  The effective lower bound on a short term interest rate may not constrain a
central bank's capacity to achieve its objectives if unconventional monetary
policy (UMP) is powerful enough. We formalize this `irrelevance hypothesis'
using a dynamic stochastic general equilibrium model with UMP and test it
empirically for the United States and Japan using a structural vector
autoregressive model that includes variables subject to occasionally binding
constraints. The hypothesis is strongly rejected for both countries. However, a
comparison of the impulse responses to a monetary policy shock across regimes
shows that UMP has had strong delayed effects in each country.
