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Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions

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  • Rustam Ibragimov

Abstract

The structure of many models in economics and finance depends on majorization properties of convolutions of distributions. In this paper, we analyze robustness of these properties and the models based on them to heavy-tailedness assumptions. We show, in particular, that majorization properties of linear combinations of log-concavely distributed signals are reversed for very long-tailed distributions. As applications of the results, we study robustness of monotone consistency of the sample mean, value at risk analysis and the model of demand-driven innovation and spatial competition as well as that of optimal bundling strategies for a multiproduct monopolist in the case of an arbitrary degree of complementarity or substitutability among the goods. The implications of the models remain valid for not too heavy-tailed distributions. However, their main properties are reversed in the very thick-tailed setting

Suggested Citation

  • Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
  • Handle: RePEc:ecm:latm04:105
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    References listed on IDEAS

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    Cited by:

    1. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    2. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    3. René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.

    More about this item

    Keywords

    Robustness; heavy-tailed distributions; innovation and spatial competition; firm growth; Gibrat's law; optimal bundling strategies; multiproduct monopolist; Vickrey auction; value at risk; coherent measures of risk; monotone consistency;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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