Im a student in econometrics and Im currently working on vector error correction models (VECM).
Im facing a problem with correction error coefficients signs. My teacher stated that they must be negative and significant. But I found out that their signs depend on the choice of the normalized coefficient.
For example, if the Johansen test tells me that there is one relation of cointegration between 3 variables (all I(1)), the sign of each error correction term will depends on the way I'm estimating. If I'm estimating a VECM between X Y Z, the first cointegrated coefficient (X) will be used for the normalization. If I'm running it in this order (Y Z X), the cointegrated coefficient of Y will be used.
Changing the order, usually change signs (global estimation results are the same but coefficients are different), so I'd like to know if there is a trick to know if my correction error terms are actually negative even if I change the order ?
As all variables are supposed endogenous, the order shouldn't be a problem.