Convexity of the central bank's loss function and dependence between monetary instruments

In this paper we obtain conditions under which the central bank loss function is strictly convex in four different states of the economy: booming economy, recession, high inflation and high output. Moreover, we found that when inflation and output are linear functions of the monetary policy instrument, convexity is guaranteed for any of the four states mentioned. When we extend our analysis to the case of many instruments, we found that only linearity is not sufficient to guarantee the shape of loss function. Our results also provide conditions under which there exists dependence between instruments of monetary policy.