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Re: st: AKAIKE formula


From   Paulo Regis <pauloregis.ar@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: AKAIKE formula
Date   Tue, 13 Apr 2010 17:14:54 +0800

Ok, i got the main point.

Now, what if the issue involves nested models in a panel. Model A:

Y = B X + e

Then, we have the "nested" model B

Y = B X +c Y(-1) + e

if Y(-1) were any variable, no problem: the t-statistic. However,
there is endogeneity and now i have that i need to use IV. That is the
reason I wanted to use AIC.

Actually, I made the two mdoels very simple. I add other variables in
addition to Y(-1) so I should look at the F-statistic or a fit
measure.

Kind Regards

Paulo


On Tue, Apr 13, 2010 at 4:06 PM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- On Tue, 13/4/10, Paulo Regis wrote:
>> I have a question about Akaike Info Criterion. Stata
>> calculates aic (using "estac ic" after the regression
>> command) with the formula:
>>
>> AIC = -2 * log (likelihood) + 2 * (k+1)  ;  k=
>> number of parameters
>>
>>
>> In the linear regression model, this is similar to use the
>> formula:
>>
>> AIC = n*ln(RSS/n) +2*(k+1),   RSS = residuals SS
>>
>> This was addressed before in this list by the following
>> post:
>>
>> http://www.stata.com/statalist/archive/2003-09/msg00365.html
>>
>> However, my problem is that I want to compare OLS with IV
>> models using AKAIKE. The command "estac ic" is not available
>> for -ivreg. Can I compute the AIC by myself using the second
>> formula?
>
> The logic behind this is that in a linear regression the
> log likelihood is a function of the RSS. So, you would need
> to argue that in -ivreg- the likelihood would need to derive
> the likelihood of your model and show that it is a similar
> function of the RSS. I haven't done so, but I am doubtful
> that that is the case.
>
> Moreover, differences in fit statistic are not a good way of
> choosing between an IV model and an non-IV model like -regress-.
> The whole point of IV models, as I understand them, is that
> you believe some of the association between a variable of
> interest x and the dependent variable y is spurious, and you
> use instrumental variables to throw away the spurious
> association and (hopefully) keep the "real" association. A
> fit statistic cannot distinguish between "real" and "spurious"
> association, so a non-IV model should "fit" better because it
> doesn't throw the spurious part of the association away. So,
> differences in fit statistic cannot help you in choosing
> between these models, at best they tell you how much
> information is being thrown away by the IV method, but since
> throwing away information is the whole point of IV methods
> (because you have a theory that this information is "bad"),
> that does not help much.
>
> -- Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> --------------------------
>
>
>
>
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