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A normalized value for information purchases

Author

Listed:
  • Antonio Cabrales

    (University College London)

  • Olivier Gossner

    (CREST; Ecole Polytechnique; London School of Economics)

  • Roberto Serrano

    (Brown University)

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.

Suggested Citation

  • Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2017. "A normalized value for information purchases," Working Papers 2017-51, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2017-51
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    References listed on IDEAS

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    1. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
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    9. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
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    Cited by:

    1. Corgnet, Brice & Deck, Cary & DeSantis, Mark & Porter, David, 2018. "Information (non)aggregation in markets with costly signal acquisition," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 286-320.
    2. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    3. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "The cost of information," Papers 1812.04211, arXiv.org, revised Dec 2020.
    4. Michel De Lara & Olivier Gossner, 2017. "An instrumental approach to the value of information," Working Papers 2017-49, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    Informativeness; Information purchases; Kullback–Leibler divergence; Relative entropy; No-arbitrageinvestment; Blackwell ordering;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D00 - Microeconomics - - General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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