Some Implications of a Quartic Loss Function

Motivated by a central banker with a symmetric inflation zone target, we assume in this letter that the loss function of a policy maker can be approximated by the quartic form. For non-normal distributions, we show that such a loss function implies a systematic inflation bias even when the bank targets the natural rate. Moreover, we illustrate that the weights in an optimal combination of forecasts will differ from that under quadratic loss. We illustrate these differences via simulated data and data from the Livingston Surveys of Professional Forecasters