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Monte Carlo Simulation of Macroeconomic Risk with a Continuum Agents : The General Case

Author

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  • Hammond, Peter J.

    (Department of Economics, University of Warwick)

  • Sun, Yeneng

    (Department of Economics, National University of Singapore)

Abstract

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a ran-dom process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence.

Suggested Citation

  • Hammond, Peter J. & Sun, Yeneng, 2007. "Monte Carlo Simulation of Macroeconomic Risk with a Continuum Agents : The General Case," The Warwick Economics Research Paper Series (TWERPS) 803, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:803
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    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_803.pdf
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    References listed on IDEAS

    as
    1. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    2. 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.
    3. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
    4. Palfrey, Thomas R. & Srivastava, Sanjay, 1986. "Private information in large economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 34-58, June.
    5. Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
    6. Peter J. Hammond & Yeneng Sun, 2000. "Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables," Working Papers 00008, Stanford University, Department of Economics.
    7. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
    8. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    9. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    10. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Perfect competition in asymmetric information economies: compatibility of efficiency and incentives," Journal of Economic Theory, Elsevier, vol. 134(1), pages 175-194, May.
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    Cited by:

    1. Hammond, Peter J. & Sun, Yeneng, 2007. "Characterization of Risk : A Sharp Law of Large Numbers," The Warwick Economics Research Paper Series (TWERPS) 806, University of Warwick, Department of Economics.

    More about this item

    Keywords

    large economy ; event-wise measurable conditional probabilities ; ex-changeability ; conditional independence ; Monte Carlo convergence ; Monte Carlo-algebra ; stochastic macro structure;

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