A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules and are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler (1989), and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent (1995). To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and non-sequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.

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An ordinary differential equation (ODE) gives the mean dynamics that govern the convergence to self-confirming equilibria of self-referential systems under discounted least squares learning. Another ODE governs escape dynamics that recurrently propel away from a selfconfirming equilibrium. In a model with a unique self-confirming equilibrium, the escape dynamics make the government discover too strong a version of the natural rate hypothesis. The escape route dynamics cause recurrent outcomes close to the Ramsey (commitment) inflation rate in a model with an adaptive government.''If an unlikely event occurs, it is very likely to occur in the most likely way.'' Michael Harrison

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We use a micro-founded macroeconometric modeling framework to investigate the design of monetary policy when the central bank faces uncertainty about the true structure of the economy. We apply Bayesian methods to estimate the parameters of the baseline specification using postwar U.S. data, and then determine the policy under commitment that maximizes household welfare. We find that the performance of the optimal policy is closely matched by a simple operational rule that focuses solely on stabilizing nominal wage inflation. Furthermore, this simple wage stabilization rule is remarkably robust to uncertainty about the model parameters and to various assumptions regarding the nature and incidence of the innovations. However, the characteristics of optimal policy are very sensitive to the specification of the wage contracting mechanism, thereby highlighting the importance of additional research regarding the structure of labor markets and wage determination.