COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1296 Measurability Is Not about Information Juan Dubra and Federico Echenique March 2001 We comment on the relation between models of information based on signals/partitions, and those based on sigma-algebras. We show that more informative signals need not generate finer sigma-algebras, hence that Blackwell's theorem fails if information is modeled as sigma-algebras. The reason is that the sigma-algebra generated by a partition does not contain all the events that can be known from the information provided by the signal. We also show that there is a non-conventional sigma-algebra that can be associated to a signal which does preserve its information content. Further, expectations and conditional expectations may depend on the choice of sigma-algebra that is associated to a signal. We provide a simple characterization of when the model is robust to changes in the sigma-algebras. Keywords: Blackwell's theorem, measurability, models of information, partitions, information-preserving sigma-algebras JEL Classification: C60, C70, G12 |
