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Faculty & Research


Common Knowledge: The Case of Linear Regression

Nielsen L. (1996). 
Common Knowledge: The Case of Linear Regression.
 Journal of Mathematical Economics26(3), pp285-304.
Journal Article
This paper reinterprets the multivariate McKelvey-Page theorem as a special case of a result about orthogonal projections in a Hilbert space. When information is given by linear signals and the distribution of payoffs and signals is elliptical, it is shown how information matrices, and the multivariate McKelvey-Page theorem is reinterpreted as a result about matrix algebra can represent common and pooled information. Applied to a version of Grossman’s securities market model with asymmetric information, the result implies that the equilibrium price is common knowledge only if all investors agree on their conditional expectations of payoffs. Combined with a result about pooling of linear signals, this observation implies that the linear rational expectations equilibrium is unique.