Minimax Analysis of Monetary Policy Under Model Uncertainty

Recently there have been several studies that examined monetary policy under model uncertainty. These studies formulated uncertainty in a number of different ways. One of the prominent ways to formulate model uncertainty is to form a non-parametric set of perturbations around some nominal model where the set is structured so that the uncertainty is focused on potentially important weaknesses of the model. Unfortunately, previous efforts were unable to compute exact optimal policy rules under this general formulation of uncertainty. Moreover, for those special cases when the robust rules were computed, the degree of their aggressiveness was often counterintuitive in light of conventional Brainard/Bayesian wisdom that policy under uncertainty should be conservative. This paper,therefore, consists of three different exercises concerning minimax analysis of policy rules under model uncertainty. First, the minimax approach is compared with the Bayesian one in a stylized Brainard (1967) setting. Strong similarities between recommendations of the two approaches are found. Next, a more realistic setting such as in Onatski and Stock (1999) is considered. A characterization of the worst possible models corresponding to the max part of the minimax scheme is given. It is shown that the worst possible models for very aggressive rules, such as the H-infinity rule, have realistic economic structure whereas those for passive rules, such as the actual Fed's policy, are not plausible. Thus, the results of minimax analysis presented in Onatski and Stock (1999) might be biased against the passive rules. Finally, exact optimal minimax policy rules for the case of slowly time-varying uncertainty in the case of the Rudebusch and Svensson's (1998) model are computed. The optimal rule under certainty turns out to be robust to moderate deviations from Rudebusch and Svensson's model.