# [Gretl-users] Heteroskedasticity / correction

Riccardo (Jack) Lucchetti r.lucchetti at univpm.it
Fri Jan 10 13:12:19 EST 2014

```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
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 ***

Test statistic: TR^2 = 24.309362,
with p-value = P(Chi-square(1) > 24.309362) = 0.000001
</output>

-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)

Università Politecnica delle Marche
(formerly known as Università di Ancona)

r.lucchetti at univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
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