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Theoretically, VAR, or its ramifications are able to identify patterns within the data, including Granger causality test of panel data.
However, there are numerious variations in practice, which makes VAR not as competent as expected, to be listed here a few cases illustrating my point:
1. short-term data, if your panel data is pooled by two panels, VAR is not sufficient to generate any time variation.
2. unbalanced panel, though large number of observations can compensate by using 'fancy techniques ' which focus more on the asymptotic properties of the statistical process, note that unfriendly data can make extant robust models impotent.
3. the implications/meaning of variables at the aggregrate level are not explicitly self-evident, nor does it convey any policy message. Be such the case, it is safer to go through the rudimentary basics and understand what is going on behind the package. This is extremely common in program evaluation design and implementation where the long-term data is simply non-existing or not reliable (in that many other interventions are influencing the outcome as well).
By saying so, I am not intending to discount the importance of VAR model whatsoever. I am simply emphasising and suggesting that understanding your data matters a lot. And please bear in mind that the gist of modelling is not to make matters complex, but clean, clear and simple.
Counter-arguments with examples welcome.
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