The equivalence of two rational expectations equilibrium economies with different approaches to processing neighbors’ information

We consider a finite-agent Hellwig (1980) economy with an extension to allow traders to observe their neighbors’ signals in an exogenously given social network. There are two potential approaches for traders to process observed signals: directly infer information about the fundamentals from the complete collection of observed signals, or indirectly from an average of observed signals. The two approaches lead to different information sets for traders. In this study, we investigate whether the two economies corresponding to the two approaches are equivalent in the sense that they have the same market equilibrium. For general network and signal structures, we present a necessary and sufficient condition for the equivalence, revealing that the two finite-agent economies are not equivalent in general unless the network structure and signal structure coordinate well. When traders have homogeneous preferences and the signal structure takes the classical form in the literature, we find that the two finite-agent economies are equivalent for regular graphs, but not for chain and star graphs. Finally, for the classical signal structure, we show that the two large economies, defined as the limit of a sequence of replica finite-agent economies, are equivalent for any network structure.