If I have 4 variables in a model and I want to check for causality between the two variables say X and Y. These two variables are not cointegrated based on Engle-Granger Residual test for cointegration and Johansen's Cointegration test based on only these 2 variables.
But when I consider all the 4 variables and check again for cointegration then, there exists 2 cointegrating vectors as indicated by trace and eigen value test. As my aim is to check for causality between X & Y, should I estimate a VAR model as these 2 variables of interest are not cointegrated or should I go forward with VECM as the variables are cointegrated when I consider all the variables?
Thanks in advance.