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Understanding Central Bank Loss Functions: Implied and Delegated Targets


  • Huiping Yuan

    (Xiamen University)

  • Stephen M. Miller

    (University of Connecticut)


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.

Suggested Citation

  • Huiping Yuan & Stephen M. Miller, 2009. "Understanding Central Bank Loss Functions: Implied and Delegated Targets," Working papers 2009-39, University of Connecticut, Department of Economics.
  • Handle: RePEc:uct:uconnp:2009-39
    Note: Professor Yuan gratefully acknowledges the financial support from the National Social Science Foundation of China, the China Scholarship Council, and the Wang Yanan Institute for Studies in Economics, Xiamen University.

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    References listed on IDEAS

    1. Henrik Jensen, 2002. "Targeting Nominal Income Growth or Inflation?," American Economic Review, American Economic Association, vol. 92(4), pages 928-956, September.
    2. Vestin, David, 2006. "Price-level versus inflation targeting," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1361-1376, October.
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    More about this item


    Optimal Policy; Central Bank Loss Functions; Policy Rules;

    JEL classification:

    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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