More specifically, it is a question of finding the interest rate that will minimise the squared forecast deviations during the forecast period between actual inflation and the inflation target and between actual and normal resource utilisation, where the latter deviation is weighted by λ – a bit of a tongue-twister to put into words. But it can be illustrated relatively conveniently with the aid of a figure. The figure measures the variation in inflation along the horizontal axel and the variation in the real economy along the vertical axel. The variations are measured using the mean squared gap, that is, the average squared deviation across the forecast horizon. Such mean squared gaps can be calculated for various possible interest rate paths and one can then compare different interest rate paths by marking the mean squared gap in the figure. The closer to origo, or the further south-west in the figure, the smaller the two mean squared gaps are, and the better success the accompanying interest rate path has in stabilising inflation and the real economy.2 We say that inflation targeting, or the interest rate path, is effective if it is not possible to reduce one of the mean squared gaps without the other gap increasing in size at the same time. Theoretically, we could imagine there is a very large number of effective points. These points form a “front” as illustrated in the figure.
The loss function can be written as  , is the forecast where π is the forecast for inflation, π* is the inflation target and deviation between actual resource utilisation in the economy and the long-run sustainable, or  BIS central bankers’ speeches  1  “normal” level of resource utilisation.1 The first term represents the central bank’s target of stabilising inflation and the second its ambition to stabilise the real economy. The parameter λ represents the importance the central bank gives to stabilising the economy in relation to stabilising inflation. If λ were zero, this would mean that the central bank does not care at all about developments in the real economy, but merely tries to bring inflation as close to the target as possible. If λ is large, this means that the central bank places great emphasis on stabilising the real economy in relation to stabilising inflation. The term loss function comes from the fact that the larger the deviation, or “gap”, the further away we are from where we want to be, and thereby the greater the “loss”. In this theoretical description the central bank’s task is described in slightly more detail than the general wording of “finding a suitable balance between stabilising inflation and stabilising the real economy”.