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I am wondering if I could include, in a VECM, exogenous variable in both level and first-difference, such as : $\Delta X_t = \alpha \beta^{'} X_{t-1} + \Delta X_{t-1} + Y_t + \Delta Y_t + U_t$

Is there any collinearity issue including both $Y_t$ and $\Delta Y_t$?

I have a second question : I'm using exchange rates (EURUSD, USDMYR and EURMYR) : EURMYR is built from the 2 first exchange rates, so I know I can't include all 3 in my model due to collinearity issue, but is it possible to include the 3 of them if I use them in first difference ?

Thanks a lot for your help,

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