We show how information acquisition costs can be identified using observable choice data. Identifying information costs from behavior is especially relevant when these costs depend on factors-such as time, effort, and cognitive resources-that are difficult to observe directly, as in models of rational inattention. Using willingness-to-pay data for opportunity sets-which require more or less information to make choices-we establish a set of canonical properties that are necessary and sufficient to identify information costs. We also provide an axiomatic characterization of the induced rationally inattentive preferences and show how they reveal the amount of information a decision-maker acquires.Keywords. Information costs, Blackwell order, information acquisition, menu choice, rational inattention. JEL classification. D81, D83. This paper merges our independent works, previously circulated as "Axiomatic Foundations for Rational Inattention" (de Oliveira), "Rational Inattention: A Decision-Theoretic Perspective" (Denti), and "Decision Making with Rational Inattention" (Mihm and Ozbek). We are grateful to Larry Blume, Simone CerreiaVioglio, Eddie Dekel, Fabio Maccheroni, Paola Manzini, Massimo Marinacci, Marco Mariotti, Tapan Mitra, Todd Sarver, and Joerg Stoye for invaluable guidance and support. We also thank Nabil Al-Najjar, Andrew Caplin, Aaron Bodoh-Creed, Giulia Brancaccio, Enrico Cantoni, Mark Dean, David Easley, Ludovica Gazzé, Peter Klibanoff, John Leahy, Samreen Malik, Jawwad Noor, Efe Ok, Pietro Ortoleva, Luciano Pomatto, Debraj Ray, Marciano Siniscalchi, Juuso Toikka, Mirko Wiederholt, Muhamet Yildiz, various seminar and conference participants, the editor and three anonymous reviewers for helpful comments and suggestions.

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The medical charts of patients sequentially treated for frontal sinus fractures by obliteration with autogenous cancellous iliac crest bone in the Oral and Maxillofacial Surgery Division of this institution were reviewed. From those, eight had complete records and adequately described long-term follow-up. All were operated by the same surgical team. Those patients were recalled and independently evaluated by 2 examiners. Radiographs and/or CT scans were available for this evaluation. Associated fractures and complications were noted. The average postoperative follow-up was 7 years, ranging from 3 to 16 years. The main complication was infection. Four patients (50%) had uneventful long-term follow-ups and four (50%) experienced complications requiring reoperation. Based on the studied sample studied the authors conclude that the obliteration with autogenous bone presented a high percentage of complications in this series.

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