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Common knowledge of a multivariate aggregate statistic

Author: Nielsen, Lars Tyge INSEAD Area: Finance Series: Working Paper ; 90/57/FIN/EPS/TM Publisher: Fontainebleau : INSEAD, 1990.Language: EnglishDescription: 43 p.Type of document: INSEAD Working Paper Online Access: Click here Abstract: If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge, then all the individuals must agree on their expectations. This result generalises the theorem of Nielsen, Brandenburger, Geanakoplos, McKelvey and Page (1989) from random variables to random vectors. It holds for general information structures given by sigma-algebras. In the illustrative case of normal distributions and linear signals, it is a statement about linear algebra, and it can be interpreted geometrically. Applied to a version of Grossman's (1975, 1976, 1978) securities market model with asymmetric information, the result implies that the equilibrium price is common knowledge only if all investors agree on their conditional distributions of asset returns. Combined with a result about pooling of linear signals, this observation implies that the linear rational expectations equilibrium is unique
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If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge, then all the individuals must agree on their expectations. This result generalises the theorem of Nielsen, Brandenburger, Geanakoplos, McKelvey and Page (1989) from random variables to random vectors. It holds for general information structures given by sigma-algebras. In the illustrative case of normal distributions and linear signals, it is a statement about linear algebra, and it can be interpreted geometrically. Applied to a version of Grossman's (1975, 1976, 1978) securities market model with asymmetric information, the result implies that the equilibrium price is common knowledge only if all investors agree on their conditional distributions of asset returns. Combined with a result about pooling of linear signals, this observation implies that the linear rational expectations equilibrium is unique

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