regression in engle and granger cointegration

[KPSS2010]

Hello,

I have a question regarding the regression in STEP2 in the engle and granger approach. When I do the OLS-regression of two I(1) variables to check the resids, does it matter which variable is the dependent variable in the OLS? Resids will differ, depending on the variable used as an dependent, so it can even happen that in one case they are cointegrated and in the other they are not. In this case, how do I decide for cointegration?

with many regards
Julius

[utah777]

Though this may sound counter-intuitive, it does matter which one of the two -- or three, or five -- variables you choose as a dependent variable. In general, you will follow the stats from Engle/Granger single equation test and choose the variable that is strongest in rejecting H0 (in humane language it is the variable with lowest p-value, usually below 10 or 5%, depending on your preferences).

You may notice as well that unless Cointegrating equation (CE) has a time trend in it, you may always choose a variable with lowest volatility as the dependent variable.

Regards