Consider the following m regression equation system:
$$r^i = X^i \beta^i + \epsilon^i \;\;\; \text{for} \;i=1,2,3,..,T$$
where $r^i$ is a $(T\times 1)$ vector of the T observations of the dependent variable, $X^i$ is a $(T\times k)$ matrix of independent variables, $\beta^i$ is a $(k\times1)$ vector of the regression coefficients and $\epsilon^i$ is the vector of errors for the $T$ observations of the $i^{th}$ regression.
If the above is an SUR model (seemingly unrelated regressions), does it make sense to compute the BIC (Bayesian Information Criterion) for the model?
If so, how would that be computed? Should the dependent variables be stacked into one vector, in order to get only one regression equation?