Key points of Engle Granger approach for cointegration

It is important to point out some drawbacks of the EG approach. First, if you have more than three variables, there might be more than one cointegrating relationship. The EG two step procedure does not allow for estimation of more than one cointegrating regression. It may be noted here that if we are dealing with n variables,there can be at most (n – 1) cointegrating relationships. To find that out, we will have to use tests developed by Johansen.

Another problem with the EG test is the order in which variables enter the  cointegrating regression. When we have more than two variables, how do we decide which is the regressand and which ones are the regressors? For example, if we have three variables Y, X, and Z and suppose we regress Y on X and Z and find cointegration. There is no guarantee that if we regress X on Y and Z we will necessarily find cointegration.

Another problem with the EG methodology in dealing with multiple time series is that we not only have to consider finding more than one cointegrating relationship, but then we will also have to deal with the error correction term for each cointegrating relationship. As a result, the simple, or bivariate, error correction model will not work. We have to then consider what is known as the vector error correction model (VECM).

All these problems can be handled if we use the Johansen methodology[1]. 

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[1] Source: D.Dujarati Econometrics by Examples.p 235-236