Aggregation and the Law of Large Numbers in Economies with a Continuum of Agents
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.
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- Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
- 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.
- Harald Uhlig, 1996.
"A law of large numbers for large economies (*),"
Springer, vol. 8(1), pages 41-50.
- 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.
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