Summary.
Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo \( \sigma \)-algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved.
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Received: October 29, 2001; revised version: April 24, 2002
RID="*"
ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape.
Correspondence to: P.J. Hammond
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Hammond, P., Sun, Y. Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case. Econ Theory 21, 743–766 (2003). https://doi.org/10.1007/s00199-002-0302-y
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DOI: https://doi.org/10.1007/s00199-002-0302-y