We propose a test for time-varying impulse responses in heteroskedastic structural vector autoregressions that can be used when the shocks are identified by external proxy variables as a group but not necessarily individually. The test is robust to the identification scheme for identifying the shocks individually and can be used even if the shocks are not identified individually. The asymptotic analysis is supported by small sample simulations which show good properties of the test. An investigation of the impact of productivity shocks in a small macroeconomic model for the U.S. illustrates the importance of the issue for empirical work.
