hi. i believe that you can use this method for your estimation.

Strictly speaking, the Pedroni tests investigate whether there is cointegration or not, but does not provide an estimate for the long run. This is done in a second step, where you use Panel FMOLS, Panel DOLS etc.

For the cointegration result (first step), stationary variables do not play a role, as they cannot include the same stochastic trend as the I(1) variables, by definition. But I tend to consider them, at least in the estimation of the cointegration vector (second step) as you might get more efficient estimates of the long run parameters, i.e. the coefficients of the I(1) variables. 

Dear Prof Christian Dreger,

Thank you very much for your respone. Which method do you think is the most appropriate for cointegration in this case?

Given you have a panel, you could apply the Westerlund tests, see below. Of course, you can test for cointegration between the two I(1) variables. Alternatively, you can also test for cointegration between the 4 variables. In fact, the stationary variables might be seen to be part of the short run dynamics and therefore, cointegration can be analysed in a more efficient way. So, the stationary variables might be embedded in the VAR, but not in the long run vector. 

I would prefer the Westerlund test. The Pedroni tests are based on the residuals obtained from a static relationship. Simulation studies have shown that  residual based tests have less power compared to those based on a dynamic model. Moreover, you can account for cross section correlation in the Westerlund approach rather easily,  since it is an option in the STATA program available for this task. 

Thank you very much Prof Christian Dreger.

Thank you Rajesh Sharma and Ali Adeli for your answers.

Dear Prof Dreger,

Thanks I have also learned a little more from your response to Pavlos. Would it be possible to understand either by another reference (research paper/book) or possibly your explain a little more on the following statement (particularly "short run dynamics" and "embedded in VAR but not in long run vector")  given in your answer above?

"In fact, the stationary variables might be seen to be part of the short run dynamics and therefore, cointegration can be analysed in a more efficient way. So, the stationary variables might be embedded in the VAR, but not in the long run vector. "

Thanks,

Brinda

Well, if your long run relationship does not come from theory and it's all about statistical identification of the cointegrated relationship (apart from I(0) and I(1) consideration, you can use the Pesaran CGE estimator (2006), where the only condition to check is that the residual of your panel relationship do not have a unit root. It is more robust to break and take cross sectional dependence between country into account.

The Pesaran CCE estimator could be more appropriate since it relaxes the assumption of cross-sectional independence (which is rare in panel set up) presumed in the cases of Kao as well as Pedroni.

Westerlund approach seems to be a better option and it can be easily applied in Stata software. It should be installed before applying.

SJ-8-2 st0146 . . Error-correction-based cointegration tests for panel data

(help xtwest if installed) . . . . . . . D. Persyn and J. Westerlund

Q2/08 SJ 8(2):232--241

implements the four error-correction-based panel

cointegration tests developed by Westerlund

Conceded for Westerlund approach.

Dear Christian Dreger, i have 8 explanatory variables, and when i run the Pedroni or Westerlund tests, an error appears showing that "number of regressors may not exceed 7". how to perform pedroni or westurlund tests on more than seven regressors ?

thanks in anticipation

I would try to reduce the number of regressors. Note that the Pedroni and Westerlund tests are constructed for a single cointegration vector - if there is any. If you include too many variables, the chance for multiple cointegration vectors will increase.

Dear Christian Dreger

Is it necessary to take log form of data and conduct panel cointegration method? Christian Dreger

I have 2 variables ( GDP and Financial development). When I conduct unit root tests in the level they are both non-stationary. Now I want to use Pedroni cointegration method. Do I need to log or first difference of the both variables before conduct the panel cointegration test?

In my view, the log form is not necessary. However, you have several advantages if you take logs:

The log transformation converts exponential trends to linear ones, the latter often assumed in the alternative hypothesis of unit root tests. Moreover, a multiplicative seasonal pattern will be converted to an additive pattern, which is better to handle. In logs, the regression parameters can be interpreted as elasticities. If you calculate growth rates, you only need to take first differences.

I really appreciate for your reply. Christian Dreger

I also want to ask one more question. I already calculated GDP growth but it is stationary in level. So I used GDP and financial development indicator and their unit root tests are non-stationary. Then can I convert them to log form to conduct Pedroni cointegration? Is that possible?