How good is a forecast? (Many outputs)
The MSE is essentially a squared Euclidean distance between two vectors, say $\mathbf y$ and $\hat{\mathbf y}$, where $\mathbf y$ is the actual economic data over $T$ periods and $\hat{\mathbf{y}}$ the predicted values. A natural extension of this to matrices $\mathbf Y=(y_{it})$ and $\widehat{\mathbf Y}=(\hat y_{it})$ where $i=1,\dots,n$ and $t=1,\dots,T$ ($n$ variables over $T$ periods) would be
\begin{equation}
\text{MSE}^*=\frac{1}{nT}\sum_{i=1}^n\sum_{t=1}^T(y_{it}-\hat y_{it})^2.
\end{equation}
But beware of the pitfall. Of course there are other matrix norms available as well.