What would be the difference of estimating a variable inside and outside a VAR model? Namely, if I know the relevant explanatory variables to model a certain variable in a time series framework, what's wrong with estimating a distributed lag instead of a VAR?
Edit: For me it's clear the limitations in terms of forecasting and impulse-response analysis. I'm not sure about the impacts on coefficients and residuals.
EDIT: I believe that an answer for my question is that it would be a specification error if we estimated an ADL model for a set of variables (in which only one would enter endogenously) that we know to affect each other in a contemporaneous way. In that case, some type of VAR is the correct approach since we'd need to take into account the multivariate covariance matrix of the residuals for appropriate inference.