VECM – Constructing a Vector Error Correction Model with a Mix of I(0) and I(1) Variables

cointegrationtime seriesvector-autoregressionvector-error-correction-model

I've been using the Johansen Procedure to check and correct for cointegration in my model, by estimating a VECM instead of VAR. But now I want to estimate a new model, in which I expect the same cointegrated relationships, however, some of my variables are now stationary (because they are one of the former variables, split into growth and decay), is there a way to construct the Error Correction Term and insert it into my differenced data, and then estimate the VECM by ordinary VAR?

And what are the implications of ignoring cointegrated relationships and just estimating the VAR? Is my model subject to bias or inconsistency?

Best Answer

VECM is a VAR with the (lagged) error correction term. The error correction term is the one you obtained from the cointegrating equation or the long run equilibrium equation. With only two variables, for cointegration, they both need to be I(1). But, with more than two variables, I think it can be a mix of I(0) and I(1). If you mix, you will see that effect in the number of cointegrating equation.

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