Target Controllability, Time Consistency, and the Tinbergen Rule

Abstract

The Tinbergen Rule states that achieving the desired targets requires an equal number of instruments. This paper shows that time inconsistency does not exist in the case of an equal number of instruments and targets. Target uncontrollability and time inconsistency, however, emerge as problems in the case of fewer instruments than targets. In this case, we obtain a necessary and sufficient condition for joint asymptotic controllability of target values. The condition is identical under commitment and under discretion. We observe that the constant average inflation bias comes from fewer instruments than targets, rather than from time inconsistency as the literature stresses. Policy makers must address target uncontrollability before addressing time inconsistency to avoid entanglement of the two problems when addressing time inconsistency. The paper solves both problems by designing the central bank loss function that determines the central bank’s long- and short-run target values of inflation and output as well as the relative weight between stabilizing inflation and output. Intuitively, a proper target value trade-off solves target uncontrollability, whereas a proper relative weight between target stabilizations achieves optimal target variability trade-off and solves time inconsistency. As a result, target values are moderate and controllable, establishing monetary policy credibility. Discretionary policy under the designed loss function, which replicates optimal policy under the social loss function, proves optimal and time-consistent. In addition, we identify two situations where the delegated weight equals the social weight -- one-decision-maker models and static models, providing additional insight into time inconsistency.