A colleague of mine is using a VAR for quarterly data (deseasonalized). Typically it is customary to use lag of 4 or 5. However, they used two lags based on a single test result, the SC criteria. Of course, there may be a degrees of freedom problem if they decide to go with the longer 4-quarter lag. What is the best way to explain their rationale to them?
If it's an economic forecasting, then their rationale is simpler than that: they don't have enough data to go beyond 2 lags. Look at the number of parameters to estimate, including covariance of errors.
In economic forecasting we always struggle with limited sample sizes.