# 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?

## 1 Answer

A regular VAR has no identification restrictions, except for setting the contemporaneous relation matrix to an identity matrix (which need not be a problem with regards to theoretical neutrality). Meanwhile, a structural VAR (a SVAR) is another story.

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.

A related question you may want to think about deals with observationally equivalent representations of a given model. One has to be careful not to draw conclusions based on some particular representation(s) that do not hold for all the possible equivalent representations. If a statement can be derived from some particular representation(s) but not from all of them, then the statement is not driven by the data but by the representation(s). In other words, the conclusion(s) would then follow from the assumptions regardless of the data... You may find more about it in an enlightening paper: Gilbert "State Space and ARMA Models: An Overview of the Equivalence" (1993).

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