In Engle-Granger 2-step ECM model,
if there are cointegration relationships then OLS result(1st step) shows a long-run relationship between variables.
Short-run relationship is expressed by ECM(2nd step) with error correction terms which we get from OLS(1st step).
E-G is the simplest case that there is only one cointegration relationship.
We also can get a cointegration equation (for specific one, especially the first variable) from VECM with rank=1.
I wonder the cointegration equation from VECM with rank=1 is equal to OLS?
I think it should be but in my model they are different.
How can I fix it?
Best Answer
In your VECM, the cointegrating relationship might have been obtained by maximum likelihood via Johansen procedure, thus the difference. You do not have to fix the discrepancy between that and what you obtained from OLS, since Johansen procedure need not be wrong (or more wrong than Engle-Granger).