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Aggregation and the Law of Large Numbers in Economies with a Continuum of Agents

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  • Nabil Al-Najjar

Abstract

This paper develops a framework in which a model with a continuum of agents and with individual and aggregate risks can be viewed as an idealization of large finite economies. The paper identifies conditions under which a sequence of finite economies gives rise to a limiting continuum economy in which uncertainty has a simple structure. The state space is the product of aggregate states and micro-states; aggregate states represent economy-wide random aggregate fluctuations, while micro-states reflect individual shocks which fluctuate independently around aggregate states and have no further discernible structure. In the special case where shocks in the finite economies are exchangable, the limiting economy satisfies a continuum-version of de Finetti's Theorem. The paper then uses this framework to derive implications for the interpretations of the Strong Law of Large Numbers and the Pettis Integral.

Suggested Citation

  • Nabil Al-Najjar, 1996. "Aggregation and the Law of Large Numbers in Economies with a Continuum of Agents," Discussion Papers 1160, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1160
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1160.pdf
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    References listed on IDEAS

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    1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    2. Al-Najjar, Nabil Ibraheem, 1995. "Decomposition and Characterization of Risk with a Continuum of Random Variables," Econometrica, Econometric Society, vol. 63(5), pages 1195-1224, September.
    3. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    4. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
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    Cited by:

    1. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, EconWPA.
    2. Heifetz, Aviad & Minelli, Enrico, 2002. "Informational smallness in rational expectations equilibria," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 197-218, September.
    3. Matthew O. Jackson & Thomas R. Palfrey, 1998. "Efficiency and Voluntary Implementation in Markets with Repeated Pairwise Bargaining," Econometrica, Econometric Society, vol. 66(6), pages 1353-1388, November.
    4. James D. Dana & Jr., 1998. "Advance-Purchase Discounts and Price Discrimination in Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 395-422, April.

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