Re: Re: st: information criterions after -xtreg, re-

["Filippo Maria D'Arcangelo" <filippo.darcangelo@unibocconi.it>]

Hi Alfonso,

thank you very much. I'd prefer to use -xtreg, re- to calculate my s.e. because of some assumptions on my error distribution.
If I understood it correctly, I can perform the FGLS estimation of my random effect model, while computing the likelihood by estimating the (equivalent) ML model. 
In case the estimates of coefficients differ from -re- and -mle- I should suspect that something is going on and probably refuse to use the AIC calculated by ML for choosing between FGLS models.
I hope it makes sense.
My doubts originated from the fact that Stata stores log-likelihood after many least-squares estimations (such as after -regress-), and I wondered why it was not the case with -xtreg, re-.

f.

>Hi Filippo,
>
>If you want to estimate random effects -xtreg, mle- does that using maximum likelihood. -xtreg, re- uses feasible GLS 
>to do the random effects estimation. In many cases the maximum likelihood is more efficient and iterated FGLS 
>converges to the maximum likelihood estimate. I say many cases because this doesn't always hold. So if you're 
>interested in a comparison criterion for different random effects models you can always estimate them with -mle- and 
>use AIC. You can always check how close your estimates of the coefficients are between a -re-and an -mle- estimation 
>by running both.
>
>Best,
>
>Alfonso Sanchez-Penalver

>> On Jan 22, 2014, at 5:40 AM, "Filippo Maria D'Arcangelo" <filippo.darcangelo@unibocconi.it> wrote:
>> 
>> Dear statlisters,
>> 
>> I have a panel dataset and I am running a set of regressions.
>> They are "nested", in the sense of Wooldridge(2005), i.e. the covariates varies incrementally from a simpler model to a more "rich" one.
>> For this purpose, I am using -xtreg, re-, assuming random effects toward the panel groups.
>> I want to compare the regressions, using some sort of (not too fancy) criterion.
>> 
>> I know that a useful criterion could be Akaike's Information Criterion (AIC). I am also aware that there are a few alternatives, mostly relying on Kullback–Leibler divergence, which in turns (to the extent of my limited knowledge) relies on a likelihood calculation.  
>> 
>> However, -xtreg, re- does not store any likelihood measure (and therefore, no AIC). 
>> Other options of -xtreg- do have this feature (e.g. [, fe] and definitely [, mle]).
>> Is there any theoretical reason for the likelihood not to be calculated after a random effect regression?
>> 
>> Should I use something different instead, such as a goodness-to-fit criterion, i.e. adjusted-R^2? If yes, does anybody of you knows how to correct determine this parameter (adj-R^2) for panel data?
>> Thank you,
>> 
>> 
>> Filippo Maria D'Arcangelo
>> 
>> 
>> Reference: Wooldridge, Jeffrey M. (2005) "Introductory Econometrics. A Modern Approach". p. 193

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