Before revision:  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.
After revision:  We formalize this `irrelevance hypothesis ,' based on a simple idea that under the hypothesis, the short rate can be excluded in any empirical model that accounts for alternative measures of monetary policy. We develop a theoretical model that underpins this hypothesis, and test it empirically for the United States and Japan using a structural vector autoregressive model that includes variables subject to occasionally binding constraints.