A Law of Large Numbers for Large Economies

Creator Series Issue number
  • 342
Date Created
  • 1988-08
  • [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.

Subject (JEL) Palavra-chave Date Modified
  • 07/15/2019
Corporate Author
  • Federal Reserve Bank of Minneapolis. Research Department
  • Federal Reserve Bank of Minneapolis
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