I'm trying to examine the relationship between money and output in the united kingdom and the money supply and income, and trying to establish whether the results are in line with the Quantity theory of Money for my dissertation.

I've run into a bit of a problem though, my monetary aggregate M4 needs to be differenced twice to become stationary. My supervisor told me: "If M4 is I(2) and the other variables are I(1) then there is an imbalance in their orders of integration. The growth rate of M4 (the first-difference in the logs) will be I(1) but including this in the model is then not consistent with the theory (MV=PY). If the ADF test for M4 is only a marginal non-rejection of the I(2) null hypothesis then you could make an argument for treating it as being I(1)."

So what do I do now? I'm so confused I'm trying to read up on it but I'm struggling. All my other variables are stationary by the first difference so I can follow the usual procedure for them. This would be an Johansen coi-ntegration test and then constructing a VAR then a VEC model to test the restrictions of the quantity theory of money. Unfortuantely the rejection of I(2) is not marginal. I'm totally at a loss what to do then. Just need to get over this problem and I know I can figure the rest out. Can i just ignore it?

Any genuine attempt at helping me would be greatly appreciated. Thanks in advance. :-)

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