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Some implications of a quartic loss function

Author

Listed:
  • Kevin Aretz

    (Lancaster University)

  • David Peel

    (Lancaster University)

Abstract

Motivated by a central banker with a symmetric but non-quadratic loss function, we show in this note that the approximations of two plausible loss functions of this type will include a quartic term. For skewed distributions, we establish that such a loss function implies a systematic inflation bias even when the bank targets the natural rate. Moreover, we show that the weights in an optimal combination of forecasts will differ from that under quadratic loss. We illustrate these differences using simulated data and data from the Livingston Surveys of Professional Forecasters.

Suggested Citation

  • Kevin Aretz & David Peel, 2007. "Some implications of a quartic loss function," Economics Bulletin, AccessEcon, vol. 7(13), pages 1-7.
    • Handle: RePEc:ebl:ecbull:eb-07g10011
    as

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    References listed on IDEAS

    as
    1. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    2. Francisco J. Ruge-Murcia, 2000. "Uncovering financial markets' beliefs about inflation targets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 483-512.
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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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