st: RE: Re: RE: Fixed-effects, unbalanced panel and time-invariant variable

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

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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