2:02 a.m.
How is the LM test calculated for Gretl for just a standard model.
I just ran a model
Model 5: OLS, using observations 1-2017
Dependent variable: nettfa
coefficient std. error t-ratio p-value
---------------------------------------------------------
const -20.9850 2.47202 -8.489 3.98e-017 ***
inc 0.770583 0.0614520 12.54 8.73e-035 ***
age25 0.0251267 0.00259339 9.689 9.96e-022 ***
male 2.47793 2.04778 1.210 0.2264
e401k 6.88622 2.12327 3.243 0.0012 ***
Mean dependent var 13.59498 S.D. dependent var 47.59058
Sum squared resid 3982124 S.E. of regression 44.48805
R-squared 0.127868 Adjusted R-squared 0.126134
F(4, 2012) 73.74763 P-value(F) 2.18e-58
Log-likelihood -10514.46 Akaike criterion 21038.91
Schwarz criterion 21066.96 Hannan-Quinn 21049.21
When I save the residuals squared to run the Pagan test I get this
Model 6: OLS, using observations 1-2017
Dependent variable: usq5
Coefficient
Std. Error
t-ratio
p-value
const
-4573.55
1848.7
-2.4739
0.01345
**
inc
112.358
45.9568
2.4449
0.01458
**
age25
4.84866
1.93946
2.5000
0.01250
**
male
2331.25
1531.43
1.5223
0.12810
e401k
1164.83
1587.89
0.7336
0.46330
Mean dependent var
1974.280
S.D. dependent var
33367.52
Sum squared resid
2.23e+12
S.E. of regression
33270.33
R-squared
0.007789
Adjusted R-squared
0.005817
F(4, 2012)
3.948695
P-value(F)
0.003387
Log-likelihood
-23861.35
Akaike criterion
47732.70
Schwarz criterion
47760.75
Hannan-Quinn
47742.99
The LM test from my understanding is n*r^2, which here would be 15.71
Using gretl's built in test I get the following:
Breusch-Pagan test for heteroskedasticity
OLS, using observations 1-2017
Dependent variable: scaled uhat^2
coefficient std. error t-ratio p-value
--------------------------------------------------------
const -2.31657 0.936391 -2.474 0.0134 **
inc 0.0569109 0.0232777 2.445 0.0146 **
age25 0.00245591 0.000982363 2.500 0.0125 **
male 1.18081 0.775689 1.522 0.1281
e401k 0.590001 0.804287 0.7336 0.4633
Explained sum of squares = 4485.49
Test statistic: LM = 2242.746588,
with p-value = P(Chi-square(4) > 2242.746588) = 0.000000
How did the LM test become so big for this model?
10:30 a.m.
On Thu, 14 Nov 2013, Mark wrote:
How is the LM test calculated for Gretl for just a standard model.
The Breusch-Pagan LM test for heteroskedasticity is calculated as per the
authors' 1979 Econometrica article (vol. 47, no. 5). That is, it is one
half of the explained sum of squares from a regression of the squared
residuals from the original OLS model, scaled by the MLE of the error
variance, on the original regressors.
Manual computation of the test statistic would look like this:
<hansl>
ols y const X
series u2 = $uhat^2
scalar sigma2 = $ess/$T
series g = u2/sigma2
ols g const X
scalar RSS = sst(g) - $ess
scalar LM = 0.5 * RSS
</hansl>
Allin Cottrell
10:40 a.m.
Thanks! I am teaching this in my next MBA Stats class, so I am going to use your script as
an example (with proper citation of course).
Cheers!
Logan
-----Original Message-----
From: gretl-users-bounces(a)lists.wfu.edu [mailto:gretl-users-bounces@lists.wfu.edu] On
Behalf Of Allin Cottrell
Sent: Thursday, November 14, 2013 9:31 AM
To: Gretl list
Subject: Re: [Gretl-users] LM Test
On Thu, 14 Nov 2013, Mark wrote:
How is the LM test calculated for Gretl for just a standard model.
The Breusch-Pagan LM test for heteroskedasticity is calculated as per the authors'
1979 Econometrica article (vol. 47, no. 5). That is, it is one half of the explained sum
of squares from a regression of the squared residuals from the original OLS model, scaled
by the MLE of the error variance, on the original regressors.
Manual computation of the test statistic would look like this:
<hansl>
ols y const X
series u2 = $uhat^2
scalar sigma2 = $ess/$T
series g = u2/sigma2
ols g const X
scalar RSS = sst(g) - $ess
scalar LM = 0.5 * RSS
</hansl>
Allin Cottrell
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11:05 a.m.
Hi,
the version of the test that Mark computed is the same version discussed
by Wooldridge (2013) under the header of Breusch-Pagan test.
But this form of the test was suggested by Koenker (1981)
and it is a generalization of the heteroskedasticity test proposed by
Breusch and Pagan (1979).
The original Breusch-Pagan LM test (the one computed using the
hettest command in Stata and the gretl built-in command) is less general
as it requires normality of the errors.
The two tests can have different outcomes.
See you
Giuseppe
O
n Thu, 2013-11-14 at 15:30 +0000, Allin Cottrell wrote:
> How is the LM test calculated for Gretl for just a standard model.
The Breusch-Pagan LM test for heteroskedasticity is calculated as per the
authors' 1979 Econometrica article (vol. 47, no. 5). That is, it is one
half of the explained sum of squares from a regression of the squared
residuals from the original OLS model, scaled by the MLE of the error
variance, on the original regressors.
Manual computation of the test statistic would look like this:
<hansl>
ols y const X
series u2 = $uhat^2
scalar sigma2 = $ess/$T
series g = u2/sigma2
ols g const X
scalar RSS = sst(g) - $ess
scalar LM = 0.5 * RSS
</hansl>
Allin Cottrell
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
11:28 a.m.
On Thu, 14 Nov 2013, Giuseppe Vittucci wrote:
Hi,
the version of the test that Mark computed is the same version discussed
by Wooldridge (2013) under the header of Breusch-Pagan test.
But this form of the test was suggested by Koenker (1981)
and it is a generalization of the heteroskedasticity test proposed by
Breusch and Pagan (1979).
The original Breusch-Pagan LM test (the one computed using the
hettest command in Stata and the gretl built-in command) is less general
as it requires normality of the errors.
But note also that gretl implements Koenker's robust variant of the 1979
B-P test (you add the --robust option to modtest --breusch-pagan).
Allin
11:53 a.m.
On Thu, 14 Nov 2013, Giuseppe Vittucci wrote:
> Hi,
>
> the version of the test that Mark computed is the same version discussed
> by Wooldridge (2013) under the header of Breusch-Pagan test.
>
> But this form of the test was suggested by Koenker (1981)
> and it is a generalization of the heteroskedasticity test proposed by
> Breusch and Pagan (1979).
>
> The original Breusch-Pagan LM test (the one computed using the
> hettest command in Stata and the gretl built-in command) is less general
> as it requires normality of the errors.
But note also that gretl implements Koenker's robust variant of the 1979
B-P test (you add the --robust option to modtest --breusch-pagan).
Touché ;-)
Giuseppe
Allin
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5 comments
4 participants
participants (4)
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Allin Cottrell -
Giuseppe Vittucci -
Logan Kelly -
Mark