IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/1160.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1160.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, University Library of Munich, Germany.
    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. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers vie9807, University of Vienna, Department of Economics.
    5. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers 9807, University of Vienna, Department of Economics.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Al-Najjar, Nabil I., 2008. "Large games and the law of large numbers," Games and Economic Behavior, Elsevier, vol. 64(1), pages 1-34, September.
    2. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    3. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    4. Rabault, Guillaume, 1999. "The Decomposition of Risk in Denumerable Populations with ex ante Identical Individuals," Journal of Economic Theory, Elsevier, vol. 85(1), pages 157-165, March.
    5. Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
    6. Andreas Ramsauer, 1999. "Heterogeneous Discount Factors in an Assignment Model with Search Frictions," Vienna Economics Papers vie9807, University of Vienna, Department of Economics.
    7. Jain, Sanjay & Majumdar, Sumon & Mukand, Sharun W, 2014. "Walk the line: Conflict, state capacity and the political dynamics of reform," Journal of Development Economics, Elsevier, vol. 111(C), pages 150-166.
    8. Zimmerman, Peter, 2020. "Blockchain structure and cryptocurrency prices," Bank of England working papers 855, Bank of England.
    9. Ryan Chahrour, 2014. "Public Communication and Information Acquisition," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(3), pages 73-101, July.
    10. Christensen, Peter Ove & Larsen, Kasper & Munk, Claus, 2012. "Equilibrium in securities markets with heterogeneous investors and unspanned income risk," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1035-1063.
    11. Kam, Timothy & Stauber, Ronald, 2016. "Solving dynamic public insurance games with endogenous agent distributions: Theory and computational approximation," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 77-98.
    12. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    13. Luo, Yulei & Young, Eric, 2013. "Rational Inattention in Macroeconomics: A Survey," MPRA Paper 54267, University Library of Munich, Germany.
    14. Drautzburg, Thorsten, 2019. "Entrepreneurial tail risk: Implications for employment dynamics," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 85-100.
    15. William Diamond, 2020. "Safety Transformation and the Structure of the Financial System," Journal of Finance, American Finance Association, vol. 75(6), pages 2973-3012, December.
    16. Heifetz, Aviad & Minelli, Enrico, 2002. "Informational smallness in rational expectations equilibria," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 197-218, September.
    17. Hans Gersbach, 2002. "Democratic Mechanisms: Double Majority Rules and Flexible Agenda Costs," CESifo Working Paper Series 749, CESifo.
    18. Jerez, Belen, 2003. "A dual characterization of incentive efficiency," Journal of Economic Theory, Elsevier, vol. 112(1), pages 1-34, September.
    19. Roozbeh Hosseini, 2015. "Adverse Selection in the Annuity Market and the Role for Social Security," Journal of Political Economy, University of Chicago Press, vol. 123(4), pages 941-984.
    20. Nehring, Klaus, 1998. "Incentive-compatibility in large games," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 57-67, January.
    21. Yann Braouezec & John Cagnol, 2023. "Theoretical Foundations of Community Rating by a Private Monopolist Insurer: Framework, Regulation, and Numerical Analysis," Papers 2309.15269, arXiv.org, revised Dec 2023.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:1160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.