SVAR performs a "test" for local identification based on the estimated parameters of the estimated asymptotic covariance matrix of the B matrix. Specifically, it uses the necessary and sufficient condition for local identification that is given in Amisano and Giannini (1997); see chapter 2 for an example. Let the identifying restrictions on B be given by
and let the asymptotic covariance matrix for B be given by Σ(B). With n being the number of endogenous variables, the test consists of evaluating the rank of the matrix
If the model is locally identified at B(0), the true value of B, then V evaluated at B(0) has rank n*n. Similarly, if the rank of V is less than n*n, then B is not locally identified at B(0). This condition is further refined by Amisano and Giannini but SVAR doesn't examine the refinement.