Paying (for) Attention: The Impact of Information Processing Costs on Bayesian Inference∗

Human information processing is often modeled as costless Bayesian inference. However, research in psychology shows that attention is a computationally costly and potentially limited resource. We study a Bayesian individual for whom computing posterior beliefs is costly. Such an agent faces a tradeoff between economizing on attention costs and having more accurate beliefs. We show that even small processing costs can lead to significant departures from the standard costless processing model. There exist situations where beliefs can cycle persistently and never converge. In addition, when updating is costly, agents are more sensitive to signals about rare events than to signals about common events. Thus, these individuals can permanently overestimate the likelihood of rare events (e.g., the probability of a plane crash). There is a commonly held assumption in economics that individuals will converge to correct beliefs/optimal behavior given sufficient experience. Our results contribute to a growing literature in psychology, neuroscience, and behavioral economics suggesting that this assumption is both theoretically and empirically fragile. ∗The authors appreciate the helpful comments of Alessandro Bonatti, Roland Fryer, Drew Fudenberg, Martin Nowak, Larry Samuelson, Andrei Shleifer, Jakub Steiner, Juuso Toikka, and seminar audiences at the Massachusetts Institute of Technology. Kominers appreciates the hospitality of Microsoft Research New England, which hosted him during parts of this research, and gratefully acknowledges the support of NSF Grants CCF-1216095 and SES-1459912, the Harvard Milton Fund, an AMS–Simons travel grant, and the Human Capital and Economic Opportunity Working Group sponsored by the Institute for New Economic Thinking. †Society of Fellows, Department of Economics, Center of Mathematical Sciences and Applications, Center for Research on Computation and Society, and Program for Evolutionary Dynamics, Harvard University, Harvard Business School, and National Bureau of Economic Research. ‡Department of Economics, Harvard University. §Human Cooperation Lab, Yale University.