IDEAS home Printed from https://ideas.repec.org/p/inu/caeprp/2023007.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2023-007.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bartosz Mackowiak & Mirko Wiederholt, 2009. "Optimal Sticky Prices under Rational Inattention," American Economic Review, American Economic Association, vol. 99(3), pages 769-803, June.
    2. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    3. Jurado, Kyle, 2023. "Rational inattention in the frequency domain," Journal of Economic Theory, Elsevier, vol. 208(C).
    4. Kenneth Kasa, 2000. "Forecasting the Forecasts of Others in the Frequency Domain," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 726-756, October.
    5. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-248, April.
    6. Hellwig, Christian & Venkateswaran, Venky, 2009. "Setting the right prices for the wrong reasons," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 57-77.
    7. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    8. Guido Lorenzoni, 2009. "A Theory of Demand Shocks," American Economic Review, American Economic Association, vol. 99(5), pages 2050-2084, December.
    9. Taub, Bart, 1989. "Aggregate fluctuations as an information transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 113-150, January.
    10. Phelps, Edmund S, 1969. "The New Microeconomics in Inflation and Employment Theory," American Economic Review, American Economic Association, vol. 59(2), pages 147-160, May.
    11. Zhao Han & Xiaohan Ma & Ruoyun Mao, 2023. "The Role of Dispersed Information in Inflation and Inflation Expectations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 48, pages 72-106, April.
    12. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rondina, Giacomo & Walker, Todd B., 2021. "Confounding dynamics," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Han, Zhao & Tan, Fei & Wu, Jieran, 2022. "Analytic policy function iteration," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Todd Walker, 2017. "Confounding Dynamics," 2017 Meeting Papers 141, Society for Economic Dynamics.
    4. Jonathan J Adams, 2019. "Macroeconomic Models with Incomplete Information and Endogenous Signals," Working Papers 001004, University of Florida, Department of Economics.
    5. George-Marios Angeletos & Chen Lian, 2018. "Forward Guidance without Common Knowledge," American Economic Review, American Economic Association, vol. 108(9), pages 2477-2512, September.
    6. George‐Marios Angeletos & Fabrice Collard & Harris Dellas, 2018. "Quantifying Confidence," Econometrica, Econometric Society, vol. 86(5), pages 1689-1726, September.
    7. George-Marios Angeletos, 2018. "Frictional Coordination," Journal of the European Economic Association, European Economic Association, vol. 16(3), pages 563-603.
    8. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    9. George-Marios Angeletos & Chen Lian, 2016. "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination," NBER Working Papers 22297, National Bureau of Economic Research, Inc.
    10. Jurado, Kyle, 2023. "Rational inattention in the frequency domain," Journal of Economic Theory, Elsevier, vol. 208(C).
    11. Atahan Afsar; José Elías Gallegos; Richard Jaimes; Edgar Silgado Gómez & José Elías Gallegos & Richard Jaimes & Edgar Silgado Gómez, 2020. "Reconciling Empirics and Theory: The Behavioral Hybrid New Keynesian Model," Vniversitas Económica 18560, Universidad Javeriana - Bogotá.
    12. Born, Benjamin & Enders, Zeno & Müller, Gernot J., 2023. "On FIRE, news, and expectations," Working Papers 42, German Research Foundation's Priority Programme 1859 "Experience and Expectation. Historical Foundations of Economic Behaviour", Humboldt University Berlin.
    13. Giacomo Rondina & Todd Walker, 2016. "Learning and Informational Stability of Dynamic REE with Incomplete Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 147-159, July.
    14. Zhao Han & Xiaohan Ma & Ruoyun Mao, 2023. "The Role of Dispersed Information in Inflation and Inflation Expectations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 48, pages 72-106, April.
    15. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    16. Jianjun Miao & Dongling Su, 2023. "Asset market equilibrium under rational inattention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 1-30, January.
    17. Camille Cornand & Paul Hubert, 2021. "Information frictions in inflation expectations among five types of economic agents," Working Papers halshs-03351632, HAL.
    18. Benhima, Kenza, 2019. "Booms and busts with dispersed information," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 32-47.
    19. Walker, Todd B., 2007. "How equilibrium prices reveal information in a time series model with disparately informed, competitive traders," Journal of Economic Theory, Elsevier, vol. 137(1), pages 512-537, November.
    20. Acharya, Sushant & Benhabib, Jess & Huo, Zhen, 2021. "The anatomy of sentiment-driven fluctuations," Journal of Economic Theory, Elsevier, vol. 195(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inu:caeprp:2023007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Center for Applied Economics and Policy Research (email available below). General contact details of provider: https://edirc.repec.org/data/caeprus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.