The mean squared gap for inflation is calculated as   [ (t   , t )   *] / (T  1) , where π(t+τ,t) denotes the forecast in quarter t of inflation in quarter t +  and T  2  0  *  denotes  the  inflation  target.  0 [ y(t   , t )  y *(t   , t )]2 / (T  1)  The  mean  squared  gap  for  output  is  calculated  as  T  , where y(t+τ,t) denotes the forecast in quarter t of output in quarter t + τ and y*(t+τ,t) denotes the forecast in quarter t of potential output in quarter t + τ, and T is the forecast horizon (normally 12 quarters). 4  BIS central bankers’ speeches  inflation target of 2.5 percent but resource utilization worse (better). The Qvigstad (2005) necessary (but not sufficient) condition for optimal policy is satisfied, namely that the inflation gap and the output gap should be of opposite signs. The bottom left panel, with the mean squared gap for inflation plotted along the horizontal axis and the mean squared gap for output plotted along the vertical axis, has been added by me. The closer the mean squared gap for inflation and output is to zero, the better inflation or the output gap is stabilized.
However, let us suppose that the appropriate and effective instruments for ensuring financial stability are not available, for instance because of serious problems with the regulatory and supervisory framework that cannot be remedied in the short run. In such a second-best situation, if there is a threat to financial stability, one may argue that, to the extent that policy rates do have an impact on financial stability, this impact should be taken into consideration when choosing the policy-rate path to best stabilise inflation and resource utilisation. Such considerations could result in a lower or higher policy-rate path than otherwise, in order to trade off less effective stabilisation of inflation and resource utilisation for more financial stability. 2 To the best of my knowledge, the evidence so far indicates that in normal times such a trade-off is very unfavourable, in the sense that the impact of policy rates on financial stability is quite small and the impact on inflation and resource utilisation is significantly greater. Then, in normal times an optimal trade-off would still result in policy rates directed towards stabilizing inflation and resource utilization with little impact on financial stability. In particular, it seems clear that monetary policy should not be used to target housing prices. A considerable amount of research has concluded that policy rates have a modest impact on housing prices but a substantial impact on output, implying high real costs for using the policy rate for this purpose (Assenmacher-Wesche and Gerlach 2010).