We estimate a time-varying structural VAR that describes the dynamic responses of a number of U.S. macro variables to different identified shocks. We find no significant changes in the estimated responses over the period when the federal funds rate attained the zero lower bound (ZLB). This result is consistent with the hypothesis of "perfect substitutability" between conventional and unconventional monetary policies. Montecarlo simulations based on artificial time series generated from a standard New Keynesian model point to the validity of our empirical approach to detect the changes in equilibrium dynamics associated with ZLB episodes.