Thank you, Mark, your explanations are very clear and useful. Barbara.
-----Message d'origine-----
De : owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] De la part de Schaffer, Mark E
Envoyé : jeudi 19 octobre 2006 15:25
À : statalist@hsphsun2.harvard.edu
Objet : st: RE: Re: RE: Fixed-effects, unbalanced panel and time-invariant variable
Barbara,
I think the problem you face comes down to the implication of failing the Hausman fe-vs.-re test.
The FE estimator uses only the orthogonality conditions that the regressors are uncorrelated with the idiosyncratic error e_ij.
The RE estimator uses these, plus the orthogonality condition that the regressors are also uncorrelated with the shared group error u_j.
The null of the Hausman test is that both sets of orthogonality conditions are valid. The usual interpretation of a failure of the Hausman test is that the regressors are uncorrelated with e_ij (maintained under the null and alternative) but correlated with u_j (used by RE).
The FE estimator is able to get consistent estimates for coeffs on time-varying variables because the within transformation wipes out the u_j, but of course this also wipes out the time-invariant variables.
If I understand the situation correctly, there are two ways around the problem.
First, the correlation of the u_j might not involve the TI variables. This is the FE+BE suggestion of Rodrigo (I think - hopefully he'll correct me if I'm wrong). FE gets you consistent coeffs on the TV variables, and BE gets you consistent coeffs on the TI variables. ...But only if you're willing to believe that E(x u_j)=0 for all the TI xs.
Second, you can use IV if you have instruments that are correlated with the TI variables and not with the u_j.
I am not sure I understand your reference to xthtayor and "no endogenous variables". The failure of the Hausman test suggests that some regressors are correlated with the u_j; this makes them endogenous by definition.
HTH.
Cheers,
Mark
________________________________
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of PETITT Barbara
Sent: Wednesday, October 18, 2006 8:40 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: Re: RE: Fixed-effects, unbalanced panel and time-invariant variable
Thanks for your feedback. In fact, I think there are two problems. The first one is to find a way to estimate the coefficient for TI variables when xtreg, re is not an option (the Hausman test is
rejected) and when I do not think xthtaylor is an option either (no endogenous variables). I like the idea of xtfevd, but there is a problem with the standard errors and so far, I am not sure where the problem comes from.
The second problem is whether the fact that it is an unbalanced panel creates a potential bias vs if it were a balanced panel.
I guess the other issue is that I am new to Stata. I tried to run your example, but could not manage T2+T3 as when I get to "predict aux1, r", I get the error message "option r not allowed".
Last, if I may, would xtgee be an option as well? Thanks.
Barbara.
________________________________
From: owner-statalist@hsphsun2.harvard.edu on behalf of Rodrigo A. Alfaro
Sent: Tue 10/17/2006 6:11 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Re: RE: Fixed-effects, unbalanced panel and time-invariant variable
Dear Mark,
RE estimation is more restrictive than the current FE+BE. For RE we need
that time variant (TV) and time invariant (TI) variables have to be
uncorrelated with the cross sectional unobservable (u_i)), if the assumption
if false the TV and TI estimates are inconsistent. But for this procedure
(FE+BE) only TI estimates will be inconsistent (Hsiao 2003, page 52-53). Of
course under not correlation RE is more efficient. The following example
show you the 3 methods: FE+BE, RE and LS.
In T1 we have the xtfevd output, T2+T3 the FE+BE without any adjustment (the
constant is added to T3 therefore the constant in T2 is irrelevant). T4 is
GLS RE, T5 is the LS and T6 is MLE RE. It seems that std errors fot TI in T1
are too much small in compare with other methods, maybe there is a typo in
the ado-file. T2+T3 give us a more reliable result that we can compare with
T4, T5 and T6. Look fem estimate (gender dummy), GLS RE is similar to LS
even that 75% of the total variance is explained by u_i. For T6 the results
are close to FE in the case of coef but very different in the std error of
TI... any idea?
Best, Rodrigo.
/******************** Example **************************************/
qui {
webuse psidextract
tsset id t
xtfevd lwage wks south smsa ms exp exp2 occ ind union fem blk ed,
invariant(fem blk ed)
est store T1
xtreg lwage wks south smsa ms exp exp2 occ ind union, fe
est store T2
predict aux1, r
bysort id: egen aux2=mean(aux1)
replace aux2=aux2+_b[_cons]
reg aux2 fem blk ed
est store T3
xtreg lwage wks south smsa ms exp exp2 occ ind union fem blk ed, re
est store T4
reg lwage wks south smsa ms exp exp2 occ ind union fem blk ed, re
est store T5
xtreg lwage wks south smsa ms exp exp2 occ ind union fem blk ed, mle
est store T6
}
est table T*, se
/******************** Example **************************************/
----- Original Message -----
From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, October 17, 2006 11:12 AM
Subject: st: RE: Fixed-effects, unbalanced panel and time-invariant variable
Barbara,
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> PETITT Barbara
> Sent: 17 October 2006 14:47
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Fixed-effects, unbalanced panel and
> time-invariant variable
>
> Hello,
>
> I have an unbalanced panel (for some firms, I have three
> years of data, for others, two years or even only one year).
> One of my independent variables is a time-invariant variable
> and with fixed-effects models, its gets dropped. I
> contemplated using the fixed effects vector decomposition
> (xtfevd), but does it work for unbalanced panel?
> Otherwise, is there any alternative?
Maybe I am missing something obvious, but why won't the standard random
effects estimator work for you? -xtreg,re- etc.
--Mark
Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
> Thank you.
>
> Barbara.
>
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