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Equivalence Results With Endogenous Signal Extraction

Author

Listed:
  • Giacomo Rondina

    (UCSD)

  • Todd Walker

    (Indiana University)

Abstract

We derive equivalence results in dynamic models with information frictions to help solve for equilibrium and facilitate interpretation. Our primary theorem delivers an equivalence, in the aggregate, between models 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 form in models with dispersed information and endogenous signal extraction.

Suggested Citation

  • Giacomo Rondina & Todd Walker, 2023. "Equivalence Results With Endogenous Signal Extraction," CAEPR Working Papers 2023-007 Classification-, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2023007
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    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2023-007.pdf
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    References listed on IDEAS

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