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A Law of Large Numbers for Large Economies

Working Paper 342 | Published August 1, 1988

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Harald Uhlig

A Law of Large Numbers for Large Economies


[Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X---- a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers (*) Xdl = U. In this paper we propose to interpret (*) as a Pettis integral. Using the corresponding Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vector-valued version of the law of large numbers for economies.

Published in: _Economic Theory_ (vol. 8, 1996, pp. 41-50),