This paper investigates the potential sources of the mixed evidence found in the empirical literature studying asymmetries in the response of output to monetary policy shocks of different magnitudes. Further, it argues that such mixed evidence is a consequence of the exogenous imposition of the threshold that classifies monetary shocks as small or large. To address this issue, I propose an unobserved-components model of output, augmented by a monetary policy variable, which allows the threshold to be endogenously estimated. The results show strong statistical evidence that the effect of monetary policy on output varies disproportionately with the size of the monetary shock once the threshold is estimated. Meanwhile, the estimates of the model are consistent with a key implication of menu-cost models: smaller monetary shocks trigger a larger response on output.