# [Gretl-users] White's test for heteroskedasticity (GUI)

Henrique henrique.coelho at gmail.com
Thu Jun 18 00:19:58 EDT 2009

```> On Wed, 17 Jun 2009, Sven Schreiber wrote:
> > I don't quite see why the current behavior would be confusing. But maybe
> > I didn't understand what you expected instead.

Let's suppose I've estimated a model like this:

EQUATION 1:     Y = const + beta_1*X1 + beta_2*X2 + u

If we perform "White's test for heteroskedasticity" Gretl will
estimate the following equation:

EQUATION 2:     uhat^2 = const + alfa_1*X1 + alfa_2*X2 + alfa_3*sq_X1
+ alfa_4*sq_X2 + alfa_5*X1*X2

And if we perform "White's test for heteroskedasticity (squared only)"
Gretl will estimate the
following equation:

EQUATION 3:     uhat^2 = const + alfa_1*X1 + alfa_2*X2 + alfa_3*sq_X1
+ alfa_4*sq_X2

The last term of "equation 2", the cross-product, can only exist if we
have more than one
non-constant regressor, ok? So, if we have a model with just one
non-constant regressor,
like this:

EQUATION 4:     Y = const + beta_1*X1 + u

In that case I think it's impossible to perform "White's test for
heteroskedasticity" because
in that test we need the cross-product term.

> On Wed, 18 Jun 2009, Allin wrote
> My original thought on reading Henrique's message was this: if you
> have estimated a model with only one non-constant regressor, then
> cross-products are not applicable, so it might be confusing to
> be faced with a choice of two versions of White's test (regular,
> and "squares only"), as in the Tests menu in the model window.

Yes, this is what I thought.

> My solution was to disable the "squares only" option in this case
> since it is redundant.

I disagree. I suppose that the best solution is to disable "White's
test for heteroskedasticity"
(the regular version), because in the "one non-constant regressor"
case we just can perform
the "White's test for heteroskedasticity (squared only)".

> But looking again at the bit of Henrique's message quoted above,
> I'm not so sure: he says, "Gretl shows me _only_ the "White's test
> for heteroskedasticity (squared only)" [emphasis added].

In the Tests menu the two versions of White's test appears. But when I
perform them Gretl
shows the same information to me. It is something like this:

I'd estimated "EQUATION 4" (presented above) and now I want to test
for heteroskedasticity using
White's test. I now that the only possible version of the test that I
can use is the "White's test for
heteroskedasticity (squared only)", because I have only non-constant
regressor, ok?

But if I try to perform the two versions of the White's test anyway,
Gretl prints only one in the
model window. The problem is that Gretl prints "White's test for
heteroskedasticity" (in the title)
and shows the results of the "White's test for heteroskedasticity
(squared only)".

I hope I could be clearer now :)

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