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##### Abstract

We derive equivalence results in dynamic models with information frictions to help solve for equilibriumand facilitate interpretation. Our primary theoremdelivers an equivalence, in the aggregate, betweenmodels with dispersed and hierarchical information. Optimal signal extraction, in the dispersed case, suggests agents treat the signal as true with probability equal to the signal-to-noise ratio, and false with the complementary probability. Equivalence follows when the share of informed agents, in the hierarchical model, is set equal to the signal-to-noise ratio in the dispersed economy. The value of this theorem is due to the hierarchical model being much easier to solve and interpret, especially when agents infer information from endogenous sources. We also generalize the ubiquitous Hansen-Sargent formula to models with incomplete information and derive equivalence-class representations as a function of information. We use our results to study the behavior of higher-order beliefs and information transmission in closed forminmodels with dispersed information and endogenous signal extraction.

##### Figure 1: Existence Space of Equilibrium with Dispersed Information

##### Citation

Giacomo Rondina and Todd B. Walker, 2023. “Equivalence Results with Endogenous Signal Extraction”