I understand that when your variables are integrated/cointegrated as oppose to the stable VAR, the Wald test does not have standard Chi-square distribution. A lot of test appearing recently in literature are proposed. Am new in this area and the more I try to read different literature on this, the more I get confused, perhaps I do know the right literature yet.
I also like to know whether a suggested Wald test perform Granger causality only in the short run or include both the cointegration equation in the analysis. As in EVIEWS, I guess it's only the short run.
Lastly any perfect paper or book that provides that mathematical intuition to the Wald test in this case?
These papers (especially the second one) may help you to better understand:
Clarke, J. A. and S. Mirza (2006). A comparison of some common methods for detecting Granger noncausality. Journal of Statistical Computation and Simulation, 76, 207-231.
Dolado, J. J and H. Lütkepohl (1996). Making Wald tests work for cointegrated VAR systems. Econometric Reviews, 15, 369-386.
I suggest also to visit this link:
http://davegiles.blogspot.com/2011/10/var-or-vecm-when-testing-for-granger.html
Best regards,
In the vector autoregressive (VAR) framework, the Wald test for testing restrictions on the coefficients are known to have nonstandard asymptotic properties for integrated and cointegrated systems of variables. This means that tests for Granger-causality may have non-standard asymptotic properties if the variables considered in the VAR system are integrated or cointegrated. Park and Phillips (1989) and Toda and Phillips (1993 a,b), among others, have illustrated the difficulties in dealing with the levels estimation of such variables.
To overcome this problem, a possible solution is to condition the testing procedure on the estimation of unit roots, cointegration rank and Cointegrating vectors. Another simple method is proposed by Dolado and Lütkepohl (1996), in what follows DL, which guarantees standard asymptotics for the Wald tests performed on the coefficients of integrated or cointegrated VAR processes with I(1) variables and avoids possible pretest biases.
DL’s simple procedure can be stated as follows: if the true generating process is a VAR(p), it is proposed to fit a VAR(p +1) to the data and perform a Wald test on the coefficient of the first p lags only. DL show that this simple method leads to Wald tests with standard asymptotic -distributions, and with this modification the tests may be performed on the least squares (LS) coefficients of the VAR system specified in the levels of the variables.
So Easy to do this with Eviews.
Read also my papper:
A Graphical Investigation of the Size and Power of the Granger-Causality Tests in Integrated-Cointegrated VAR Systems
Good Luck!
When you perform VEC(p) using adecuate lags, you have to see the coefficient of Cointegration equation. If the coefficient is negative, the independent variable cause Granger the dependent variable. It is very easy using Eviews.
Thank you very much Refk, Panagiotis and Manuel. I have performed the test in Eviews based on the VECM. My issue has to do with the interpretation whether it describe Granger causality in the short only or it involves the cointegration equation, in this case the whole model. I haven't gotten the mathematical intuition of the exact Wald test described in the Eviews to know whether its the short run only or it involves causality in the long run.
Can you also tell me the statistical package which performs the Wald test in the one proposed by Dolado and Lutkepohl? Because apart from the theoretical understanding, I also have to perform the test to see the result.
And lastly, what about the idea of first differencing the integrated series and perform the Granger causality in VAR before going back to estimate the VECM. I see people do that.
yes, you can perform Granger causality test before going to estimate the VECM in an instance where you are not sure of the nature of the r/ship that exist among the variables under consideration.
By using Eviews, you can easily perform Granger short and long run causality tests within the VECM framework. The steps of the procedure are as follow: First, determine the degree of the integration of variables in the study by using ADF, PP, KPSS and ng ğerron unit root tests. Second, if the results of unit root tets indiate that variables are I(1), then, use Johansen cointegration test to determine whether variables are cointegrated. Third,If they are cointegrated, estimate a VECM and then perform Granger causality test. For the short run causality, use Wald test and for the long run causality test the statistical significance of coefficient of error correction term in equation in VECM.
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