Monetary policy shocks derived from VARs often suggest that monetary policymakers regularly react to an unexpected increase that they induced in the federal funds rate with additional increases. This puzzling pattern can be called the “policy innovation paradox” because there is no obvious explanation for such a pattern. This article shows that the policy innovation paradox is most likely an artifact of failing to account for the discreteness of changes that policymakers make to the target federal funds rate. Misspecified VARs that fail to account for discrete target changes imply the policy innovation paradox, whereas a model that uses information from discrete policy changes does not.