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Blackwell Informativeness and Sufficient Statistics with Applications to Financial Markets and Multiperson Agencies

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Economic Analysis of Information and Contracts

Abstract

This paper has two purposes. The first is partly tutorial: I want to develop Blackwell’s theory of information value in a way that makes the essential intuition transparent. In the process I will present a generalization of Blackwell’s [1951] seminal result on informativeness that is related to Marschak and Miyasawa’s [1968] concept of garbling 1,2 More important, I want to show that garbling is intimately linked to the more useful and general theory of sufficient statistics, which has been at the center stage of progress in statistical theory ever since the concept was proposed by Fisher [1922] and cast into its present form by the factorization theorem of Halmos and Savage [1949]. While the garbling idea has intuitive appeal for initiation into information economics, I believe that too much mental reliance on it tends to obscure the important point that both Blackwell’s concept and sufficient statistics essentially arise from properties of the conditional probability measures given the statistics. Consequently, I want to highlight this aspect and show the connections between the Blackwell theory and sufficient statistics that become apparent if we focus on the meaning and properties of these conditional measures. Later in the paper I exploit these connections when I discuss applications to financial markets and agencies.

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Authors
  1. Amin H. Amershi
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Editors and Affiliations

  1. University of British Columbia, Canada

    Gerald A. Feltham  & William T. Ziemba  & 

  2. University of Minnesota, USA

    Amin H. Amershi

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© 1988 Kluwer Academic Publishers, Boston

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Amershi, A.H. (1988). Blackwell Informativeness and Sufficient Statistics with Applications to Financial Markets and Multiperson Agencies. In: Feltham, G.A., Amershi, A.H., Ziemba, W.T. (eds) Economic Analysis of Information and Contracts. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2667-7_3

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  • DOI: https://doi.org/10.1007/978-94-009-2667-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7702-6

  • Online ISBN: 978-94-009-2667-7

  • eBook Packages: Springer Book Archive

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