Tests for identification through heteroskedasticity in structural vector autoregressive analysis are developed for models with two volatility states where the time point of volatility change is known. The tests are Wald type tests for which only the unrestricted model including the covariance matrices of the two volatility states have to be estimated. The residuals of the model are assumed to be from the class of elliptical distributions which includes Gaussian models. The asymptotic null distributions of the test statistics are derived and simulations are used to explore their small sample properties. Two empirical examples illustrate the usefulness of the tests.