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 _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users

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(a)gmx.net&gt; *To:* gretl-users(a)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 > > > > _______________________________________________ > Gretl-users mailing list > Gretl-users(a)lists.wfu.edu <mailto:Gretl-users@lists.wfu.edu> > http://lists.wfu.edu/mailman/listinfo/gretl-users _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu <mailto:Gretl-users@lists.wfu.edu> http://lists.wfu.edu/mailman/listinfo/gretl-users _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users

Count me as one such! The Engle-Granger test regressions are not rocket science and if one wants to do something non-standard that's fine, but there's little point in larding the "coint" command with additional options.

slightly modifies the critical values. Curiously enough, including the trend in the cointegrated equation also modifies the critical values of the DF test on the residuals (i.e., according to my simulation, both sets of simulated CV are different to the EG critical values).

2.- I agree with Riccardo (Jack) that if the outcome of the test changes when a few observations are removed, then the test is not quite reliable. But that was not my argument. If you have 120 obs, why should we only use 90 obs. to draw inference? Sven said that getting the same sample sizes for all the variables would make possible a comparison between the ADF tests. I would rather say that the main point of doing ADF tests to the observed variables is to be sure that the variables are I(1), and not to compare the tests. It's always better to draw inference using all the available information.

3.- Allin said the test cannot be considered as rocket science and I agree. That said, it remains an option in Gretl, next to the Johansen test. The latter allows the user to include/remove deterministic elements in the cointegrating vector. Why would that not be possible with the EG?