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Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case

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  • Peter Hammond
  • Yeneng Sun

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.
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  • Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    • Handle: RePEc:spr:joecth:v:36:y:2008:i:2:p:303-325
    DOI: 10.1007/s00199-007-0279-7
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    6. 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.
    7. 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.
    8. 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.
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    10. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    11. 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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    Citations

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    Cited by:

    1. Sun, Yeneng & Wu, Lei & Yannelis, Nicholas C., 2012. "Existence, incentive compatibility and efficiency of the rational expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 76(1), pages 329-339.
    2. Olga Gorelkina & Ioanna Grypari & Erin Hengel, 2023. "The theory of straight ticket voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 365-381, April.
    3. Hammond, Peter J. & Sun, Yeneng, 2016. "The One-way Fubini Property and Conditional Independence : An Equivalence Result," CRETA Online Discussion Paper Series 22, Centre for Research in Economic Theory and its Applications CRETA.
    4. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    5. Peter J. Hammond, 2017. "Designing a strategyproof spot market mechanism with many traders: twenty-two steps to Walrasian equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 1-50, January.
    6. Peter J. Hammond & Lei Qiao & Yeneng Sun, 2021. "Monte Carlo sampling processes and incentive compatible allocations in large economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1161-1187, April.
    7. Subramanian, Ajay & Wang, Jinjing, 2021. "Capital, aggregate risk, insurance prices and regulation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 156-192.
    8. Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
    9. 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.
    10. Martin F. Hellwig, 2021. "Public-Good Provision with Macro Uncertainty about Preferences: Efficiency, Budget Balance, and Robustness," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2021_19, Max Planck Institute for Research on Collective Goods.
    11. Sun, Xiang & Sun, Yeneng & Wu, Lei & Yannelis, Nicholas C., 2017. "Equilibria and incentives in private information economies," Journal of Economic Theory, Elsevier, vol. 169(C), pages 474-488.
    12. Yeneng Sun & Lei Wu & Nicholas C. Yannelis, 2011. "Existence, Incentive Compatibility and Efficiency of the Rational Expectations Equilibrium," Economics Discussion Paper Series 1108, Economics, The University of Manchester.
    13. Ahmad Peivandi & Mohammad Abbas Rezaei & Ajay Subramanian, 2023. "Optimal design of bank regulation under aggregate risk," Mathematics and Financial Economics, Springer, volume 17, number 2, February.

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    More about this item

    Keywords

    Large economy; Event-wise measurable conditional probabilities; Exchangeability; Conditional independence; Monte Carlo convergence; Monte Carlo σ-algebra; Stochastic macro structure; C00; D80; E00;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

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