# Are VAR and VEC models theoretically neutral?

I have recently been introduced to Vector Autoregression (VAR) and Vector Error Correction (VEC) models in an Econometrics class, where both approaches were presented as a neutral way to test economic theory. To my knowledge, however, VAR/VEC models always require a Cholesky Decomposition or sign restrictions for identification, and it seems to me that these greatly influence the results. For example, the direction of the effects and the implied causality will often change depending on ordering and/or sign decisions.

In short: If the design of these models influences the results to this extent, how can one ever provide evidence for/against a certain theory on this basis?

A regular VECM only requires normalization restrictions for the matrix consisting of cointegrating vectors (usually denoted as $\beta$ matrix), e.g. set the first element of each vector to one; even this is not necessary if you do not care about the loading matrix $\alpha$ and the cointegrating vectors matrix $\beta$ so that you are satisfied with estimating a product of the two $\Pi$ without decomposing it into the two factors. The normalization need not cause a problem in the sense of theoretical neutrality, if I understand it correctly. Again, a structural VECM (a SVECM) is another story.