The papers collected in this issue are united in a common view that it is rational to recognize that we have a poor perception of the constraints we face when making economic decisions and hence we employ decision rules that are robust. Robustness can be interpreted in different ways but generally it implies that our decision rules should not depend critically on an exact description of these constraints but they should perform well over a prespecified range of potential variations in the assumed economic environment. So, we are interested in deriving optimal and hence rational decisions where our utility or loss function incorporates the need for robustness in the face of a misspecified model. This misspecification can involve placing simple bounds on deviations from the parameters we assume for a nominal model, or misspecified dynamics, neglected nonlinearities, time variation, or quite general arbitrary misspecification in the transfer function between the input uncertainties and the output variables in which we are ultimately interested.

The theme of this paper is that the simple concept of risk sensitivity raises ideas, shows associations, and forces clarification of issues that one would have thought quite unrelated.

We review several control problems, all related to robust control in some way, that lead to a minimax linear quadratic problem. We stress the fact that although an augmented performance index appears, containing an L2 norm of a disturbance signal, only the nonaugmented quadratic performance index is of interest per se in each case.

A planner and agent in a permanent-income economy cannot observe part of the state, regard their model as an approximation, and value decision rules that are robust across a set of models. They use robust decision theory to choose allocations. Equilibrium prices reflect the preference for robustness and so embody a “market price of Knightian uncertainty.” We compute market prices of risk and compare them with a model that assumes that the state is fully observed. We use detection error probabilities to constrain a single parameter that governs the taste for robustness.

This paper examines monetary policy in a two-equation macroeconomic model when the policymaker recognizes that the model is an approximation and is uncertain about the quality of that approximation. It is argued that the minimax approach of robust control provides a general and tractable alternative to the conventional Bayesian decision theoretic approach. Robust control techniques are used to construct robust monetary policies. In most (but not all) cases, these robust policies are more aggressive than the optimal policies absent model uncertainty. The specific robust policies depend strongly on the formulation of model uncertainty used, and we make some suggestions about which formulation is most relevant for monetary policy applications.

This paper proposes a general method based on a property of zero-sum two-player games to derive robust optimal monetary policy rules—the best rules among those that yield an acceptable performance in a specified range of models—when the true model is unknown and model uncertainty is viewed as uncertainty about parameters of the structural model. The method is applied to characterize robust optimal Taylor rules in a simple forward-looking macroeconomic model that can be derived from first principles. Although it is commonly believed that monetary policy should be less responsive when there is parameter uncertainty, we show that robust optimal Taylor rules prescribe in general a stronger response of the interest rate to fluctuations in inflation and the output gap than is the case in the absence of uncertainty. Thus model uncertainty does not necessarily justify a relatively small response of actual monetary policy.

Using results from the literature on H∞ control, this paper incorporates model uncertainty into a frequency-domain approach to stabilization policy. The derived policies guarantee a minimum performance level even in the worst of (a bounded set of) circumstances. Robust H∞ policies are shown to be more “activist” than H2 policies in the sense that their impulse responses are larger. Robust policies also tend to be more autocorrelated. Consequently, the premium associated with being able to commit is greater under model uncertainty. Without commitment, the policymaker is not able to (credibly) smooth his response to the degree that he would like. A contribution of this paper is its analysis of robust control in a model featuring a forward-looking state transition equation, which arises from the fact that the private sector bases its decisions on expectations of future government policy. Existing applications of H∞ control in economics follow the engineering literature, and only consider backward-looking state transition equations.

In this paper, we reconsider the theoretical basis for the Lucas critique from the point of view of robust decision theory. We first emphasize that the Lucas critique rests on a weak theoretical paradigm in that it fails to consider the motivation for the policy change by the government and hence inconsistently assumes limited rationality by the government. When placed in a proper dynamic general equilibrium framework of a dynamic game between the government and the private sector, much of the force of the critique simply vanishes. We also reconsider the critique by adopting an alternative theoretical paradigm and notion of rationality based on robust decision theory. This view of rationality might be regarded as more relevant than the nonrobust rationality employed by Lucas and, critically, it is one in which the Lucas critique can be shown simply not to apply, provided the private sector has adopted suitably robust decision rules.