sdprice=r(sd)
reg we pr len he, beta
di in red /*
*/ "Coeff multiplied by sd / divided" /*
*/ " by sd of dependent: " /*
*/ `=_b[pr]*`sdprice'/`sdwe''

gen lnpr=log(pr)
su lnpr
loc sdlogprice=r(sd)
reg we lnpr len he, beta
di in red /*
*/ "Coeff multiplied by sd / divided" /*
*/ " by sd of dependent: "/*
*/ `=_b[lnpr]*`sdlogprice'/`sdwe''
*************

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 16:29
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: AW: Economic Significance and Logged Independent Variables

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:
>
> <>
>
>
>
initially
> 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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```