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# Re: st: AW: mfx-Elasticity for a dummy variable

 From A Loumiotis To statalist@hsphsun2.harvard.edu Subject Re: st: AW: mfx-Elasticity for a dummy variable Date Thu, 10 Jun 2010 12:11:33 +0300

your model is (correct me if i'm wrong):

ln(y) = a + b ln(x) + c T + dZ + error

The elasticity of y with respect to T is
(dy/y)/(dT/T)=dln(y)/(dT/T)=(dln(y)/dT)/T=c/T.

So, the elasticity of y with respect to T does not depend on the means
of ln(x) and ln(y).  As I said in my previous reply it is equal to the
coefficient of the dummy variable T divided by T (= c / T).  So the
elasticity will be equal to "c"  only if you calculate it at T=1 and
not at the mean of T.  It is your call but you should consider the
drawbacks of computing elasticities with respect to dummy(discrete)
variables.

Antonis

On Wed, Jun 9, 2010 at 6:15 PM, Nyasha Tirivayi <ntirivayi@gmail.com> wrote:
> Dear Antonis and Martin
>
> Thanks for your reply. If you recall my model is as follows:
>
> ln(y) = a + b ln(x) + T + D Z
>
> I intend to calculate elasticity for T at T=1 and at means of ln(x)
> and ln(Y). And if I do that the elasticity is the same as the
> coefficient of T.
>
> Should I proceed with that as the answer?
>
>
> Nyasha Tirivayi
> Maastricht University
>
> On Tue, Jun 8, 2010 at 1:27 PM, A Loumiotis <antonis.loumiotis@gmail.com> wrote:
>> Yes I agree... although one can compute it at the mean point of T
>> which is different from 0 or 1.  But as I said in my first response
>> elasticities with respect to dummy variables have no meaningful
>> interpretation.
>>
>> On Tue, Jun 8, 2010 at 2:18 PM, Martin Weiss <martin.weiss1@gmx.de> wrote:
>>>
>>> <>
>>>
>>> " ...will be the coefficient of the dummy
>>>  variable T divided by the dummy variable itself."
>>>
>>>
>>> I do not get this sentence. The dummy is either 0 or 1, as you said.
>>> Dividing by zero is not permissible, and dividing by one does not change
>>> anything, does it?
>>>
>>>
>>>
>>> HTH
>>> Martin
>>>
>>> -----Ursprüngliche Nachricht-----
>>> Von: owner-statalist@hsphsun2.harvard.edu
>>> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von A Loumiotis
>>> Gesendet: Dienstag, 8. Juni 2010 13:15
>>> An: statalist@hsphsun2.harvard.edu
>>> Betreff: Re: st: AW: mfx-Elasticity for a dummy variable
>>>
>>>  The elasticity of y with respect to the dummy variable in the way that
>>>  you have defined your regression will be the coefficient of the dummy
>>>  variable T divided by the dummy variable itself.
>>>
>>> On Tue, Jun 8, 2010 at 2:05 PM, A Loumiotis <antonis.loumiotis@gmail.com>
>>> wrote:
>>>> Nyasha,
>>>>
>>>> The elasticity of y with respect to the dummy variable in the way that
>>>> you have defined your regression will be the coefficient of the dummy
>>>> variable T times the dummy variable itself.  If you calculate it at
>>>> the mean point of T then it will be different from the coefficient of
>>>> the dummy variable.  If you calculate it at T=1, it will be the same.
>>>>
>>>> However elasticities with respect to dummy variables have no
>>>> meaningful interpretation because the dummy variable changes in a
>>>> discrete fashion (from 0 to 1).
>>>>
>>>> Antonis Loumiotis
>>>>
>>>> On Mon, Jun 7, 2010 at 6:24 PM, Nyasha Tirivayi <ntirivayi@gmail.com>
>>> wrote:
>>>>> Dear Martin
>>>>>
>>>>> Thanks for the code. Now the results are different. I was using the
>>>>> wrong code i.e mfx , dyex at(mean) instead of mfx compute,
>>>>> varlist(logweight) dyex at(mean).
>>>>>
>>>>> Regards
>>>>>
>>>>> Nyasha Tirivayi
>>>>> Maastricht University
>>>>>
>>>>>
>>>>>
>>>>> On Mon, Jun 7, 2010 at 9:16 AM, Martin Weiss <martin.weiss1@gmx.de>
>>> wrote:
>>>>>>
>>>>>> <>
>>>>>>
>>>>>> What is the difference of your example to this one - where the marginal
>>>>>> effects do seem to change:
>>>>>>
>>>>>>
>>>>>> *************
>>>>>> sysuse auto, clear
>>>>>> gen logprice=log(price)
>>>>>> gen logweight=log(weight)
>>>>>> reg logprice length logweight foreign
>>>>>> mfx compute, varlist(logweight) dydx at(mean)
>>>>>> mfx compute, varlist(logweight) eyex at(mean)
>>>>>> mfx compute, varlist(logweight) dyex at(mean)
>>>>>> mfx compute, varlist(logweight) eydx at(mean)
>>>>>> *************
>>>>>>
>>>>>>
>>>>>>
>>>>>> HTH
>>>>>> Martin
>>>>>>
>>>>>> -----Ursprüngliche Nachricht-----
>>>>>> Von: owner-statalist@hsphsun2.harvard.edu
>>>>>> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Nyasha
>>> Tirivayi
>>>>>> Gesendet: Montag, 7. Juni 2010 02:50
>>>>>> An: statalist@hsphsun2.harvard.edu
>>>>>> Betreff: st: mfx-Elasticity for a dummy variable
>>>>>>
>>>>>> Dear All
>>>>>>
>>>>>> I am trying to estimate elasticity for a dummy explanatory variable in
>>>>>> the following model
>>>>>>
>>>>>> ln(y) = a + b ln(x) + T + D Z
>>>>>>
>>>>>>
>>>>>>
>>>>>> I am interested in calculating the elasticity for T a dummy variable
>>>>>> for a "treatment". What is the formula in stata? Is it mfx,dy/dx or
>>>>>> mfx,dyex?
>>>>>>
>>>>>>
>>>>>>
>>>>>> I have done mfx,dyex and the result still remains the coefficient for
>>>>>> T. Could it be that simple? Or there is another way ?
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> Nyasha Tirivayi
>>>>>>
>>>>>> Maastricht University
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