Target Controllability and Time Consistency: Complement to the Tinbergen Rule

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, which complements the Tinbergen rule. The condition is identical under commitment and under discretion. If the condition does not hold, the steady-state values of target variables regress to their respective target values. The paper solves both problems by determining the central bank’s 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 achieves optimal target variability trade-off and solves time inconsistency. As a result, target values are controllable, establishing monetary policy credibility. Discretionary policy under the designed loss function, which replicates optimal policy under the social loss function, proves time-consistent. In addition, we identify two situations where the delegated weight equals the social weight, providing additional insight into time inconsistency.