The Central Bank Loss Function and Quantitative Easing as a Stackelberg Game

Abstract

The central bank loss function implies that the central bank’s benefit of QE is that of reputation enhancement of controlled inflation and strong economic growth. The loss function is quadratic capturing the deviation of the actual inflation and actual GDP from their socially desirable targets. The loss function at any time t is given by

$$ {L}_t=\frac{1}{2}\left[{\left({\pi}_t-{\pi}^{*}\right)}^2+\theta {\left({y}_t-{y}^{*}\right)}^2\right], $$