4:43 p.m.
I am doing a panel-data exercise from Greene (5th. ed. ) exercise 13.1
Why do I get precisely the same estimates in pooled OLS as in the
random-effects panel model?
Best regards
Helgi Tomasson
The data is below.
I get the following
Model 2: Random-effects (GLS), using 30 observations
Included 3 cross-sectional units
Time-series length = 10
Dependent variable: y
coefficient std. error t-ratio p-value
--------------------------------------------------------
const −0.747476 0.955953 −0.7819 0.4408
x 1.05896 0.0586557 18.05 5.84e-17 ***
Mean dependent var 15.09667 S.D. dependent var 7.252441
Sum squared resid 120.6687 S.E. of regression 2.039850
Log-likelihood −63.44593 Akaike criterion 130.8919
Schwarz criterion 133.6942 Hannan-Quinn 131.7884
'Within' variance = 3.0455
'Between' variance = 0.113088
theta used for quasi-demeaning = 0
GRETL gives me precicel the same answer on pooled-estimate and on
randome-effects estimate. I have done this exercise before with an older
vers
i t y x
1 1 13.32 12.85
2 1 20.30 22.93
3 1 8.85 8.65
1 2 26.30 25.69
2 2 17.47 17.96
3 2 19.60 16.55
1 3 2.62 5.48
2 3 9.31 9.16
3 3 3.87 1.47
1 4 14.94 13.79
2 4 18.01 18.73
3 4 24.19 24.91
1 5 15.80 15.41
2 5 7.63 11.31
3 5 3.99 5.01
1 6 12.20 12.59
2 6 19.84 21.15
3 6 5.73 8.34
1 7 14.93 16.64
2 7 13.76 16.13
3 7 26.68 22.70
1 8 29.82 26.45
2 8 10.00 11.61
3 8 11.49 8.36
1 9 20.32 19.64
2 9 19.51 19.55
3 9 18.49 15.44
1 10 4.77 5.43
2 10 18.32 17.06
3 10 20.84 17.87
6:10 p.m.
On Thu, 16 Feb 2012, Helgi Tomasson wrote:
I am doing a panel-data exercise from Greene (5th. ed. ) exercise
13.1
Why do I get precisely the same estimates in pooled OLS as in the
random-effects panel model?
Here's the answer to your question
'Within' variance = 3.0455
'Between' variance = 0.113088
theta used for quasi-demeaning = 0
In finite samples, it may well happen that the estimate for theta goes
outside its 'natural' limits (the 0-1 interval), in which case it's force
d to 0. See any textbook for details (eg Greene --- used to be section
13.4 in the 5th edition, don't known in more recent versions).
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
7 p.m.
On Thu, 16 Feb 2012, Riccardo (Jack) Lucchetti wrote:
On Thu, 16 Feb 2012, Helgi Tomasson wrote:
> I am doing a panel-data exercise from Greene (5th. ed. ) exercise 13.1
> Why do I get precisely the same estimates in pooled OLS as in the
> random-effects panel model?
Here's the answer to your question
> 'Within' variance = 3.0455
> 'Between' variance = 0.113088
> theta used for quasi-demeaning = 0
In finite samples, it may well happen that the estimate for theta goes
outside its 'natural' limits (the 0-1 interval), in which case it's force d
to 0. See any textbook for details (eg Greene --- used to be section 13.4 in
the 5th edition, don't known in more recent versions).
Footnote: stata's "xtreg" command produces the same result as
gretl on the data Helgi posted, for the random effects model.
Allin Cottrell
10:49 a.m.
Of course it is a question of how Omega is calculated. The R-program
offers the following options:
plm(y~x,data=datap,model="random",random.method="nerlove")
Model Formula: y ~ x
Coefficients:
(Intercept) x
-1.3212 1.0973
plm(y~x,data=datap,model="random",random.method="walhus")
Model Formula: y ~ x
Coefficients:
(Intercept) x
-1.2388 1.0918
plm(y~x,data=datap,model="random",random.method="amemiya")
Model Formula: y ~ x
Coefficients:
(Intercept) x
-1.2534 1.0928
plm(y~x,data=datap,model="random",random.method="swar")
Error in
swar(object, data, effect) :
the estimated variance of the individual effect is negative
My own programming in R of the formulas in Greene (edition 5) gives
-1.262934 1.09341
My estimate of var(beta) is 0.002613184, whereas the R-alternatives give
0.002514221, 0.002653728, 0.00262924.
Of these, only the first (Nerlove's method of calculating Omega) will
give a positive Hausman test statistic.
Some years ago I had my students do this exercise in GRETL. Then GRETL
gave results that were very similar to mine, except that GRETL gave a
positive Hausman statistic. I suspect that sometimes in the last couple
of years GRETL has gone from estimating Omega with one of
Nerlove/Walus/Amemiya to SWAR (the R default).
Is it possible to choose a method for calculating Omega in GRETL?
best regards
Helgi Tomasson
On Thu, 2012-02-16 at 14:00 -0500, Allin Cottrell wrote:
On Thu, 16 Feb 2012, Riccardo (Jack) Lucchetti wrote:
> On Thu, 16 Feb 2012, Helgi Tomasson wrote:
>
>> I am doing a panel-data exercise from Greene (5th. ed. ) exercise 13.1
>> Why do I get precisely the same estimates in pooled OLS as in the
>> random-effects panel model?
>
> Here's the answer to your question
>
>> 'Within' variance = 3.0455
>> 'Between' variance = 0.113088
>> theta used for quasi-demeaning = 0
>
> In finite samples, it may well happen that the estimate for theta goes
> outside its 'natural' limits (the 0-1 interval), in which case it's
force d
> to 0. See any textbook for details (eg Greene --- used to be section 13.4 in
> the 5th edition, don't known in more recent versions).
Footnote: stata's "xtreg" command produces the same result as
gretl on the data Helgi posted, for the random effects model.
Allin Cottrell
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Gretl-users(a)lists.wfu.edu
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8:37 p.m.
On Fri, 17 Feb 2012, Helgi Tomasson wrote:
Of course it is a question of how Omega is calculated. The R-program
offers the following options [...]
Some years ago I had my students do this exercise in GRETL. Then GRETL
gave results that were very similar to mine, except that GRETL gave a
positive Hausman statistic. I suspect that sometimes in the last couple
of years GRETL has gone from estimating Omega with one of
Nerlove/Walus/Amemiya to SWAR (the R default).
We started out using a different variant, but gretl has used
Swamy-Arora for the last 5+ years.
Is it possible to choose a method for calculating Omega in GRETL?
In CVS and snapshots I've added a --nerlove option for use
with the "panel" command (plus the --random-effects option).
The others are somewhat complicated and, it seems to me,
little used.
Allin Cottrell
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4 comments
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participants (3)
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Allin Cottrell -
Helgi Tomasson -
Riccardo (Jack) Lucchetti