We compare responses to two alternative indicators of monetary policy with an approach that directly embeds rational expectations into a low-dimensional structural vector autoregression. Our method constructs clouds of responses of inflation and economic activity in a modern sample encompassing the Great Financial Crisis of 2007 and the COVID-19 shock of 2020. We find large regions of puzzling responses to innovations in the federal funds rate. Regions of sensible responses are far larger when considering a broad Divisia monetary aggregate as an alternative indicator of policy. We conclude that a Taylor rule characterization of monetary policy shocks requires a painstaking search over the parameter space to elicit sensible responses. A money growth rule characterization, with Divisia M4 as an indicator of policy, can reasonably approximate responses to an interest rule—particularly, when allowing for long horizons in the formation of inflation expectations in the policy rule along with an adherence to the Taylor Principle.