Robust Control with Commitment: A Modification to Hansen-Sargent

This paper examines the Hansen and Sargent (2003) formulation of the robust Stackelberg problem and shows that their method of constructing the approximating equilibrium, which is central to any robust control exercise, is generally invalid. The paper then turns to the Hansen and Sargent (2007) treatment, which, responding to the problems raised in this paper, changes subtly, but importantly, how the robust Stackelberg problem is formulated. This paper proves, first, that their method for obtaining the approximating equilibrium is now equivalent to the one developed in this paper, and, second, that the worst-case specification errors are not subject to a time-inconsistency problem. Analyzing robust monetary policy in two New Keynesian business cycle models, the paper demonstrates that a robust central bank should primarily fear that the supply side of its approximating model is misspecified and that attenuation characterizes robust policymaking. Depending on how the robust Stackelberg problem is formulated, this paper shows that the Hansen-Sargent approximating equilibrium can be dynamically unstable and that robustness can be irrelevant, i.e., that the robust policy can coincide with the rational expectations policy.