Structural VAR Models
Identifying assumptions for structural VARs can be imposed on both the contemporaneous effects of shocks and on the long-run effects. The program is able to handle over-identifying restrictions as long as they don't imply that the covariance matrix of the reduced-form residuals is singular. Before any structural form is estimated SVAR tests for local identification by drawing random values for the free parameters of the restricted matrices. The exact procedure for the local identification test is discussed by e.g. Amisano and Giannini (1997).
To achieve exact identification the number of identifying restrictions must be equal to the number of variables squared, i.e., n*n. Of these SVAR automatically uses n*(n+1)/2 by setting the covariance matrix for the structural shocks to the identity. Hence, there remains n*(n-1)/2 restrictions for the user to select. These must then be such that the effects, whether contemporaneous or long-run, on the endogenous variables are unique for each shock.
While the case of contemporaneous restrictions is straightforward to understand since it only involves one matrix, the long-run restrictions are trickier in the case of cointegration. The reason is that the restrictions are imposed on a product of two matrices and, for example, under cointegration (fewer cointegration relations than endogenous variables but at least one such relation) one of these matrices is of reduced rank while the other is not. In two of the subsections about common trends type models (common trends - part 1 and common trends - part 2) I will therefore confine myself to long-run identifying restrictions. One exception to this is the final subsection where a specific issue concerning over-identification is discussed.
Cointegration Space
A related topic to identification of shocks in Structural VAR models is the identification of the cointegration vectors. SVAR always performs a test for generic identification (cf. Johansen, 1995) when exact and over-identifying restrictions have been selected for the β matrix and you attempt to estimate this matrix. In the event that the test for generic identification fails, you'll be notified by SVAR with hints about which vectors are affected and the software aborts estimation of the restricted β matrix.