Essays on Microfoundations, Macroeconomic Applications and Economic History in Honor of Axel Leijonhufvud
Edited by Roger E.A. Farmer
7. Time inconsistency of robust control? Lars Peter Hansen and Thomas J. Sargent* INTRODUCTION 7.1 This chapter responds to criticisms by Chen and Epstein (2002) and Epstein and Schneider (2003) of the decision-theoretic foundations of our work that builds on robust control theory. Epstein, Chen and Schneider focus on what they regard as an undesirable dynamic inconsistency in the preferences that robust control theorists implicitly impute to the decisionmaker. This chapter describes representations of robust control theory as two-player zero-sum games, provides senses of time consistency that robust control theories do and do not satisfy, and asserts our opinion that the dynamic inconsistency that concerns Epstein and his co-authors is not particularly troublesome for economic applications. Hansen et al. (2006) used ideas from robust control theory1 to form a set of time-zero multiple priors for the min–max expected utility theory of Gilboa and Schmeidler (1989). They express the set of priors as a family of perturbations to a single explicitly stated benchmark model. Hansen et al. (2006) call the resulting min–max preferences the ‘constraint preferences’ because they are formulated directly in terms of a set of priors represented via a constraint on the magnitude of allowable perturbations from the benchmark model. In this way, Hansen et al. (2006) connected Gilboa and Schmeidler’s approach to uncertainty aversion with the literature on robust control. Hansen et al. (2006) show that the control law that solves the time-zero robust control problem can also be expressed in terms of a recursive representation...
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