Re: [Gretl-users] Heteroskedasticity / correction
On Fri, 10 Jan 2014, Ana Amaro ISG wrote:
Hi everyone
I need some help on this topic:
1- simple model one regressor (x)
2- error is heteroskedastic (and residual analysis shows that the error variance
increases with x variable)
3- rerun the analysis dividing both model members by the sqrt(x) - no constant
Eviews runs the white test with a constant
Gretl runs the white test with no constant!
The decision is, of course, different.
Which software is doing it the right way? Eviews, right?
Uhm, this is not what I'm seeing here.
<hansl>
nulldata 100
set seed 987
x = normal()
e = normal() * sqrt(1 + x^2)
y = x + e
ols y x
modtest --white
</hansl>
Of course, generating data which _does_ contain heterskedasticity is
totally irrelevant here: if I understand the point correctly, the issue
here is on whether a constant should be present or not in the auxiliary
regression for the White test. And the answer is: yes, the constant should
be there. And that's what gretl does:
<output>
? ols y x
Model 1: OLS, using observations 1-100
Dependent variable: y
coefficient std. error t-ratio p-value
--------------------------------------------------------
x 0.955352 0.128086 7.459 3.40e-11 ***
Mean dependent var 0.340859 S.D. dependent var 1.747793
Sum squared resid 201.0589 S.E. of regression 1.425096
R-squared 0.359770 Adjusted R-squared 0.359770
F(1, 99) 55.63201 P-value(F) 3.40e-11
Log-likelihood −176.8152 Akaike criterion 355.6305
Schwarz criterion 358.2357 Hannan-Quinn 356.6849
? modtest --white
White's test for heteroskedasticity
OLS, using observations 1-100
Dependent variable: uhat^2
coefficient std. error t-ratio p-value
--------------------------------------------------------
x −0.103511 0.315278 −0.3283 0.7434
sq_x 0.798762 0.152451 5.239 9.24e-07 ***
Unadjusted R-squared = 0.243094
Test statistic: TR^2 = 24.309362,
with p-value = P(Chi-square(1) > 24.309362) = 0.000001
</output>
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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