8 Tinbergen’s result is correct if the targets have to be achieved exactly, but it is not correct if there are tradeoffs among the goals of policy, and the central bank utility or loss function includes the costs of missing each of the targets and the interactions among them.
9 Based on the Tinbergen result, central banks whose mandated goals are narrow, such as having only an inflation target, are often considered to have more independence than central banks with additional targets or with multifaceted objectives. In practice, I doubt that any central bank targets inflation to the exclusion of all other outcomes.