Stochastic Optimisation and Worst Case Analysis in Monetary Policy Design

In this paper, we show how stochastic optimisation and worst-case analysis can be used together in order to provide central banks with a straightforward tool for selecting a policy rule that limits worst-case outcomes while at the same time providing reasonably good performance on average. We conduct this analysis within a simple estimated model of the euro area with adaptive expectations. In particular, we consider not only uncertainty due to additive shocks but also uncertainty with respect to all the parameters of the model, including multiplicative parameters and potential nonlinearities in the inflation-output relationship. In terms of monetary policy we focus on the optimal choice of response coefficients in a Taylor-style interest rate rule that responds to inflation and the output gap and we evaluate the performance of this type of rule by means of a standard quadratic loss function in output and inflation. We then compare the rules obtained by the two different methods by comparing their respective performance in the worst-case scenario as well as the overall expected performance given the empirical probability distributions.