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A Normalized Value for Information Purchases

Cabrales, A; Gossner, O; Serrano, R; (2017) A Normalized Value for Information Purchases. Journal of Economic Theory , 170 pp. 266-288. 10.1016/j.jet.2017.05.007. Green open access

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Abstract

Consider agents who are heterogeneous in their preferences and wealth levels. These agents may acquire information prior to choosing an investment that has a property of no-arbitrage, and each piece of information bears a corresponding cost. We associate a numeric index to each information purchase (information-cost pair). This index describes the normalized value of the information purchase: it is the risk-aversion level of the unique CARA agent who is indifferent between accepting and rejecting the purchase, and it is characterized by a “duality” principle that states that agents with a stronger preference for information should engage more often in information purchases. No agent more risk-averse than the index finds it profitable to acquire the information, whereas all agents less risk-averse than the index do. Given an empirically measured range of degrees of risk aversion in a competitive economy with no-arbitrage investments, our model therefore comes close to describing an inverse demand for information, by predicting what pieces of information are acquired by agents and which ones are not. Among several desirable properties, the normalized-value formula induces a complete ranking of information structures that extends Blackwell's classic ordering.

Type: Article
Title: A Normalized Value for Information Purchases
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jet.2017.05.007
Publisher version: http://doi.org/10.1016/j.jet.2017.05.007
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Informativeness, Information purchases, Kullback–Leibler divergence, Relative entropy, No-arbitrage investment, Blackwell ordering
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1556270
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