In this paper we examine implications of model uncertainty due to robustness (RB) for consumption decisions, aggregate savings, and welfare under limited information-processing capacity (rational inattention or RI) in an otherwise standard permanent income model with filtering. We first show that RB and risk-sensitivity (RS) are observationally equivalent (OE) under imperfect information due to RI in the sense that they lead to the same consumption and saving decisions if consumers use the regular Kalman filter to extract signals. Second, we find that once allowing RS consumers to use the risk-sensitive filter and RB consumers to use the robust Kalman filter to extract signals, the absolute and linear OE between RB and RS no longer holds; instead, we find a conditional and nonlinear OE between RB and RS. Furthermore, we find that in the filtering problem, either a stronger preference for robustness in the Kalman gain, a stronger risk-sensitive preference, or higher channel capacity can increase the Kalman gain. Finally, we explore how RB in the filtering problem interacts with RI and affects consumption dynamics, aggregate savings, and the welfare costs of uncertainty. JEL Classification Numbers: C61, D81, E21. ∗We would like to thank Richard Dennis, Larry Epstein, Ken Kasa, Tasos Karantounias, Jun Nie, Kevin Salyer, Tom Sargent, Martin Schneider, Chris Sims, Laura Veldkamp, and Mirko Wiederholt, as well as seminar and conference participants at UC Davis, The Hong Kong University of Science and Technology, University of Toyko, Shanghai University of Finance and Economics, the conference on “Putting Information Into (or Taking it out of) Macroeconomics”organized by LAEF of UCSB, and the 2011 Summer Meeting of Econometric Society for helpful discussions and comments. Luo thanks the General Research Fund (GRF) in Hong Kong and the HKU seed funding program for basic research for financial support. All errors are the responsibility of the authors. †Corresponding author. School of Economics and Finance, University of Hong Kong, Hong Kong. Email address: email@example.com. ‡Department of Economics, University of Virginia, Charlottesville, VA 22904. E-mail: firstname.lastname@example.org.