IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/104116.html
   My bibliography  Save this paper

A maximum likelihood approach to combining forecasts

Author

Listed:
  • Levy, Gilat
  • Razin, Ronny

Abstract

We model an individual who wants to learn about a state of the world. The individual has a prior belief and has data that consist of multiple forecasts about the state of the world. Our key assumption is that the decision maker identifies explanations that could have generated this data and among these focuses on those that maximize the likelihood of observing the data. The decision maker then bases her final prediction about the state on one of these maximum likelihood explanations. We show that in all the maximum likelihood explanations, moderate forecasts are just statistical derivatives of extreme ones. Therefore, the decision maker will base her final prediction only on the information conveyed in the relatively extreme forecasts. We show that this approach to combining forecasts leads to a unique prediction, and a simple and dynamically consistent way to aggregate opinions.

Suggested Citation

  • Levy, Gilat & Razin, Ronny, 2021. "A maximum likelihood approach to combining forecasts," LSE Research Online Documents on Economics 104116, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:104116
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/104116/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Gilat Levy & Ronny Razin, 2012. "When do simple policies win?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(3), pages 621-637, April.
    3. Benjamin Golub & Matthew O. Jackson, 2012. "How Homophily Affects the Speed of Learning and Best-Response Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1287-1338.
    4. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    5. Ran Spiegler, 2016. "Bayesian Networks and Boundedly Rational Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1243-1290.
    6. Levy, Gilat & Razin, Ronny, 2013. "Dynamic legislative decision making when interest groups control the agenda," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1862-1890.
    7. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 730-778.
    8. , & , & ,, 2016. "Fragility of asymptotic agreement under Bayesian learning," Theoretical Economics, Econometric Society, vol. 11(1), January.
    9. Roberta De Filippis & Antonio Guarino & Philippe Jehiel & Toru Kitagawa, 2016. "Updating ambiguous beliefs in a social learning experiment," CeMMAP working papers 18/16, Institute for Fiscal Studies.
    10. Pietro Ortoleva, 2012. "Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News," American Economic Review, American Economic Association, vol. 102(6), pages 2410-2436, October.
    11. Benjamin Enke & Florian Zimmermann, 2019. "Correlation Neglect in Belief Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 313-332.
    12. Jeffrey S. Rosenthal & Martin J. Osborne & Matthew A. Turner, 2000. "Meetings with Costly Participation," American Economic Review, American Economic Association, vol. 90(4), pages 927-943, September.
    13. repec:diw:diwwpp:dp1104 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Olivier Compte, 2023. "Belief formation and the persistence of biased beliefs," Papers 2310.08466, arXiv.org.
    2. Marcos R. Fernandes, 2024. "Combining Combined Forecasts: a Network Approach," Papers 2406.13749, arXiv.org.
    3. Kfir Eliaz & Simone Galperti & Ran Spiegler, 2022. "False Narratives and Political Mobilization," Papers 2206.12621, arXiv.org.

    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. Cheng, Ing-Haw & Hsiaw, Alice, 2022. "Distrust in experts and the origins of disagreement," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. Jawwad Noor, 2019. "Intuitive Beliefs," Cowles Foundation Discussion Papers 2216, Cowles Foundation for Research in Economics, Yale University.
    3. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    4. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.
    5. J. Aislinn Bohren & Daniel N. Hauser, 2021. "Learning With Heterogeneous Misspecified Models: Characterization and Robustness," Econometrica, Econometric Society, vol. 89(6), pages 3025-3077, November.
    6. Levy, Gilat & Razin, Ronny, 2018. "Information diffusion in networks with the Bayesian Peer Influence heuristic," Games and Economic Behavior, Elsevier, vol. 109(C), pages 262-270.
    7. Kai Barron, 2021. "Belief updating: does the ‘good-news, bad-news’ asymmetry extend to purely financial domains?," Experimental Economics, Springer;Economic Science Association, vol. 24(1), pages 31-58, March.
    8. Dasaratha, Krishna & He, Kevin, 2020. "Network structure and naive sequential learning," Theoretical Economics, Econometric Society, vol. 15(2), May.
    9. Inés Moreno de Barreda & Gilat Levy & Ronny Razin, 2017. "Persuasion with Correlation Neglect: Media Power via Correlation of News Content," Economics Series Working Papers 836, University of Oxford, Department of Economics.
    10. Kai Barron & Tilman Fries, 2023. "Narrative Persuasion," Rationality and Competition Discussion Paper Series 469, CRC TRR 190 Rationality and Competition.
    11. Ing-Haw Cheng & Alice Hsiaw, 2016. "Trust in Signals and the Origins of Disagreement," Working Papers 110R4, Brandeis University, Department of Economics and International Business School, revised Dec 2018.
    12. Mauersberger, Felix, 2021. "Monetary policy rules in a non-rational world: A macroeconomic experiment," Journal of Economic Theory, Elsevier, vol. 197(C).
    13. Gilboa, Itzhak & Wang, Fan, 2019. "Rational status quo," Journal of Economic Theory, Elsevier, vol. 181(C), pages 289-308.
    14. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    15. Pinger, Pia & Schäfer, Sebastian & Schumacher, Heiner, 2018. "Locus of control and consistent investment choices," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 75(C), pages 66-75.
    16. Benjamin Enke, 2020. "What You See Is All There Is," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1363-1398.
    17. Aislinn Bohren & Daniel Hauser, 2018. "Social Learning with Model Misspeciification: A Framework and a Robustness Result," PIER Working Paper Archive 18-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jul 2018.
    18. Bogaçhan Çelen & Sen Geng & Huihui Li, 2018. "Belief Error and Non-Bayesian Social Learning: An Experimental Evidence," GRU Working Paper Series GRU_2018_022, City University of Hong Kong, Department of Economics and Finance, Global Research Unit.
    19. Simon Board & Moritz Meyer‐ter‐Vehn, 2021. "Learning Dynamics in Social Networks," Econometrica, Econometric Society, vol. 89(6), pages 2601-2635, November.
    20. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.

    More about this item

    Keywords

    maximum likelihood; combining forecasts; misspecified models;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:104116. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.