Hi,
Many thanks. So, for the DF tests on the original variables, the Engle-Granger uses the smallest available sample size. I understand the argument and it seems to be the strongest one. However, considering that the ultimate goal is to identify unit roots in the variables, it also could be argued that using all the available information is better than just using a part of it; It's true, the tests will not be strictly comparable, but the goal is not to compare them; what the practitioner should do is to ensure that the ADF tests correctly rejects/does not reject the null. Anyway, that's not the main issue: suppose you use the Engle-Granger test and include constant term and trend for the ADF tests on the variables. It turns out that the specification of the cointegration equation  includes exactly the same deterministic components. It's quite easy to imagine a number of data-generating processes for, say, x_t and y_t, that do not fit the model used by GRETL: x_{t}=m+x_{t-1}+u_{t} (unit root with drift, i.e. deterministic trend); y_{t}=a+b*x_{t}+w_{t} with w_t~I(0). To test for the unit root in x, you need to include constant term and trend; the same goes for y, since it includes x. Nevertheless, the cointegration equation does not have trend. Maybe I am missing something really obvious (and I'm sorry if that's the case), but I think you should be able to decide, as a separate option, what deterministic elements should be included in the ADF tests and in the cointegration equation.
Friendly,
Daniel

From: Sven Schreiber <svetosch@gmx.net>
To: gretl-users@lists.wfu.edu
Sent: Tuesday, May 8, 2012 4:52 AM
Subject: Re: [Gretl-users] issues with the DF/EG tests

Hi,

to make the results strictly comparable the same sample should arguably
be used, and that's what gretl does.

OLS residuals have mean zero by construction and deterministics do not
make sense there (modulo some initial-value problems if you do not use
the same sample, but that's not what gretl does as we have just discussed).

Hope I understood your questions correctly,

cheers,
sven

Am 08.05.2012 02:27, schrieb Daniel Ventosa S.:
> Hello,
> I am teaching a basic course in Econometrics, and, as usual, I use Gretl
> for all empirical applications. A week ago, a couple of students
> (Alejandra Pérez and Natividad Aguilera) discovered something weird when
> using the DF test in the residuals or the Engle-Granger test. They know
> that, although the test is the same, critical are not. Anyway, the value
> of the t-ratio should be the same whether you use the EG option or do
> the test by yourself using the DF-test. They showed to me their example
> and I think they might be right. In their own words:
> "Dear Sir or Madam,
> We have some points that we would like to have clarified about the
> Engle-Granger cointegration test (coint ) and the Augmented
> Dickey-Fuller test (adf ) using two variables.
> First, in the coint test, there is an option to allow Gretl to determine
> the number of lags of the dependent variable used in the adf test (from
> a maximum number of lags established by the user) and in the first step
> it reduces the sample according to this. Then the same sample is used to
> run the adf test on the other variable. Why Gretl does not use a sample
> according to the significant lags in each case/variable as if it were
> doing the adf test individually?
> Second, once the sample is reduced in the first step, the ADFperformed
> on residuals (second step) is done with the same reduced sample.
> Inference is not drawn using the original sample size. Why?
> Third, when we run the coint test it is not possible to do the test for
> the residuals with different deterministic components. However, it is
> possible that the variables with unitary root have a tendency and the
> residuals series not. Why is it not possible to select different
> deterministic components for initial adf test and the adf test on the
> residuals?
> Thank you for your attention to this message.
> Yours faithfully,
> Natividad Aguilera, economic’s master student from University of
> Guanajuato (UG) &
> Alejandra Pérez, economic’s undergraduate student from Center for
> Reseach and Teaching in Economics (CIDE)."
> Many thanks for your attention. You can corroborate this using any pair
> of time series (the number of lags must be fixed for both variables, the
> ADF and the EG).
> Friendly Daniel
>
>
>
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> Gretl-users@lists.wfu.edu
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