Robustness and information processing

This paper considers a standard Kalman filtering problem subject to model uncertainty and information-processing constraints. It draws a connection between robust filtering [Hansen and Sargent, 2004. Robust control and economic model uncertainty. Monograph. In press] and Rational Inattention [Sims, 2003. Implications of rational inattention, Journal of Monetary Economics 50 (3), 665–690]. Considered separately, robustness and Rational Inattention are shown to be observationally equivalent, in the sense that a higher filter gain can either be interpreted as an increased preference for robustness, or an increased ability to process information. However, it is more interesting to consider them jointly. In this case, it is argued that an increased preference for robustness can be interpreted as an increased demand for information processing, while Sims' model of Rational Inattention can be interpreted as placing a constraint on the available supply. This suggests that the way agents actually implement robust decision rules is by allocating some of their scarce information processing capacity to problems that are characterized by high degrees of model uncertainty and risk-sensitivity.