Understanding Central Bank Loss Functions: Implied and Delegated Targets

The paper studies the dynamic nature of optimal solutions under commitment in Barro-Gordon and new-Keynesian models and, finds two interesting parameters -- the implied targets and the persistence parameter that governs the adjustment toward the implied targets. The implied targets generally differ from the social ones, but exhibit a trade-off between targets and equal the long-run equilibrium values of target variables. The implied targets prove consistent with the models and the social targets do not. Moreover, the implied targets emerge in the long run according to the persistence parameter. As such, the government delegates to the central bank short-term, state-contingent targets, which guide discretionary policy to evolve along optimal paths as these targets converge to their long-run implied targets. For the Barro-Gordon model with output persistence, the correct delegated targets eliminate the constant average and state-contingent inflation biases, and a weight-liberal central bank removes the stabilization bias. For the new-Keynesian models, delegated targets, combined with the appropriate weight-liberal or -conservative central bank, can eliminate all three biases. The delegated targets may reflect backward- or forward-looking behavior, depending on the model.