# Johansen Cointegration in Pairwise Model but No Cointegration When Put in a Multiple Variable Model

I have tested for cointegration between two variables, REIT returns and direct property returns, which are cointegrated. However, when I add variables to this Johansen cointegration test (i.e. economic variables), the test is returning that there is no cointegration. All variables are I(1).

Does this make any sense? Shouldn't there be at least one cointegrating relationship in the multiple variable cointegration test, since the REIT and direct property variables are cointegrated on their own?

Shouldn't there be at least one cointegrating relationship in the multiple variable Cointegration test, since the REIT and direct property variables are cointegrated on their own?

No. Cointegration among a number of $$I(d)$$ variables occurs when their linear combination is $$I(d')$$ where $$d'. A caveat is that weights in the linear combination are not allowed to be zero. In other words, you cannot simply exclude some of the variables from the linear combination. Otherwise your point would make perfect sense.

• Thanks for the answer. So even though the property returns are cointegrated alone, this does not necessary mean a cointegrating relationship should arise when they are placed in another Cointegration test with additional variables? Do we say that multiple variables share a I(d') linear combination when r>0? Sep 18 '19 at 10:11
• And if Johansen returns zero cointegrating relationships for Eigen test starts, and 1 relationship for Trace test, are we able to run with Eigen? Sep 18 '19 at 10:18
• @James, Regarding your first question, I think that is correct. Regarding the second one, you have conflicting results. You should argue why one result is more convincing than another and then proceed with it cautiously. Actually, these are new questions which can (should) be asked separately. They would have better visibility and better focus when asked separately. Sep 18 '19 at 11:09