When a continuous time model is estimated from its non-recursive discrete approximation, the presence of identities and exogenous variables in the system does not preclude the use of standard procedures. However, if we wish to use the exact discrete model for estimation purposes, the treatment of identities and exogenous variables is not so staightforward. It is found that the procedure based on the exact discrete model is unlikely to be affected by the presence of identities, but when exogenous variables occur in the system some sort of approximation is usually necessary before the model can be estimated with discrete data. An approximate model is constructed to deal with the latter case and the asymptotic properties of estimators derived from this model are investigated.